# Entrants' Sample Solutions

## ATPBoost 1.0

Bartosz Piotrowski
University of Warsaw, Poland

### Sample solution for HL400001_5

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('HL400001_5.p', conj_thm_2Ebool_2ETRUTH)).
fof(c_0_1, negated_conjecture, ~(\$true), inference(assume_negation,[status(cth)],[conj_thm_2Ebool_2ETRUTH])).
fof(c_0_2, negated_conjecture, ~\$true, inference(fof_simplification,[status(thm)],[c_0_1])).
cnf(c_0_3, negated_conjecture, (\$false), inference(split_conjunct,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (\$false), inference(cn,[status(thm)],[c_0_3]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001_4

```# SZS output start CNFRefutation
tff(thm_2Ebool_2ETRUTH, conjecture, p(mono_2Ec_2Ebool_2ET_2E0), file('HL400001_4.p', thm_2Ebool_2ETRUTH)).
tff(reserved_2Eho_2Etruth, axiom, p(mono_2Ec_2Ebool_2ET_2E0), file('Axioms/HL4002_4.ax', reserved_2Eho_2Etruth)).
tff(c_0_2, negated_conjecture, ~(p(mono_2Ec_2Ebool_2ET_2E0)), inference(assume_negation,[status(cth)],[thm_2Ebool_2ETRUTH])).
tff(c_0_3, negated_conjecture, ~p(mono_2Ec_2Ebool_2ET_2E0), inference(fof_simplification,[status(thm)],[c_0_2])).
tcf(c_0_4, negated_conjecture, ~p(mono_2Ec_2Ebool_2ET_2E0), inference(split_conjunct,[status(thm)],[c_0_3])).
tcf(c_0_5, plain, p(mono_2Ec_2Ebool_2ET_2E0), inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth])).
cnf(c_0_6, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_4, c_0_5])]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001+5

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('HL400001+5.p', conj_thm_2Ebool_2ETRUTH)).
fof(c_0_1, negated_conjecture, ~(\$true), inference(assume_negation,[status(cth)],[conj_thm_2Ebool_2ETRUTH])).
fof(c_0_2, negated_conjecture, ~\$true, inference(fof_simplification,[status(thm)],[c_0_1])).
cnf(c_0_3, negated_conjecture, (\$false), inference(split_conjunct,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (\$false), inference(cn,[status(thm)],[c_0_3]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001+4

```# SZS output start CNFRefutation
fof(thm_2Ebool_2ETRUTH, conjecture, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('HL400001+4.p', thm_2Ebool_2ETRUTH)).
fof(reserved_2Eho_2Etruth, axiom, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('Axioms/HL4002+4.ax', reserved_2Eho_2Etruth)).
fof(c_0_2, negated_conjecture, ~(p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(assume_negation,[status(cth)],[thm_2Ebool_2ETRUTH])).
fof(c_0_3, negated_conjecture, ~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), inference(fof_simplification,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(split_conjunct,[status(thm)],[c_0_3])).
cnf(c_0_5, plain, (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth])).
cnf(c_0_6, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_4, c_0_5])]), ['proof']).
# SZS output end CNFRefutation
```

## CSE 1.3

### Sample solution for SEU140+2

```% Proof found
% SZS status Theorem for SEU140+2
% SZS output start Proof
%ClaNum:116(EqnAxiom:34)
%VarNum:417(SingletonVarNum:163)
%MaxLitNum:4
%MaxfuncDepth:2
%SharedTerms:12
%goalClause: 37 38 55
%singleGoalClaCount:3
[35]P1(a1)
[36]P1(a2)
[37]P3(a3,a5)
[38]P2(a5,a6)
[54]~P1(a13)
[55]~P2(a3,a6)
[40]P3(a1,x401)
[43]P3(x431,x431)
[56]~P4(x561,x561)
[39]E(f12(a1,x391),a1)
[41]E(f16(x411,a1),x411)
[42]E(f12(x421,a1),x421)
[44]E(f16(x441,x441),x441)
[46]E(f12(x461,f12(x461,a1)),a1)
[49]E(f12(x491,f12(x491,x491)),x491)
[45]E(f16(x451,x452),f16(x452,x451))
[47]P3(x471,f16(x471,x472))
[48]P3(f12(x481,x482),x481)
[50]E(f16(x501,f12(x502,x501)),f16(x501,x502))
[51]E(f12(f16(x511,x512),x512),f12(x511,x512))
[52]E(f12(x521,f12(x521,x522)),f12(x522,f12(x522,x521)))
[57]~P1(x571)+E(x571,a1)
[61]~P3(x611,a1)+E(x611,a1)
[62]P5(f7(x621),x621)+E(x621,a1)
[60]~E(x601,x602)+P3(x601,x602)
[63]~P5(x632,x631)+~E(x631,a1)
[64]~P4(x641,x642)+~E(x641,x642)
[65]~P1(x651)+~P5(x652,x651)
[70]~P4(x701,x702)+P3(x701,x702)
[71]~P2(x712,x711)+P2(x711,x712)
[74]~P5(x742,x741)+~P5(x741,x742)
[75]~P4(x752,x751)+~P4(x751,x752)
[76]~P3(x762,x761)+~P4(x761,x762)
[67]~P3(x671,x672)+E(f12(x671,x672),a1)
[69]P3(x691,x692)+~E(f12(x691,x692),a1)
[72]~P3(x721,x722)+E(f16(x721,x722),x722)
[78]P1(x781)+~P1(f16(x782,x781))
[79]P1(x791)+~P1(f16(x791,x792))
[80]P3(x801,x802)+P5(f8(x801,x802),x801)
[81]P2(x811,x812)+P5(f14(x811,x812),x812)
[82]P2(x821,x822)+P5(f14(x821,x822),x821)
[96]P3(x961,x962)+~P5(f8(x961,x962),x962)
[88]~P2(x881,x882)+E(f12(x881,f12(x881,x882)),a1)
[89]~P3(x891,x892)+E(f16(x891,f12(x892,x891)),x892)
[90]~P3(x901,x902)+E(f12(x901,f12(x901,x902)),x901)
[95]P2(x951,x952)+~E(f12(x951,f12(x951,x952)),a1)
[104]P2(x1041,x1042)+P5(f4(x1041,x1042),f12(x1041,f12(x1041,x1042)))
[99]~P3(x991,x993)+P3(f12(x991,x992),f12(x993,x992))
[106]~P2(x1061,x1062)+~P5(x1063,f12(x1061,f12(x1061,x1062)))
[107]~P3(x1071,x1073)+P3(f12(x1071,f12(x1071,x1072)),f12(x1073,f12(x1073,x1072)))
[58]~P1(x582)+~P1(x581)+E(x581,x582)
[73]P4(x731,x732)+~P3(x731,x732)+E(x731,x732)
[77]~P3(x772,x771)+~P3(x771,x772)+E(x771,x772)
[97]E(x971,x972)+P5(f15(x971,x972),x972)+P5(f15(x971,x972),x971)
[103]E(x1031,x1032)+~P5(f15(x1031,x1032),x1032)+~P5(f15(x1031,x1032),x1031)
[83]~P3(x833,x832)+P5(x831,x832)+~P5(x831,x833)
[84]~P3(x841,x843)+P3(x841,x842)+~P3(x843,x842)
[91]~P2(x913,x912)+~P5(x911,x912)+~P5(x911,x913)
[98]~P3(x982,x983)+~P3(x981,x983)+P3(f16(x981,x982),x983)
[108]P5(f10(x1082,x1083,x1081),x1081)+P5(f10(x1082,x1083,x1081),x1082)+E(x1081,f12(x1082,x1083))
[111]P5(f10(x1112,x1113,x1111),x1111)+~P5(f10(x1112,x1113,x1111),x1113)+E(x1111,f12(x1112,x1113))
[113]~P5(f9(x1132,x1133,x1131),x1131)+~P5(f9(x1132,x1133,x1131),x1133)+E(x1131,f16(x1132,x1133))
[114]~P5(f9(x1142,x1143,x1141),x1141)+~P5(f9(x1142,x1143,x1141),x1142)+E(x1141,f16(x1142,x1143))
[105]~P3(x1051,x1053)+~P3(x1051,x1052)+P3(x1051,f12(x1052,f12(x1052,x1053)))
[109]P5(f11(x1092,x1093,x1091),x1091)+P5(f11(x1092,x1093,x1091),x1093)+E(x1091,f12(x1092,f12(x1092,x1093)))
[110]P5(f11(x1102,x1103,x1101),x1101)+P5(f11(x1102,x1103,x1101),x1102)+E(x1101,f12(x1102,f12(x1102,x1103)))
[85]~P5(x851,x854)+P5(x851,x852)+~E(x852,f16(x853,x854))
[86]~P5(x861,x863)+P5(x861,x862)+~E(x862,f16(x863,x864))
[87]~P5(x871,x873)+P5(x871,x872)+~E(x873,f12(x872,x874))
[92]~P5(x924,x923)+~P5(x924,x921)+~E(x921,f12(x922,x923))
[100]~P5(x1001,x1003)+P5(x1001,x1002)+~E(x1003,f12(x1004,f12(x1004,x1002)))
[112]P5(f9(x1122,x1123,x1121),x1121)+P5(f9(x1122,x1123,x1121),x1123)+P5(f9(x1122,x1123,x1121),x1122)+E(x1121,f16(x1122,x1123))
[115]P5(f10(x1152,x1153,x1151),x1153)+~P5(f10(x1152,x1153,x1151),x1151)+~P5(f10(x1152,x1153,x1151),x1152)+E(x1151,f12(x1152,x1153))
[116]~P5(f11(x1162,x1163,x1161),x1161)+~P5(f11(x1162,x1163,x1161),x1163)+~P5(f11(x1162,x1163,x1161),x1162)+E(x1161,f12(x1162,f12(x1162,x1163)))
[93]~P5(x931,x934)+P5(x931,x932)+P5(x931,x933)+~E(x932,f12(x934,x933))
[94]~P5(x941,x944)+P5(x941,x942)+P5(x941,x943)+~E(x944,f16(x943,x942))
[102]~P5(x1021,x1024)+~P5(x1021,x1023)+P5(x1021,x1022)+~E(x1022,f12(x1023,f12(x1023,x1024)))
%EqnAxiom
[1]E(x11,x11)
[2]E(x22,x21)+~E(x21,x22)
[3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
[4]~E(x41,x42)+E(f12(x41,x43),f12(x42,x43))
[5]~E(x51,x52)+E(f12(x53,x51),f12(x53,x52))
[6]~E(x61,x62)+E(f16(x61,x63),f16(x62,x63))
[7]~E(x71,x72)+E(f16(x73,x71),f16(x73,x72))
[8]~E(x81,x82)+E(f11(x81,x83,x84),f11(x82,x83,x84))
[9]~E(x91,x92)+E(f11(x93,x91,x94),f11(x93,x92,x94))
[10]~E(x101,x102)+E(f11(x103,x104,x101),f11(x103,x104,x102))
[11]~E(x111,x112)+E(f15(x111,x113),f15(x112,x113))
[12]~E(x121,x122)+E(f15(x123,x121),f15(x123,x122))
[13]~E(x131,x132)+E(f8(x131,x133),f8(x132,x133))
[14]~E(x141,x142)+E(f8(x143,x141),f8(x143,x142))
[15]~E(x151,x152)+E(f10(x151,x153,x154),f10(x152,x153,x154))
[16]~E(x161,x162)+E(f10(x163,x161,x164),f10(x163,x162,x164))
[17]~E(x171,x172)+E(f10(x173,x174,x171),f10(x173,x174,x172))
[18]~E(x181,x182)+E(f9(x181,x183,x184),f9(x182,x183,x184))
[19]~E(x191,x192)+E(f9(x193,x191,x194),f9(x193,x192,x194))
[20]~E(x201,x202)+E(f9(x203,x204,x201),f9(x203,x204,x202))
[21]~E(x211,x212)+E(f14(x211,x213),f14(x212,x213))
[22]~E(x221,x222)+E(f14(x223,x221),f14(x223,x222))
[23]~E(x231,x232)+E(f4(x231,x233),f4(x232,x233))
[24]~E(x241,x242)+E(f4(x243,x241),f4(x243,x242))
[25]~E(x251,x252)+E(f7(x251),f7(x252))
[26]~P1(x261)+P1(x262)+~E(x261,x262)
[27]P5(x272,x273)+~E(x271,x272)+~P5(x271,x273)
[28]P5(x283,x282)+~E(x281,x282)+~P5(x283,x281)
[29]P3(x292,x293)+~E(x291,x292)+~P3(x291,x293)
[30]P3(x303,x302)+~E(x301,x302)+~P3(x303,x301)
[31]P2(x312,x313)+~E(x311,x312)+~P2(x311,x313)
[32]P2(x323,x322)+~E(x321,x322)+~P2(x323,x321)
[33]P4(x332,x333)+~E(x331,x332)+~P4(x331,x333)
[34]P4(x343,x342)+~E(x341,x342)+~P4(x343,x341)

%-------------------------------------------
cnf(118,plain,
(~P5(x1181,a1)),
inference(equality_inference,[],[63])).
cnf(120,plain,
(~P5(x1201,x1202)+P5(x1201,f16(x1203,x1202))),
inference(equality_inference,[],[85])).
cnf(121,plain,
(~P5(x1211,x1212)+P5(x1211,f16(x1212,x1213))),
inference(equality_inference,[],[86])).
cnf(122,plain,
(~P5(x1221,f12(x1222,x1223))+P5(x1221,x1222)),
inference(equality_inference,[],[87])).
cnf(123,plain,
(~P5(x1231,x1232)+~P5(x1231,f12(x1233,x1232))),
inference(equality_inference,[],[92])).
cnf(124,plain,
(~P5(x1241,x1242)+P5(x1241,f12(x1242,x1243))+P5(x1241,x1243)),
inference(equality_inference,[],[93])).
cnf(125,plain,
(~P5(x1251,f16(x1252,x1253))+P5(x1251,x1253)+P5(x1251,x1252)),
inference(equality_inference,[],[94])).
cnf(126,plain,
(~P5(x1261,f12(x1262,f12(x1262,x1263)))+P5(x1261,x1263)),
inference(equality_inference,[],[100])).
cnf(127,plain,
(~P5(x1271,x1272)+~P5(x1271,x1273)+P5(x1271,f12(x1273,f12(x1273,x1272)))),
inference(equality_inference,[],[102])).
cnf(128,plain,
(E(x1281,f16(x1281,x1281))),
inference(scs_inference,[],[44,2])).
cnf(131,plain,
(~P5(x1311,f12(a1,x1312))),
inference(scs_inference,[],[118,44,2,126,122])).
cnf(133,plain,
(P2(x1331,a1)),
inference(scs_inference,[],[118,44,2,126,122,104])).
cnf(138,plain,
(~P2(a6,a3)),
inference(scs_inference,[],[118,55,44,39,2,126,122,104,95,71])).
cnf(142,plain,
(~P5(x1421,a2)),
inference(scs_inference,[],[118,55,36,44,39,46,2,126,122,104,95,71,69,65])).
cnf(147,plain,
(E(f16(x1471,x1471),x1471)),
inference(rename_variables,[],[44])).
cnf(149,plain,
(~E(a1,a6)),
inference(scs_inference,[],[118,55,36,44,39,46,2,126,122,104,95,71,69,65,64,63,32])).
cnf(150,plain,
(~E(a5,a3)),
inference(scs_inference,[],[118,38,55,36,44,39,46,2,126,122,104,95,71,69,65,64,63,32,31])).
cnf(155,plain,
(E(f16(x1551,x1551),x1551)),
inference(rename_variables,[],[44])).
cnf(156,plain,
(~E(a1,f16(a6,a6))),   inference(scs_inference,[],[43,40,118,38,55,36,54,44,147,155,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3])).
cnf(157,plain,
(E(f16(x1571,x1571),x1571)),
inference(rename_variables,[],[44])).
cnf(165,plain,
(~P3(a6,a1)),   inference(scs_inference,[],[37,43,40,118,38,55,36,54,44,147,155,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77])).
cnf(166,plain,
(P3(a1,x1661)),
inference(rename_variables,[],[40])).
cnf(174,plain,
(E(f16(x1741,x1741),x1741)),
inference(rename_variables,[],[44])).
cnf(175,plain,
(~P5(x1751,a1)),
inference(rename_variables,[],[118])).
cnf(178,plain,
(E(f16(x1781,x1781),x1781)),
inference(rename_variables,[],[44])).
cnf(180,plain,
(P5(f9(a6,a6,a1),a6)),   inference(scs_inference,[],[37,43,40,166,118,175,38,55,35,36,54,44,147,155,157,174,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112])).
cnf(181,plain,
(~P5(x1811,a1)),
inference(rename_variables,[],[118])).
cnf(184,plain,
(E(f16(x1841,x1841),x1841)),
inference(rename_variables,[],[44])).
cnf(186,plain,
(~P5(x1861,f16(f16(a1,a1),f16(a1,a1)))),   inference(scs_inference,[],[37,43,40,166,118,175,181,38,55,35,36,54,44,147,155,157,174,178,184,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94])).
cnf(187,plain,
(E(f16(x1871,x1871),x1871)),
inference(rename_variables,[],[44])).
cnf(190,plain,
(E(f16(x1901,x1901),x1901)),
inference(rename_variables,[],[44])).
cnf(191,plain,
(~P5(x1911,a1)),
inference(rename_variables,[],[118])).
cnf(225,plain,
(E(f12(a5,f12(a5,a6)),a1)),   inference(scs_inference,[],[37,43,40,166,118,175,181,38,55,35,36,54,44,147,155,157,174,178,184,187,190,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88])).
cnf(237,plain,
(~P4(a5,a3)),   inference(scs_inference,[],[37,43,40,166,118,175,181,38,55,35,36,54,44,147,155,157,174,178,184,187,190,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76])).
cnf(245,plain,
(E(f12(a3,a5),a1)),   inference(scs_inference,[],[37,43,40,166,118,175,181,38,55,35,36,54,44,147,155,157,174,178,184,187,190,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76,75,74,72,67])).
cnf(254,plain,
(E(f16(x2541,x2541),x2541)),
inference(rename_variables,[],[44])).
cnf(255,plain,
(~P5(f15(a2,f16(a1,a1)),f16(a2,a2))),   inference(scs_inference,[],[37,43,56,40,166,118,175,181,38,55,35,36,54,44,147,155,157,174,178,184,187,190,254,45,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76,75,74,72,67,57,60,34,33,28])).
cnf(256,plain,
(E(f16(x2561,x2561),x2561)),
inference(rename_variables,[],[44])).
cnf(259,plain,
(P5(f9(a6,a6,a1),f12(a6,f12(a6,a6)))),   inference(scs_inference,[],[37,43,56,40,166,118,175,181,38,55,35,36,54,44,147,155,157,174,178,184,187,190,254,256,45,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76,75,74,72,67,57,60,34,33,28,27,127])).
cnf(261,plain,
(P5(f9(a6,a6,a1),f12(a6,a1))),   inference(scs_inference,[],[37,43,56,40,166,118,175,181,191,38,55,35,36,54,44,147,155,157,174,178,184,187,190,254,256,45,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76,75,74,72,67,57,60,34,33,28,27,127,124])).
cnf(262,plain,
(~P5(x2621,a1)),
inference(rename_variables,[],[118])).
cnf(265,plain,
(~P5(x2651,a1)),
inference(rename_variables,[],[118])).
cnf(269,plain,
(~P5(x2691,a1)),
inference(rename_variables,[],[118])).
cnf(273,plain,
(~P5(x2731,a1)),
inference(rename_variables,[],[118])).
cnf(275,plain,
(E(a1,f12(a1,x2751))),   inference(scs_inference,[],[37,43,56,40,166,118,175,181,191,262,265,269,273,38,55,35,36,54,44,147,155,157,174,178,184,187,190,254,256,45,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76,75,74,72,67,57,60,34,33,28,27,127,124,111,110,109,108])).
cnf(283,plain,
(~P5(f9(a6,a6,a1),a5)),   inference(scs_inference,[],[37,43,56,40,166,118,175,181,191,262,265,269,273,38,55,35,36,54,44,147,155,157,174,178,184,187,190,254,256,45,47,39,46,2,126,122,104,95,71,69,65,64,63,32,31,30,29,26,3,125,97,84,77,73,58,100,87,112,102,94,93,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,106,99,90,89,88,82,81,80,79,78,76,75,74,72,67,57,60,34,33,28,27,127,124,111,110,109,108,105,98,91])).
cnf(313,plain,
(P2(a2,x3131)),
inference(scs_inference,[],[55,142,261,186,259,62,121,120,123,106,104,95,82])).
cnf(314,plain,
(~P5(x3141,a2)),
inference(rename_variables,[],[142])).
cnf(317,plain,
(~P5(x3171,a2)),
inference(rename_variables,[],[142])).
cnf(320,plain,
(~P5(x3201,a2)),
inference(rename_variables,[],[142])).
cnf(322,plain,
(~P5(f12(a6,a1),f9(a6,a6,a1))),   inference(scs_inference,[],[55,142,314,317,261,186,259,62,121,120,123,106,104,95,82,81,80,74])).
cnf(333,plain,
(~P5(x3331,a2)),
inference(rename_variables,[],[142])).
cnf(334,plain,
(~P5(x3341,a1)),
inference(rename_variables,[],[118])).
cnf(337,plain,
(~P5(x3371,a2)),
inference(rename_variables,[],[142])).
cnf(338,plain,
(~P5(x3381,a1)),
inference(rename_variables,[],[118])).
cnf(342,plain,
(~P5(x3421,a1)),
inference(rename_variables,[],[118])).
cnf(350,plain,
(~P5(x3501,a1)),
inference(rename_variables,[],[118])).
cnf(357,plain,
(~P5(x3571,a1)),
inference(rename_variables,[],[118])).
cnf(359,plain,
(~P3(a5,a3)),   inference(scs_inference,[],[37,48,118,334,338,342,350,38,55,142,314,317,320,333,337,149,150,237,261,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73])).
cnf(362,plain,
(~P5(x3621,f12(a1,x3622))),
inference(rename_variables,[],[131])).
cnf(364,plain,
(~P5(x3641,a1)),
inference(rename_variables,[],[118])).
cnf(367,plain,
(~P5(x3671,a1)),
inference(rename_variables,[],[118])).
cnf(371,plain,
(~P5(x3711,a1)),
inference(rename_variables,[],[118])).
cnf(373,plain,
(~E(f12(f12(a6,a1),a1),a1)),   inference(scs_inference,[],[37,48,118,334,338,342,350,357,364,367,38,55,142,314,317,320,333,337,149,150,237,261,131,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69])).
cnf(377,plain,
(~E(a6,a1)),   inference(scs_inference,[],[37,48,118,334,338,342,350,357,364,367,38,55,142,314,317,320,333,337,149,150,165,237,261,131,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60])).
cnf(386,plain,
(~E(f12(a6,a1),f12(x3861,f12(x3861,a1)))),   inference(scs_inference,[],[37,48,40,118,334,338,342,350,357,364,367,371,38,55,142,314,317,320,333,337,149,150,165,237,261,131,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100])).
cnf(387,plain,
(~P5(x3871,a1)),
inference(rename_variables,[],[118])).
cnf(389,plain,
(~E(f12(a6,a1),f12(a1,x3891))),   inference(scs_inference,[],[37,48,40,118,334,338,342,350,357,364,367,371,387,38,55,142,314,317,320,333,337,149,150,165,237,261,131,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87])).
cnf(390,plain,
(~P5(x3901,a1)),
inference(rename_variables,[],[118])).
cnf(392,plain,
(~E(f12(a6,a1),f16(a1,a1))),   inference(scs_inference,[],[37,48,40,118,334,338,342,350,357,364,367,371,387,390,38,55,142,314,317,320,333,337,149,150,165,237,261,131,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94])).
cnf(398,plain,
(~P4(x3981,f16(x3981,a1))),   inference(scs_inference,[],[37,48,41,56,40,118,334,338,342,350,357,364,367,371,387,390,38,55,142,314,317,320,333,337,149,150,165,237,261,131,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94,5,2,34])).
cnf(399,plain,
(E(f16(x3991,a1),x3991)),
inference(rename_variables,[],[41])).
cnf(400,plain,
(~P2(a3,f16(a6,a1))),   inference(scs_inference,[],[37,48,41,399,56,40,118,334,338,342,350,357,364,367,371,387,390,38,55,142,314,317,320,333,337,149,150,165,237,261,131,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94,5,2,34,32])).
cnf(401,plain,
(E(f16(x4011,a1),x4011)),
inference(rename_variables,[],[41])).
cnf(403,plain,
(E(f16(x4031,a1),x4031)),
inference(rename_variables,[],[41])).
cnf(405,plain,
(E(f16(x4051,a1),x4051)),
inference(rename_variables,[],[41])).
cnf(408,plain,
(E(x4081,f16(x4081,x4081))),
inference(rename_variables,[],[128])).
cnf(410,plain,
(E(f16(x4101,a1),x4101)),
inference(rename_variables,[],[41])).
cnf(413,plain,
(~P5(x4131,f12(f16(a1,x4132),x4132))),   inference(scs_inference,[],[37,48,41,399,401,403,405,410,51,56,35,40,118,334,338,342,350,357,364,367,371,387,390,54,38,55,142,314,317,320,333,337,149,150,165,237,128,261,131,362,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94,5,2,34,32,31,30,26,3,33,29,28])).
cnf(415,plain,
(P5(f16(f9(a6,a6,a1),f9(a6,a6,a1)),f12(a6,a1))),   inference(scs_inference,[],[37,48,41,399,401,403,405,410,51,56,35,40,118,334,338,342,350,357,364,367,371,387,390,54,38,55,142,314,317,320,333,337,149,150,165,237,128,408,261,131,362,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94,5,2,34,32,31,30,26,3,33,29,28,27])).
cnf(421,plain,
(P5(f4(a3,a6),a6)),   inference(scs_inference,[],[37,48,41,399,401,403,405,410,51,56,35,40,118,334,338,342,350,357,364,367,371,387,390,54,38,55,142,314,317,320,333,337,149,150,165,237,128,408,261,131,362,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94,5,2,34,32,31,30,26,3,33,29,28,27,70,61,126])).
cnf(423,plain,
(P5(f4(a3,a6),a3)),   inference(scs_inference,[],[37,48,41,399,401,403,405,410,51,56,35,40,118,334,338,342,350,357,364,367,371,387,390,54,38,55,142,314,317,320,333,337,149,150,165,237,128,408,261,131,362,255,156,186,259,62,121,120,123,106,104,95,82,81,80,74,71,67,63,57,110,109,108,105,98,97,92,91,83,73,112,102,93,69,65,60,125,84,77,100,87,94,5,2,34,32,31,30,26,3,33,29,28,27,70,61,126,122])).
cnf(456,plain,
(E(f12(x4561,a1),x4561)),
inference(rename_variables,[],[42])).
cnf(475,plain,
(~E(f12(a6,a1),f12(a1,x4751))),
inference(rename_variables,[],[389])).
cnf(476,plain,
(~P5(x4761,a1)),
inference(rename_variables,[],[118])).
cnf(479,plain,
(~P5(x4791,a1)),
inference(rename_variables,[],[118])).
cnf(482,plain,
(~P5(x4821,a1)),
inference(rename_variables,[],[118])).
cnf(491,plain,
(~P5(x4911,a1)),
inference(rename_variables,[],[118])).
cnf(495,plain,
(~P5(x4951,a1)),
inference(rename_variables,[],[118])).
cnf(498,plain,
(E(f12(x4981,a1),x4981)),
inference(rename_variables,[],[42])).
cnf(503,plain,
(E(f12(x5031,a1),x5031)),
inference(rename_variables,[],[42])).
cnf(512,plain,
(E(f12(x5121,a1),x5121)),
inference(rename_variables,[],[42])).
cnf(518,plain,
(~P5(x5181,a1)),
inference(rename_variables,[],[118])).
cnf(521,plain,
(~P5(x5211,a1)),
inference(rename_variables,[],[118])).
cnf(526,plain,
(E(x5261,f16(x5261,x5261))),
inference(rename_variables,[],[128])).
cnf(528,plain,
(P3(x5281,x5281)),
inference(rename_variables,[],[43])).
cnf(530,plain,
(E(f12(x5301,a1),x5301)),
inference(rename_variables,[],[42])).
cnf(532,plain,
(E(f12(x5321,a1),x5321)),
inference(rename_variables,[],[42])).
cnf(544,plain,
(\$false), inference(scs_inference,[],[37,42,456,498,503,512,530,532,49,52,50,43,528,47,48,118,476,479,482,491,495,518,521,54,38,377,133,313,359,138,180,392,415,322,398,389,475,283,423,245,275,421,400,413,386,225,373,128,526,62,123,106,74,71,67,63,92,83,93,82,81,80,65,60,127,110,109,108,73,126,97,112,94,69,100,77,122,87,124,86,85,5,32,31,30,26,3,2,29,28,27,104,57,91]),
['proof']).
% SZS output end Proof
```

## CSE_E 1.2

### Sample solution for SEU140+2

```% Proof found!
% SZS status Theorem for SEU140+2.p
% SZS output start Proof
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t63_xboole_1)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', t3_xboole_0)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', d4_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', l32_xboole_1)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/home/ars01/Desktop/dist/problems/SEU140+2.p', d1_xboole_0)).
fof(c_0_5, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
fof(c_0_6, lemma, ![X101, X102, X104, X105, X106]:(((in(esk9_2(X101,X102),X101)|disjoint(X101,X102))&(in(esk9_2(X101,X102),X102)|disjoint(X101,X102)))&(~in(X106,X104)|~in(X106,X105)|~disjoint(X104,X105))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])).
fof(c_0_7, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])).
fof(c_0_8, plain, ![X43, X44, X45, X46, X47, X48, X49, X50]:((((in(X46,X43)|~in(X46,X45)|X45!=set_difference(X43,X44))&(~in(X46,X44)|~in(X46,X45)|X45!=set_difference(X43,X44)))&(~in(X47,X43)|in(X47,X44)|in(X47,X45)|X45!=set_difference(X43,X44)))&((~in(esk5_3(X48,X49,X50),X50)|(~in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X49))|X50=set_difference(X48,X49))&((in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))&(~in(esk5_3(X48,X49,X50),X49)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])).
fof(c_0_9, lemma, ![X63, X64]:((set_difference(X63,X64)!=empty_set|subset(X63,X64))&(~subset(X63,X64)|set_difference(X63,X64)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
fof(c_0_10, plain, ![X15, X16, X17]:((X15!=empty_set|~in(X16,X15))&(in(esk1_1(X17),X17)|X17=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])).
cnf(c_0_11, lemma, (~in(X1,X2)|~in(X1,X3)|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6])).
cnf(c_0_12, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_7])).
cnf(c_0_13, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_7])).
cnf(c_0_14, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6])).
cnf(c_0_15, plain, (in(X1,X3)|in(X1,X4)|~in(X1,X2)|X4!=set_difference(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_16, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_17, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_7])).
cnf(c_0_18, plain, (X1!=empty_set|~in(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_19, negated_conjecture, (~in(X1,esk13_0)|~in(X1,esk12_0)), inference(spm,[status(thm)],[c_0_11, c_0_12])).
cnf(c_0_20, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_13, c_0_14])).
cnf(c_0_21, plain, (in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2)), inference(er,[status(thm)],[c_0_15])).
cnf(c_0_22, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_16, c_0_17])).
cnf(c_0_23, plain, (~in(X1,empty_set)), inference(er,[status(thm)],[c_0_18])).
cnf(c_0_24, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6])).
cnf(c_0_25, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_19, c_0_20])).
cnf(c_0_26, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22]), c_0_23])).
cnf(c_0_27, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_13, c_0_24])).
cnf(c_0_28, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])]), ['proof']).
% SZS output end Proof
```

## CVC4 1.8

Andrew Reynolds
University of Iowa, USA

### Sample proof for SET014^4

```% SZS output start Proof for SET014^4
(skolem (forall ((BOUND_VARIABLE_714 |u_(-> \$\$unsorted Bool)|) (BOUND_VARIABLE_710 |u_(-> \$\$unsorted Bool)|) (BOUND_VARIABLE_705 |u_(-> \$\$unsorted Bool)|) (BOUND_VARIABLE_673 \$\$unsorted)) (or (not (forall ((BOUND_VARIABLE_620 \$\$unsorted)) (or (not (ho_1 BOUND_VARIABLE_714 BOUND_VARIABLE_620)) (ho_1 BOUND_VARIABLE_705 BOUND_VARIABLE_620)) )) (not (forall ((BOUND_VARIABLE_628 \$\$unsorted)) (or (not (ho_1 BOUND_VARIABLE_710 BOUND_VARIABLE_628)) (ho_1 BOUND_VARIABLE_705 BOUND_VARIABLE_628)) )) (and (not (ho_1 BOUND_VARIABLE_714 BOUND_VARIABLE_673)) (not (ho_1 BOUND_VARIABLE_710 BOUND_VARIABLE_673))) (ho_1 BOUND_VARIABLE_705 BOUND_VARIABLE_673)) )
( skv_2 skv_3 skv_4 skv_5 )
)
(instantiation (forall ((BOUND_VARIABLE_620 \$\$unsorted)) (or (not (ho_1 skv_2 BOUND_VARIABLE_620)) (ho_1 skv_4 BOUND_VARIABLE_620)) )
( skv_5 )
)
(instantiation (forall ((BOUND_VARIABLE_628 \$\$unsorted)) (or (not (ho_1 skv_3 BOUND_VARIABLE_628)) (ho_1 skv_4 BOUND_VARIABLE_628)) )
( skv_5 )
)
% SZS output end Proof for SET014^4
```

### Sample proof for DAT013=1

```% SZS output start Proof for DAT013=1
(skolem (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_404 Int)) (let ((_let_0 (* (- 1) BOUND_VARIABLE_404))) (or (not (forall ((X Int)) (let ((_let_0 (* (- 1) X))) (or (>= (+ V _let_0) 1) (not (>= (+ W _let_0) 0)) (>= (read U X) 1))) )) (>= (+ V _let_0) (- 2)) (not (>= (+ W _let_0) 0)) (>= (read U BOUND_VARIABLE_404) 1))) )
( skv_1 skv_2 skv_3 skv_4 )
)
(instantiation (forall ((X Int)) (or (not (>= (+ X (* (- 1) skv_2)) 0)) (>= (+ X (* (- 1) skv_3)) 1) (>= (read skv_1 X) 1)) )
( skv_4 )
)
% SZS output end Proof for DAT013=1
```

### Sample proof for SEU140+2

```% SZS output start Proof for SEU140+2
(skolem (forall ((A \$\$unsorted)) (not (empty A)) )
( skv_1 )
)
(skolem (forall ((A \$\$unsorted)) (empty A) )
( skv_2 )
)
(skolem (forall ((A \$\$unsorted) (B \$\$unsorted) (C \$\$unsorted)) (or (not (subset A B)) (not (disjoint B C)) (disjoint A C)) )
( skv_3 skv_4 skv_5 )
)
(skolem (forall ((C \$\$unsorted)) (or (not (in C skv_3)) (not (in C skv_5))) )
( skv_6 )
)
(skolem (forall ((C \$\$unsorted)) (not (in C (set_intersection2 skv_3 skv_5))) )
( skv_7 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (= A B) (and (subset A B) (subset B A))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (proper_subset A B) (and (subset A B) (not (= A B)))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (subset (set_intersection2 A B) A) )
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_5 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (subset (set_difference A B) A) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (subset A (set_union2 A B)) )
( skv_3, skv_4 )
( skv_3, (set_difference skv_4 skv_3) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (in A B)) (not (in B A))) )
( skv_3, skv_6 )
( skv_5, skv_6 )
( (set_intersection2 skv_3 skv_5), skv_7 )
( skv_6, skv_3 )
( skv_6, skv_5 )
( skv_7, (set_intersection2 skv_3 skv_5) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (proper_subset A B)) (not (proper_subset B A))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (set_union2 B A) (set_union2 A B)) )
( skv_3, skv_4 )
( skv_3, (set_difference skv_4 skv_3) )
( skv_4, skv_3 )
( (set_difference skv_4 skv_3), skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (set_intersection2 B A) (set_intersection2 A B)) )
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_3 )
( skv_4, skv_5 )
( skv_5, skv_3 )
( skv_5, skv_4 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (subset A B) (forall ((C \$\$unsorted)) (or (not (in C A)) (in C B)) )) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (disjoint A B) (= empty_set (set_intersection2 A B))) )
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_5 )
( skv_5, skv_3 )
( skv_5, skv_4 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (empty A) (not (empty (set_union2 A B)))) )
( skv_3, skv_4 )
( skv_3, (set_difference skv_4 skv_3) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (empty A) (not (empty (set_union2 B A)))) )
( skv_4, skv_3 )
( (set_difference skv_4 skv_3), skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (= empty_set (set_difference A B)) (subset A B)) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (disjoint A B)) (disjoint B A)) )
( skv_3, skv_5 )
( skv_4, skv_5 )
( skv_5, skv_3 )
( skv_5, skv_4 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (= B (set_union2 A B))) )
( skv_3, skv_4 )
( skv_3, (set_difference skv_4 skv_3) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (C \$\$unsorted)) (or (not (subset A B)) (not (subset A C)) (subset A (set_intersection2 B C))) )
( skv_4, skv_3, skv_4 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (= A (set_intersection2 A B))) )
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_5 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (set_union2 A B) (set_union2 A (set_difference B A))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((BOUND_VARIABLE_847 \$\$unsorted) (BOUND_VARIABLE_848 \$\$unsorted)) (or (disjoint BOUND_VARIABLE_847 BOUND_VARIABLE_848) (not (forall ((C \$\$unsorted)) (or (not (in C BOUND_VARIABLE_847)) (not (in C BOUND_VARIABLE_848))) ))) )
( skv_3, skv_5 )
( skv_5, skv_3 )
)
(instantiation (forall ((BOUND_VARIABLE_860 \$\$unsorted) (BOUND_VARIABLE_861 \$\$unsorted) (BOUND_VARIABLE_874 \$\$unsorted)) (or (not (disjoint BOUND_VARIABLE_860 BOUND_VARIABLE_861)) (not (in BOUND_VARIABLE_874 BOUND_VARIABLE_860)) (not (in BOUND_VARIABLE_874 BOUND_VARIABLE_861))) )
( skv_5, skv_4, skv_6 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (set_difference A B) (set_difference (set_union2 A B) B)) )
( skv_3, skv_4 )
( skv_3, (set_difference skv_4 skv_3) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (= B (set_union2 A (set_difference B A)))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (= (set_intersection2 A B) (set_difference A (set_difference A B))) )
( skv_3, skv_4 )
( skv_3, skv_5 )
( skv_4, skv_5 )
)
(instantiation (forall ((BOUND_VARIABLE_913 \$\$unsorted) (BOUND_VARIABLE_914 \$\$unsorted)) (or (disjoint BOUND_VARIABLE_913 BOUND_VARIABLE_914) (not (forall ((C \$\$unsorted)) (not (in C (set_intersection2 BOUND_VARIABLE_913 BOUND_VARIABLE_914))) ))) )
( skv_3, skv_5 )
( skv_5, skv_3 )
)
(instantiation (forall ((BOUND_VARIABLE_924 \$\$unsorted) (BOUND_VARIABLE_925 \$\$unsorted) (BOUND_VARIABLE_936 \$\$unsorted)) (or (not (in BOUND_VARIABLE_936 (set_intersection2 BOUND_VARIABLE_924 BOUND_VARIABLE_925))) (not (disjoint BOUND_VARIABLE_924 BOUND_VARIABLE_925))) )
( skv_3, skv_4, skv_6 )
( skv_3, skv_5, skv_7 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (not (proper_subset B A))) )
( skv_3, skv_4 )
( skv_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted)) (or (not (empty A)) (= empty_set A)) )
( empty_set )
( skv_1 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (in A B)) (not (empty B))) )
( skv_6, skv_3 )
( skv_6, skv_5 )
( skv_7, (set_intersection2 skv_3 skv_5) )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (empty A)) (= A B) (not (empty B))) )
( empty_set, empty_set )
( empty_set, skv_1 )
( skv_1, empty_set )
( skv_1, skv_1 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (C \$\$unsorted)) (or (not (subset A B)) (not (subset C B)) (subset (set_union2 A C) B)) )
( skv_3, skv_3, (set_difference skv_4 skv_3) )
)
(instantiation (forall ((C \$\$unsorted)) (or (not (in C skv_3)) (in C skv_4)) )
( skv_6 )
)
% SZS output end Proof for SEU140+2
```

### Sample proof for NLP042+1

```% SZS output start FiniteModel for NLP042+1
(define-fun woman ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun female ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun human_person ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun animate ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun human ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun organism ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun living ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))
(define-fun impartial ((BOUND_VARIABLE_7737 \$\$unsorted) (BOUND_VARIABLE_7738 \$\$unsorted)) Bool true)
(define-fun entity ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)) true (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2))))
(define-fun mia_forename ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun forename ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun abstraction ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun unisex ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)) true (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)) true (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))))
(define-fun general ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun nonhuman ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun thing ((BOUND_VARIABLE_7737 \$\$unsorted) (BOUND_VARIABLE_7738 \$\$unsorted)) Bool true)
(define-fun relation ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun relname ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)))
(define-fun object ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)))
(define-fun nonliving ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)))
(define-fun existent ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)) true (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2))))
(define-fun specific ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)) true (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)) true (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_0 \$x2)))))
(define-fun substance_matter ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)))
(define-fun food ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)))
(define-fun beverage ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)))
(define-fun shake_beverage ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$x2)))
(define-fun order ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))
(define-fun event ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))
(define-fun eventuality ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))
(define-fun nonexistent ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))
(define-fun singleton ((BOUND_VARIABLE_7737 \$\$unsorted) (BOUND_VARIABLE_7738 \$\$unsorted)) Bool true)
(define-fun act ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))
(define-fun of ((BOUND_VARIABLE_7793 \$\$unsorted) (BOUND_VARIABLE_7794 \$\$unsorted) (BOUND_VARIABLE_7795 \$\$unsorted)) Bool true)
(define-fun nonreflexive ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted)) Bool (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2)))
(define-fun agent ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted) (\$x3 \$\$unsorted)) Bool (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2) (= @uc_\$\$unsorted_2 \$x3)) false (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2) (= @uc_\$\$unsorted_1 \$x3)) false (not (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2) (= @uc_\$\$unsorted_3 \$x3))))))
(define-fun patient ((\$x1 \$\$unsorted) (\$x2 \$\$unsorted) (\$x3 \$\$unsorted)) Bool (not (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_3 \$x2) (= @uc_\$\$unsorted_0 \$x3))))
(define-fun actual_world ((BOUND_VARIABLE_7806 \$\$unsorted)) Bool true)
(define-fun past ((BOUND_VARIABLE_7737 \$\$unsorted) (BOUND_VARIABLE_7738 \$\$unsorted)) Bool true)
; cardinality of \$\$unsorted is 4
(declare-sort \$\$unsorted 0)
; rep: @uc_\$\$unsorted_0
; rep: @uc_\$\$unsorted_1
; rep: @uc_\$\$unsorted_2
; rep: @uc_\$\$unsorted_3
% SZS output end FiniteModel for NLP042+1
```

### Sample proof for SWV017+1

```% SZS output start FiniteModel for SWV017+1
(define-fun at () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun t () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun key ((BOUND_VARIABLE_1613 \$\$unsorted) (BOUND_VARIABLE_1614 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun a_holds ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun a () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun party_of_protocol ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun b () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun an_a_nonce () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun pair ((BOUND_VARIABLE_1613 \$\$unsorted) (BOUND_VARIABLE_1614 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun sent ((BOUND_VARIABLE_1632 \$\$unsorted) (BOUND_VARIABLE_1633 \$\$unsorted) (BOUND_VARIABLE_1634 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun message ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun a_stored ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun quadruple ((BOUND_VARIABLE_1649 \$\$unsorted) (BOUND_VARIABLE_1650 \$\$unsorted) (BOUND_VARIABLE_1651 \$\$unsorted) (BOUND_VARIABLE_1652 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun encrypt ((BOUND_VARIABLE_1613 \$\$unsorted) (BOUND_VARIABLE_1614 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun triple ((BOUND_VARIABLE_1632 \$\$unsorted) (BOUND_VARIABLE_1633 \$\$unsorted) (BOUND_VARIABLE_1634 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun bt () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun b_holds ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun fresh_to_b ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun generate_b_nonce ((BOUND_VARIABLE_1667 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun generate_expiration_time ((BOUND_VARIABLE_1667 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
(define-fun b_stored ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun a_key ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool (= @uc_\$\$unsorted_1 BOUND_VARIABLE_1621))
(define-fun t_holds ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun a_nonce ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool (= @uc_\$\$unsorted_0 BOUND_VARIABLE_1621))
(define-fun generate_key ((BOUND_VARIABLE_1667 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_1)
(define-fun intruder_message ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun intruder_holds ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun an_intruder_nonce () \$\$unsorted @uc_\$\$unsorted_0)
(define-fun fresh_intruder_nonce ((BOUND_VARIABLE_1621 \$\$unsorted)) Bool true)
(define-fun generate_intruder_nonce ((BOUND_VARIABLE_1667 \$\$unsorted)) \$\$unsorted @uc_\$\$unsorted_0)
; cardinality of \$\$unsorted is 2
(declare-sort \$\$unsorted 0)
; rep: @uc_\$\$unsorted_0
; rep: @uc_\$\$unsorted_1
% SZS output end FiniteModel for SWV017+1
```

## E 2.4

Stephan Schulz
DHBW Stuttgart, Germany

### Sample solution for BOO001-1

```# SZS output start CNFRefutation
cnf(associativity, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('/Users/schulz/EPROVER/TPTP_7.2.0_FLAT/Axioms/BOO001-0.ax', associativity)).
cnf(ternary_multiply_1, axiom, (multiply(X1,X2,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.2.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_1)).
cnf(right_inverse, axiom, (multiply(X1,X2,inverse(X2))=X1), file('/Users/schulz/EPROVER/TPTP_7.2.0_FLAT/Axioms/BOO001-0.ax', right_inverse)).
cnf(ternary_multiply_2, axiom, (multiply(X1,X1,X2)=X1), file('/Users/schulz/EPROVER/TPTP_7.2.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_2)).
cnf(left_inverse, axiom, (multiply(inverse(X1),X1,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.2.0_FLAT/Axioms/BOO001-0.ax', left_inverse)).
cnf(prove_inverse_is_self_cancelling, negated_conjecture, (inverse(inverse(a))!=a), file('/Users/schulz/EPROVER/TPTP_7.2.0_FLAT/BOO001-1.p', prove_inverse_is_self_cancelling)).
cnf(c_0_6, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), associativity).
cnf(c_0_7, axiom, (multiply(X1,X2,X2)=X2), ternary_multiply_1).
cnf(c_0_8, plain, (multiply(multiply(X1,X2,X3),X4,X2)=multiply(X1,X2,multiply(X3,X4,X2))), inference(spm,[status(thm)],[c_0_6, c_0_7])).
cnf(c_0_9, axiom, (multiply(X1,X2,inverse(X2))=X1), right_inverse).
cnf(c_0_10, plain, (multiply(X1,X2,X3)=multiply(X1,X3,multiply(inverse(X3),X2,X3))), inference(spm,[status(thm)],[c_0_8, c_0_9])).
cnf(c_0_11, axiom, (multiply(X1,X1,X2)=X1), ternary_multiply_2).
cnf(c_0_12, axiom, (multiply(inverse(X1),X1,X2)=X2), left_inverse).
cnf(c_0_13, plain, (multiply(X1,inverse(X2),X2)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_9])).
cnf(c_0_14, negated_conjecture, (inverse(inverse(a))!=a), prove_inverse_is_self_cancelling).
cnf(c_0_15, plain, (inverse(inverse(X1))=X1), inference(spm,[status(thm)],[c_0_12, c_0_13])).
cnf(c_0_16, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])]), ['proof']).
# SZS output end CNFRefutation
```

## E 2.5

Stephan Schulz
DHBW Stuttgart, Germany

### Sample proof for SEU140+2

```# SZS output start CNFRefutation
fof(t4_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t4_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t48_xboole_1)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d1_xboole_0)).
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d3_xboole_0)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(subset(X1,X2)&subset(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d10_xboole_0)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t36_xboole_1)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_boole)).
fof(c_0_11, lemma, ![X115, X116, X118, X119, X120]:((disjoint(X115,X116)|in(esk10_2(X115,X116),set_intersection2(X115,X116)))&(~in(X120,set_intersection2(X118,X119))|~disjoint(X118,X119))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_xboole_0])])])])])])).
fof(c_0_12, lemma, ![X112, X113]:set_difference(X112,set_difference(X112,X113))=set_intersection2(X112,X113), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_13, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
cnf(c_0_14, lemma, (~in(X1,set_intersection2(X2,X3))|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_15, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])).
fof(c_0_16, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])).
cnf(c_0_17, lemma, (~disjoint(X2,X3)|~in(X1,set_difference(X2,set_difference(X2,X3)))), inference(rw,[status(thm)],[c_0_14, c_0_15])).
cnf(c_0_18, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
fof(c_0_19, plain, ![X15, X16, X17]:((X15!=empty_set|~in(X16,X15))&(in(esk1_1(X17),X17)|X17=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])).
fof(c_0_20, plain, ![X34, X35, X36, X37, X38, X39, X40, X41]:((((in(X37,X34)|~in(X37,X36)|X36!=set_intersection2(X34,X35))&(in(X37,X35)|~in(X37,X36)|X36!=set_intersection2(X34,X35)))&(~in(X38,X34)|~in(X38,X35)|in(X38,X36)|X36!=set_intersection2(X34,X35)))&((~in(esk4_3(X39,X40,X41),X41)|(~in(esk4_3(X39,X40,X41),X39)|~in(esk4_3(X39,X40,X41),X40))|X41=set_intersection2(X39,X40))&((in(esk4_3(X39,X40,X41),X39)|in(esk4_3(X39,X40,X41),X41)|X41=set_intersection2(X39,X40))&(in(esk4_3(X39,X40,X41),X40)|in(esk4_3(X39,X40,X41),X41)|X41=set_intersection2(X39,X40))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_21, plain, ![X43, X44, X45, X46, X47, X48, X49, X50]:((((in(X46,X43)|~in(X46,X45)|X45!=set_difference(X43,X44))&(~in(X46,X44)|~in(X46,X45)|X45!=set_difference(X43,X44)))&(~in(X47,X43)|in(X47,X44)|in(X47,X45)|X45!=set_difference(X43,X44)))&((~in(esk5_3(X48,X49,X50),X50)|(~in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X49))|X50=set_difference(X48,X49))&((in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))&(~in(esk5_3(X48,X49,X50),X49)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])).
fof(c_0_22, lemma, ![X101, X102, X104, X105, X106]:(((in(esk9_2(X101,X102),X101)|disjoint(X101,X102))&(in(esk9_2(X101,X102),X102)|disjoint(X101,X102)))&(~in(X106,X104)|~in(X106,X105)|~disjoint(X104,X105))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])).
fof(c_0_23, lemma, ![X63, X64]:((set_difference(X63,X64)!=empty_set|subset(X63,X64))&(~subset(X63,X64)|set_difference(X63,X64)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_24, negated_conjecture, (~in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0)))), inference(spm,[status(thm)],[c_0_17, c_0_18])).
cnf(c_0_25, plain, (in(esk1_1(X1),X1)|X1=empty_set), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_26, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_27, plain, (~in(X1,X2)|~in(X1,X3)|X3!=set_difference(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_28, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
cnf(c_0_29, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_30, plain, ![X13, X14]:(((subset(X13,X14)|X13!=X14)&(subset(X14,X13)|X13!=X14))&(~subset(X13,X14)|~subset(X14,X13)|X13=X14)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])).
cnf(c_0_31, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_32, negated_conjecture, (set_difference(esk12_0,set_difference(esk12_0,esk13_0))=empty_set), inference(spm,[status(thm)],[c_0_24, c_0_25])).
fof(c_0_33, lemma, ![X94, X95]:subset(set_difference(X94,X95),X94), inference(variable_rename,[status(thm)],[t36_xboole_1])).
cnf(c_0_34, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_26, c_0_15])).
cnf(c_0_35, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_36, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
fof(c_0_37, plain, ![X100]:set_difference(X100,empty_set)=X100, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_38, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_27])).
cnf(c_0_39, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_28, c_0_29])).
cnf(c_0_40, plain, (X1=X2|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_41, lemma, (subset(esk12_0,set_difference(esk12_0,esk13_0))), inference(spm,[status(thm)],[c_0_31, c_0_32])).
cnf(c_0_42, lemma, (subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_33])).
cnf(c_0_43, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_34])).
cnf(c_0_44, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_35, c_0_36])).
cnf(c_0_45, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_46, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_47, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0))), inference(spm,[status(thm)],[c_0_38, c_0_39])).
cnf(c_0_48, lemma, (set_difference(esk12_0,esk13_0)=esk12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42])])).
cnf(c_0_49, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45])).
cnf(c_0_50, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_28, c_0_46])).
cnf(c_0_51, lemma, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_47, c_0_48])).
cnf(c_0_52, negated_conjecture, (\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_51]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```# SZS output start Saturation
fof(ax26, axiom, ![X1, X2]:(beverage(X1,X2)=>food(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax26)).
fof(ax27, axiom, ![X1, X2]:(shake_beverage(X1,X2)=>beverage(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax27)).
fof(ax15, axiom, ![X1, X2]:(relname(X1,X2)=>relation(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax15)).
fof(ax16, axiom, ![X1, X2]:(forename(X1,X2)=>relname(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax16)).
fof(ax25, axiom, ![X1, X2]:(food(X1,X2)=>substance_matter(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax25)).
fof(co1, conjecture, ~(?[X1]:(actual_world(X1)&?[X2, X3, X4, X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', co1)).
fof(ax41, axiom, ![X1, X2]:(specific(X1,X2)=>~(general(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax41)).
fof(ax21, axiom, ![X1, X2]:(entity(X1,X2)=>specific(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax21)).
fof(ax39, axiom, ![X1, X2]:(nonhuman(X1,X2)=>~(human(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax39)).
fof(ax12, axiom, ![X1, X2]:(abstraction(X1,X2)=>nonhuman(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax12)).
fof(ax14, axiom, ![X1, X2]:(relation(X1,X2)=>abstraction(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax14)).
fof(ax42, axiom, ![X1, X2]:(unisex(X1,X2)=>~(female(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax42)).
fof(ax10, axiom, ![X1, X2]:(abstraction(X1,X2)=>unisex(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax10)).
fof(ax24, axiom, ![X1, X2]:(substance_matter(X1,X2)=>object(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax24)).
fof(ax31, axiom, ![X1, X2]:(eventuality(X1,X2)=>specific(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax31)).
fof(ax34, axiom, ![X1, X2]:(event(X1,X2)=>eventuality(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax34)).
fof(ax6, axiom, ![X1, X2]:(organism(X1,X2)=>entity(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax6)).
fof(ax7, axiom, ![X1, X2]:(human_person(X1,X2)=>organism(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax7)).
fof(ax8, axiom, ![X1, X2]:(woman(X1,X2)=>human_person(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax8)).
fof(ax11, axiom, ![X1, X2]:(abstraction(X1,X2)=>general(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax11)).
fof(ax40, axiom, ![X1, X2]:(nonliving(X1,X2)=>~(living(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax40)).
fof(ax19, axiom, ![X1, X2]:(object(X1,X2)=>nonliving(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax19)).
fof(ax37, axiom, ![X1, X2]:(animate(X1,X2)=>~(nonliving(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax37)).
fof(ax17, axiom, ![X1, X2]:(object(X1,X2)=>unisex(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax17)).
fof(ax38, axiom, ![X1, X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax38)).
fof(ax30, axiom, ![X1, X2]:(eventuality(X1,X2)=>nonexistent(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax30)).
fof(ax29, axiom, ![X1, X2]:(eventuality(X1,X2)=>unisex(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax29)).
fof(ax44, axiom, ![X1, X2, X3, X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>X3!=X4), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax44)).
fof(ax43, axiom, ![X1, X2, X3]:(((entity(X1,X2)&forename(X1,X3))&of(X1,X3,X2))=>~(?[X4]:((forename(X1,X4)&X4!=X3)&of(X1,X4,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax43)).
fof(ax3, axiom, ![X1, X2]:(human_person(X1,X2)=>human(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax3)).
fof(ax1, axiom, ![X1, X2]:(woman(X1,X2)=>female(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax1)).
fof(ax4, axiom, ![X1, X2]:(organism(X1,X2)=>living(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax4)).
fof(ax2, axiom, ![X1, X2]:(human_person(X1,X2)=>animate(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax2)).
fof(ax20, axiom, ![X1, X2]:(entity(X1,X2)=>existent(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax20)).
fof(ax23, axiom, ![X1, X2]:(object(X1,X2)=>entity(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax23)).
fof(ax35, axiom, ![X1, X2]:(act(X1,X2)=>event(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax35)).
fof(ax28, axiom, ![X1, X2]:(order(X1,X2)=>event(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax28)).
fof(ax36, axiom, ![X1, X2]:(order(X1,X2)=>act(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax36)).
fof(ax32, axiom, ![X1, X2]:(thing(X1,X2)=>singleton(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax32)).
fof(ax9, axiom, ![X1, X2]:(mia_forename(X1,X2)=>forename(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax9)).
fof(ax33, axiom, ![X1, X2]:(eventuality(X1,X2)=>thing(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax33)).
fof(ax13, axiom, ![X1, X2]:(abstraction(X1,X2)=>thing(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax13)).
fof(ax22, axiom, ![X1, X2]:(entity(X1,X2)=>thing(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax22)).
fof(ax18, axiom, ![X1, X2]:(object(X1,X2)=>impartial(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax18)).
fof(ax5, axiom, ![X1, X2]:(organism(X1,X2)=>impartial(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/NLP042+1.p', ax5)).
fof(c_0_45, plain, ![X56, X57]:(~beverage(X56,X57)|food(X56,X57)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])).
fof(c_0_46, plain, ![X58, X59]:(~shake_beverage(X58,X59)|beverage(X58,X59)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])).
fof(c_0_47, plain, ![X34, X35]:(~relname(X34,X35)|relation(X34,X35)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])).
fof(c_0_48, plain, ![X36, X37]:(~forename(X36,X37)|relname(X36,X37)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])).
fof(c_0_49, plain, ![X54, X55]:(~food(X54,X55)|substance_matter(X54,X55)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])).
cnf(c_0_50, plain, (food(X1,X2)|~beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_51, plain, (beverage(X1,X2)|~shake_beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46]), ['final']).
fof(c_0_52, negated_conjecture, ~(~(?[X1]:(actual_world(X1)&?[X2, X3, X4, X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))))), inference(assume_negation,[status(cth)],[co1])).
fof(c_0_53, plain, ![X86, X87]:(~specific(X86,X87)|~general(X86,X87)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax41])])])).
fof(c_0_54, plain, ![X46, X47]:(~entity(X46,X47)|specific(X46,X47)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])).
fof(c_0_55, plain, ![X82, X83]:(~nonhuman(X82,X83)|~human(X82,X83)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax39])])])).
fof(c_0_56, plain, ![X28, X29]:(~abstraction(X28,X29)|nonhuman(X28,X29)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])).
fof(c_0_57, plain, ![X32, X33]:(~relation(X32,X33)|abstraction(X32,X33)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])])).
cnf(c_0_58, plain, (relation(X1,X2)|~relname(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_47]), ['final']).
cnf(c_0_59, plain, (relname(X1,X2)|~forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
fof(c_0_60, plain, ![X88, X89]:(~unisex(X88,X89)|~female(X88,X89)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax42])])])).
fof(c_0_61, plain, ![X24, X25]:(~abstraction(X24,X25)|unisex(X24,X25)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax10])])).
fof(c_0_62, plain, ![X52, X53]:(~substance_matter(X52,X53)|object(X52,X53)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])])).
cnf(c_0_63, plain, (substance_matter(X1,X2)|~food(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
cnf(c_0_64, plain, (food(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_50, c_0_51]), ['final']).
fof(c_0_65, plain, ![X66, X67]:(~eventuality(X66,X67)|specific(X66,X67)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])).
fof(c_0_66, plain, ![X72, X73]:(~event(X72,X73)|eventuality(X72,X73)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])])).
fof(c_0_67, negated_conjecture, (actual_world(esk1_0)&((((((((((of(esk1_0,esk3_0,esk2_0)&woman(esk1_0,esk2_0))&mia_forename(esk1_0,esk3_0))&forename(esk1_0,esk3_0))&shake_beverage(esk1_0,esk4_0))&event(esk1_0,esk5_0))&agent(esk1_0,esk5_0,esk2_0))&patient(esk1_0,esk5_0,esk4_0))&past(esk1_0,esk5_0))&nonreflexive(esk1_0,esk5_0))&order(esk1_0,esk5_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])).
fof(c_0_68, plain, ![X16, X17]:(~organism(X16,X17)|entity(X16,X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])).
fof(c_0_69, plain, ![X18, X19]:(~human_person(X18,X19)|organism(X18,X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])).
fof(c_0_70, plain, ![X20, X21]:(~woman(X20,X21)|human_person(X20,X21)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])).
cnf(c_0_71, plain, (~specific(X1,X2)|~general(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_53]), ['final']).
cnf(c_0_72, plain, (specific(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54]), ['final']).
fof(c_0_73, plain, ![X26, X27]:(~abstraction(X26,X27)|general(X26,X27)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])).
cnf(c_0_74, plain, (~nonhuman(X1,X2)|~human(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_55]), ['final']).
cnf(c_0_75, plain, (nonhuman(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_56]), ['final']).
cnf(c_0_76, plain, (abstraction(X1,X2)|~relation(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_57]), ['final']).
cnf(c_0_77, plain, (relation(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_58, c_0_59]), ['final']).
cnf(c_0_78, plain, (~unisex(X1,X2)|~female(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_79, plain, (unisex(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61]), ['final']).
fof(c_0_80, plain, ![X84, X85]:(~nonliving(X84,X85)|~living(X84,X85)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax40])])])).
fof(c_0_81, plain, ![X42, X43]:(~object(X42,X43)|nonliving(X42,X43)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])).
cnf(c_0_82, plain, (object(X1,X2)|~substance_matter(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62]), ['final']).
cnf(c_0_83, plain, (substance_matter(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_63, c_0_64]), ['final']).
fof(c_0_84, plain, ![X78, X79]:(~animate(X78,X79)|~nonliving(X78,X79)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax37])])])).
fof(c_0_85, plain, ![X38, X39]:(~object(X38,X39)|unisex(X38,X39)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax17])])).
fof(c_0_86, plain, ![X80, X81]:(~existent(X80,X81)|~nonexistent(X80,X81)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax38])])])).
fof(c_0_87, plain, ![X64, X65]:(~eventuality(X64,X65)|nonexistent(X64,X65)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])])).
cnf(c_0_88, plain, (specific(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_65]), ['final']).
cnf(c_0_89, plain, (eventuality(X1,X2)|~event(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_90, negated_conjecture, (event(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
fof(c_0_91, plain, ![X62, X63]:(~eventuality(X62,X63)|unisex(X62,X63)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])).
cnf(c_0_92, plain, (entity(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_68]), ['final']).
cnf(c_0_93, plain, (organism(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_69]), ['final']).
cnf(c_0_94, plain, (human_person(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_70]), ['final']).
cnf(c_0_95, negated_conjecture, (woman(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
fof(c_0_96, plain, ![X94, X95, X96, X97]:(~nonreflexive(X94,X95)|~agent(X94,X95,X96)|~patient(X94,X95,X97)|X96!=X97), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])).
cnf(c_0_97, plain, (~general(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_71, c_0_72]), ['final']).
cnf(c_0_98, plain, (general(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_73]), ['final']).
cnf(c_0_99, plain, (~abstraction(X1,X2)|~human(X1,X2)), inference(spm,[status(thm)],[c_0_74, c_0_75]), ['final']).
cnf(c_0_100, plain, (abstraction(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_76, c_0_77]), ['final']).
cnf(c_0_101, plain, (~abstraction(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_78, c_0_79]), ['final']).
cnf(c_0_102, plain, (~nonliving(X1,X2)|~living(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_80]), ['final']).
cnf(c_0_103, plain, (nonliving(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_81]), ['final']).
cnf(c_0_104, plain, (object(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_82, c_0_83]), ['final']).
cnf(c_0_105, negated_conjecture, (shake_beverage(esk1_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_106, plain, (~animate(X1,X2)|~nonliving(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_84]), ['final']).
cnf(c_0_107, plain, (unisex(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85]), ['final']).
cnf(c_0_108, plain, (~existent(X1,X2)|~nonexistent(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86]), ['final']).
cnf(c_0_109, plain, (nonexistent(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_87]), ['final']).
cnf(c_0_110, plain, (~eventuality(X1,X2)|~general(X1,X2)), inference(spm,[status(thm)],[c_0_71, c_0_88]), ['final']).
cnf(c_0_111, negated_conjecture, (eventuality(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_89, c_0_90]), ['final']).
cnf(c_0_112, plain, (unisex(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_91]), ['final']).
fof(c_0_113, plain, ![X90, X91, X92, X93]:(~entity(X90,X91)|~forename(X90,X92)|~of(X90,X92,X91)|(~forename(X90,X93)|X93=X92|~of(X90,X93,X91))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])).
cnf(c_0_114, plain, (entity(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_92, c_0_93]), ['final']).
cnf(c_0_115, negated_conjecture, (human_person(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_94, c_0_95]), ['final']).
cnf(c_0_116, plain, (~nonreflexive(X1,X2)|~agent(X1,X2,X3)|~patient(X1,X2,X4)|X3!=X4), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_117, plain, (~abstraction(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_97, c_0_98]), ['final']).
cnf(c_0_118, plain, (~forename(X1,X2)|~human(X1,X2)), inference(spm,[status(thm)],[c_0_99, c_0_100]), ['final']).
cnf(c_0_119, negated_conjecture, (forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
fof(c_0_120, plain, ![X10, X11]:(~human_person(X10,X11)|human(X10,X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])).
cnf(c_0_121, plain, (~forename(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_101, c_0_100]), ['final']).
fof(c_0_122, plain, ![X6, X7]:(~woman(X6,X7)|female(X6,X7)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])).
cnf(c_0_123, plain, (~object(X1,X2)|~living(X1,X2)), inference(spm,[status(thm)],[c_0_102, c_0_103]), ['final']).
cnf(c_0_124, negated_conjecture, (object(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_104, c_0_105]), ['final']).
fof(c_0_125, plain, ![X12, X13]:(~organism(X12,X13)|living(X12,X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])).
cnf(c_0_126, plain, (~object(X1,X2)|~animate(X1,X2)), inference(spm,[status(thm)],[c_0_106, c_0_103]), ['final']).
fof(c_0_127, plain, ![X8, X9]:(~human_person(X8,X9)|animate(X8,X9)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])).
cnf(c_0_128, plain, (~object(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_78, c_0_107]), ['final']).
cnf(c_0_129, plain, (~eventuality(X1,X2)|~existent(X1,X2)), inference(spm,[status(thm)],[c_0_108, c_0_109]), ['final']).
fof(c_0_130, plain, ![X44, X45]:(~entity(X44,X45)|existent(X44,X45)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])).
cnf(c_0_131, negated_conjecture, (~general(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_110, c_0_111]), ['final']).
cnf(c_0_132, plain, (~eventuality(X1,X2)|~female(X1,X2)), inference(spm,[status(thm)],[c_0_78, c_0_112]), ['final']).
fof(c_0_133, plain, ![X50, X51]:(~object(X50,X51)|entity(X50,X51)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])).
cnf(c_0_134, plain, (X4=X3|~entity(X1,X2)|~forename(X1,X3)|~of(X1,X3,X2)|~forename(X1,X4)|~of(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_113]), ['final']).
cnf(c_0_135, negated_conjecture, (of(esk1_0,esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_136, negated_conjecture, (entity(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_114, c_0_115]), ['final']).
fof(c_0_137, plain, ![X74, X75]:(~act(X74,X75)|event(X74,X75)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])])).
fof(c_0_138, plain, ![X60, X61]:(~order(X60,X61)|event(X60,X61)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])).
fof(c_0_139, plain, ![X76, X77]:(~order(X76,X77)|act(X76,X77)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])).
fof(c_0_140, plain, ![X68, X69]:(~thing(X68,X69)|singleton(X68,X69)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])])).
fof(c_0_141, plain, ![X22, X23]:(~mia_forename(X22,X23)|forename(X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])).
fof(c_0_142, plain, ![X70, X71]:(~eventuality(X70,X71)|thing(X70,X71)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])])).
fof(c_0_143, plain, ![X30, X31]:(~abstraction(X30,X31)|thing(X30,X31)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])).
fof(c_0_144, plain, ![X48, X49]:(~entity(X48,X49)|thing(X48,X49)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])])).
fof(c_0_145, plain, ![X40, X41]:(~object(X40,X41)|impartial(X40,X41)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])).
fof(c_0_146, plain, ![X14, X15]:(~organism(X14,X15)|impartial(X14,X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])).
cnf(c_0_147, plain, (~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)), inference(er,[status(thm)],[c_0_116]), ['final']).
cnf(c_0_148, negated_conjecture, (patient(esk1_0,esk5_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_149, negated_conjecture, (nonreflexive(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_150, plain, (~forename(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_117, c_0_100]), ['final']).
cnf(c_0_151, negated_conjecture, (~human(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_118, c_0_119]), ['final']).
cnf(c_0_152, plain, (human(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_120]), ['final']).
cnf(c_0_153, negated_conjecture, (~female(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_121, c_0_119]), ['final']).
cnf(c_0_154, plain, (female(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_122]), ['final']).
cnf(c_0_155, negated_conjecture, (~living(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_123, c_0_124]), ['final']).
cnf(c_0_156, plain, (living(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_125]), ['final']).
cnf(c_0_157, negated_conjecture, (~animate(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_126, c_0_124]), ['final']).
cnf(c_0_158, plain, (animate(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_127]), ['final']).
cnf(c_0_159, negated_conjecture, (~female(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_128, c_0_124]), ['final']).
cnf(c_0_160, negated_conjecture, (~existent(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_129, c_0_111]), ['final']).
cnf(c_0_161, plain, (existent(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_130]), ['final']).
cnf(c_0_162, negated_conjecture, (~abstraction(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_131, c_0_98]), ['final']).
cnf(c_0_163, negated_conjecture, (~female(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_132, c_0_111]), ['final']).
cnf(c_0_164, plain, (entity(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_133]), ['final']).
cnf(c_0_165, negated_conjecture, (X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135]), c_0_119])]), c_0_136])]), ['final']).
cnf(c_0_166, plain, (event(X1,X2)|~act(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_137]), ['final']).
cnf(c_0_167, plain, (event(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_138]), ['final']).
cnf(c_0_168, plain, (act(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_139]), ['final']).
cnf(c_0_169, plain, (singleton(X1,X2)|~thing(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_140]), ['final']).
cnf(c_0_170, plain, (forename(X1,X2)|~mia_forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_141]), ['final']).
cnf(c_0_171, plain, (thing(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_142]), ['final']).
cnf(c_0_172, plain, (thing(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_143]), ['final']).
cnf(c_0_173, plain, (thing(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_144]), ['final']).
cnf(c_0_174, plain, (impartial(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_145]), ['final']).
cnf(c_0_175, plain, (impartial(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_146]), ['final']).
cnf(c_0_176, negated_conjecture, (~agent(esk1_0,esk5_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_148]), c_0_149])]), ['final']).
cnf(c_0_177, negated_conjecture, (~entity(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_150, c_0_119]), ['final']).
cnf(c_0_178, negated_conjecture, (~human_person(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_151, c_0_152]), ['final']).
cnf(c_0_179, negated_conjecture, (~woman(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_153, c_0_154]), ['final']).
cnf(c_0_180, negated_conjecture, (~organism(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_155, c_0_156]), ['final']).
cnf(c_0_181, negated_conjecture, (~human_person(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_157, c_0_158]), ['final']).
cnf(c_0_182, negated_conjecture, (~woman(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_159, c_0_154]), ['final']).
cnf(c_0_183, negated_conjecture, (~entity(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_160, c_0_161]), ['final']).
cnf(c_0_184, negated_conjecture, (~forename(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_162, c_0_100]), ['final']).
cnf(c_0_185, negated_conjecture, (~woman(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_163, c_0_154]), ['final']).
cnf(c_0_186, negated_conjecture, (entity(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_164, c_0_124]), ['final']).
cnf(c_0_187, negated_conjecture, (agent(esk1_0,esk5_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_188, negated_conjecture, (past(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_189, negated_conjecture, (order(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_190, negated_conjecture, (mia_forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_191, negated_conjecture, (actual_world(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
# SZS output end Saturation
```

### Sample solution for SWV017+1

```# SZS output start Saturation
fof(server_t_generates_key, axiom, ![X1, X2, X3, X4, X5, X6, X7]:((((message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6))))&t_holds(key(X6,X1)))&t_holds(key(X7,X3)))&a_nonce(X4))=>message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', server_t_generates_key)).
fof(b_creates_freash_nonces_in_time, axiom, ![X1, X2]:((message(sent(X1,b,pair(X1,X2)))&fresh_to_b(X2))=>(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
fof(t_holds_key_at_for_a, axiom, t_holds(key(at,a)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
fof(intruder_can_record, axiom, ![X1, X2, X3]:(message(sent(X1,X2,X3))=>intruder_message(X3)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_can_record)).
fof(a_sent_message_i_to_b, axiom, message(sent(a,b,pair(a,an_a_nonce))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)).
fof(nonce_a_is_fresh_to_b, axiom, fresh_to_b(an_a_nonce), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(a_forwards_secure, axiom, ![X1, X2, X3, X4, X5, X6]:((message(sent(t,a,triple(encrypt(quadruple(X5,X6,X3,X2),at),X4,X1)))&a_stored(pair(X5,X6)))=>(message(sent(a,X5,pair(X4,encrypt(X1,X3))))&a_holds(key(X3,X5)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_forwards_secure)).
fof(t_holds_key_bt_for_b, axiom, t_holds(key(bt,b)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(intruder_message_sent, axiom, ![X1, X2, X3]:(((intruder_message(X1)&party_of_protocol(X2))&party_of_protocol(X3))=>message(sent(X2,X3,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(intruder_decomposes_triples, axiom, ![X1, X2, X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_decomposes_triples)).
fof(a_stored_message_i, axiom, a_stored(pair(b,an_a_nonce)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_stored_message_i)).
fof(an_a_nonce_is_a_nonce, axiom, a_nonce(an_a_nonce), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(b_is_party_of_protocol, axiom, party_of_protocol(b), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_is_party_of_protocol)).
fof(intruder_composes_pairs, axiom, ![X1, X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(t_is_party_of_protocol, axiom, party_of_protocol(t), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', t_is_party_of_protocol)).
fof(intruder_composes_triples, axiom, ![X1, X2, X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_composes_triples)).
fof(a_is_party_of_protocol, axiom, party_of_protocol(a), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
fof(b_accepts_secure_session_key, axiom, ![X2, X4, X5]:(((message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))&a_key(X2))&b_stored(pair(X4,X5)))=>b_holds(key(X2,X4))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(intruder_decomposes_pairs, axiom, ![X1, X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(intruder_key_encrypts, axiom, ![X1, X2, X3]:(((intruder_message(X1)&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(encrypt(X1,X2))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_key_encrypts)).
fof(intruder_holds_key, axiom, ![X2, X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(generated_keys_are_keys, axiom, ![X1]:a_key(generate_key(X1)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', generated_keys_are_keys)).
fof(fresh_intruder_nonces_are_fresh_to_b, axiom, ![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)).
fof(can_generate_more_fresh_intruder_nonces, axiom, ![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)).
fof(intruder_interception, axiom, ![X1, X2, X3]:(((intruder_message(encrypt(X1,X2))&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', intruder_interception)).
fof(nothing_is_a_nonce_and_a_key, axiom, ![X1]:~((a_key(X1)&a_nonce(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)).
fof(generated_keys_are_not_nonces, axiom, ![X1]:~(a_nonce(generate_key(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
fof(an_intruder_nonce_is_a_fresh_intruder_nonce, axiom, fresh_intruder_nonce(an_intruder_nonce), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(generated_times_and_nonces_are_nonces, axiom, ![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(b_hold_key_bt_for_t, axiom, b_holds(key(bt,t)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)).
fof(a_holds_key_at_for_t, axiom, a_holds(key(at,t)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
fof(c_0_33, plain, ![X19, X20, X21, X22, X23, X24, X25]:(~message(sent(X19,t,triple(X19,X20,encrypt(triple(X21,X22,X23),X24))))|~t_holds(key(X24,X19))|~t_holds(key(X25,X21))|~a_nonce(X22)|message(sent(t,X21,triple(encrypt(quadruple(X19,X22,generate_key(X22),X23),X25),encrypt(triple(X21,generate_key(X22),X23),X24),X20)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[server_t_generates_key])])).
fof(c_0_34, plain, ![X14, X15]:((message(sent(b,t,triple(b,generate_b_nonce(X15),encrypt(triple(X14,X15,generate_expiration_time(X15)),bt))))|(~message(sent(X14,b,pair(X14,X15)))|~fresh_to_b(X15)))&(b_stored(pair(X14,X15))|(~message(sent(X14,b,pair(X14,X15)))|~fresh_to_b(X15)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_creates_freash_nonces_in_time])])])).
cnf(c_0_36, plain, (t_holds(key(at,a))), inference(split_conjunct,[status(thm)],[t_holds_key_at_for_a]), ['final']).
fof(c_0_37, plain, ![X26, X27, X28]:(~message(sent(X26,X27,X28))|intruder_message(X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_can_record])])).
cnf(c_0_38, plain, (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~message(sent(X2,b,pair(X2,X1)))|~fresh_to_b(X1)), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']).
cnf(c_0_39, plain, (message(sent(a,b,pair(a,an_a_nonce)))), inference(split_conjunct,[status(thm)],[a_sent_message_i_to_b]), ['final']).
cnf(c_0_40, plain, (fresh_to_b(an_a_nonce)), inference(split_conjunct,[status(thm)],[nonce_a_is_fresh_to_b]), ['final']).
cnf(c_0_42, plain, (message(sent(t,a,triple(encrypt(quadruple(X1,X2,generate_key(X2),X3),at),encrypt(triple(a,generate_key(X2),X3),X4),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(X1,t,triple(X1,X5,encrypt(triple(a,X2,X3),X4))))), inference(spm,[status(thm)],[c_0_35, c_0_36]), ['final']).
cnf(c_0_43, plain, (t_holds(key(bt,b))), inference(split_conjunct,[status(thm)],[t_holds_key_bt_for_b]), ['final']).
fof(c_0_44, plain, ![X50, X51, X52]:(~intruder_message(X50)|~party_of_protocol(X51)|~party_of_protocol(X52)|message(sent(X51,X52,X50))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_message_sent])])).
fof(c_0_45, plain, ![X31, X32, X33]:(((intruder_message(X31)|~intruder_message(triple(X31,X32,X33)))&(intruder_message(X32)|~intruder_message(triple(X31,X32,X33))))&(intruder_message(X33)|~intruder_message(triple(X31,X32,X33)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_triples])])])).
cnf(c_0_46, plain, (intruder_message(X3)|~message(sent(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_37]), ['final']).
cnf(c_0_47, plain, (message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])]), ['final']).
cnf(c_0_49, plain, (a_stored(pair(b,an_a_nonce))), inference(split_conjunct,[status(thm)],[a_stored_message_i]), ['final']).
cnf(c_0_50, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(a,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_42, c_0_43]), ['final']).
cnf(c_0_51, plain, (a_nonce(an_a_nonce)), inference(split_conjunct,[status(thm)],[an_a_nonce_is_a_nonce]), ['final']).
cnf(c_0_52, plain, (b_stored(pair(X1,X2))|~message(sent(X1,b,pair(X1,X2)))|~fresh_to_b(X2)), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']).
cnf(c_0_53, plain, (message(sent(X2,X3,X1))|~intruder_message(X1)|~party_of_protocol(X2)|~party_of_protocol(X3)), inference(split_conjunct,[status(thm)],[c_0_44]), ['final']).
cnf(c_0_54, plain, (party_of_protocol(b)), inference(split_conjunct,[status(thm)],[b_is_party_of_protocol]), ['final']).
fof(c_0_55, plain, ![X38, X39]:(~intruder_message(X38)|~intruder_message(X39)|intruder_message(pair(X38,X39))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_pairs])])).
cnf(c_0_56, plain, (party_of_protocol(t)), inference(split_conjunct,[status(thm)],[t_is_party_of_protocol]), ['final']).
fof(c_0_57, plain, ![X40, X41, X42]:(~intruder_message(X40)|~intruder_message(X41)|~intruder_message(X42)|intruder_message(triple(X40,X41,X42))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_triples])])).
cnf(c_0_58, plain, (intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_59, plain, (intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))), inference(spm,[status(thm)],[c_0_46, c_0_47]), ['final']).
cnf(c_0_60, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2)))), inference(spm,[status(thm)],[c_0_48, c_0_49]), ['final']).
cnf(c_0_61, plain, (party_of_protocol(a)), inference(split_conjunct,[status(thm)],[a_is_party_of_protocol]), ['final']).
cnf(c_0_62, plain, (message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_47]), c_0_51])]), ['final']).
fof(c_0_63, plain, ![X16, X17, X18]:(~message(sent(X17,b,pair(encrypt(triple(X17,X16,generate_expiration_time(X18)),bt),encrypt(generate_b_nonce(X18),X16))))|~a_key(X16)|~b_stored(pair(X17,X18))|b_holds(key(X16,X17))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_accepts_secure_session_key])])).
cnf(c_0_64, plain, (b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54])]), ['final']).
cnf(c_0_65, plain, (intruder_message(pair(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(split_conjunct,[status(thm)],[c_0_55]), ['final']).
fof(c_0_66, plain, ![X29, X30]:((intruder_message(X29)|~intruder_message(pair(X29,X30)))&(intruder_message(X30)|~intruder_message(pair(X29,X30)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_pairs])])])).
cnf(c_0_67, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_53]), c_0_56]), c_0_54])]), ['final']).
cnf(c_0_68, plain, (intruder_message(triple(X1,X2,X3))|~intruder_message(X1)|~intruder_message(X2)|~intruder_message(X3)), inference(split_conjunct,[status(thm)],[c_0_57]), ['final']).
cnf(c_0_69, plain, (intruder_message(b)), inference(spm,[status(thm)],[c_0_58, c_0_59]), ['final']).
cnf(c_0_70, plain, (intruder_message(X1)|~intruder_message(triple(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_71, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_53]), c_0_61]), c_0_56])]), ['final']).
cnf(c_0_72, plain, (intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))), inference(spm,[status(thm)],[c_0_46, c_0_62]), ['final']).
cnf(c_0_73, plain, (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(pair(X2,X1))|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_53]), c_0_54])]), ['final']).
cnf(c_0_74, plain, (b_holds(key(X2,X1))|~message(sent(X1,b,pair(encrypt(triple(X1,X2,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X2))))|~a_key(X2)|~b_stored(pair(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_63]), ['final']).
cnf(c_0_75, plain, (b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_64, c_0_65]), ['final']).
fof(c_0_76, plain, ![X55, X56, X57]:(~intruder_message(X55)|~intruder_holds(key(X56,X57))|~party_of_protocol(X57)|intruder_message(encrypt(X55,X56))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_key_encrypts])])).
fof(c_0_77, plain, ![X53, X54]:(~intruder_message(X53)|~party_of_protocol(X54)|intruder_holds(key(X53,X54))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_holds_key])])).
cnf(c_0_78, plain, (intruder_message(X1)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_79, plain, (intruder_message(pair(a,an_a_nonce))), inference(spm,[status(thm)],[c_0_46, c_0_39]), ['final']).
cnf(c_0_80, plain, (message(sent(t,b,triple(encrypt(quadruple(X1,X2,generate_key(X2),X3),bt),encrypt(triple(b,generate_key(X2),X3),X4),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(X1,t,triple(X1,X5,encrypt(triple(b,X2,X3),X4))))), inference(spm,[status(thm)],[c_0_35, c_0_43]), ['final']).
cnf(c_0_81, plain, (b_stored(pair(a,an_a_nonce))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_39]), c_0_40])]), ['final']).
cnf(c_0_82, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69])]), ['final']).
cnf(c_0_83, plain, (intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_70, c_0_59]), ['final']).
cnf(c_0_84, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X3,X4),at))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_71, c_0_68]), ['final']).
cnf(c_0_85, plain, (intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))), inference(spm,[status(thm)],[c_0_58, c_0_72]), ['final']).
cnf(c_0_86, plain, (message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_73, c_0_65]), ['final']).
cnf(c_0_87, plain, (b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_74, c_0_75]), ['final']).
cnf(c_0_88, plain, (intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_holds(key(X2,X3))|~party_of_protocol(X3)), inference(split_conjunct,[status(thm)],[c_0_76]), ['final']).
cnf(c_0_89, plain, (intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_90, plain, (intruder_message(a)), inference(spm,[status(thm)],[c_0_78, c_0_79]), ['final']).
cnf(c_0_91, plain, (message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))), inference(spm,[status(thm)],[c_0_60, c_0_62]), ['final']).
cnf(c_0_92, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(b,X1,X2),bt))))), inference(spm,[status(thm)],[c_0_80, c_0_43]), ['final']).
cnf(c_0_93, plain, (b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))), inference(spm,[status(thm)],[c_0_74, c_0_81]), ['final']).
cnf(c_0_95, plain, (message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_51])]), ['final']).
cnf(c_0_96, plain, (message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_84, c_0_85]), ['final']).
cnf(c_0_97, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(a,X1,X2),at))))), inference(spm,[status(thm)],[c_0_42, c_0_36]), ['final']).
cnf(c_0_98, plain, (intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_46, c_0_86]), ['final']).
cnf(c_0_99, plain, (b_holds(key(X1,X2))|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_53]), c_0_54])]), ['final']).
cnf(c_0_100, plain, (intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_88, c_0_89])).
cnf(c_0_101, plain, (intruder_message(X1)|~intruder_message(triple(X2,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_102, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_86]), c_0_90]), c_0_61])]), ['final']).
fof(c_0_103, plain, ![X61]:a_key(generate_key(X61)), inference(variable_rename,[status(thm)],[generated_keys_are_keys])).
cnf(c_0_104, plain, (intruder_message(X1)|~intruder_message(pair(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_105, plain, (intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))), inference(spm,[status(thm)],[c_0_46, c_0_91]), ['final']).
cnf(c_0_106, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(b,X1,X2),at))))), inference(spm,[status(thm)],[c_0_80, c_0_36]), ['final']).
cnf(c_0_107, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_53]), c_0_56]), c_0_54])]), ['final']).
cnf(c_0_108, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_86]), c_0_69]), c_0_54])]), ['final']).
cnf(c_0_109, plain, (b_holds(key(X1,a))|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_53]), c_0_54]), c_0_61])]), ['final']).
cnf(c_0_110, plain, (a_holds(key(X1,b))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4)))), inference(spm,[status(thm)],[c_0_94, c_0_49]), ['final']).
fof(c_0_111, plain, ![X63]:((fresh_to_b(X63)|~fresh_intruder_nonce(X63))&(intruder_message(X63)|~fresh_intruder_nonce(X63))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fresh_intruder_nonces_are_fresh_to_b])])])).
cnf(c_0_112, plain, (message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_60, c_0_95]), ['final']).
cnf(c_0_113, plain, (intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_96]), ['final']).
cnf(c_0_114, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_53]), c_0_56]), c_0_61])]), ['final']).
cnf(c_0_115, plain, (intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_70, c_0_98]), ['final']).
cnf(c_0_116, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_99, c_0_65]), ['final']).
cnf(c_0_117, plain, (intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_100, c_0_54]), ['final']).
cnf(c_0_118, plain, (intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_101, c_0_98]), ['final']).
cnf(c_0_119, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_102]), ['final']).
cnf(c_0_120, plain, (a_key(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_103]), ['final']).
cnf(c_0_121, plain, (intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))), inference(spm,[status(thm)],[c_0_104, c_0_105]), ['final']).
cnf(c_0_122, plain, (intruder_message(an_a_nonce)), inference(spm,[status(thm)],[c_0_104, c_0_79]), ['final']).
cnf(c_0_123, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_53]), c_0_56]), c_0_61])]), ['final']).
cnf(c_0_124, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_68]), c_0_69])]), ['final']).
cnf(c_0_125, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_108]), ['final']).
cnf(c_0_126, plain, (b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~a_key(X1)), inference(spm,[status(thm)],[c_0_109, c_0_65]), ['final']).
cnf(c_0_127, plain, (intruder_message(generate_b_nonce(an_a_nonce))), inference(spm,[status(thm)],[c_0_101, c_0_59]), ['final']).
cnf(c_0_128, plain, (a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_53]), c_0_61]), c_0_56])]), ['final']).
fof(c_0_129, plain, ![X62]:(~fresh_intruder_nonce(X62)|fresh_intruder_nonce(generate_intruder_nonce(X62))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[can_generate_more_fresh_intruder_nonces])])).
cnf(c_0_130, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_73, c_0_105]), ['final']).
cnf(c_0_131, plain, (fresh_to_b(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_111]), ['final']).
cnf(c_0_132, plain, (intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_112]), ['final']).
cnf(c_0_133, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_73, c_0_113]), ['final']).
cnf(c_0_134, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_68]), c_0_90])]), ['final']).
cnf(c_0_135, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_115]), c_0_90]), c_0_61])]), ['final']).
cnf(c_0_136, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_96]), c_0_90])]), ['final']).
cnf(c_0_137, plain, (b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_64, c_0_105]), ['final']).
cnf(c_0_138, plain, (b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_118]), ['final']).
cnf(c_0_139, plain, (intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_101, c_0_119]), ['final']).
cnf(c_0_140, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_113]), c_0_120])]), c_0_118]), ['final']).
cnf(c_0_141, plain, (b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_64, c_0_113]), ['final']).
cnf(c_0_142, plain, (b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_96]), c_0_90])]), ['final']).
cnf(c_0_143, plain, (intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_104, c_0_113])).
cnf(c_0_144, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_121]), c_0_122]), c_0_120]), c_0_40])]), ['final']).
cnf(c_0_145, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_68]), c_0_90])]), ['final']).
cnf(c_0_146, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_115]), c_0_69]), c_0_54])]), ['final']).
cnf(c_0_147, plain, (intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_101, c_0_125]), ['final']).
cnf(c_0_148, plain, (b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~a_key(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_117]), c_0_127])]), ['final']).
cnf(c_0_149, plain, (a_holds(key(X1,b))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X1,X2),at))|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_128, c_0_68]), ['final']).
fof(c_0_151, plain, ![X47, X48, X49]:(~intruder_message(encrypt(X47,X48))|~intruder_holds(key(X48,X49))|~party_of_protocol(X49)|intruder_message(X48)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_interception])])).
cnf(c_0_153, plain, (intruder_message(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_111]), ['final']).
cnf(c_0_154, plain, (fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_129]), ['final']).
fof(c_0_155, plain, ![X60]:(~a_key(X60)|~a_nonce(X60)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[nothing_is_a_nonce_and_a_key])])).
fof(c_0_156, plain, ![X58]:~a_nonce(generate_key(X58)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[generated_keys_are_not_nonces])])).
cnf(c_0_157, plain, (fresh_intruder_nonce(an_intruder_nonce)), inference(split_conjunct,[status(thm)],[an_intruder_nonce_is_a_fresh_intruder_nonce]), ['final']).
fof(c_0_158, plain, ![X59]:(a_nonce(generate_expiration_time(X59))&a_nonce(generate_b_nonce(X59))), inference(variable_rename,[status(thm)],[generated_times_and_nonces_are_nonces])).
cnf(c_0_159, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_130, c_0_131]), ['final']).
cnf(c_0_160, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_73, c_0_132]), ['final']).
cnf(c_0_161, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_133, c_0_131]), ['final']).
cnf(c_0_162, plain, (message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_134, c_0_117]), ['final']).
cnf(c_0_163, plain, (message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_82, c_0_117]), ['final']).
cnf(c_0_164, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_135]), ['final']).
cnf(c_0_165, plain, (b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_64, c_0_132]), ['final']).
cnf(c_0_166, plain, (intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_46, c_0_95]), ['final']).
cnf(c_0_167, plain, (message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_136, c_0_131]), ['final']).
cnf(c_0_168, plain, (b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_137, c_0_131]), ['final']).
cnf(c_0_169, plain, (intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_58, c_0_119]), ['final']).
cnf(c_0_170, plain, (b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_139]), c_0_90]), c_0_120]), c_0_61])]), ['final']).
cnf(c_0_171, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140, c_0_117]), c_0_58]), ['final']).
cnf(c_0_172, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_140, c_0_115]), ['final']).
cnf(c_0_173, plain, (b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)), inference(spm,[status(thm)],[c_0_141, c_0_131]), ['final']).
cnf(c_0_174, plain, (b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_142, c_0_131]), ['final']).
cnf(c_0_175, plain, (intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_143, c_0_72]), ['final']).
cnf(c_0_176, plain, (b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_117]), c_0_58]), ['final']).
cnf(c_0_177, plain, (message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_145, c_0_117]), ['final']).
cnf(c_0_178, plain, (message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)), inference(spm,[status(thm)],[c_0_124, c_0_117]), ['final']).
cnf(c_0_179, plain, (intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_46, c_0_146]), ['final']).
cnf(c_0_180, plain, (intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_58, c_0_125]), ['final']).
cnf(c_0_181, plain, (b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_147]), c_0_69]), c_0_120]), c_0_54])]), ['final']).
cnf(c_0_182, plain, (intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_70, c_0_125]), ['final']).
cnf(c_0_183, plain, (b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_117]), c_0_101]), c_0_58]), ['final']).
cnf(c_0_184, plain, (b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_138, c_0_115]), ['final']).
cnf(c_0_185, plain, (message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(quadruple(b,an_a_nonce,X3,X4))|~intruder_message(at)|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_84, c_0_117]), ['final']).
cnf(c_0_186, plain, (b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_117]), c_0_101]), ['final']).
cnf(c_0_187, plain, (b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_83]), c_0_122])]), ['final']).
cnf(c_0_188, plain, (a_holds(key(X1,b))|~intruder_message(quadruple(b,an_a_nonce,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~intruder_message(X4)), inference(spm,[status(thm)],[c_0_149, c_0_117]), ['final']).
cnf(c_0_190, plain, (intruder_message(X2)|~intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~party_of_protocol(X3)), inference(split_conjunct,[status(thm)],[c_0_151]), ['final']).
cnf(c_0_195, plain, (intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(spm,[status(thm)],[c_0_153, c_0_154]), ['final']).
cnf(c_0_196, plain, (~a_key(X1)|~a_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_155]), ['final']).
cnf(c_0_197, plain, (~a_nonce(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_156]), ['final']).
cnf(c_0_198, plain, (b_holds(key(generate_key(an_a_nonce),b))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_147]), c_0_69]), c_0_54]), c_0_122]), c_0_51]), c_0_40])]), ['final']).
cnf(c_0_199, plain, (intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_78, c_0_105]), ['final']).
cnf(c_0_200, plain, (b_holds(key(generate_key(an_a_nonce),a))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_91]), c_0_122]), c_0_90]), c_0_120]), c_0_40]), c_0_61])]), ['final']).
cnf(c_0_201, plain, (a_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_110, c_0_62]), ['final']).
cnf(c_0_202, plain, (b_holds(key(bt,t))), inference(split_conjunct,[status(thm)],[b_hold_key_bt_for_t]), ['final']).
cnf(c_0_203, plain, (a_holds(key(at,t))), inference(split_conjunct,[status(thm)],[a_holds_key_at_for_t]), ['final']).
cnf(c_0_204, plain, (intruder_message(an_intruder_nonce)), inference(spm,[status(thm)],[c_0_153, c_0_157]), ['final']).
cnf(c_0_205, plain, (a_nonce(generate_expiration_time(X1))), inference(split_conjunct,[status(thm)],[c_0_158]), ['final']).
cnf(c_0_206, plain, (a_nonce(generate_b_nonce(X1))), inference(split_conjunct,[status(thm)],[c_0_158]), ['final']).
# SZS output end Saturation
```

### Sample solution for BOO001-1

```# SZS output start CNFRefutation
cnf(associativity, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', associativity)).
cnf(ternary_multiply_1, axiom, (multiply(X1,X2,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_1)).
cnf(right_inverse, axiom, (multiply(X1,X2,inverse(X2))=X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', right_inverse)).
cnf(ternary_multiply_2, axiom, (multiply(X1,X1,X2)=X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', ternary_multiply_2)).
cnf(left_inverse, axiom, (multiply(inverse(X1),X1,X2)=X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/Axioms/BOO001-0.ax', left_inverse)).
cnf(prove_inverse_is_self_cancelling, negated_conjecture, (inverse(inverse(a))!=a), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/BOO001-1.p', prove_inverse_is_self_cancelling)).
cnf(c_0_6, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), associativity).
cnf(c_0_7, axiom, (multiply(X1,X2,X2)=X2), ternary_multiply_1).
cnf(c_0_8, plain, (multiply(multiply(X1,X2,X3),X4,X2)=multiply(X1,X2,multiply(X3,X4,X2))), inference(spm,[status(thm)],[c_0_6, c_0_7])).
cnf(c_0_9, axiom, (multiply(X1,X2,inverse(X2))=X1), right_inverse).
cnf(c_0_10, plain, (multiply(X1,X2,X3)=multiply(X1,X3,multiply(inverse(X3),X2,X3))), inference(spm,[status(thm)],[c_0_8, c_0_9])).
cnf(c_0_11, axiom, (multiply(X1,X1,X2)=X1), ternary_multiply_2).
cnf(c_0_12, axiom, (multiply(inverse(X1),X1,X2)=X2), left_inverse).
cnf(c_0_13, plain, (multiply(X1,inverse(X2),X2)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_9])).
cnf(c_0_14, negated_conjecture, (inverse(inverse(a))!=a), prove_inverse_is_self_cancelling).
cnf(c_0_15, plain, (inverse(inverse(X1))=X1), inference(spm,[status(thm)],[c_0_12, c_0_13])).
cnf(c_0_16, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001_5

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('/Users/schulz/Desktop/HL400001_5.p', conj_thm_2Ebool_2ETRUTH)).
fof(c_0_1, negated_conjecture, ~(\$true), inference(assume_negation,[status(cth)],[conj_thm_2Ebool_2ETRUTH])).
fof(c_0_2, negated_conjecture, ~\$true, inference(fof_simplification,[status(thm)],[c_0_1])).
cnf(c_0_3, negated_conjecture, (\$false), inference(split_conjunct,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (\$false), inference(cn,[status(thm)],[c_0_3]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001_4

```# SZS output start CNFRefutation
tff(thm_2Ebool_2ETRUTH, conjecture, p(mono_2Ec_2Ebool_2ET_2E0), file('/Users/schulz/Desktop/HL400001_4.p', thm_2Ebool_2ETRUTH)).
tff(reserved_2Eho_2Etruth, axiom, p(mono_2Ec_2Ebool_2ET_2E0), file('/Users/schulz/Desktop/Axioms/HL4002_4.ax', reserved_2Eho_2Etruth)).
tff(c_0_2, negated_conjecture, ~(p(mono_2Ec_2Ebool_2ET_2E0)), inference(assume_negation,[status(cth)],[thm_2Ebool_2ETRUTH])).
tff(c_0_3, negated_conjecture, ~p(mono_2Ec_2Ebool_2ET_2E0), inference(fof_simplification,[status(thm)],[c_0_2])).
tcf(c_0_4, negated_conjecture, ~p(mono_2Ec_2Ebool_2ET_2E0), inference(split_conjunct,[status(thm)],[c_0_3])).
tcf(c_0_5, plain, p(mono_2Ec_2Ebool_2ET_2E0), inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth])).
cnf(c_0_6, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_4, c_0_5])]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001+5

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('/Users/schulz/Desktop/HL400001+5.p', conj_thm_2Ebool_2ETRUTH)).
fof(c_0_1, negated_conjecture, ~(\$true), inference(assume_negation,[status(cth)],[conj_thm_2Ebool_2ETRUTH])).
fof(c_0_2, negated_conjecture, ~\$true, inference(fof_simplification,[status(thm)],[c_0_1])).
cnf(c_0_3, negated_conjecture, (\$false), inference(split_conjunct,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (\$false), inference(cn,[status(thm)],[c_0_3]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001+4

```# SZS output start CNFRefutation
fof(thm_2Ebool_2ETRUTH, conjecture, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('/Users/schulz/Desktop/HL400001+4.p', thm_2Ebool_2ETRUTH)).
fof(reserved_2Eho_2Etruth, axiom, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('/Users/schulz/Desktop/Axioms/HL4002+4.ax', reserved_2Eho_2Etruth)).
fof(c_0_2, negated_conjecture, ~(p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(assume_negation,[status(cth)],[thm_2Ebool_2ETRUTH])).
fof(c_0_3, negated_conjecture, ~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), inference(fof_simplification,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(split_conjunct,[status(thm)],[c_0_3])).
cnf(c_0_5, plain, (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth])).
cnf(c_0_6, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_4, c_0_5])]), ['proof']).
# SZS output end CNFRefutation
```

## Enigma 0.5.1

Jan Jakubuv
Czech Technical University in Prague, Czech Republic

### Sample proof for SEU140+2

```# SZS output start CNFRefutation
fof(t4_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t4_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t48_xboole_1)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d1_xboole_0)).
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d3_xboole_0)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(subset(X1,X2)&subset(X2,X1))), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', d10_xboole_0)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1), file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t36_xboole_1)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_7.3.0_FLAT/SEU140+2.p', t3_boole)).
fof(c_0_11, lemma, ![X115, X116, X118, X119, X120]:((disjoint(X115,X116)|in(esk10_2(X115,X116),set_intersection2(X115,X116)))&(~in(X120,set_intersection2(X118,X119))|~disjoint(X118,X119))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_xboole_0])])])])])])).
fof(c_0_12, lemma, ![X112, X113]:set_difference(X112,set_difference(X112,X113))=set_intersection2(X112,X113), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_13, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
cnf(c_0_14, lemma, (~in(X1,set_intersection2(X2,X3))|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_15, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])).
fof(c_0_16, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])).
cnf(c_0_17, lemma, (~disjoint(X2,X3)|~in(X1,set_difference(X2,set_difference(X2,X3)))), inference(rw,[status(thm)],[c_0_14, c_0_15])).
cnf(c_0_18, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
fof(c_0_19, plain, ![X15, X16, X17]:((X15!=empty_set|~in(X16,X15))&(in(esk1_1(X17),X17)|X17=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])).
fof(c_0_20, plain, ![X34, X35, X36, X37, X38, X39, X40, X41]:((((in(X37,X34)|~in(X37,X36)|X36!=set_intersection2(X34,X35))&(in(X37,X35)|~in(X37,X36)|X36!=set_intersection2(X34,X35)))&(~in(X38,X34)|~in(X38,X35)|in(X38,X36)|X36!=set_intersection2(X34,X35)))&((~in(esk4_3(X39,X40,X41),X41)|(~in(esk4_3(X39,X40,X41),X39)|~in(esk4_3(X39,X40,X41),X40))|X41=set_intersection2(X39,X40))&((in(esk4_3(X39,X40,X41),X39)|in(esk4_3(X39,X40,X41),X41)|X41=set_intersection2(X39,X40))&(in(esk4_3(X39,X40,X41),X40)|in(esk4_3(X39,X40,X41),X41)|X41=set_intersection2(X39,X40))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_21, plain, ![X43, X44, X45, X46, X47, X48, X49, X50]:((((in(X46,X43)|~in(X46,X45)|X45!=set_difference(X43,X44))&(~in(X46,X44)|~in(X46,X45)|X45!=set_difference(X43,X44)))&(~in(X47,X43)|in(X47,X44)|in(X47,X45)|X45!=set_difference(X43,X44)))&((~in(esk5_3(X48,X49,X50),X50)|(~in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X49))|X50=set_difference(X48,X49))&((in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))&(~in(esk5_3(X48,X49,X50),X49)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])).
fof(c_0_22, lemma, ![X101, X102, X104, X105, X106]:(((in(esk9_2(X101,X102),X101)|disjoint(X101,X102))&(in(esk9_2(X101,X102),X102)|disjoint(X101,X102)))&(~in(X106,X104)|~in(X106,X105)|~disjoint(X104,X105))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])).
fof(c_0_23, lemma, ![X63, X64]:((set_difference(X63,X64)!=empty_set|subset(X63,X64))&(~subset(X63,X64)|set_difference(X63,X64)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_24, negated_conjecture, (~in(X1,set_difference(esk12_0,set_difference(esk12_0,esk13_0)))), inference(spm,[status(thm)],[c_0_17, c_0_18])).
cnf(c_0_25, plain, (in(esk1_1(X1),X1)|X1=empty_set), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_26, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_27, plain, (~in(X1,X2)|~in(X1,X3)|X3!=set_difference(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_28, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
cnf(c_0_29, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_30, plain, ![X13, X14]:(((subset(X13,X14)|X13!=X14)&(subset(X14,X13)|X13!=X14))&(~subset(X13,X14)|~subset(X14,X13)|X13=X14)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])).
cnf(c_0_31, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_32, negated_conjecture, (set_difference(esk12_0,set_difference(esk12_0,esk13_0))=empty_set), inference(spm,[status(thm)],[c_0_24, c_0_25])).
fof(c_0_33, lemma, ![X94, X95]:subset(set_difference(X94,X95),X94), inference(variable_rename,[status(thm)],[t36_xboole_1])).
cnf(c_0_34, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_26, c_0_15])).
cnf(c_0_35, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_36, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
fof(c_0_37, plain, ![X100]:set_difference(X100,empty_set)=X100, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_38, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_27])).
cnf(c_0_39, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk13_0)), inference(spm,[status(thm)],[c_0_28, c_0_29])).
cnf(c_0_40, plain, (X1=X2|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_41, lemma, (subset(esk12_0,set_difference(esk12_0,esk13_0))), inference(spm,[status(thm)],[c_0_31, c_0_32])).
cnf(c_0_42, lemma, (subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_33])).
cnf(c_0_43, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_34])).
cnf(c_0_44, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_35, c_0_36])).
cnf(c_0_45, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_46, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_47, negated_conjecture, (~in(esk9_2(esk11_0,esk13_0),set_difference(X1,esk13_0))), inference(spm,[status(thm)],[c_0_38, c_0_39])).
cnf(c_0_48, lemma, (set_difference(esk12_0,esk13_0)=esk12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42])])).
cnf(c_0_49, negated_conjecture, (in(X1,esk12_0)|~in(X1,esk11_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45])).
cnf(c_0_50, negated_conjecture, (in(esk9_2(esk11_0,esk13_0),esk11_0)), inference(spm,[status(thm)],[c_0_28, c_0_46])).
cnf(c_0_51, lemma, (~in(esk9_2(esk11_0,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_47, c_0_48])).
cnf(c_0_52, negated_conjecture, (\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_51]), ['proof']).
# SZS output end CNFRefutation
```

## Etableau 0.2

John Hester
University of Florida, USA

### Sample solution for SEU140+2

```# SZS output start CNFRefutation for /tmp/SystemOnTPTP26112/SEU140+2.tptp
# Begin clausification derivation
fof(d3_xboole_0, axiom, ![X1, X2, X3]:(X3=set_intersection2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&in(X4,X2)))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d3_xboole_0)).
fof(t48_xboole_1, lemma, ![X1, X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t48_xboole_1)).
fof(t2_boole, axiom, ![X1]:set_intersection2(X1,empty_set)=empty_set, file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t2_boole)).
fof(t26_xboole_1, lemma, ![X1, X2, X3]:(subset(X1,X2)=>subset(set_intersection2(X1,X3),set_intersection2(X2,X3))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t26_xboole_1)).
fof(d2_xboole_0, axiom, ![X1, X2, X3]:(X3=set_union2(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)|in(X4,X2)))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d2_xboole_0)).
fof(t19_xboole_1, lemma, ![X1, X2, X3]:((subset(X1,X2)&subset(X1,X3))=>subset(X1,set_intersection2(X2,X3))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t19_xboole_1)).
fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=set_difference(X1,X2)<=>![X4]:(in(X4,X3)<=>(in(X4,X1)&~(in(X4,X2))))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d4_xboole_0)).
fof(t4_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~(in(X3,set_intersection2(X1,X2)))))&~((?[X3]:in(X3,set_intersection2(X1,X2))&disjoint(X1,X2)))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t4_xboole_0)).
fof(t28_xboole_1, lemma, ![X1, X2]:(subset(X1,X2)=>set_intersection2(X1,X2)=X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t28_xboole_1)).
fof(d7_xboole_0, axiom, ![X1, X2]:(disjoint(X1,X2)<=>set_intersection2(X1,X2)=empty_set), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d7_xboole_0)).
fof(d1_xboole_0, axiom, ![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d1_xboole_0)).
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t63_xboole_1)).
fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', commutativity_k3_xboole_0)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t3_boole)).
fof(t2_tarski, axiom, ![X1, X2]:(![X3]:(in(X3,X1)<=>in(X3,X2))=>X1=X2), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t2_tarski)).
fof(t33_xboole_1, lemma, ![X1, X2, X3]:(subset(X1,X2)=>subset(set_difference(X1,X3),set_difference(X2,X3))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t33_xboole_1)).
fof(t8_xboole_1, lemma, ![X1, X2, X3]:((subset(X1,X2)&subset(X3,X2))=>subset(set_union2(X1,X3),X2)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t8_xboole_1)).
fof(t3_xboole_0, lemma, ![X1, X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t3_xboole_0)).
fof(d3_tarski, axiom, ![X1, X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d3_tarski)).
fof(d8_xboole_0, axiom, ![X1, X2]:(proper_subset(X1,X2)<=>(subset(X1,X2)&X1!=X2)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d8_xboole_0)).
fof(t1_xboole_1, lemma, ![X1, X2, X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t1_xboole_1)).
fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(subset(X1,X2)&subset(X2,X1))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', d10_xboole_0)).
fof(t12_xboole_1, lemma, ![X1, X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t12_xboole_1)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', l32_xboole_1)).
fof(fc2_xboole_0, axiom, ![X1, X2]:(~(empty(X1))=>~(empty(set_union2(X1,X2)))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', fc2_xboole_0)).
fof(fc3_xboole_0, axiom, ![X1, X2]:(~(empty(X1))=>~(empty(set_union2(X2,X1)))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', fc3_xboole_0)).
fof(t8_boole, axiom, ![X1, X2]:~(((empty(X1)&X1!=X2)&empty(X2))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t8_boole)).
fof(symmetry_r1_xboole_0, axiom, ![X1, X2]:(disjoint(X1,X2)=>disjoint(X2,X1)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', symmetry_r1_xboole_0)).
fof(antisymmetry_r2_xboole_0, axiom, ![X1, X2]:(proper_subset(X1,X2)=>~(proper_subset(X2,X1))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', antisymmetry_r2_xboole_0)).
fof(antisymmetry_r2_hidden, axiom, ![X1, X2]:(in(X1,X2)=>~(in(X2,X1))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', antisymmetry_r2_hidden)).
fof(t60_xboole_1, lemma, ![X1, X2]:~((subset(X1,X2)&proper_subset(X2,X1))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t60_xboole_1)).
fof(t3_xboole_1, lemma, ![X1]:(subset(X1,empty_set)=>X1=empty_set), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t3_xboole_1)).
fof(t6_boole, axiom, ![X1]:(empty(X1)=>X1=empty_set), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t6_boole)).
fof(t7_boole, axiom, ![X1, X2]:~((in(X1,X2)&empty(X2))), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t7_boole)).
fof(irreflexivity_r2_xboole_0, axiom, ![X1, X2]:~(proper_subset(X1,X1)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', irreflexivity_r2_xboole_0)).
fof(rc2_xboole_0, axiom, ?[X1]:~(empty(X1)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', rc2_xboole_0)).
fof(commutativity_k2_xboole_0, axiom, ![X1, X2]:set_union2(X1,X2)=set_union2(X2,X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', commutativity_k2_xboole_0)).
fof(t40_xboole_1, lemma, ![X1, X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t40_xboole_1)).
fof(t39_xboole_1, lemma, ![X1, X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t39_xboole_1)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t36_xboole_1)).
fof(t7_xboole_1, lemma, ![X1, X2]:subset(X1,set_union2(X1,X2)), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t7_xboole_1)).
fof(idempotence_k2_xboole_0, axiom, ![X1, X2]:set_union2(X1,X1)=X1, file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', idempotence_k2_xboole_0)).
fof(t1_boole, axiom, ![X1]:set_union2(X1,empty_set)=X1, file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t1_boole)).
fof(t4_boole, axiom, ![X1]:set_difference(empty_set,X1)=empty_set, file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t4_boole)).
fof(reflexivity_r1_tarski, axiom, ![X1, X2]:subset(X1,X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', reflexivity_r1_tarski)).
fof(t2_xboole_1, lemma, ![X1]:subset(empty_set,X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', t2_xboole_1)).
fof(rc1_xboole_0, axiom, ?[X1]:empty(X1), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', rc1_xboole_0)).
fof(fc1_xboole_0, axiom, empty(empty_set), file('/tmp/SystemOnTPTP26112/SEU140+2.tptp', fc1_xboole_0)).
fof(c_0_48, plain, ![X34, X35, X36, X37, X38, X39, X40, X41]:((((in(X37,X34)|~in(X37,X36)|X36!=set_intersection2(X34,X35))&(in(X37,X35)|~in(X37,X36)|X36!=set_intersection2(X34,X35)))&(~in(X38,X34)|~in(X38,X35)|in(X38,X36)|X36!=set_intersection2(X34,X35)))&((~in(esk4_3(X39,X40,X41),X41)|(~in(esk4_3(X39,X40,X41),X39)|~in(esk4_3(X39,X40,X41),X40))|X41=set_intersection2(X39,X40))&((in(esk4_3(X39,X40,X41),X39)|in(esk4_3(X39,X40,X41),X41)|X41=set_intersection2(X39,X40))&(in(esk4_3(X39,X40,X41),X40)|in(esk4_3(X39,X40,X41),X41)|X41=set_intersection2(X39,X40))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])).
fof(c_0_49, lemma, ![X112, X113]:set_difference(X112,set_difference(X112,X113))=set_intersection2(X112,X113), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_50, plain, ![X86]:set_intersection2(X86,empty_set)=empty_set, inference(variable_rename,[status(thm)],[t2_boole])).
fof(c_0_51, lemma, ![X81, X82, X83]:(~subset(X81,X82)|subset(set_intersection2(X81,X83),set_intersection2(X82,X83))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])])).
fof(c_0_52, plain, ![X19, X20, X21, X22, X23, X24, X25, X26]:(((~in(X22,X21)|(in(X22,X19)|in(X22,X20))|X21!=set_union2(X19,X20))&((~in(X23,X19)|in(X23,X21)|X21!=set_union2(X19,X20))&(~in(X23,X20)|in(X23,X21)|X21!=set_union2(X19,X20))))&(((~in(esk2_3(X24,X25,X26),X24)|~in(esk2_3(X24,X25,X26),X26)|X26=set_union2(X24,X25))&(~in(esk2_3(X24,X25,X26),X25)|~in(esk2_3(X24,X25,X26),X26)|X26=set_union2(X24,X25)))&(in(esk2_3(X24,X25,X26),X26)|(in(esk2_3(X24,X25,X26),X24)|in(esk2_3(X24,X25,X26),X25))|X26=set_union2(X24,X25)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])])).
cnf(c_0_53, plain, (in(X1,X4)|~in(X1,X2)|~in(X1,X3)|X4!=set_intersection2(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_54, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_49])).
fof(c_0_55, lemma, ![X74, X75, X76]:(~subset(X74,X75)|~subset(X74,X76)|subset(X74,set_intersection2(X75,X76))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])])).
fof(c_0_56, plain, ![X43, X44, X45, X46, X47, X48, X49, X50]:((((in(X46,X43)|~in(X46,X45)|X45!=set_difference(X43,X44))&(~in(X46,X44)|~in(X46,X45)|X45!=set_difference(X43,X44)))&(~in(X47,X43)|in(X47,X44)|in(X47,X45)|X45!=set_difference(X43,X44)))&((~in(esk5_3(X48,X49,X50),X50)|(~in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X49))|X50=set_difference(X48,X49))&((in(esk5_3(X48,X49,X50),X48)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))&(~in(esk5_3(X48,X49,X50),X49)|in(esk5_3(X48,X49,X50),X50)|X50=set_difference(X48,X49))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])).
fof(c_0_57, lemma, ![X115, X116, X118, X119, X120]:((disjoint(X115,X116)|in(esk10_2(X115,X116),set_intersection2(X115,X116)))&(~in(X120,set_intersection2(X118,X119))|~disjoint(X118,X119))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_xboole_0])])])])])])).
cnf(c_0_58, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_intersection2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
fof(c_0_59, lemma, ![X84, X85]:(~subset(X84,X85)|set_intersection2(X84,X85)=X84), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])).
fof(c_0_60, plain, ![X52, X53]:((~disjoint(X52,X53)|set_intersection2(X52,X53)=empty_set)&(set_intersection2(X52,X53)!=empty_set|disjoint(X52,X53))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])).
fof(c_0_61, plain, ![X15, X16, X17]:((X15!=empty_set|~in(X16,X15))&(in(esk1_1(X17),X17)|X17=empty_set)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])).
fof(c_0_62, negated_conjecture, ~(![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), inference(assume_negation,[status(cth)],[t63_xboole_1])).
fof(c_0_63, plain, ![X11, X12]:set_intersection2(X11,X12)=set_intersection2(X12,X11), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).
cnf(c_0_64, plain, (set_intersection2(X1,empty_set)=empty_set), inference(split_conjunct,[status(thm)],[c_0_50])).
fof(c_0_65, plain, ![X100]:set_difference(X100,empty_set)=X100, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_66, plain, (X3=set_intersection2(X1,X2)|~in(esk4_3(X1,X2,X3),X3)|~in(esk4_3(X1,X2,X3),X1)|~in(esk4_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_67, plain, (in(esk4_3(X1,X2,X3),X1)|in(esk4_3(X1,X2,X3),X3)|X3=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_68, plain, (in(esk4_3(X1,X2,X3),X2)|in(esk4_3(X1,X2,X3),X3)|X3=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_69, lemma, (subset(set_intersection2(X1,X3),set_intersection2(X2,X3))|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_51])).
fof(c_0_70, plain, ![X87, X88]:((~in(esk8_2(X87,X88),X87)|~in(esk8_2(X87,X88),X88)|X87=X88)&(in(esk8_2(X87,X88),X87)|in(esk8_2(X87,X88),X88)|X87=X88)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])).
cnf(c_0_71, plain, (in(X1,X3)|in(X1,X4)|~in(X1,X2)|X2!=set_union2(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_52])).
cnf(c_0_72, plain, (in(X1,X4)|X4!=set_difference(X2,set_difference(X2,X3))|~in(X1,X3)|~in(X1,X2)), inference(rw,[status(thm)],[c_0_53, c_0_54])).
cnf(c_0_73, lemma, (subset(X1,set_intersection2(X2,X3))|~subset(X1,X2)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_55])).
cnf(c_0_74, plain, (in(X1,X3)|in(X1,X4)|~in(X1,X2)|X4!=set_difference(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_56])).
cnf(c_0_75, lemma, (disjoint(X1,X2)|in(esk10_2(X1,X2),set_intersection2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_57])).
cnf(c_0_76, plain, (in(X1,X2)|X3!=set_difference(X4,set_difference(X4,X2))|~in(X1,X3)), inference(rw,[status(thm)],[c_0_58, c_0_54])).
fof(c_0_77, lemma, ![X91, X92, X93]:(~subset(X91,X92)|subset(set_difference(X91,X93),set_difference(X92,X93))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])])).
cnf(c_0_78, plain, (in(X1,X3)|~in(X1,X2)|X3!=set_union2(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_52])).
cnf(c_0_79, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_difference(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_56])).
cnf(c_0_80, plain, (in(X1,X3)|~in(X1,X2)|X3!=set_union2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_52])).
fof(c_0_81, lemma, ![X133, X134, X135]:(~subset(X133,X134)|~subset(X135,X134)|subset(set_union2(X133,X135),X134)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])])).
fof(c_0_82, lemma, ![X101, X102, X104, X105, X106]:(((in(esk9_2(X101,X102),X101)|disjoint(X101,X102))&(in(esk9_2(X101,X102),X102)|disjoint(X101,X102)))&(~in(X106,X104)|~in(X106,X105)|~disjoint(X104,X105))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])).
fof(c_0_83, plain, ![X28, X29, X30, X31, X32]:((~subset(X28,X29)|(~in(X30,X28)|in(X30,X29)))&((in(esk3_2(X31,X32),X31)|subset(X31,X32))&(~in(esk3_2(X31,X32),X32)|subset(X31,X32)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])).
cnf(c_0_84, lemma, (set_intersection2(X1,X2)=X1|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59])).
fof(c_0_85, plain, ![X54, X55]:(((subset(X54,X55)|~proper_subset(X54,X55))&(X54!=X55|~proper_subset(X54,X55)))&(~subset(X54,X55)|X54=X55|proper_subset(X54,X55))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])])).
cnf(c_0_86, plain, (set_intersection2(X1,X2)=empty_set|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_60])).
fof(c_0_87, lemma, ![X78, X79, X80]:(~subset(X78,X79)|~subset(X79,X80)|subset(X78,X80)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])).
cnf(c_0_88, plain, (disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_60])).
fof(c_0_89, plain, ![X13, X14]:(((subset(X13,X14)|X13!=X14)&(subset(X14,X13)|X13!=X14))&(~subset(X13,X14)|~subset(X14,X13)|X13=X14)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])).
cnf(c_0_90, plain, (~in(X1,X2)|~in(X1,X3)|X3!=set_difference(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_56])).
fof(c_0_91, lemma, ![X70, X71]:(~subset(X70,X71)|set_union2(X70,X71)=X71), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])).
fof(c_0_92, lemma, ![X63, X64]:((set_difference(X63,X64)!=empty_set|subset(X63,X64))&(~subset(X63,X64)|set_difference(X63,X64)=empty_set)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])).
cnf(c_0_93, lemma, (~in(X1,set_intersection2(X2,X3))|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_57])).
fof(c_0_94, plain, ![X56, X57]:(empty(X56)|~empty(set_union2(X56,X57))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_xboole_0])])])).
fof(c_0_95, plain, ![X58, X59]:(empty(X58)|~empty(set_union2(X59,X58))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc3_xboole_0])])])).
fof(c_0_96, plain, ![X131, X132]:(~empty(X131)|X131=X132|~empty(X132)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])])).
fof(c_0_97, plain, ![X68, X69]:(~disjoint(X68,X69)|disjoint(X69,X68)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])).
fof(c_0_98, plain, ![X7, X8]:(~proper_subset(X7,X8)|~proper_subset(X8,X7)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0])])])).
fof(c_0_99, plain, ![X5, X6]:(~in(X5,X6)|~in(X6,X5)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden])])])).
fof(c_0_100, lemma, ![X121, X122]:(~subset(X121,X122)|~proper_subset(X122,X121)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])])).
fof(c_0_101, lemma, ![X107]:(~subset(X107,empty_set)|X107=empty_set), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])])).
fof(c_0_102, plain, ![X126]:(~empty(X126)|X126=empty_set), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])).
fof(c_0_103, plain, ![X127, X128]:(~in(X127,X128)|~empty(X128)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])).
cnf(c_0_104, plain, (X1!=empty_set|~in(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_61])).
fof(c_0_105, plain, ![X62]:~proper_subset(X62,X62), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0])])).
fof(c_0_106, plain, ~empty(esk7_0), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[rc2_xboole_0])])])).
fof(c_0_107, negated_conjecture, ((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~disjoint(esk11_0,esk13_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])).
cnf(c_0_108, plain, (set_intersection2(X1,X2)=set_intersection2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_63])).
fof(c_0_109, plain, ![X9, X10]:set_union2(X9,X10)=set_union2(X10,X9), inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_110, lemma, ![X108, X109]:set_difference(set_union2(X108,X109),X109)=set_difference(X108,X109), inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_111, lemma, ![X98, X99]:set_union2(X98,set_difference(X99,X98))=set_union2(X98,X99), inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_112, plain, (set_difference(X1,set_difference(X1,empty_set))=empty_set), inference(rw,[status(thm)],[c_0_64, c_0_54])).
cnf(c_0_113, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_65]), ['final']).
fof(c_0_114, lemma, ![X94, X95]:subset(set_difference(X94,X95),X94), inference(variable_rename,[status(thm)],[t36_xboole_1])).
fof(c_0_115, lemma, ![X129, X130]:subset(X129,set_union2(X129,X130)), inference(variable_rename,[status(thm)],[t7_xboole_1])).
fof(c_0_116, plain, ![X60]:set_union2(X60,X60)=X60, inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])])).
fof(c_0_117, plain, ![X77]:set_union2(X77,empty_set)=X77, inference(variable_rename,[status(thm)],[t1_boole])).
fof(c_0_118, plain, ![X114]:set_difference(empty_set,X114)=empty_set, inference(variable_rename,[status(thm)],[t4_boole])).
fof(c_0_119, plain, ![X67]:subset(X67,X67), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])])).
fof(c_0_120, lemma, ![X90]:subset(empty_set,X90), inference(variable_rename,[status(thm)],[t2_xboole_1])).
fof(c_0_121, plain, empty(esk6_0), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])])).
cnf(c_0_122, plain, (in(esk2_3(X1,X2,X3),X3)|in(esk2_3(X1,X2,X3),X1)|in(esk2_3(X1,X2,X3),X2)|X3=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_52]), ['final']).
cnf(c_0_123, plain, (in(esk5_3(X1,X2,X3),X2)|X3=set_difference(X1,X2)|~in(esk5_3(X1,X2,X3),X3)|~in(esk5_3(X1,X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_56]), ['final']).
cnf(c_0_124, plain, (X3=set_difference(X1,set_difference(X1,X2))|~in(esk4_3(X1,X2,X3),X3)|~in(esk4_3(X1,X2,X3),X2)|~in(esk4_3(X1,X2,X3),X1)), inference(rw,[status(thm)],[c_0_66, c_0_54]), ['final']).
cnf(c_0_125, plain, (X3=set_difference(X1,set_difference(X1,X2))|in(esk4_3(X1,X2,X3),X3)|in(esk4_3(X1,X2,X3),X1)), inference(rw,[status(thm)],[c_0_67, c_0_54]), ['final']).
cnf(c_0_126, plain, (X3=set_difference(X1,set_difference(X1,X2))|in(esk4_3(X1,X2,X3),X3)|in(esk4_3(X1,X2,X3),X2)), inference(rw,[status(thm)],[c_0_68, c_0_54]), ['final']).
cnf(c_0_127, plain, (in(esk5_3(X1,X2,X3),X1)|in(esk5_3(X1,X2,X3),X3)|X3=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_56]), ['final']).
cnf(c_0_128, lemma, (subset(set_difference(X1,set_difference(X1,X3)),set_difference(X2,set_difference(X2,X3)))|~subset(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_54]), c_0_54]), ['final']).
cnf(c_0_129, plain, (in(esk5_3(X1,X2,X3),X3)|X3=set_difference(X1,X2)|~in(esk5_3(X1,X2,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_56]), ['final']).
cnf(c_0_130, plain, (X3=set_union2(X1,X2)|~in(esk2_3(X1,X2,X3),X1)|~in(esk2_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_52]), ['final']).
cnf(c_0_131, plain, (X3=set_union2(X1,X2)|~in(esk2_3(X1,X2,X3),X2)|~in(esk2_3(X1,X2,X3),X3)), inference(split_conjunct,[status(thm)],[c_0_52]), ['final']).
cnf(c_0_132, plain, (in(esk8_2(X1,X2),X1)|in(esk8_2(X1,X2),X2)|X1=X2), inference(split_conjunct,[status(thm)],[c_0_70]), ['final']).
cnf(c_0_133, plain, (in(X1,X2)|in(X1,X3)|~in(X1,set_union2(X3,X2))), inference(er,[status(thm)],[c_0_71]), ['final']).
cnf(c_0_134, plain, (in(X1,set_difference(X2,set_difference(X2,X3)))|~in(X1,X3)|~in(X1,X2)), inference(er,[status(thm)],[c_0_72]), ['final']).
cnf(c_0_135, lemma, (subset(X1,set_difference(X2,set_difference(X2,X3)))|~subset(X1,X3)|~subset(X1,X2)), inference(rw,[status(thm)],[c_0_73, c_0_54]), ['final']).
cnf(c_0_136, plain, (in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2)), inference(er,[status(thm)],[c_0_74]), ['final']).
cnf(c_0_137, plain, (X1=X2|~in(esk8_2(X1,X2),X1)|~in(esk8_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_70]), ['final']).
cnf(c_0_138, lemma, (disjoint(X1,X2)|in(esk10_2(X1,X2),set_difference(X1,set_difference(X1,X2)))), inference(rw,[status(thm)],[c_0_75, c_0_54]), ['final']).
cnf(c_0_139, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2)))), inference(er,[status(thm)],[c_0_76]), ['final']).
cnf(c_0_140, lemma, (subset(set_difference(X1,X3),set_difference(X2,X3))|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_141, plain, (in(X1,set_union2(X2,X3))|~in(X1,X2)), inference(er,[status(thm)],[c_0_78]), ['final']).
cnf(c_0_142, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3))), inference(er,[status(thm)],[c_0_79]), ['final']).
cnf(c_0_143, plain, (in(X1,set_union2(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_80]), ['final']).
cnf(c_0_144, lemma, (subset(set_union2(X1,X3),X2)|~subset(X1,X2)|~subset(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_81]), ['final']).
cnf(c_0_145, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_82]), ['final']).
cnf(c_0_146, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_82]), ['final']).
cnf(c_0_147, plain, (in(esk3_2(X1,X2),X1)|subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_83]), ['final']).
cnf(c_0_148, lemma, (set_difference(X1,set_difference(X1,X2))=X1|~subset(X1,X2)), inference(rw,[status(thm)],[c_0_84, c_0_54]), ['final']).
cnf(c_0_149, plain, (X1=X2|proper_subset(X1,X2)|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85]), ['final']).
cnf(c_0_150, plain, (set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2)), inference(rw,[status(thm)],[c_0_86, c_0_54]), ['final']).
cnf(c_0_151, lemma, (subset(X1,X3)|~subset(X1,X2)|~subset(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_87]), ['final']).
cnf(c_0_152, plain, (disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set), inference(rw,[status(thm)],[c_0_88, c_0_54]), ['final']).
cnf(c_0_153, plain, (subset(X1,X2)|~in(esk3_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_83]), ['final']).
cnf(c_0_154, plain, (X1=X2|~subset(X1,X2)|~subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_89]), ['final']).
cnf(c_0_155, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3)), inference(er,[status(thm)],[c_0_90]), ['final']).
cnf(c_0_156, plain, (in(X3,X2)|~subset(X1,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_83]), ['final']).
cnf(c_0_157, lemma, (set_union2(X1,X2)=X2|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_91]), ['final']).
cnf(c_0_158, plain, (in(esk1_1(X1),X1)|X1=empty_set), inference(split_conjunct,[status(thm)],[c_0_61]), ['final']).
cnf(c_0_159, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_92]), ['final']).
cnf(c_0_160, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_92]), ['final']).
cnf(c_0_161, lemma, (~disjoint(X2,X3)|~in(X1,set_difference(X2,set_difference(X2,X3)))), inference(rw,[status(thm)],[c_0_93, c_0_54]), ['final']).
cnf(c_0_162, plain, (empty(X1)|~empty(set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_94]), ['final']).
cnf(c_0_163, plain, (empty(X1)|~empty(set_union2(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_95]), ['final']).
cnf(c_0_164, lemma, (~in(X1,X2)|~in(X1,X3)|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_82]), ['final']).
cnf(c_0_165, plain, (X1=X2|~empty(X1)|~empty(X2)), inference(split_conjunct,[status(thm)],[c_0_96]), ['final']).
cnf(c_0_166, plain, (disjoint(X2,X1)|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_97]), ['final']).
cnf(c_0_167, plain, (subset(X1,X2)|~proper_subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85]), ['final']).
cnf(c_0_168, plain, (~proper_subset(X1,X2)|~proper_subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_98]), ['final']).
cnf(c_0_169, plain, (~in(X1,X2)|~in(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_99]), ['final']).
cnf(c_0_170, lemma, (~subset(X1,X2)|~proper_subset(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_100]), ['final']).
cnf(c_0_171, lemma, (X1=empty_set|~subset(X1,empty_set)), inference(split_conjunct,[status(thm)],[c_0_101]), ['final']).
cnf(c_0_172, plain, (X1=empty_set|~empty(X1)), inference(split_conjunct,[status(thm)],[c_0_102]), ['final']).
cnf(c_0_173, plain, (~in(X1,X2)|~empty(X2)), inference(split_conjunct,[status(thm)],[c_0_103]), ['final']).
cnf(c_0_174, plain, (~in(X1,empty_set)), inference(er,[status(thm)],[c_0_104]), ['final']).
cnf(c_0_175, plain, (~proper_subset(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_105]), ['final']).
cnf(c_0_176, plain, (~empty(esk7_0)), inference(split_conjunct,[status(thm)],[c_0_106]), ['final']).
cnf(c_0_177, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_107]), ['final']).
cnf(c_0_178, plain, (set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108, c_0_54]), c_0_54]), ['final']).
cnf(c_0_179, plain, (set_union2(X1,X2)=set_union2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_109]), ['final']).
cnf(c_0_180, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_110]), ['final']).
cnf(c_0_181, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_111]), ['final']).
cnf(c_0_182, plain, (set_difference(X1,X1)=empty_set), inference(rw,[status(thm)],[c_0_112, c_0_113]), ['final']).
cnf(c_0_183, lemma, (subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_114]), ['final']).
cnf(c_0_184, lemma, (subset(X1,set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_115]), ['final']).
cnf(c_0_185, plain, (set_union2(X1,X1)=X1), inference(split_conjunct,[status(thm)],[c_0_116]), ['final']).
cnf(c_0_186, plain, (set_union2(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_117]), ['final']).
cnf(c_0_187, plain, (set_difference(empty_set,X1)=empty_set), inference(split_conjunct,[status(thm)],[c_0_118]), ['final']).
cnf(c_0_188, plain, (subset(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_119]), ['final']).
cnf(c_0_189, lemma, (subset(empty_set,X1)), inference(split_conjunct,[status(thm)],[c_0_120]), ['final']).
cnf(c_0_190, plain, (empty(esk6_0)), inference(split_conjunct,[status(thm)],[c_0_121]), ['final']).
cnf(c_0_191, plain, (empty(empty_set)), inference(split_conjunct,[status(thm)],[fc1_xboole_0]), ['final']).
cnf(c_0_192, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_107]), ['final']).
cnf(c_0_193, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_107]), ['final']).

# End clausification derivation
# Begin listing active clauses obtained from FOF to CNF conversion
cnf(i_0_82, negated_conjecture, (subset(esk11_0,esk12_0))).
cnf(i_0_81, negated_conjecture, (disjoint(esk12_0,esk13_0))).
cnf(i_0_40, plain, (empty(empty_set))).
cnf(i_0_48, plain, (empty(esk6_0))).
cnf(i_0_62, lemma, (subset(empty_set,X1))).
cnf(i_0_50, plain, (subset(X1,X1))).
cnf(i_0_76, plain, (set_difference(empty_set,X1)=empty_set)).
cnf(i_0_55, plain, (set_union2(X1,empty_set)=X1)).
cnf(i_0_68, plain, (set_difference(X1,empty_set)=X1)).
cnf(i_0_43, plain, (set_union2(X1,X1)=X1)).
cnf(i_0_85, lemma, (subset(X1,set_union2(X1,X2)))).
cnf(i_0_64, lemma, (subset(set_difference(X1,X2),X1))).
cnf(i_0_59, plain, (set_difference(X1,X1)=empty_set)).
cnf(i_0_67, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2))).
cnf(i_0_73, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2))).
cnf(i_0_3, plain, (set_union2(X1,X2)=set_union2(X2,X1))).
cnf(i_0_4, plain, (set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1)))).
cnf(i_0_80, negated_conjecture, (~disjoint(esk11_0,esk13_0))).
cnf(i_0_49, plain, (~empty(esk7_0))).
cnf(i_0_45, plain, (~proper_subset(X1,X1))).
cnf(i_0_9, plain, (~in(X1,empty_set))).
cnf(i_0_84, plain, (~empty(X1)|~in(X2,X1))).
cnf(i_0_83, plain, (X1=empty_set|~empty(X1))).
cnf(i_0_72, lemma, (X1=empty_set|~subset(X1,empty_set))).
cnf(i_0_79, lemma, (~subset(X1,X2)|~proper_subset(X2,X1))).
cnf(i_0_1, plain, (~in(X1,X2)|~in(X2,X1))).
cnf(i_0_2, plain, (~proper_subset(X1,X2)|~proper_subset(X2,X1))).
cnf(i_0_35, plain, (subset(X1,X2)|~proper_subset(X1,X2))).
cnf(i_0_51, plain, (disjoint(X1,X2)|~disjoint(X2,X1))).
cnf(i_0_86, plain, (X1=X2|~empty(X2)|~empty(X1))).
cnf(i_0_69, lemma, (~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1))).
cnf(i_0_42, plain, (empty(X1)|~empty(set_union2(X2,X1)))).
cnf(i_0_41, plain, (empty(X1)|~empty(set_union2(X1,X2)))).
cnf(i_0_77, lemma, (~disjoint(X1,X2)|~in(X3,set_difference(X1,set_difference(X1,X2))))).
cnf(i_0_47, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set)).
cnf(i_0_46, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2))).
cnf(i_0_8, plain, (X1=empty_set|in(esk1_1(X1),X1))).
cnf(i_0_52, lemma, (set_union2(X1,X2)=X2|~subset(X1,X2))).
cnf(i_0_18, plain, (in(X1,X2)|~subset(X3,X2)|~in(X1,X3))).
cnf(i_0_29, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3))).
cnf(i_0_5, plain, (X1=X2|~subset(X2,X1)|~subset(X1,X2))).
cnf(i_0_16, plain, (subset(X1,X2)|~in(esk3_2(X1,X2),X2))).
cnf(i_0_31, plain, (disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set)).
cnf(i_0_56, lemma, (subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3))).
cnf(i_0_32, plain, (set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2))).
cnf(i_0_33, plain, (X1=X2|proper_subset(X1,X2)|~subset(X1,X2))).
cnf(i_0_58, lemma, (set_difference(X1,set_difference(X1,X2))=X1|~subset(X1,X2))).
cnf(i_0_17, plain, (subset(X1,X2)|in(esk3_2(X1,X2),X1))).
cnf(i_0_70, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X2))).
cnf(i_0_71, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),X1))).
cnf(i_0_87, lemma, (subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3))).
cnf(i_0_13, plain, (in(X1,set_union2(X2,X3))|~in(X1,X3))).
cnf(i_0_30, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3)))).
cnf(i_0_14, plain, (in(X1,set_union2(X2,X3))|~in(X1,X2))).
cnf(i_0_63, lemma, (subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3))).
cnf(i_0_23, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2))))).
cnf(i_0_78, lemma, (disjoint(X1,X2)|in(esk10_2(X1,X2),set_difference(X1,set_difference(X1,X2))))).
cnf(i_0_61, plain, (X1=X2|~in(esk8_2(X1,X2),X2)|~in(esk8_2(X1,X2),X1))).
cnf(i_0_28, plain, (in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2))).
cnf(i_0_54, lemma, (subset(X1,set_difference(X2,set_difference(X2,X3)))|~subset(X1,X3)|~subset(X1,X2))).
cnf(i_0_22, plain, (in(X1,set_difference(X2,set_difference(X2,X3)))|~in(X1,X3)|~in(X1,X2))).
cnf(i_0_15, plain, (in(X1,X2)|in(X1,X3)|~in(X1,set_union2(X3,X2)))).
cnf(i_0_60, plain, (X1=X2|in(esk8_2(X1,X2),X1)|in(esk8_2(X1,X2),X2))).
cnf(i_0_11, plain, (X1=set_union2(X2,X3)|~in(esk2_3(X2,X3,X1),X1)|~in(esk2_3(X2,X3,X1),X3))).
cnf(i_0_12, plain, (X1=set_union2(X2,X3)|~in(esk2_3(X2,X3,X1),X1)|~in(esk2_3(X2,X3,X1),X2))).
cnf(i_0_25, plain, (X1=set_difference(X2,X3)|in(esk5_3(X2,X3,X1),X1)|~in(esk5_3(X2,X3,X1),X3))).
cnf(i_0_57, lemma, (subset(set_difference(X1,set_difference(X1,X2)),set_difference(X3,set_difference(X3,X2)))|~subset(X1,X3))).
cnf(i_0_26, plain, (X1=set_difference(X2,X3)|in(esk5_3(X2,X3,X1),X2)|in(esk5_3(X2,X3,X1),X1))).
cnf(i_0_19, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk4_3(X2,X3,X1),X3)|in(esk4_3(X2,X3,X1),X1))).
cnf(i_0_20, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk4_3(X2,X3,X1),X2)|in(esk4_3(X2,X3,X1),X1))).
cnf(i_0_21, plain, (X1=set_difference(X2,set_difference(X2,X3))|~in(esk4_3(X2,X3,X1),X1)|~in(esk4_3(X2,X3,X1),X3)|~in(esk4_3(X2,X3,X1),X2))).
cnf(i_0_27, plain, (X1=set_difference(X2,X3)|in(esk5_3(X2,X3,X1),X3)|~in(esk5_3(X2,X3,X1),X1)|~in(esk5_3(X2,X3,X1),X2))).
cnf(i_0_10, plain, (X1=set_union2(X2,X3)|in(esk2_3(X2,X3,X1),X2)|in(esk2_3(X2,X3,X1),X3)|in(esk2_3(X2,X3,X1),X1))).
# End listing active clauses.  There is an equivalent clause to each of these in the clausification!
# Begin printing tableau
# 2,0,0,1  x c
cnf(i_0_118, plain, (disjoint(esk11_0,esk13_0))).
# 1,2,51,0
cnf(i_0_101, plain, (~disjoint(esk11_0,esk13_0))).
# 0,1,80,0
cnf(i_0_80, watchlist, (~disjoint(esk11_0,esk13_0))).

# 2,0,0,0  c s
cnf(i_0_119, plain, (~disjoint(esk13_0,esk11_0))).
# 1,2,51,0
cnf(i_0_101, plain, (~disjoint(esk11_0,esk13_0))).
# 0,1,80,0
cnf(i_0_80, watchlist, (~disjoint(esk11_0,esk13_0))).

# End printing tableau
# SZS output end CNFRefutation for /tmp/SystemOnTPTP26112/SEU140+2.tptp
```

### Sample solution for BOO001-1

```# SZS output start CNFRefutation for /tmp/SystemOnTPTP26176/BOO001-1.tptp
# Begin clausification derivation
cnf(prove_inverse_is_self_cancelling, negated_conjecture, (inverse(inverse(a))!=a), file('/tmp/SystemOnTPTP26176/BOO001-1.tptp', prove_inverse_is_self_cancelling)).
cnf(associativity, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', associativity)).
cnf(left_inverse, axiom, (multiply(inverse(X1),X1,X2)=X2), file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', left_inverse)).
cnf(right_inverse, axiom, (multiply(X1,X2,inverse(X2))=X1), file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', right_inverse)).
cnf(ternary_multiply_2, axiom, (multiply(X1,X1,X2)=X1), file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', ternary_multiply_2)).
cnf(ternary_multiply_1, axiom, (multiply(X1,X2,X2)=X2), file('/exp/home/tptp/TPTP/Axioms/BOO001-0.ax', ternary_multiply_1)).
cnf(c_0_6, negated_conjecture, (inverse(inverse(a))!=a), prove_inverse_is_self_cancelling, ['final']).
cnf(c_0_7, axiom, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5))), associativity, ['final']).
cnf(c_0_8, axiom, (multiply(inverse(X1),X1,X2)=X2), left_inverse, ['final']).
cnf(c_0_9, axiom, (multiply(X1,X2,inverse(X2))=X1), right_inverse, ['final']).
cnf(c_0_10, axiom, (multiply(X1,X1,X2)=X1), ternary_multiply_2, ['final']).
cnf(c_0_11, axiom, (multiply(X1,X2,X2)=X2), ternary_multiply_1, ['final']).

# End clausification derivation
# Begin listing active clauses obtained from FOF to CNF conversion
cnf(i_0_8, plain, (multiply(X1,X2,X2)=X2)).
cnf(i_0_9, plain, (multiply(X1,X1,X2)=X1)).
cnf(i_0_11, plain, (multiply(X1,X2,inverse(X2))=X1)).
cnf(i_0_10, plain, (multiply(inverse(X1),X1,X2)=X2)).
cnf(i_0_7, plain, (multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))=multiply(X1,X2,multiply(X3,X4,X5)))).
cnf(i_0_12, negated_conjecture, (inverse(inverse(a))!=a)).
# End listing active clauses.  There is an equivalent clause to each of these in the clausification!
# Begin printing tableau
# 2,0,0,1  x c
cnf(i_0_29, plain, (inverse(inverse(a))=a)).
# 1,3,22,0
cnf(i_0_23, plain, (inverse(inverse(a))!=a)).
# 0,1,12,0
cnf(i_0_12, watchlist, (inverse(inverse(a))!=a)).

# 2,0,0,0  c
cnf(i_0_30, plain, (inverse(inverse(a))!=multiply(X15,inverse(inverse(a)),inverse(inverse(a))))).
# 1,3,22,0
cnf(i_0_23, plain, (inverse(inverse(a))!=a)).
# 0,1,12,0
cnf(i_0_12, watchlist, (inverse(inverse(a))!=a)).

# 2,0,0,0  c s
cnf(i_0_31, plain, (multiply(X15,inverse(inverse(a)),inverse(inverse(a)))!=a)).
# 1,3,22,0
cnf(i_0_23, plain, (inverse(inverse(a))!=a)).
# 0,1,12,0
cnf(i_0_12, watchlist, (inverse(inverse(a))!=a)).

# End printing tableau
# SZS output end CNFRefutation for /tmp/SystemOnTPTP26176/BOO001-1.tptp
```

## GKC 0.5.1

Tanel Tammet
Tallin University of Technology, Estonia
```GKC does not print any other distinguished strings: if the previous one is not found in the
ouput, this only means that no proof has been found. In particular, GKC does not attempt
to show non-provability.

GKC proofs consist of a list of formulas or clauses, each on one line, with the following structure:

input_formula_identifier [derivation method, parent formula identifier, clause class] derived_formula_in_fof.
clause_number [derivation method, input formula id or parent clause numbers, clause class] derived_clause_in_cnf.

The input formula identifier may be prefixed by \$imp:: indicating it stems from the imported file,
or suffixed by _\$sk, indicating that it is a result of pushing negation inward and skolemization.

We use the = sign for equality, minus sign for negation and | for logical or.
Words starting with an uppercase character or a question mark ? denote variables.
Clauses are terminated with a period.

Input formulas and their clausifications occur in the first part of the
proof output, followed by the derivations from clauses. Each raw input formula
passes some obvious simplifications followed by pushing negation inward and skolemization:
the result of negation-pushing and skolemization is stored an output in proof as
a separate derived formula. Finally, distribution and further obvious simplifications

The derivation method can be:

* axiom, lemma, conjecture, negated_conjecture: input formula with only obvious simplifications done
* sk: formula obtained from the previous formula by pushing negation inward, skolemization and obvious simplifications
* cnf: input clause or a clause obtained by distribution and obvious simplifications from the skolemized formula
* in: input clause followed by its name.
* mp: resolution upon next two parent numbers.
* merge: factorization upon the next parent number.
* =: paramodulation from the next parent number to the following.
* =r: reflexivity of equality applied to the first parent number,
* simp: first parent number is demodulated and/or units are cut off with the following parents,
without instantianting the first parent.

The rest of the parent clause numbers, if present, are simplifiers:
clauses used as demodulators and/or cutting off units, without instantianting
the result of the derivation method.

The final part of [....] indicates the class of the derived clause related to initial
axioms/external axioms/assumptions/goal  structure and is purely informational:
the derived clause does not depend upon it.

A clause number may be a chain of numbers separated by a period, like 15.1 or 12.0.1 or 11.0.R.

* The first number is the clause number proper.

* The second indicates the number of literal operated upon, with 0 being the first number
(0 is omitted if nothing follows).

* The third indicates the concrete subterm operated upon (used by paramodulation),
from left to right.

* Instead of the third number, paramodulation uses R to indicate that paramodulation
is performed from right.
```

### Sample solution for SEU140+2

```% SZS output start CNFRefutation for /opt/TPTP/Problems/SEU/SEU140+2.p
d7_xboole_0_\$sk: [sk,d7_xboole_0] ((~disjoint(X2,X1) | (set_intersection2(X2,X1) = empty_set)) & (disjoint(X4,X3) | ~(set_intersection2(X4,X3) = empty_set)))
d7_xboole_0: [axiom] (! [A,B] : (disjoint(A,B) <=> (set_intersection2(A,B) = empty_set)))
t6_boole_\$sk: [sk,t6_boole] ((X1 = empty_set) | ~empty(X1))
t6_boole: [axiom] (! [A] : (empty(A) => (A = empty_set)))
rc1_xboole_0_\$sk: [sk,rc1_xboole_0] empty(\$sk9)
rc1_xboole_0: [axiom] (? [A] : empty(A))
t63_xboole_1_\$sk: [sk,t63_xboole_1] (~disjoint(\$sk3,\$sk2) & (disjoint(\$sk1,\$sk2) & subset(\$sk3,\$sk1)))
t63_xboole_1: [conjecture] (! [A,B,C] : ((subset(A,B) & disjoint(B,C)) => disjoint(A,C)))
t28_xboole_1_\$sk: [sk,t28_xboole_1] ((set_intersection2(X2,X1) = X2) | ~subset(X2,X1))
t28_xboole_1: [lemma] (! [A,B] : (subset(A,B) => (set_intersection2(A,B) = A)))
t7_xboole_1_\$sk: [sk,t7_xboole_1] subset(X2,set_union2(X2,X1))
t7_xboole_1: [lemma] (! [A,B] : subset(A,set_union2(A,B)))
commutativity_k3_xboole_0_\$sk: [sk,commutativity_k3_xboole_0] (set_intersection2(X2,X1) = set_intersection2(X1,X2))
commutativity_k3_xboole_0: [axiom] (! [A,B] : (set_intersection2(A,B) = set_intersection2(B,A)))
t48_xboole_1_\$sk: [sk,t48_xboole_1] (set_difference(X2,set_difference(X2,X1)) = set_intersection2(X2,X1))
t48_xboole_1: [lemma] (! [A,B] : (set_difference(A,set_difference(A,B)) = set_intersection2(A,B)))
commutativity_k2_xboole_0_\$sk: [sk,commutativity_k2_xboole_0] (set_union2(X2,X1) = set_union2(X1,X2))
commutativity_k2_xboole_0: [axiom] (! [A,B] : (set_union2(A,B) = set_union2(B,A)))
t40_xboole_1_\$sk: [sk,t40_xboole_1] (set_difference(set_union2(X2,X1),X1) = set_difference(X2,X1))
t40_xboole_1: [lemma] (! [A,B] : (set_difference(set_union2(A,B),B) = set_difference(A,B)))
t39_xboole_1_\$sk: [sk,t39_xboole_1] (set_union2(X2,set_difference(X1,X2)) = set_union2(X2,X1))
t39_xboole_1: [lemma] (! [A,B] : (set_union2(A,set_difference(B,A)) = set_union2(A,B)))
t33_xboole_1_\$sk: [sk,t33_xboole_1] (subset(set_difference(X3,X2),set_difference(X1,X2)) | ~subset(X3,X1))
t33_xboole_1: [lemma] (! [A,B,C] : (subset(A,B) => subset(set_difference(A,C),set_difference(B,C))))
l32_xboole_1_\$sk: [sk,l32_xboole_1] ((~(set_difference(X2,X1) = empty_set) | subset(X2,X1)) & ((set_difference(X4,X3) = empty_set) | ~subset(X4,X3)))
l32_xboole_1: [lemma] (! [A,B] : ((set_difference(A,B) = empty_set) <=> subset(A,B)))
t1_boole_\$sk: [sk,t1_boole] (set_union2(X1,empty_set) = X1)
t1_boole: [axiom] (! [A] : (set_union2(A,empty_set) = A))
t26_xboole_1_\$sk: [sk,t26_xboole_1] (subset(set_intersection2(X3,X2),set_intersection2(X1,X2)) | ~subset(X3,X1))
t26_xboole_1: [lemma] (! [A,B,C] : (subset(A,B) => subset(set_intersection2(A,C),set_intersection2(B,C))))
t1_xboole_1_\$sk: [sk,t1_xboole_1] (subset(X3,X2) | (~subset(X1,X2) | ~subset(X3,X1)))
t1_xboole_1: [lemma] (! [A,B,C] : ((subset(A,B) & subset(B,C)) => subset(A,C)))
t3_boole_\$sk: [sk,t3_boole] (set_difference(X1,empty_set) = X1)
t3_boole: [axiom] (! [A] : (set_difference(A,empty_set) = A))
1: [cnf,d7_xboole_0_\$sk, axiom] =(set_intersection2(?0,?1),empty_set) | -disjoint(?0,?1).
2: [cnf,t6_boole_\$sk, axiom] =(X,empty_set) | -empty(X).
3: [cnf,rc1_xboole_0_\$sk, axiom] empty(\$sk9).
4: [mp, 2.1, 3, fromaxiom] =(\$sk9,empty_set).
5: [simp, 1, 4, fromaxiom] =(set_intersection2(X,Y),\$sk9) | -disjoint(X,Y).
6: [cnf,t63_xboole_1_\$sk, goal] disjoint(\$sk1,\$sk2).
7: [mp, 5.1, 6, fromgoal] =(set_intersection2(\$sk1,\$sk2),\$sk9).
8: [cnf,t28_xboole_1_\$sk, axiom] =(set_intersection2(X,Y),X) | -subset(X,Y).
9: [cnf,t7_xboole_1_\$sk, axiom] subset(X,set_union2(X,Y)).
10: [mp, 8.1, 9, fromaxiom] =(set_intersection2(X,set_union2(X,Y)),X).
11: [cnf,commutativity_k3_xboole_0_\$sk, axiom] =(set_intersection2(X,Y),set_intersection2(Y,X)).
12: [=, 10, 11.0.4, fromaxiom] =(set_intersection2(set_union2(X,Y),X),X).
13: [cnf,t48_xboole_1_\$sk, axiom] =(set_difference(X,set_difference(X,Y)),set_intersection2(X,Y)).
14: [=, 12, 13.0.6, fromaxiom] =(set_difference(set_union2(X3,Y3),set_difference(set_union2(X3,Y3),X3)),X3).
15: [cnf,commutativity_k2_xboole_0_\$sk, axiom] =(set_union2(X,Y),set_union2(Y,X)).
16: [cnf,t40_xboole_1_\$sk, axiom] =(set_difference(set_union2(X,Y),Y),set_difference(X,Y)).
17: [=, 15, 16.0.2, fromaxiom] =(set_difference(set_union2(X,Y),X),set_difference(Y,X)).
18: [cnf,t39_xboole_1_\$sk, axiom] =(set_union2(X,set_difference(Y,X)),set_union2(X,Y)).
19: [=, 18, 16.0.2, fromaxiom] =(set_difference(set_union2(X,Y),set_difference(Y,X)),set_difference(X,set_difference(Y,X))).
20: [simp, 14, 17, 19, fromaxiom] =(set_difference(X,set_difference(Y,X)),X).
21: [cnf,t33_xboole_1_\$sk, axiom] subset(set_difference(X,Y),set_difference(Z,Y)) | -subset(X,Z).
22: [cnf,t63_xboole_1_\$sk, goal] subset(\$sk3,\$sk1).
23: [mp, 21.1, 22, fromgoal] subset(set_difference(\$sk3,X),set_difference(\$sk1,X)).
24: [cnf,l32_xboole_1_\$sk, axiom] =(set_difference(?0,?1),empty_set) | -subset(?0,?1).
25: [simp, 24, 4, fromaxiom] =(set_difference(X,Y),\$sk9) | -subset(X,Y).
26: [mp, 23, 25.1, fromgoal] =(set_difference(set_difference(\$sk3,X),set_difference(\$sk1,X)),\$sk9).
27: [=, 20, 26.0.5, fromgoal] =(set_difference(set_difference(\$sk3,set_difference(X,\$sk1)),\$sk1),\$sk9).
28: [=, 15, 18.0.1, fromaxiom] =(set_union2(set_difference(X,Y),Y),set_union2(Y,X)).
29: [=, 27, 28.0.2, fromgoal] =(set_union2(\$sk9,\$sk1),set_union2(\$sk1,set_difference(\$sk3,set_difference(X3,\$sk1)))).
30: [cnf,t1_boole_\$sk, axiom] =(set_union2(X,empty_set),X).
31: [=, 4.0.R, 30.0.3, fromaxiom] =(set_union2(X,\$sk9),X).
32: [=, 15, 31.0.1, fromaxiom] =(set_union2(\$sk9,X),X).
33: [simp, 29, 32, fromgoal] =(\$sk1,set_union2(\$sk1,set_difference(\$sk3,set_difference(X,\$sk1)))).
34: [cnf,t26_xboole_1_\$sk, axiom] subset(set_intersection2(X,Y),set_intersection2(Z,Y)) | -subset(X,Z).
35: [cnf,t1_xboole_1_\$sk, axiom] -subset(X,Y) | -subset(Y,Z) | subset(X,Z).
36: [mp, 35, 22, fromgoal] subset(\$sk3,X) | -subset(\$sk1,X).
37: [mp, 36.1, 9, fromgoal] subset(\$sk3,set_union2(\$sk1,X)).
38: [mp, 34.1, 37, fromgoal] subset(set_intersection2(\$sk3,X),set_intersection2(set_union2(\$sk1,Y),X)).
39: [mp, 38, 25.1, fromgoal] =(set_difference(set_intersection2(\$sk3,X),set_intersection2(set_union2(\$sk1,Y),X)),\$sk9).
40: [=, 33.0.R, 39.0.6, fromgoal] =(set_difference(set_intersection2(\$sk3,X),set_intersection2(\$sk1,X)),\$sk9).
41: [=, 7, 40.0.5, fromgoal] =(set_difference(set_intersection2(\$sk3,\$sk2),\$sk9),\$sk9).
42: [cnf,t3_boole_\$sk, axiom] =(set_difference(X,empty_set),X).
43: [=, 4.0.R, 42.0.3, fromaxiom] =(set_difference(X,\$sk9),X).
44: [simp, 41, 43, fromgoal] =(set_intersection2(\$sk3,\$sk2),\$sk9).
45: [cnf,d7_xboole_0_\$sk, axiom] -=(set_intersection2(?0,?1),empty_set) | disjoint(?0,?1).
46: [simp, 45, 4, fromaxiom] -=(set_intersection2(X,Y),\$sk9) | disjoint(X,Y).
47: [cnf,t63_xboole_1_\$sk, goal] -disjoint(\$sk3,\$sk2).
48: [mp, 44, 46, 47, fromgoal] false
% SZS output end CNFRefutation for /opt/TPTP/Problems/SEU/SEU140+2.p
```

### Sample solution for BOO001-1

```% SZS output start CNFRefutation for /opt/TPTP/Problems/BOO/BOO001-1.p
1: [cnf,\$imp::right_inverse_\$sk, extaxiom] =(multiply(X,Y,inverse(Y)),X).
2: [cnf,\$imp::ternary_multiply_1_\$sk, extaxiom] =(multiply(X,Y,Y),Y).
3: [cnf,\$imp::associativity_\$sk, extaxiom] =(multiply(multiply(X,Y,Z),U,multiply(X,Y,V)),multiply(X,Y,multiply(Z,U,V))).
4: [=, 2, 3.0.2, fromaxiom] =(multiply(X,Y,multiply(Z,X,U)),multiply(Z,X,multiply(X,Y,U))).
5: [cnf,\$imp::ternary_multiply_2_\$sk, extaxiom] =(multiply(X,X,Y),X).
6: [=, 3, 5.0.1, fromaxiom] =(multiply(X,Y,multiply(Z,multiply(X,Y,Z),U)),multiply(X,Y,Z)).
7: [=, 1, 6.0.6, fromaxiom] =(multiply(X3,Y3,multiply(inverse(Y3),X3,Z3)),multiply(X3,Y3,inverse(Y3))).
8: [simp, 7, 1, fromaxiom] =(multiply(X,Y,multiply(inverse(Y),X,Z)),X).
9: [=, 4, 8.0.1, fromaxiom] =(multiply(inverse(X),Y,multiply(Y,X,Z)),Y).
10: [=, 2, 9.0.5, fromaxiom] =(multiply(inverse(X),Y,X),Y).
11: [cnf,prove_inverse_is_self_cancelling_\$sk, goal] -=(inverse(inverse(a)),a).
12: [=, 1, 10.0.1, 11, fromaxiom] false
% SZS output end CNFRefutation for /opt/TPTP/Problems/BOO/BOO001-1.p
```

### Sample solution for HL400001+5

```% SZS output start CNFRefutation for Examples/HL400001+5.p
conj_thm_2Ebool_2ETRUTH_\$sk: [sk,conj_thm_2Ebool_2ETRUTH] ~\$true
conj_thm_2Ebool_2ETRUTH: [conjecture] \$true
ax_thm_2Ebool_2ET__DEF_\$sk: [sk,ax_thm_2Ebool_2ET__DEF] ((~\$true | (i(bool) = i(bool))) & (\$true | ~(i(bool) = i(bool))))
ax_thm_2Ebool_2ET__DEF: [axiom] (\$true <=> (i(bool) = i(bool)))
1: [cnf,conj_thm_2Ebool_2ETRUTH_\$sk, goal] -\$pr(\$true).
2: [cnf,ax_thm_2Ebool_2ET__DEF_\$sk, axiom] \$pr(\$true).
3: [simp, 1, 2, fromgoal] false
% SZS output end CNFRefutation for Examples/HL400001+5.p
```

### Sample solution for HL400001+4

```% SZS output start CNFRefutation for Examples/HL400001+4.p
thm_2Ebool_2ETRUTH_\$sk: [sk,thm_2Ebool_2ETRUTH] ~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
thm_2Ebool_2ETRUTH: [conjecture] p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
reserved_2Eho_2Etruth: [axiom] p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
1: [cnf,thm_2Ebool_2ETRUTH_\$sk, goal] -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)).
2: [cnf,reserved_2Eho_2Etruth_\$sk, axiom] p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)).
3: [simp, 1, 2, fromgoal] false
% SZS output end CNFRefutation for Examples/HL400001+4.p
```

## iProver 3.3

Konstantin Korovin
University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS output start CNFRefutation for SEU140+2.p

fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('/shareddata/TPTP-v7.3.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f67,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X1) | ~in(X2,X0)))),
inference(ennf_transformation,[],[f8])).

fof(f105,plain,(
! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X2] : (in(X2,X1) | ~in(X2,X0)) | ~subset(X0,X1)))),
inference(nnf_transformation,[],[f67])).

fof(f106,plain,(
! [X0,X1] : ((subset(X0,X1) | ? [X2] : (~in(X2,X1) & in(X2,X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
inference(rectify,[],[f105])).

fof(f107,plain,(
! [X1,X0] : (? [X2] : (~in(X2,X1) & in(X2,X0)) => (~in(sK2(X0,X1),X1) & in(sK2(X0,X1),X0)))),
introduced(choice_axiom,[])).

fof(f108,plain,(
! [X0,X1] : ((subset(X0,X1) | (~in(sK2(X0,X1),X1) & in(sK2(X0,X1),X0))) & (! [X3] : (in(X3,X1) | ~in(X3,X0)) | ~subset(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f106,f107])).

fof(f150,plain,(
( ! [X0,X3,X1] : (in(X3,X1) | ~in(X3,X0) | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f108])).

fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('/shareddata/TPTP-v7.3.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f62,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).

fof(f82,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f62])).

fof(f129,plain,(
! [X1,X0] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
introduced(choice_axiom,[])).

fof(f130,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).

fof(f199,plain,(
( ! [X2,X0,X1] : (~disjoint(X0,X1) | ~in(X2,X1) | ~in(X2,X0)) )),
inference(cnf_transformation,[],[f130])).

fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).

fof(f198,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).

fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('/shareddata/TPTP-v7.3.0/Problems/SEU/SEU140+2.p',unknown)).

fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).

fof(f87,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).

fof(f88,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f87])).

fof(f133,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
introduced(choice_axiom,[])).

fof(f134,plain,(
~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).

fof(f210,plain,(
~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f134])).

fof(f209,plain,(
disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f134])).

fof(f208,plain,(
subset(sK10,sK11)),
inference(cnf_transformation,[],[f134])).

cnf(c_17,plain,
( ~ subset(X0,X1) | ~ in(X2,X0) | in(X2,X1) ),
inference(cnf_transformation,[],[f150]) ).

cnf(c_3235,plain,
( ~ subset(sK10,X0)
| in(sK8(sK10,sK12),X0)
| ~ in(sK8(sK10,sK12),sK10) ),
inference(instantiation,[status(thm)],[c_17]) ).

cnf(c_5304,plain,
( ~ subset(sK10,sK11)
| in(sK8(sK10,sK12),sK11)
| ~ in(sK8(sK10,sK12),sK10) ),
inference(instantiation,[status(thm)],[c_3235]) ).

cnf(c_62,plain,
( ~ disjoint(X0,X1) | ~ in(X2,X1) | ~ in(X2,X0) ),
inference(cnf_transformation,[],[f199]) ).

cnf(c_3194,plain,
( ~ disjoint(X0,sK12)
| ~ in(sK8(sK10,sK12),X0)
| ~ in(sK8(sK10,sK12),sK12) ),
inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_5199,plain,
( ~ disjoint(sK11,sK12)
| ~ in(sK8(sK10,sK12),sK11)
| ~ in(sK8(sK10,sK12),sK12) ),
inference(instantiation,[status(thm)],[c_3194]) ).

cnf(c_64,plain,
( disjoint(X0,X1) | in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f197]) ).

cnf(c_3001,plain,
( disjoint(sK10,sK12) | in(sK8(sK10,sK12),sK10) ),
inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_63,plain,
( disjoint(X0,X1) | in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f198]) ).

cnf(c_2998,plain,
( disjoint(sK10,sK12) | in(sK8(sK10,sK12),sK12) ),
inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_72,negated_conjecture,
( ~ disjoint(sK10,sK12) ),
inference(cnf_transformation,[],[f210]) ).

cnf(c_73,negated_conjecture,
( disjoint(sK11,sK12) ),
inference(cnf_transformation,[],[f209]) ).

cnf(c_74,negated_conjecture,
( subset(sK10,sK11) ),
inference(cnf_transformation,[],[f208]) ).

( \$false ),
inference(minisat,
[status(thm)],
[c_5304,c_5199,c_3001,c_2998,c_72,c_73,c_74]) ).

% SZS output end CNFRefutation for SEU140+2.p
```

### Sample solution for NLP042+1

```% SZS output start Model for NLP042+1.p

%------ Negative definition of equality_sorted
fof(lit_def,axiom,
(! [X0_0,X0_2,X1_2] :
( ~(equality_sorted(X0_0,X0_2,X1_2)) <=>
(
(
( X0_0=iProver_forename_2_\$i & X0_66=sK4 & X1_66=sK3 )
)

|
(
( X0_0=iProver_forename_2_\$i & X0_66=sK4 & X1_66=sK1 )
)

|
(
( X0_0=iProver_forename_2_\$i & X0_66=sK3 )
&
( X1_66!=sK3 )
)

|
(
( X0_0=iProver_forename_2_\$i & X0_66=sK3 & X1_66=sK1 )
)

|
(
( X0_0=iProver_forename_2_\$i & X0_66=sK1 )
&
( X1_66!=sK1 )
)

|
(
( X0_0=iProver_forename_2_\$i & X0_66=sK2 )
&
( X1_66!=sK2 )
)

|
(
( X0_0=iProver_forename_2_\$i & X1_66=sK3 )
&
( X0_66!=sK3 )
)

|
(
( X0_0=iProver_forename_2_\$i & X1_66=sK1 )
&
( X0_66!=sK1 )
)

|
(
( X0_0=iProver_forename_2_\$i & X1_66=sK2 )
&
( X0_66!=sK2 )
)

)
)
)
).

%------ Positive definition of woman
fof(lit_def,axiom,
(! [X0,X1] :
( woman(X0,X1) <=>
\$false
)
)
).

%------ Positive definition of forename
fof(lit_def,axiom,
(! [X0_67,X0_66] :
( forename(X0_67,X0_66) <=>
(
(
( X0_67=sK0 & X0_66=sK2 )
)

)
)
)
).

%------ Positive definition of mia_forename
fof(lit_def,axiom,
(! [X0,X1] :
( mia_forename(X0,X1) <=>
\$false
)
)
).

%------ Positive definition of shake_beverage
fof(lit_def,axiom,
(! [X0,X1] :
( shake_beverage(X0,X1) <=>
\$false
)
)
).

%------ Positive definition of event
fof(lit_def,axiom,
(! [X0,X1] :
( event(X0,X1) <=>
\$false
)
)
).

%------ Positive definition of order
fof(lit_def,axiom,
(! [X0,X1] :
( order(X0,X1) <=>
\$false
)
)
).

%------ Positive definition of of
fof(lit_def,axiom,
(! [X0_67,X0_66,X1_66] :
( of(X0_67,X0_66,X1_66) <=>
(
(
( X0_67=sK0 & X0_66=sK2 & X1_66=sK1 )
)

)
)
)
).

%------ Positive definition of patient
fof(lit_def,axiom,
(! [X0,X1,X2] :
( patient(X0,X1,X2) <=>
\$false
)
)
).

%------ Positive definition of agent
fof(lit_def,axiom,
(! [X0,X1,X2] :
( agent(X0,X1,X2) <=>
\$false
)
)
).

%------ Positive definition of nonreflexive
fof(lit_def,axiom,
(! [X0,X1] :
( nonreflexive(X0,X1) <=>
\$false
)
)
).
% SZS output end Model for NLP042+1.p
```

### Sample solution for SWV017+1

```% SZS output start Model for SWV017+1.p

%------ Negative definition of party_of_protocol
fof(lit_def,axiom,
(! [X0] :
( ~(party_of_protocol(X0)) <=>
\$false
)
)
).

%------ Negative definition of message
fof(lit_def,axiom,
(! [X0] :
( ~(message(X0)) <=>
\$false
)
)
).

%------ Negative definition of a_stored
fof(lit_def,axiom,
(! [X0] :
( ~(a_stored(X0)) <=>
\$false
)
)
).

%------ Positive definition of fresh_to_b
fof(lit_def,axiom,
(! [X0] :
( fresh_to_b(X0) <=>
\$true
)
)
).

%------ Negative definition of t_holds
fof(lit_def,axiom,
(! [X0] :
( ~(t_holds(X0)) <=>
\$false
)
)
).

%------ Positive definition of a_nonce
fof(lit_def,axiom,
(! [X0] :
( a_nonce(X0) <=>
\$false
)
)
).

%------ Positive definition of intruder_message
fof(lit_def,axiom,
(! [X0] :
( intruder_message(X0) <=>
\$true
)
)
).

%------ Negative definition of intruder_holds
fof(lit_def,axiom,
(! [X0] :
( ~(intruder_holds(X0)) <=>
\$false
)
)
).

%------ Negative definition of fresh_intruder_nonce
fof(lit_def,axiom,
(! [X0] :
( ~(fresh_intruder_nonce(X0)) <=>
\$false
)
)
).
% SZS output end Model for SWV017+1.p
```

### Sample solution for BOO001-1

```% SZS output start CNFRefutation for BOO001-1.p

cnf(c_4,plain,
( X0 = multiply(inverse(X1),X1,X0) ),
file('/shareddata/TPTP-v7.3.0/Axioms/BOO001-0.ax', left_inverse) ).

cnf(c_2,plain,
( X0 = multiply(X1,X0,X0) ),
file('/shareddata/TPTP-v7.3.0/Axioms/BOO001-0.ax', ternary_multiply_1) ).

cnf(c_3,plain,
( X0 = multiply(X0,X0,X1) ),
file('/shareddata/TPTP-v7.3.0/Axioms/BOO001-0.ax', ternary_multiply_2) ).

cnf(c_5,plain,
( X0 = multiply(X0,X1,inverse(X1)) ),
file('/shareddata/TPTP-v7.3.0/Axioms/BOO001-0.ax', right_inverse) ).

cnf(c_1,plain,
( multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)) ),
file('/shareddata/TPTP-v7.3.0/Axioms/BOO001-0.ax', associativity) ).

cnf(c_58,plain,
( multiply(X0,X1,multiply(X0,X2,X3)) = multiply(X0,X2,multiply(inverse(X2),X1,X3)) ),
inference(superposition,[status(thm)],[c_5,c_1]) ).

cnf(c_188,plain,
( multiply(X0,X1,inverse(X1)) = multiply(X0,inverse(X1),multiply(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_3,c_58]) ).

cnf(c_190,plain,
( X0 = multiply(X0,inverse(X1),multiply(X0,X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_188,c_5]) ).

cnf(c_327,plain,
( X0 = multiply(X0,inverse(X1),X1) ),
inference(superposition,[status(thm)],[c_2,c_190]) ).

cnf(c_374,plain,
( X0 = inverse(inverse(X0)) ),
inference(superposition,[status(thm)],[c_4,c_327]) ).

cnf(c_0,negated_conjecture,
( inverse(inverse(a)) != a ),
file('/shareddata/TPTP-v7.3.0/Problems/BOO/BOO001-1.p', prove_inverse_is_self_cancelling) ).

cnf(c_407,plain,
( a != a ),
inference(demodulation,[status(thm)],[c_374,c_0]) ).

cnf(c_408,plain,
( \$false ),
inference(equality_resolution_simp,[status(thm)],[c_407]) ).

% SZS output end CNFRefutation for BOO001-1.p
```

### Sample solution for HL400001+5

```% SZS output start CNFRefutation for HL400001+5.p

fof(f72,conjecture,(
\$true),
file('/shareddata/home/korovin/CASC_2020_sample_sol/HL400001+5.p',unknown)).

fof(f73,negated_conjecture,(
~\$true),
inference(negated_conjecture,[],[f72])).

fof(f131,plain,(
\$false),
inference(true_and_false_elimination,[],[f73])).

fof(f301,plain,(
\$false),
inference(cnf_transformation,[],[f131])).

cnf(c_0,negated_conjecture,
( \$false ),
inference(cnf_transformation,[],[f301]) ).

% SZS output end CNFRefutation for HL400001+5.p
```

### Sample solution for HL400001+4

```% SZS output start CNFRefutation for HL400001+4.p

fof(f102,conjecture,(
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
file('/shareddata/home/korovin/CASC_2020_sample_sol/HL400001+4.p',unknown)).

fof(f103,negated_conjecture,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(negated_conjecture,[],[f102])).

fof(f199,plain,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(flattening,[],[f103])).

fof(f532,plain,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(cnf_transformation,[],[f199])).

cnf(c_113,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[],[f533]) ).

cnf(c_178,negated_conjecture,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[],[f532]) ).

( \$false ),
inference(minisat,[status(thm)],[c_113,c_178]) ).

% SZS output end CNFRefutation for HL400001+4.p
```

## lazyCoP 0.1

Michael Rawson
University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS begin CNFRefutation
cnf(c0, axiom,
subset(sK10,sK11)).
cnf(c1, plain,
subset(sK10,sK11),
inference(start, [], [c0])).

cnf(c2, axiom,
subset(set_difference(X0,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1))) | ~subset(X0,X2)).
cnf(a0, assumption,
sK10 = X0).
cnf(a1, assumption,
sK11 = X2).
cnf(c3, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a0, a1])], [c1, c2])).
cnf(c4, plain,
subset(set_difference(X0,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1))),
inference(strict_predicate_extension, [assumptions([a0, a1])], [c1, c2])).

cnf(c5, axiom,
in(X3,X4) | ~in(X3,X5) | ~subset(X5,X4)).
cnf(a2, assumption,
set_difference(X0,set_difference(X0,X1)) = X5).
cnf(a3, assumption,
set_difference(X2,set_difference(X2,X1)) = X4).
cnf(c6, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a2, a3])], [c4, c5])).
cnf(c7, plain,
in(X3,X4) | ~in(X3,X5),
inference(strict_predicate_extension, [assumptions([a2, a3])], [c4, c5])).

cnf(c8, axiom,
~disjoint(X6,X7) | ~in(X8,set_difference(X6,set_difference(X6,X7)))).
cnf(a4, assumption,
X3 = X8).
cnf(a5, assumption,
X4 = set_difference(X6,set_difference(X6,X7))).
cnf(c9, plain,
~in(X3,X5),
inference(strict_predicate_extension, [assumptions([a4, a5])], [c7, c8])).
cnf(c10, plain,
~disjoint(X6,X7),
inference(strict_predicate_extension, [assumptions([a4, a5])], [c7, c8])).

cnf(c11, axiom,
disjoint(sK11,sK12)).
cnf(a6, assumption,
X6 = sK11).
cnf(a7, assumption,
X7 = sK12).
cnf(c12, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a6, a7])], [c10, c11])).
cnf(c13, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a6, a7])], [c10, c11])).

cnf(c14, axiom,
in(sK9(X9,X10),set_difference(X9,set_difference(X9,X10))) | disjoint(X9,X10)).
cnf(a8, assumption,
X3 = sK9(X9,X10)).
cnf(a9, assumption,
X5 = set_difference(X9,set_difference(X9,X10))).
cnf(c15, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a8, a9])], [c9, c14])).
cnf(c16, plain,
disjoint(X9,X10),
inference(strict_predicate_extension, [assumptions([a8, a9])], [c9, c14])).

cnf(c17, axiom,
~disjoint(sK10,sK12)).
cnf(a10, assumption,
X9 = sK10).
cnf(a11, assumption,
X10 = sK12).
cnf(c18, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a10, a11])], [c16, c17])).
cnf(c19, plain,
\$false,
inference(strict_predicate_extension, [assumptions([a10, a11])], [c16, c17])).

cnf(c20, plain,
\$false,
inference(constraint_solving, [
bind(X0, sK10),
bind(X1, sK12),
bind(X2, sK11),
bind(X3, sK9(X9,X10)),
bind(X4, set_difference(X6,set_difference(X6,X7))),
bind(X5, set_difference(X9,set_difference(X9,X10))),
bind(X6, sK11),
bind(X7, sK12),
bind(X8, sK9(X9,X10)),
bind(X9, sK10),
bind(X10, sK12)
],
[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11])).

% SZS end CNFRefutation
```

### Sample solution for BOO001-1

```% SZS begin CNFRefutation
cnf(c0, axiom,
a != inverse(inverse(a))).
cnf(c1, plain,
a != inverse(inverse(a)),
inference(start, [], [c0])).

cnf(c2, axiom,
multiply(X0,X1,inverse(X1)) = X0).
cnf(a0, assumption,
inverse(inverse(a)) = X0).
cnf(c3, plain,
\$false,
inference(variable_extension, [assumptions([a0])], [c1, c2])).
cnf(c4, plain,
multiply(X0,X1,inverse(X1)) != X2 | a != X2,
inference(variable_extension, [assumptions([a0])], [c1, c2])).

cnf(c5, axiom,
multiply(X3,X4,X4) = X4).
cnf(a1, assumption,
inverse(X1) = X4).
cnf(c6, plain,
a != X2,
inference(variable_extension, [assumptions([a1])], [c4, c5])).
cnf(c7, plain,
multiply(X3,X4,X4) != X5 | multiply(X0,X1,X5) != X2,
inference(variable_extension, [assumptions([a1])], [c4, c5])).

cnf(a2, assumption,
multiply(X3,X4,X4) = X5).
cnf(c8, plain,
multiply(X0,X1,X5) != X2,
inference(reflexivity, [assumptions([a2])], [c7])).

cnf(a3, assumption,
multiply(X0,X1,X5) = X2).
cnf(c9, plain,
\$false,
inference(reflexivity, [assumptions([a3])], [c8])).

cnf(c10, axiom,
multiply(X6,X7,X7) = X7).
cnf(a4, assumption,
a = X7).
cnf(c11, plain,
\$false,
inference(variable_extension, [assumptions([a4])], [c6, c10])).
cnf(c12, plain,
multiply(X6,X7,X7) != X8 | X8 != X2,
inference(variable_extension, [assumptions([a4])], [c6, c10])).

cnf(c13, axiom,
multiply(X9,X10,inverse(X10)) = X9).
cnf(a5, assumption,
multiply(X6,X7,X7) = X9).
cnf(c14, plain,
X8 != X2,
inference(variable_extension, [assumptions([a5])], [c12, c13])).
cnf(c15, plain,
multiply(X9,X10,inverse(X10)) != X11 | X11 != X8,
inference(variable_extension, [assumptions([a5])], [c12, c13])).

cnf(c16, axiom,
multiply(X12,X13,inverse(X13)) = X12).
cnf(a6, assumption,
inverse(X10) = X12).
cnf(c17, plain,
X11 != X8,
inference(variable_extension, [assumptions([a6])], [c15, c16])).
cnf(c18, plain,
multiply(X12,X13,inverse(X13)) != X14 | multiply(X9,X10,X14) != X11,
inference(variable_extension, [assumptions([a6])], [c15, c16])).

cnf(a7, assumption,
multiply(X12,X13,inverse(X13)) = X14).
cnf(c19, plain,
multiply(X9,X10,X14) != X11,
inference(reflexivity, [assumptions([a7])], [c18])).

cnf(c20, axiom,
multiply(multiply(X15,X16,X17),X18,multiply(X15,X16,X19)) = multiply(X15,X16,multiply(X17,X18,X19))).
cnf(a8, assumption,
multiply(X20,X21,X22) = multiply(X9,X10,X14)).
cnf(c21, plain,
\$false,
inference(function_extension, [assumptions([a8])], [c19, c20])).
cnf(c22, plain,
X20 != multiply(X15,X16,X17) | X21 != X18 | X22 != multiply(X15,X16,X19) | X23 != multiply(X15,X16,multiply(X17,X18,X19)) | X23 != X11,
inference(function_extension, [assumptions([a8])], [c19, c20])).

cnf(a9, assumption,
X20 = multiply(X15,X16,X17)).
cnf(c23, plain,
X21 != X18 | X22 != multiply(X15,X16,X19) | X23 != multiply(X15,X16,multiply(X17,X18,X19)) | X23 != X11,
inference(reflexivity, [assumptions([a9])], [c22])).

cnf(a10, assumption,
X21 = X18).
cnf(c24, plain,
X22 != multiply(X15,X16,X19) | X23 != multiply(X15,X16,multiply(X17,X18,X19)) | X23 != X11,
inference(reflexivity, [assumptions([a10])], [c23])).

cnf(a11, assumption,
X22 = multiply(X15,X16,X19)).
cnf(c25, plain,
X23 != multiply(X15,X16,multiply(X17,X18,X19)) | X23 != X11,
inference(reflexivity, [assumptions([a11])], [c24])).

cnf(a12, assumption,
X23 = multiply(X15,X16,multiply(X17,X18,X19))).
cnf(c26, plain,
X23 != X11,
inference(reflexivity, [assumptions([a12])], [c25])).

cnf(a13, assumption,
X23 = X11).
cnf(c27, plain,
\$false,
inference(reflexivity, [assumptions([a13])], [c26])).

cnf(a14, assumption,
X11 = X8).
cnf(c28, plain,
\$false,
inference(reflexivity, [assumptions([a14])], [c17])).

cnf(a15, assumption,
X8 = X2).
cnf(c29, plain,
\$false,
inference(reflexivity, [assumptions([a15])], [c14])).

cnf(c30, plain,
\$false,
inference(constraint_solving, [
bind(X0, inverse(X10)),
bind(X1, a),
bind(X2, multiply(X15,X16,multiply(X17,X18,X19))),
bind(X3, a),
bind(X4, inverse(X13)),
bind(X5, multiply(X17,X18,X19)),
bind(X6, inverse(X10)),
bind(X7, a),
bind(X8, multiply(X15,X16,multiply(X17,X18,X19))),
bind(X9, multiply(X15,X16,X17)),
bind(X10, inverse(X13)),
bind(X11, multiply(X15,X16,multiply(X17,X18,X19))),
bind(X12, inverse(X10)),
bind(X13, a),
bind(X14, multiply(X15,X16,X19)),
bind(X15, inverse(X10)),
bind(X16, a),
bind(X17, a),
bind(X18, inverse(X13)),
bind(X19, inverse(X13)),
bind(X23, multiply(X15,X16,multiply(X17,X18,X19))),
bind(X20, multiply(X15,X16,X17)),
bind(X21, inverse(X13)),
bind(X22, multiply(X15,X16,X19))
],
[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15])).

% SZS end CNFRefutation
```

## leanCoP 2.2

Jens Otten
University of Oslo, Norway

### Sample solution for SEU140+2

```% SZS output start Proof for SEU140+2.p

%-----------------------------------------------------
fof(t63_xboole_1,conjecture,! [_63308,_63311,_63314] : (subset(_63308,_63311) & disjoint(_63311,_63314) => disjoint(_63308,_63314)),file('SEU140+2.p',t63_xboole_1)).
fof(d3_tarski,axiom,! [_63543,_63546] : (subset(_63543,_63546) <=> ! [_63564] : (in(_63564,_63543) => in(_63564,_63546))),file('SEU140+2.p',d3_tarski)).
fof(t3_xboole_0,lemma,! [_63793,_63796] : (~ (~ disjoint(_63793,_63796) & ! [_63818] : ~ (in(_63818,_63793) & in(_63818,_63796))) & ~ (? [_63818] : (in(_63818,_63793) & in(_63818,_63796)) & disjoint(_63793,_63796))),file('SEU140+2.p',t3_xboole_0)).

cnf(1,plain,[-(subset(11^[],12^[]))],clausify(t63_xboole_1)).
cnf(2,plain,[-(disjoint(12^[],13^[]))],clausify(t63_xboole_1)).
cnf(3,plain,[disjoint(11^[],13^[])],clausify(t63_xboole_1)).
cnf(4,plain,[subset(_29177,_29233),in(_29347,_29177),-(in(_29347,_29233))],clausify(d3_tarski)).
cnf(5,plain,[-(disjoint(_40265,_40352)),-(in(9^[_40352,_40265],_40265))],clausify(t3_xboole_0)).
cnf(6,plain,[-(disjoint(_40265,_40352)),-(in(9^[_40352,_40265],_40352))],clausify(t3_xboole_0)).
cnf(7,plain,[disjoint(_40265,_40352),in(_40769,_40265),in(_40769,_40352)],clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12^[],13^[]),in(9^[13^[],11^[]],12^[]),in(9^[13^[],11^[]],13^[])],start(7,bind([[_40265,_40769,_40352],[12^[],9^[13^[],11^[]],13^[]]]))).
cnf('1.1',plain,[-(disjoint(12^[],13^[]))],extension(2)).
cnf('1.2',plain,[-(in(9^[13^[],11^[]],12^[])),subset(11^[],12^[]),in(9^[13^[],11^[]],11^[])],extension(4,bind([[_29233,_29347,_29177],[12^[],9^[13^[],11^[]],11^[]]]))).
cnf('1.2.1',plain,[-(subset(11^[],12^[]))],extension(1)).
cnf('1.2.2',plain,[-(in(9^[13^[],11^[]],11^[])),-(disjoint(11^[],13^[]))],extension(5,bind([[_40265,_40352],[11^[],13^[]]]))).
cnf('1.2.2.1',plain,[disjoint(11^[],13^[])],extension(3)).
cnf('1.3',plain,[-(in(9^[13^[],11^[]],13^[])),-(disjoint(11^[],13^[]))],extension(6,bind([[_40265,_40352],[11^[],13^[]]]))).
cnf('1.3.1',plain,[disjoint(11^[],13^[])],extension(3)).
%-----------------------------------------------------

% SZS output end Proof for SEU140+2.p
```

## LEO-II 1.7.0

Alexander Steen
University of Luxembourg, Luxembourg

### Sample solution for SET014^4

```% SZS output start CNFRefutation
thf(tp_complement,type,(complement: ((\$i>\$o)>(\$i>\$o)))).
thf(tp_disjoint,type,(disjoint: ((\$i>\$o)>((\$i>\$o)>\$o)))).
thf(tp_emptyset,type,(emptyset: (\$i>\$o))).
thf(tp_excl_union,type,(excl_union: ((\$i>\$o)>((\$i>\$o)>(\$i>\$o))))).
thf(tp_in,type,(in: (\$i>((\$i>\$o)>\$o)))).
thf(tp_intersection,type,(intersection: ((\$i>\$o)>((\$i>\$o)>(\$i>\$o))))).
thf(tp_is_a,type,(is_a: (\$i>((\$i>\$o)>\$o)))).
thf(tp_meets,type,(meets: ((\$i>\$o)>((\$i>\$o)>\$o)))).
thf(tp_misses,type,(misses: ((\$i>\$o)>((\$i>\$o)>\$o)))).
thf(tp_sK1_X,type,(sK1_X: (\$i>\$o))).
thf(tp_sK2_SY0,type,(sK2_SY0: (\$i>\$o))).
thf(tp_sK3_SY2,type,(sK3_SY2: (\$i>\$o))).
thf(tp_sK4_SX0,type,(sK4_SX0: \$i)).
thf(tp_setminus,type,(setminus: ((\$i>\$o)>((\$i>\$o)>(\$i>\$o))))).
thf(tp_singleton,type,(singleton: (\$i>(\$i>\$o)))).
thf(tp_subset,type,(subset: ((\$i>\$o)>((\$i>\$o)>\$o)))).
thf(tp_union,type,(union: ((\$i>\$o)>((\$i>\$o)>(\$i>\$o))))).
thf(tp_unord_pair,type,(unord_pair: (\$i>(\$i>(\$i>\$o))))).
thf(excl_union,definition,(excl_union = (^[X:(\$i>\$o),Y:(\$i>\$o),U:\$i]: (((X@U) & (~ (Y@U))) | ((~ (X@U)) & (Y@U))))),file('/home/mwisnie/Downloads/TPTP-v6.3.0/Problems/SET/SET014^4.p',excl_union)).
thf(2,negated_conjecture,(((![X:(\$i>\$o),Y:(\$i>\$o),A:(\$i>\$o)]: ((((subset@X)@A) & ((subset@Y)@A)) => ((subset@((union@X)@Y))@A)))=\$false)),inference(negate_conjecture,[status(cth)],[1])).
thf(3,plain,(((![SY0:(\$i>\$o),SY1:(\$i>\$o)]: ((((subset@sK1_X)@SY1) & ((subset@SY0)@SY1)) => ((subset@((union@sK1_X)@SY0))@SY1)))=\$false)),inference(extcnf_forall_neg,[status(esa)],[2])).
thf(4,plain,(((![SY2:(\$i>\$o)]: ((((subset@sK1_X)@SY2) & ((subset@sK2_SY0)@SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@SY2)))=\$false)),inference(extcnf_forall_neg,[status(esa)],[3])).
thf(5,plain,((((((subset@sK1_X)@sK3_SY2) & ((subset@sK2_SY0)@sK3_SY2)) => ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=\$false)),inference(extcnf_forall_neg,[status(esa)],[4])).
thf(6,plain,((((subset@sK1_X)@sK3_SY2)=\$true)),inference(standard_cnf,[status(thm)],[5])).
thf(7,plain,((((subset@sK2_SY0)@sK3_SY2)=\$true)),inference(standard_cnf,[status(thm)],[5])).
thf(8,plain,((((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2)=\$false)),inference(standard_cnf,[status(thm)],[5])).
thf(9,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=\$true)),inference(polarity_switch,[status(thm)],[8])).
thf(10,plain,((((subset@sK2_SY0)@sK3_SY2)=\$true)),inference(copy,[status(thm)],[7])).
thf(11,plain,((((subset@sK1_X)@sK3_SY2)=\$true)),inference(copy,[status(thm)],[6])).
thf(12,plain,(((~ ((subset@((union@sK1_X)@sK2_SY0))@sK3_SY2))=\$true)),inference(copy,[status(thm)],[9])).
thf(13,plain,(((~ (![SX0:\$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0))))=\$true)),inference(unfold_def,[status(thm)],[12,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(14,plain,(((![SX0:\$i]: ((~ (sK1_X@SX0)) | (sK3_SY2@SX0)))=\$true)),inference(unfold_def,[status(thm)],[11,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(15,plain,(((![SX0:\$i]: ((~ (sK2_SY0@SX0)) | (sK3_SY2@SX0)))=\$true)),inference(unfold_def,[status(thm)],[10,complement,disjoint,emptyset,excl_union,in,intersection,is_a,meets,misses,setminus,singleton,subset,union,unord_pair])).
thf(16,plain,(((![SX0:\$i]: ((~ ((sK1_X@SX0) | (sK2_SY0@SX0))) | (sK3_SY2@SX0)))=\$false)),inference(extcnf_not_pos,[status(thm)],[13])).
thf(17,plain,(![SV1:\$i]: ((((~ (sK1_X@SV1)) | (sK3_SY2@SV1))=\$true))),inference(extcnf_forall_pos,[status(thm)],[14])).
thf(18,plain,(![SV2:\$i]: ((((~ (sK2_SY0@SV2)) | (sK3_SY2@SV2))=\$true))),inference(extcnf_forall_pos,[status(thm)],[15])).
thf(19,plain,((((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))) | (sK3_SY2@sK4_SX0))=\$false)),inference(extcnf_forall_neg,[status(esa)],[16])).
thf(20,plain,(![SV1:\$i]: (((~ (sK1_X@SV1))=\$true) | ((sK3_SY2@SV1)=\$true))),inference(extcnf_or_pos,[status(thm)],[17])).
thf(21,plain,(![SV2:\$i]: (((~ (sK2_SY0@SV2))=\$true) | ((sK3_SY2@SV2)=\$true))),inference(extcnf_or_pos,[status(thm)],[18])).
thf(22,plain,(((~ ((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0)))=\$false)),inference(extcnf_or_neg,[status(thm)],[19])).
thf(23,plain,(((sK3_SY2@sK4_SX0)=\$false)),inference(extcnf_or_neg,[status(thm)],[19])).
thf(24,plain,(![SV1:\$i]: (((sK1_X@SV1)=\$false) | ((sK3_SY2@SV1)=\$true))),inference(extcnf_not_pos,[status(thm)],[20])).
thf(25,plain,(![SV2:\$i]: (((sK2_SY0@SV2)=\$false) | ((sK3_SY2@SV2)=\$true))),inference(extcnf_not_pos,[status(thm)],[21])).
thf(26,plain,((((sK1_X@sK4_SX0) | (sK2_SY0@sK4_SX0))=\$true)),inference(extcnf_not_neg,[status(thm)],[22])).
thf(27,plain,(((sK1_X@sK4_SX0)=\$true) | ((sK2_SY0@sK4_SX0)=\$true)),inference(extcnf_or_pos,[status(thm)],[26])).
thf(28,plain,(((\$false)=\$true)),inference(fo_atp_e,[status(thm)],[23,27,25,24])).
thf(29,plain,(\$false),inference(solved_all_splits,[solved_all_splits(join,[])],[28])).
% SZS output end CNFRefutation
```

## Leo-III 1.4

Alexander Steen
University of Luxembourg, Luxembourg

### Sample solution for HL400001^1

```% SZS output start CNFRefutation for HL400001^1.p
thf(u_type, type, u: \$tType).
thf(d_type, type, d: \$tType).
thf(du_type, type, du: \$tType).
thf(mono_2Ec_2Ebool_2ET_type, type, mono_2Ec_2Ebool_2ET: \$o).
thf(3,axiom,((mono_2Ec_2Ebool_2ET = (! [A:\$o]: (A = A)))),file('HL400001^1.p',thm_2Ebool_2ET__DEF)).
thf(5,plain,(mono_2Ec_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
thf(1,conjecture,(mono_2Ec_2Ebool_2ET),file('HL400001^1.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (mono_2Ec_2Ebool_2ET)),inference(neg_conjecture,[status(cth)],[1])).
thf(4,plain,(~ (mono_2Ec_2Ebool_2ET)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(6,plain,(\$false),inference(rewrite,[status(thm)],[5,4])).
thf(7,plain,(\$false),inference(simp,[status(thm)],[6])).
% SZS output end CNFRefutation for HL400001^1.p
```

### Sample solution for HL400001^2

```% SZS output start CNFRefutation for HL400001^2.p
thf(del_type, type, del: \$tType).
thf(1,conjecture,(\$true),file('HL400001^2.p',conj_thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (\$true)),inference(neg_conjecture,[status(cth)],[1])).
thf(16,plain,(~ (\$true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(17,plain,(\$false),inference(simp,[status(thm)],[16])).
% SZS output end CNFRefutation for HL400001^2.p
```

```TBA
```

### Sample solution for HL400001_1

```% SZS output start CNFRefutation for HL400001_1.p
thf(u_type, type, u: \$tType).
thf(d_type, type, d: \$tType).
thf(du_type, type, du: \$tType).
thf(mono_2Etyop_2Emin_2Ebool_type, type, mono_2Etyop_2Emin_2Ebool: \$tType).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: \$tType).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: \$tType).
thf(p_type, type, p: (mono_2Etyop_2Emin_2Ebool > \$o)).
thf(mono_2Ec_2Ebool_2ET_2E0_type, type, mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool).
thf(25,axiom,((p @ mono_2Ec_2Ebool_2ET_2E0)),file('HL400001_1.p',reserved_2Eho_2Etruth)).
thf(128,plain,((p @ mono_2Ec_2Ebool_2ET_2E0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
thf(1,conjecture,((p @ mono_2Ec_2Ebool_2ET_2E0)),file('HL400001_1.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,((~ (p @ mono_2Ec_2Ebool_2ET_2E0))),inference(neg_conjecture,[status(cth)],[1])).
thf(34,plain,((~ (p @ mono_2Ec_2Ebool_2ET_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(166,plain,(\$false),inference(rewrite,[status(thm)],[128,34])).
thf(167,plain,(\$false),inference(simp,[status(thm)],[166])).
% SZS output end CNFRefutation for HL400001_1.p
```

### Sample solution for HL400001_2

```% SZS output start CNFRefutation for HL400001_2.p
thf(del_type, type, del: \$tType).
thf(tp__o_type, type, tp__o: \$tType).
thf(1,conjecture,(\$true),file('HL400001_2.p',conj_thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (\$true)),inference(neg_conjecture,[status(cth)],[1])).
thf(17,plain,(~ (\$true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(18,plain,(\$false),inference(simp,[status(thm)],[17])).
% SZS output end CNFRefutation for HL400001_2.p
```

### Sample solution for HL400001_3

```% SZS output start CNFRefutation for HL400001_3.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: \$tType).
thf(p_type, type, p: (tyop_2Emin_2Ebool > \$o)).
thf(c_2Ebool_2ET_2E0_type, type, c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool).
thf(12,axiom,(((p @ c_2Ebool_2ET_2E0) <=> (! [A:tyop_2Emin_2Ebool]: (A = A)))),file('HL400001_3.p',thm_2Ebool_2ET__DEF)).
thf(60,plain,((p @ c_2Ebool_2ET_2E0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
thf(1,conjecture,((p @ c_2Ebool_2ET_2E0)),file('HL400001_3.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,((~ (p @ c_2Ebool_2ET_2E0))),inference(neg_conjecture,[status(cth)],[1])).
thf(26,plain,((~ (p @ c_2Ebool_2ET_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(128,plain,(\$false),inference(rewrite,[status(thm)],[60,26])).
thf(129,plain,(\$false),inference(simp,[status(thm)],[128])).
% SZS output end CNFRefutation for HL400001_3.p
```

### Sample solution for HL400001+1

```% SZS output start CNFRefutation for HL400001+1.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: \$i).
thf(c_2Ebool_2ET_2E0_type, type, c_2Ebool_2ET_2E0: \$i).
thf(s_type, type, s: (\$i > (\$i > \$i))).
thf(p_type, type, p: (\$i > \$o)).
thf(14,axiom,((p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0))),file('HL400001+1.p',thm_2Eextra_2Dho_2Etruth)).
thf(75,plain,((p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
thf(1,conjecture,((p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0))),file('HL400001+1.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,((~ (p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0)))),inference(neg_conjecture,[status(cth)],[1])).
thf(19,plain,((~ (p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(90,plain,(\$false),inference(rewrite,[status(thm)],[75,19])).
thf(91,plain,(\$false),inference(simp,[status(thm)],[90])).
% SZS output end CNFRefutation for HL400001+1.p
```

### Sample solution for HL400001+2

```% SZS output start CNFRefutation for HL400001+2.p

thf(1,conjecture,(\$true),file('HL400001+2.p',conj_thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (\$true)),inference(neg_conjecture,[status(cth)],[1])).
thf(16,plain,(~ (\$true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(17,plain,(\$false),inference(simp,[status(thm)],[16])).
% SZS output end CNFRefutation for HL400001+2.p
```

## Leo-III 1.5

Alexander Steen
University of Luxembourg, Luxembourg

### Sample solution for SET014^4

```% SZS output start CNFRefutation for TPTP/Problems/SET/SET014^4.p
thf(union_type, type, union: ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(union_def, definition, (union = (^ [A:(\$i > \$o),B:(\$i > \$o),C:\$i]: ((A @ C) | (B @ C))))).
thf(subset_type, type, subset: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(subset_def, definition, (subset = (^ [A:(\$i > \$o),B:(\$i > \$o)]: ! [C:\$i]: ((A @ C) => (B @ C))))).
thf(sk1_type, type, sk1: (\$i > \$o)).
thf(sk2_type, type, sk2: (\$i > \$o)).
thf(sk3_type, type, sk3: (\$i > \$o)).
thf(sk4_type, type, sk4: \$i).
thf(1,conjecture,((! [A:(\$i > \$o),B:(\$i > \$o),C:(\$i > \$o)]: (((subset @ A @ C) & (subset @ B @ C)) => (subset @ (union @ A @ B) @ C)))),file('TPTP/Problems/SET/SET014^4.p',thm)).
thf(2,negated_conjecture,((~ (! [A:(\$i > \$o),B:(\$i > \$o),C:(\$i > \$o)]: (((subset @ A @ C) & (subset @ B @ C)) => (subset @ (union @ A @ B) @ C))))),inference(neg_conjecture,[status(cth)],[1])).
thf(3,plain,((~ (! [A:(\$i > \$o),B:(\$i > \$o),C:(\$i > \$o)]: ((! [D:\$i]: ((A @ D) => (C @ D)) & ! [D:\$i]: ((B @ D) => (C @ D))) => (! [D:\$i]: (((A @ D) | (B @ D)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(5,plain,((sk1 @ sk4) | (sk2 @ sk4)),inference(cnf,[status(esa)],[3])).
thf(7,plain,(! [A:\$i] : ((~ (sk1 @ A)) | (sk3 @ A))),inference(cnf,[status(esa)],[3])).
thf(4,plain,((~ (sk3 @ sk4))),inference(cnf,[status(esa)],[3])).
thf(9,plain,(! [A:\$i] : ((~ (sk1 @ A)) | ((sk3 @ A) != (sk3 @ sk4)))),inference(paramod_ordered,[status(thm)],[7,4])).
thf(10,plain,((~ (sk1 @ sk4))),inference(pattern_uni,[status(thm)],[9:[bind(A, \$thf(sk4))]])).
thf(11,plain,(\$false | (sk2 @ sk4)),inference(rewrite,[status(thm)],[5,10])).
thf(12,plain,((sk2 @ sk4)),inference(simp,[status(thm)],[11])).
thf(6,plain,(! [A:\$i] : ((~ (sk2 @ A)) | (sk3 @ A))),inference(cnf,[status(esa)],[3])).
thf(8,plain,(! [A:\$i] : ((~ (sk2 @ A)) | (sk3 @ A))),inference(simp,[status(thm)],[6])).
thf(13,plain,(! [A:\$i] : ((~ (sk2 @ A)) | ((sk3 @ A) != (sk3 @ sk4)))),inference(paramod_ordered,[status(thm)],[8,4])).
thf(14,plain,((~ (sk2 @ sk4))),inference(pattern_uni,[status(thm)],[13:[bind(A, \$thf(sk4))]])).
thf(15,plain,(\$false),inference(rewrite,[status(thm)],[12,14])).
thf(16,plain,(\$false),inference(simp,[status(thm)],[15])).
% SZS output end CNFRefutation for TPTP/Problems/SET/SET014^4.p
```

### Sample solution for HL400001^7

```% SZS output start CNFRefutation for HL400001^7.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: \$tType).
thf(tyop_2Emin_2Eind_type, type, tyop_2Emin_2Eind: \$tType).
thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: \$o).
thf(29,axiom,((c_2Ebool_2ET = ((^ [A:\$o]: (A)) = (^ [A:\$o]: (A))))),file('HL400001^7.p',thm_2Ebool_2ET__DEF)).
thf(132,plain,(c_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
thf(1,conjecture,(c_2Ebool_2ET),file('HL400001^7.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (c_2Ebool_2ET)),inference(neg_conjecture,[status(cth)],[1])).
thf(32,plain,(~ (c_2Ebool_2ET)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(141,plain,(\$false),inference(rewrite,[status(thm)],[132,32])).
thf(142,plain,(\$false),inference(simp,[status(thm)],[141])).
% SZS output end CNFRefutation for HL400001^7.p
```

### Sample solution for HL400001^5

```% SZS output start CNFRefutation for HL400001^5.p
thf(del_type, type, del: \$tType).
thf(tp__i_type, type, tp__i: \$tType).
thf(1,conjecture,(\$true),file('HL400001^5.p',conj_thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (\$true)),inference(neg_conjecture,[status(cth)],[1])).
thf(75,plain,(~ (\$true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(76,plain,(\$false),inference(simp,[status(thm)],[75])).
% SZS output end CNFRefutation for HL400001^5.p
```

### Sample solution for HL400001^4

```% SZS output start CNFRefutation for HL400001^4.p
thf(u_type, type, u: \$tType).
thf(d_type, type, d: \$tType).
thf(du_type, type, du: \$tType).
thf(mono_2Ec_2Ebool_2ET_type, type, mono_2Ec_2Ebool_2ET: \$o).
thf(mono_2Etyop_2Emin_2Eind_type, type, mono_2Etyop_2Emin_2Eind: \$tType).
thf(77,axiom,((mono_2Ec_2Ebool_2ET = (! [A:\$o]: (A = A)))),file('HL400001^4.p',thm_2Ebool_2ET__DEF)).
thf(340,plain,(mono_2Ec_2Ebool_2ET),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
thf(1,conjecture,(mono_2Ec_2Ebool_2ET),file('HL400001^4.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (mono_2Ec_2Ebool_2ET)),inference(neg_conjecture,[status(cth)],[1])).
thf(82,plain,(~ (mono_2Ec_2Ebool_2ET)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(355,plain,(\$false),inference(rewrite,[status(thm)],[340,82])).
thf(356,plain,(\$false),inference(simp,[status(thm)],[355])).
% SZS output end CNFRefutation for HL400001^4.p
```

### Sample solution for HL400001_7

```% SZS output start CNFRefutation for HL400001_7.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: \$tType).
thf(p_type, type, p: (tyop_2Emin_2Ebool > \$o)).
thf(c_2Ebool_2ET_2E0_type, type, c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool).
thf(tyop_2Emin_2Eind_type, type, tyop_2Emin_2Eind: \$tType).
thf(50,axiom,(((p @ c_2Ebool_2ET_2E0) <=> (! [A:tyop_2Emin_2Ebool]: (A = A)))),file('HL400001_7.p',thm_2Ebool_2ET__DEF)).
thf(261,plain,((p @ c_2Ebool_2ET_2E0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
thf(1,conjecture,((p @ c_2Ebool_2ET_2E0)),file('HL400001_7.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,((~ (p @ c_2Ebool_2ET_2E0))),inference(neg_conjecture,[status(cth)],[1])).
thf(82,plain,((~ (p @ c_2Ebool_2ET_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(433,plain,(\$false),inference(rewrite,[status(thm)],[261,82])).
thf(434,plain,(\$false),inference(simp,[status(thm)],[433])).
% SZS output end CNFRefutation for HL400001_7.p
```

### Sample solution for HL400001_5

```% SZS output start CNFRefutation for HL400001_5.p
thf(del_type, type, del: \$tType).
thf(tp__o_type, type, tp__o: \$tType).
thf(tp__i_type, type, tp__i: \$tType).
thf(1,conjecture,(\$true),file('HL400001_5.p',conj_thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (\$true)),inference(neg_conjecture,[status(cth)],[1])).
thf(129,plain,(~ (\$true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(130,plain,(\$false),inference(simp,[status(thm)],[129])).
% SZS output end CNFRefutation for HL400001_5.p
```

### Sample solution for HL400001_4

```% SZS output start CNFRefutation for HL400001_4.p
thf(u_type, type, u: \$tType).
thf(d_type, type, d: \$tType).
thf(du_type, type, du: \$tType).
thf(mono_2Etyop_2Emin_2Ebool_type, type, mono_2Etyop_2Emin_2Ebool: \$tType).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: \$tType).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: \$tType).
thf(p_type, type, p: (mono_2Etyop_2Emin_2Ebool > \$o)).
thf(mono_2Ec_2Ebool_2ET_2E0_type, type, mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29_type, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29: \$tType).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_type, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29: \$tType).
thf(65,axiom,(((p @ mono_2Ec_2Ebool_2ET_2E0) <=> (! [A:mono_2Etyop_2Emin_2Ebool]: (A = A)))),file('HL400001_4.p',thm_2Ebool_2ET__DEF)).
thf(289,plain,((p @ mono_2Ec_2Ebool_2ET_2E0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
thf(1,conjecture,((p @ mono_2Ec_2Ebool_2ET_2E0)),file('HL400001_4.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,((~ (p @ mono_2Ec_2Ebool_2ET_2E0))),inference(neg_conjecture,[status(cth)],[1])).
thf(99,plain,((~ (p @ mono_2Ec_2Ebool_2ET_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(534,plain,(\$false),inference(rewrite,[status(thm)],[289,99])).
thf(535,plain,(\$false),inference(simp,[status(thm)],[534])).
% SZS output end CNFRefutation for HL400001_4.p
```

### Sample solution for HL400001+5

```% SZS output start CNFRefutation for HL400001+5.p

thf(1,conjecture,(\$true),file('HL400001+5.p',conj_thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,(~ (\$true)),inference(neg_conjecture,[status(cth)],[1])).
thf(74,plain,(~ (\$true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(75,plain,(\$false),inference(simp,[status(thm)],[74])).
% SZS output end CNFRefutation for HL400001+5.p
```

### Sample solution for HL400001+4

```% SZS output start CNFRefutation for HL400001+4.p
thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: \$i).
thf(c_2Ebool_2ET_2E0_type, type, c_2Ebool_2ET_2E0: \$i).
thf(s_type, type, s: (\$i > (\$i > \$i))).
thf(p_type, type, p: (\$i > \$o)).
thf(53,axiom,((p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0))),file('HL400001+4.p',reserved_2Eho_2Etruth)).
thf(328,plain,((p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
thf(1,conjecture,((p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0))),file('HL400001+4.p',thm_2Ebool_2ETRUTH)).
thf(2,negated_conjecture,((~ (p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0)))),inference(neg_conjecture,[status(cth)],[1])).
thf(82,plain,((~ (p @ (s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
thf(466,plain,(\$false),inference(rewrite,[status(thm)],[328,82])).
thf(467,plain,(\$false),inference(simp,[status(thm)],[466])).
% SZS output end CNFRefutation for HL400001+4.p
```

## MaLARea 0.9

Josef Urban
Czech Technical University in Prague, Czech Republic

### Sample solution for HL400001+5

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('/Users/schulz/Desktop/HL400001+5.p', conj_thm_2Ebool_2ETRUTH)).
fof(c_0_1, negated_conjecture, ~(\$true), inference(assume_negation,[status(cth)],[conj_thm_2Ebool_2ETRUTH])).
fof(c_0_2, negated_conjecture, ~\$true, inference(fof_simplification,[status(thm)],[c_0_1])).
cnf(c_0_3, negated_conjecture, (\$false), inference(split_conjunct,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (\$false), inference(cn,[status(thm)],[c_0_3]), ['proof']).
# SZS output end CNFRefutation
```

### Sample solution for HL400001+4

```# SZS output start CNFRefutation
fof(thm_2Ebool_2ETRUTH, conjecture, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('/Users/schulz/Desktop/HL400001+4.p', thm_2Ebool_2ETRUTH)).
fof(reserved_2Eho_2Etruth, axiom, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('/Users/schulz/Desktop/Axioms/HL4002+4.ax', reserved_2Eho_2Etruth)).
fof(c_0_2, negated_conjecture, ~(p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(assume_negation,[status(cth)],[thm_2Ebool_2ETRUTH])).
fof(c_0_3, negated_conjecture, ~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), inference(fof_simplification,[status(thm)],[c_0_2])).
cnf(c_0_4, negated_conjecture, (~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(split_conjunct,[status(thm)],[c_0_3])).
cnf(c_0_5, plain, (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))), inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth])).
cnf(c_0_6, negated_conjecture, (\$false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_4, c_0_5])]), ['proof']).
# SZS output end CNFRefutation
```

## Prover9 1109a

William McCune, Bob Veroff
University of New Mexico, USA

### Sample solution for SEU140+2

```8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
42 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
55 -(all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(negated_conjecture) # label(non_clause).  [assumption].
60 subset(c3,c4) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
61 disjoint(c4,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
75 disjoint(A,B) | in(f7(A,B),A) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
76 disjoint(A,B) | in(f7(A,B),B) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
92 -disjoint(c3,c5) # label(t63_xboole_1) # label(negated_conjecture).  [clausify(55)].
101 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma).  [clausify(42)].
109 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom).  [clausify(26)].
123 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom).  [clausify(8)].
273 -disjoint(c5,c3).  [ur(109,b,92,a)].
300 -in(A,c3) | in(A,c4).  [resolve(123,a,60,a)].
959 in(f7(c5,c3),c3).  [resolve(273,a,76,a)].
960 in(f7(c5,c3),c5).  [resolve(273,a,75,a)].
1084 -in(f7(c5,c3),c4).  [ur(101,b,960,a,c,61,a)].
1292 \$F.  [resolve(300,a,959,a),unit_del(a,1084)].
```

## PyRes 1.3

Stephan Schulz
DHBW Stuttgart, Germany

### Sample solution for SEU140+2

```# SZS output start CNFRefutation
fof(t63_xboole_1,conjecture,(![A]:(![B]:(![C]:((subset(A,B)&disjoint(B,C))=>disjoint(A,C))))),input).
fof(c22,negated_conjecture,(~(![A]:(![B]:(![C]:((subset(A,B)&disjoint(B,C))=>disjoint(A,C)))))),inference(assume_negation,status(cth),[t63_xboole_1])).
fof(c23,negated_conjecture,(?[A]:(?[B]:(?[C]:((subset(A,B)&disjoint(B,C))&~disjoint(A,C))))),inference(fof_nnf,status(thm),[c22])).
fof(c24,negated_conjecture,(?[X12]:(?[X13]:(?[X14]:((subset(X12,X13)&disjoint(X13,X14))&~disjoint(X12,X14))))),inference(variable_rename,status(thm),[c23])).
fof(c25,negated_conjecture,((subset(skolem0001,skolem0002)&disjoint(skolem0002,skolem0003))&~disjoint(skolem0001,skolem0003)),inference(skolemize,status(esa),[c24])).
cnf(c28,negated_conjecture,~disjoint(skolem0001,skolem0003),inference(split_conjunct,status(thm),[c25])).
fof(t3_xboole_0,plain,(![A]:(![B]:((~((~disjoint(A,B))&(![C]:(~(in(C,A)&in(C,B))))))&(~((?[C]:(in(C,A)&in(C,B)))&disjoint(A,B)))))),input).
fof(c52,plain,(![A]:(![B]:((~(~disjoint(A,B)&(![C]:(~(in(C,A)&in(C,B))))))&(~((?[C]:(in(C,A)&in(C,B)))&disjoint(A,B)))))),inference(fof_simplification,status(thm),[t3_xboole_0])).
fof(c53,plain,(![A]:(![B]:((disjoint(A,B)|(?[C]:(in(C,A)&in(C,B))))&((![C]:(~in(C,A)|~in(C,B)))|~disjoint(A,B))))),inference(fof_nnf,status(thm),[c52])).
fof(c54,plain,((![A]:(![B]:(disjoint(A,B)|(?[C]:(in(C,A)&in(C,B))))))&(![A]:(![B]:((![C]:(~in(C,A)|~in(C,B)))|~disjoint(A,B))))),inference(shift_quantors,status(thm),[c53])).
fof(c55,plain,((![X31]:(![X32]:(disjoint(X31,X32)|(?[X33]:(in(X33,X31)&in(X33,X32))))))&(![X34]:(![X35]:((![X36]:(~in(X36,X34)|~in(X36,X35)))|~disjoint(X34,X35))))),inference(variable_rename,status(thm),[c54])).
fof(c57,plain,(![X31]:(![X32]:(![X34]:(![X35]:(![X36]:((disjoint(X31,X32)|(in(skolem0005(X31,X32),X31)&in(skolem0005(X31,X32),X32)))&((~in(X36,X34)|~in(X36,X35))|~disjoint(X34,X35)))))))),inference(shift_quantors,status(thm),[fof(c56,plain,((![X31]:(![X32]:(disjoint(X31,X32)|(in(skolem0005(X31,X32),X31)&in(skolem0005(X31,X32),X32)))))&(![X34]:(![X35]:((![X36]:(~in(X36,X34)|~in(X36,X35)))|~disjoint(X34,X35))))),inference(skolemize,status(esa),[c55])).])).
fof(c58,plain,(![X31]:(![X32]:(![X34]:(![X35]:(![X36]:(((disjoint(X31,X32)|in(skolem0005(X31,X32),X31))&(disjoint(X31,X32)|in(skolem0005(X31,X32),X32)))&((~in(X36,X34)|~in(X36,X35))|~disjoint(X34,X35)))))))),inference(distribute,status(thm),[c57])).
cnf(c60,plain,disjoint(X286,X287)|in(skolem0005(X286,X287),X287),inference(split_conjunct,status(thm),[c58])).
cnf(c467,plain,in(skolem0005(skolem0001,skolem0003),skolem0003),inference(resolution,status(thm),[c60, c28])).
cnf(c27,negated_conjecture,disjoint(skolem0002,skolem0003),inference(split_conjunct,status(thm),[c25])).
fof(symmetry_r1_xboole_0,axiom,(![A]:(![B]:(disjoint(A,B)=>disjoint(B,A)))),input).
fof(c110,axiom,(![A]:(![B]:(~disjoint(A,B)|disjoint(B,A)))),inference(fof_nnf,status(thm),[symmetry_r1_xboole_0])).
fof(c111,axiom,(![X70]:(![X71]:(~disjoint(X70,X71)|disjoint(X71,X70)))),inference(variable_rename,status(thm),[c110])).
cnf(c112,axiom,~disjoint(X188,X189)|disjoint(X189,X188),inference(split_conjunct,status(thm),[c111])).
cnf(c290,plain,disjoint(skolem0003,skolem0002),inference(resolution,status(thm),[c112, c27])).
cnf(c61,plain,~in(X294,X295)|~in(X294,X296)|~disjoint(X295,X296),inference(split_conjunct,status(thm),[c58])).
cnf(c485,plain,~in(X1138,skolem0003)|~in(X1138,skolem0002),inference(resolution,status(thm),[c61, c290])).
cnf(c59,plain,disjoint(X280,X281)|in(skolem0005(X280,X281),X280),inference(split_conjunct,status(thm),[c58])).
cnf(c451,plain,in(skolem0005(skolem0001,skolem0003),skolem0001),inference(resolution,status(thm),[c59, c28])).
fof(d2_xboole_0,axiom,(![A]:(![B]:(![C]:(C=set_union2(A,B)<=>(![D]:(in(D,C)<=>(in(D,A)|in(D,B)))))))),input).
fof(c203,axiom,(![A]:(![B]:(![C]:((C!=set_union2(A,B)|(![D]:((~in(D,C)|(in(D,A)|in(D,B)))&((~in(D,A)&~in(D,B))|in(D,C)))))&((?[D]:((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))|C=set_union2(A,B)))))),inference(fof_nnf,status(thm),[d2_xboole_0])).
fof(c204,axiom,((![A]:(![B]:(![C]:(C!=set_union2(A,B)|((![D]:(~in(D,C)|(in(D,A)|in(D,B))))&(![D]:((~in(D,A)&~in(D,B))|in(D,C))))))))&(![A]:(![B]:(![C]:((?[D]:((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))|C=set_union2(A,B)))))),inference(shift_quantors,status(thm),[c203])).
fof(c205,axiom,((![X118]:(![X119]:(![X120]:(X120!=set_union2(X118,X119)|((![X121]:(~in(X121,X120)|(in(X121,X118)|in(X121,X119))))&(![X122]:((~in(X122,X118)&~in(X122,X119))|in(X122,X120))))))))&(![X123]:(![X124]:(![X125]:((?[X126]:((~in(X126,X125)|(~in(X126,X123)&~in(X126,X124)))&(in(X126,X125)|(in(X126,X123)|in(X126,X124)))))|X125=set_union2(X123,X124)))))),inference(variable_rename,status(thm),[c204])).
fof(c207,axiom,(![X118]:(![X119]:(![X120]:(![X121]:(![X122]:(![X123]:(![X124]:(![X125]:((X120!=set_union2(X118,X119)|((~in(X121,X120)|(in(X121,X118)|in(X121,X119)))&((~in(X122,X118)&~in(X122,X119))|in(X122,X120))))&(((~in(skolem0012(X123,X124,X125),X125)|(~in(skolem0012(X123,X124,X125),X123)&~in(skolem0012(X123,X124,X125),X124)))&(in(skolem0012(X123,X124,X125),X125)|(in(skolem0012(X123,X124,X125),X123)|in(skolem0012(X123,X124,X125),X124))))|X125=set_union2(X123,X124))))))))))),inference(shift_quantors,status(thm),[fof(c206,axiom,((![X118]:(![X119]:(![X120]:(X120!=set_union2(X118,X119)|((![X121]:(~in(X121,X120)|(in(X121,X118)|in(X121,X119))))&(![X122]:((~in(X122,X118)&~in(X122,X119))|in(X122,X120))))))))&(![X123]:(![X124]:(![X125]:(((~in(skolem0012(X123,X124,X125),X125)|(~in(skolem0012(X123,X124,X125),X123)&~in(skolem0012(X123,X124,X125),X124)))&(in(skolem0012(X123,X124,X125),X125)|(in(skolem0012(X123,X124,X125),X123)|in(skolem0012(X123,X124,X125),X124))))|X125=set_union2(X123,X124)))))),inference(skolemize,status(esa),[c205])).])).
fof(c208,axiom,(![X118]:(![X119]:(![X120]:(![X121]:(![X122]:(![X123]:(![X124]:(![X125]:(((X120!=set_union2(X118,X119)|(~in(X121,X120)|(in(X121,X118)|in(X121,X119))))&((X120!=set_union2(X118,X119)|(~in(X122,X118)|in(X122,X120)))&(X120!=set_union2(X118,X119)|(~in(X122,X119)|in(X122,X120)))))&((((~in(skolem0012(X123,X124,X125),X125)|~in(skolem0012(X123,X124,X125),X123))|X125=set_union2(X123,X124))&((~in(skolem0012(X123,X124,X125),X125)|~in(skolem0012(X123,X124,X125),X124))|X125=set_union2(X123,X124)))&((in(skolem0012(X123,X124,X125),X125)|(in(skolem0012(X123,X124,X125),X123)|in(skolem0012(X123,X124,X125),X124)))|X125=set_union2(X123,X124)))))))))))),inference(distribute,status(thm),[c207])).
cnf(c210,axiom,X597!=set_union2(X594,X596)|~in(X595,X594)|in(X595,X597),inference(split_conjunct,status(thm),[c208])).
cnf(c26,negated_conjecture,subset(skolem0001,skolem0002),inference(split_conjunct,status(thm),[c25])).
fof(t45_xboole_1,plain,(![A]:(![B]:(subset(A,B)=>B=set_union2(A,set_difference(B,A))))),input).
fof(c44,plain,(![A]:(![B]:(~subset(A,B)|B=set_union2(A,set_difference(B,A))))),inference(fof_nnf,status(thm),[t45_xboole_1])).
fof(c45,plain,(![X26]:(![X27]:(~subset(X26,X27)|X27=set_union2(X26,set_difference(X27,X26))))),inference(variable_rename,status(thm),[c44])).
cnf(c46,plain,~subset(X263,X264)|X264=set_union2(X263,set_difference(X264,X263)),inference(split_conjunct,status(thm),[c45])).
cnf(c399,plain,skolem0002=set_union2(skolem0001,set_difference(skolem0002,skolem0001)),inference(resolution,status(thm),[c46, c26])).
cnf(c6483,plain,~in(X3113,skolem0001)|in(X3113,skolem0002),inference(resolution,status(thm),[c399, c210])).
cnf(c21278,plain,in(skolem0005(skolem0001,skolem0003),skolem0002),inference(resolution,status(thm),[c6483, c451])).
cnf(c40528,plain,~in(skolem0005(skolem0001,skolem0003),skolem0003),inference(resolution,status(thm),[c21278, c485])).
cnf(c55305,plain,\$false,inference(resolution,status(thm),[c40528, c467])).
# SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```# SZS output start Saturation
fof(co1,conjecture,(~(?[U]:(actual_world(U)&(?[V]:(?[W]:(?[X]:(?[Y]:((((((((((of(U,W,V)&woman(U,V))&mia_forename(U,W))&forename(U,W))&shake_beverage(U,X))&event(U,Y))&agent(U,Y,V))&patient(U,Y,X))&past(U,Y))&nonreflexive(U,Y))&order(U,Y))))))))),input).
fof(c38,negated_conjecture,(~(~(?[U]:(actual_world(U)&(?[V]:(?[W]:(?[X]:(?[Y]:((((((((((of(U,W,V)&woman(U,V))&mia_forename(U,W))&forename(U,W))&shake_beverage(U,X))&event(U,Y))&agent(U,Y,V))&patient(U,Y,X))&past(U,Y))&nonreflexive(U,Y))&order(U,Y)))))))))),inference(assume_negation,status(cth),[co1])).
fof(c39,negated_conjecture,(?[U]:(actual_world(U)&(?[V]:(?[W]:(?[X]:(?[Y]:((((((((((of(U,W,V)&woman(U,V))&mia_forename(U,W))&forename(U,W))&shake_beverage(U,X))&event(U,Y))&agent(U,Y,V))&patient(U,Y,X))&past(U,Y))&nonreflexive(U,Y))&order(U,Y)))))))),inference(fof_nnf,status(thm),[c38])).
fof(c40,negated_conjecture,(?[X2]:(actual_world(X2)&(?[X3]:(?[X4]:(?[X5]:(?[X6]:((((((((((of(X2,X4,X3)&woman(X2,X3))&mia_forename(X2,X4))&forename(X2,X4))&shake_beverage(X2,X5))&event(X2,X6))&agent(X2,X6,X3))&patient(X2,X6,X5))&past(X2,X6))&nonreflexive(X2,X6))&order(X2,X6)))))))),inference(variable_rename,status(thm),[c39])).
fof(c41,negated_conjecture,(actual_world(skolem0001)&((((((((((of(skolem0001,skolem0003,skolem0002)&woman(skolem0001,skolem0002))&mia_forename(skolem0001,skolem0003))&forename(skolem0001,skolem0003))&shake_beverage(skolem0001,skolem0004))&event(skolem0001,skolem0005))&agent(skolem0001,skolem0005,skolem0002))&patient(skolem0001,skolem0005,skolem0004))&past(skolem0001,skolem0005))&nonreflexive(skolem0001,skolem0005))&order(skolem0001,skolem0005))),inference(skolemize,status(esa),[c40])).
cnf(c43,negated_conjecture,of(skolem0001,skolem0003,skolem0002),inference(split_conjunct,status(thm),[c41])).
fof(ax43,axiom,(![U]:(![V]:(![W]:(((entity(U,V)&forename(U,W))&of(U,W,V))=>(~(?[X]:((forename(U,X)&X!=W)&of(U,X,V)))))))),input).
fof(c57,axiom,(![U]:(![V]:(![W]:(((~entity(U,V)|~forename(U,W))|~of(U,W,V))|(![X]:((~forename(U,X)|X=W)|~of(U,X,V))))))),inference(fof_nnf,status(thm),[ax43])).
fof(c59,axiom,(![X11]:(![X12]:(![X13]:(![X14]:(((~entity(X11,X12)|~forename(X11,X13))|~of(X11,X13,X12))|((~forename(X11,X14)|X14=X13)|~of(X11,X14,X12))))))),inference(shift_quantors,status(thm),[fof(c58,axiom,(![X11]:(![X12]:(![X13]:(((~entity(X11,X12)|~forename(X11,X13))|~of(X11,X13,X12))|(![X14]:((~forename(X11,X14)|X14=X13)|~of(X11,X14,X12))))))),inference(variable_rename,status(thm),[c57])).])).
cnf(c60,axiom,~entity(X452,X453)|~forename(X452,X455)|~of(X452,X455,X453)|~forename(X452,X454)|X454=X455|~of(X452,X454,X453),inference(split_conjunct,status(thm),[c59])).
cnf(c361,plain,~entity(skolem0001,skolem0002)|~forename(skolem0001,X517)|~of(skolem0001,X517,skolem0002)|~forename(skolem0001,skolem0003)|skolem0003=X517,inference(resolution,status(thm),[c60, c43])).
cnf(c49,negated_conjecture,agent(skolem0001,skolem0005,skolem0002),inference(split_conjunct,status(thm),[c41])).
cnf(c50,negated_conjecture,patient(skolem0001,skolem0005,skolem0004),inference(split_conjunct,status(thm),[c41])).
fof(ax44,axiom,(![U]:(![V]:(![W]:(![X]:(((nonreflexive(U,V)&agent(U,V,W))&patient(U,V,X))=>W!=X))))),input).
fof(c54,axiom,(![U]:(![V]:(![W]:(![X]:(((~nonreflexive(U,V)|~agent(U,V,W))|~patient(U,V,X))|W!=X))))),inference(fof_nnf,status(thm),[ax44])).
fof(c55,axiom,(![X7]:(![X8]:(![X9]:(![X10]:(((~nonreflexive(X7,X8)|~agent(X7,X8,X9))|~patient(X7,X8,X10))|X9!=X10))))),inference(variable_rename,status(thm),[c54])).
cnf(c56,axiom,~nonreflexive(X445,X442)|~agent(X445,X442,X443)|~patient(X445,X442,X444)|X443!=X444,inference(split_conjunct,status(thm),[c55])).
cnf(c356,plain,~nonreflexive(skolem0001,skolem0005)|~agent(skolem0001,skolem0005,X515)|X515!=skolem0004,inference(resolution,status(thm),[c56, c50])).
cnf(c398,plain,~nonreflexive(skolem0001,skolem0005)|skolem0002!=skolem0004,inference(resolution,status(thm),[c356, c49])).
cnf(reflexivity,axiom,X99=X99,eq_axiom).
cnf(c35,plain,X426!=X423|X424!=X428|X427!=X425|~patient(X426,X424,X427)|patient(X423,X428,X425),eq_axiom).
cnf(c348,plain,skolem0001!=X509|skolem0005!=X507|skolem0004!=X508|patient(X509,X507,X508),inference(resolution,status(thm),[c35, c50])).
cnf(c394,plain,skolem0001!=X514|skolem0005!=X513|patient(X514,X513,skolem0004),inference(resolution,status(thm),[c348, reflexivity])).
cnf(c397,plain,skolem0001!=X516|patient(X516,skolem0005,skolem0004),inference(resolution,status(thm),[c394, reflexivity])).
cnf(c34,plain,X414!=X411|X412!=X416|X415!=X413|~agent(X414,X412,X415)|agent(X411,X416,X413),eq_axiom).
cnf(c343,plain,skolem0001!=X498|skolem0005!=X499|skolem0002!=X500|agent(X498,X499,X500),inference(resolution,status(thm),[c34, c49])).
cnf(c389,plain,skolem0001!=X511|skolem0005!=X510|agent(X511,X510,skolem0002),inference(resolution,status(thm),[c343, reflexivity])).
cnf(c395,plain,skolem0001!=X512|agent(X512,skolem0005,skolem0002),inference(resolution,status(thm),[c389, reflexivity])).
cnf(c32,plain,X395!=X392|X393!=X397|X396!=X394|~of(X395,X393,X396)|of(X392,X397,X394),eq_axiom).
cnf(c335,plain,skolem0001!=X491|skolem0003!=X492|skolem0002!=X493|of(X491,X492,X493),inference(resolution,status(thm),[c32, c43])).
cnf(c385,plain,skolem0001!=X505|skolem0003!=X504|of(X505,X504,skolem0002),inference(resolution,status(thm),[c335, reflexivity])).
cnf(c392,plain,skolem0001!=X506|of(X506,skolem0003,skolem0002),inference(resolution,status(thm),[c385, reflexivity])).
cnf(c51,negated_conjecture,past(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
cnf(c37,plain,X435!=X437|X436!=X434|~past(X435,X436)|past(X437,X434),eq_axiom).
cnf(c352,plain,skolem0001!=X502|skolem0005!=X501|past(X502,X501),inference(resolution,status(thm),[c37, c51])).
cnf(c390,plain,skolem0001!=X503|past(X503,skolem0005),inference(resolution,status(thm),[c352, reflexivity])).
cnf(c52,negated_conjecture,nonreflexive(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
cnf(c33,plain,X404!=X406|X405!=X403|~nonreflexive(X404,X405)|nonreflexive(X406,X403),eq_axiom).
cnf(c339,plain,skolem0001!=X495|skolem0005!=X496|nonreflexive(X495,X496),inference(resolution,status(thm),[c33, c52])).
cnf(c387,plain,skolem0001!=X497|nonreflexive(X497,skolem0005),inference(resolution,status(thm),[c339, reflexivity])).
cnf(c53,negated_conjecture,order(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
fof(ax36,axiom,(![U]:(![V]:(order(U,V)=>act(U,V)))),input).
fof(c85,axiom,(![U]:(![V]:(~order(U,V)|act(U,V)))),inference(fof_nnf,status(thm),[ax36])).
fof(c86,axiom,(![X27]:(![X28]:(~order(X27,X28)|act(X27,X28)))),inference(variable_rename,status(thm),[c85])).
cnf(c87,axiom,~order(X126,X127)|act(X126,X127),inference(split_conjunct,status(thm),[c86])).
cnf(c196,plain,act(skolem0001,skolem0005),inference(resolution,status(thm),[c87, c53])).
cnf(c31,plain,X383!=X385|X384!=X382|~act(X383,X384)|act(X385,X382),eq_axiom).
cnf(c330,plain,skolem0001!=X489|skolem0005!=X490|act(X489,X490),inference(resolution,status(thm),[c31, c196])).
cnf(c384,plain,skolem0001!=X494|act(X494,skolem0005),inference(resolution,status(thm),[c330, reflexivity])).
fof(ax32,axiom,(![U]:(![V]:(thing(U,V)=>singleton(U,V)))),input).
fof(c97,axiom,(![U]:(![V]:(~thing(U,V)|singleton(U,V)))),inference(fof_nnf,status(thm),[ax32])).
fof(c98,axiom,(![X35]:(![X36]:(~thing(X35,X36)|singleton(X35,X36)))),inference(variable_rename,status(thm),[c97])).
cnf(c99,axiom,~thing(X138,X139)|singleton(X138,X139),inference(split_conjunct,status(thm),[c98])).
cnf(c46,negated_conjecture,forename(skolem0001,skolem0003),inference(split_conjunct,status(thm),[c41])).
fof(ax16,axiom,(![U]:(![V]:(forename(U,V)=>relname(U,V)))),input).
fof(c145,axiom,(![U]:(![V]:(~forename(U,V)|relname(U,V)))),inference(fof_nnf,status(thm),[ax16])).
fof(c146,axiom,(![X67]:(![X68]:(~forename(X67,X68)|relname(X67,X68)))),inference(variable_rename,status(thm),[c145])).
cnf(c147,axiom,~forename(X198,X199)|relname(X198,X199),inference(split_conjunct,status(thm),[c146])).
cnf(c222,plain,relname(skolem0001,skolem0003),inference(resolution,status(thm),[c147, c46])).
fof(ax15,axiom,(![U]:(![V]:(relname(U,V)=>relation(U,V)))),input).
fof(c148,axiom,(![U]:(![V]:(~relname(U,V)|relation(U,V)))),inference(fof_nnf,status(thm),[ax15])).
fof(c149,axiom,(![X69]:(![X70]:(~relname(X69,X70)|relation(X69,X70)))),inference(variable_rename,status(thm),[c148])).
cnf(c150,axiom,~relname(X204,X205)|relation(X204,X205),inference(split_conjunct,status(thm),[c149])).
cnf(c224,plain,relation(skolem0001,skolem0003),inference(resolution,status(thm),[c150, c222])).
fof(ax14,axiom,(![U]:(![V]:(relation(U,V)=>abstraction(U,V)))),input).
fof(c151,axiom,(![U]:(![V]:(~relation(U,V)|abstraction(U,V)))),inference(fof_nnf,status(thm),[ax14])).
fof(c152,axiom,(![X71]:(![X72]:(~relation(X71,X72)|abstraction(X71,X72)))),inference(variable_rename,status(thm),[c151])).
cnf(c153,axiom,~relation(X206,X207)|abstraction(X206,X207),inference(split_conjunct,status(thm),[c152])).
cnf(c225,plain,abstraction(skolem0001,skolem0003),inference(resolution,status(thm),[c153, c224])).
fof(ax13,axiom,(![U]:(![V]:(abstraction(U,V)=>thing(U,V)))),input).
fof(c154,axiom,(![U]:(![V]:(~abstraction(U,V)|thing(U,V)))),inference(fof_nnf,status(thm),[ax13])).
fof(c155,axiom,(![X73]:(![X74]:(~abstraction(X73,X74)|thing(X73,X74)))),inference(variable_rename,status(thm),[c154])).
cnf(c156,axiom,~abstraction(X208,X209)|thing(X208,X209),inference(split_conjunct,status(thm),[c155])).
cnf(c226,plain,thing(skolem0001,skolem0003),inference(resolution,status(thm),[c156, c225])).
cnf(c228,plain,singleton(skolem0001,skolem0003),inference(resolution,status(thm),[c226, c99])).
cnf(c30,plain,X375!=X377|X376!=X374|~singleton(X375,X376)|singleton(X377,X374),eq_axiom).
cnf(c326,plain,skolem0001!=X485|skolem0003!=X486|singleton(X485,X486),inference(resolution,status(thm),[c30, c228])).
cnf(c381,plain,skolem0001!=X488|singleton(X488,skolem0003),inference(resolution,status(thm),[c326, reflexivity])).
fof(ax22,axiom,(![U]:(![V]:(entity(U,V)=>thing(U,V)))),input).
fof(c127,axiom,(![U]:(![V]:(~entity(U,V)|thing(U,V)))),inference(fof_nnf,status(thm),[ax22])).
fof(c128,axiom,(![X55]:(![X56]:(~entity(X55,X56)|thing(X55,X56)))),inference(variable_rename,status(thm),[c127])).
cnf(c129,axiom,~entity(X174,X175)|thing(X174,X175),inference(split_conjunct,status(thm),[c128])).
cnf(c44,negated_conjecture,woman(skolem0001,skolem0002),inference(split_conjunct,status(thm),[c41])).
fof(ax8,axiom,(![U]:(![V]:(woman(U,V)=>human_person(U,V)))),input).
fof(c169,axiom,(![U]:(![V]:(~woman(U,V)|human_person(U,V)))),inference(fof_nnf,status(thm),[ax8])).
fof(c170,axiom,(![X83]:(![X84]:(~woman(X83,X84)|human_person(X83,X84)))),inference(variable_rename,status(thm),[c169])).
cnf(c171,axiom,~woman(X231,X230)|human_person(X231,X230),inference(split_conjunct,status(thm),[c170])).
cnf(c238,plain,human_person(skolem0001,skolem0002),inference(resolution,status(thm),[c171, c44])).
fof(ax7,axiom,(![U]:(![V]:(human_person(U,V)=>organism(U,V)))),input).
fof(c172,axiom,(![U]:(![V]:(~human_person(U,V)|organism(U,V)))),inference(fof_nnf,status(thm),[ax7])).
fof(c173,axiom,(![X85]:(![X86]:(~human_person(X85,X86)|organism(X85,X86)))),inference(variable_rename,status(thm),[c172])).
cnf(c174,axiom,~human_person(X232,X233)|organism(X232,X233),inference(split_conjunct,status(thm),[c173])).
cnf(c240,plain,organism(skolem0001,skolem0002),inference(resolution,status(thm),[c174, c238])).
fof(ax6,axiom,(![U]:(![V]:(organism(U,V)=>entity(U,V)))),input).
fof(c175,axiom,(![U]:(![V]:(~organism(U,V)|entity(U,V)))),inference(fof_nnf,status(thm),[ax6])).
fof(c176,axiom,(![X87]:(![X88]:(~organism(X87,X88)|entity(X87,X88)))),inference(variable_rename,status(thm),[c175])).
cnf(c177,axiom,~organism(X239,X238)|entity(X239,X238),inference(split_conjunct,status(thm),[c176])).
cnf(c243,plain,entity(skolem0001,skolem0002),inference(resolution,status(thm),[c177, c240])).
cnf(c245,plain,thing(skolem0001,skolem0002),inference(resolution,status(thm),[c243, c129])).
cnf(c248,plain,singleton(skolem0001,skolem0002),inference(resolution,status(thm),[c245, c99])).
cnf(c325,plain,skolem0001!=X483|skolem0002!=X484|singleton(X483,X484),inference(resolution,status(thm),[c30, c248])).
cnf(c380,plain,skolem0001!=X487|singleton(X487,skolem0002),inference(resolution,status(thm),[c325, reflexivity])).
cnf(c48,negated_conjecture,event(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
fof(ax34,axiom,(![U]:(![V]:(event(U,V)=>eventuality(U,V)))),input).
fof(c91,axiom,(![U]:(![V]:(~event(U,V)|eventuality(U,V)))),inference(fof_nnf,status(thm),[ax34])).
fof(c92,axiom,(![X31]:(![X32]:(~event(X31,X32)|eventuality(X31,X32)))),inference(variable_rename,status(thm),[c91])).
cnf(c93,axiom,~event(X131,X130)|eventuality(X131,X130),inference(split_conjunct,status(thm),[c92])).
cnf(c198,plain,eventuality(skolem0001,skolem0005),inference(resolution,status(thm),[c93, c48])).
fof(ax33,axiom,(![U]:(![V]:(eventuality(U,V)=>thing(U,V)))),input).
fof(c94,axiom,(![U]:(![V]:(~eventuality(U,V)|thing(U,V)))),inference(fof_nnf,status(thm),[ax33])).
fof(c95,axiom,(![X33]:(![X34]:(~eventuality(X33,X34)|thing(X33,X34)))),inference(variable_rename,status(thm),[c94])).
cnf(c96,axiom,~eventuality(X137,X136)|thing(X137,X136),inference(split_conjunct,status(thm),[c95])).
cnf(c199,plain,thing(skolem0001,skolem0005),inference(resolution,status(thm),[c96, c198])).
cnf(c200,plain,singleton(skolem0001,skolem0005),inference(resolution,status(thm),[c99, c199])).
cnf(c324,plain,skolem0001!=X479|skolem0005!=X480|singleton(X479,X480),inference(resolution,status(thm),[c30, c200])).
cnf(c377,plain,skolem0001!=X482|singleton(X482,skolem0005),inference(resolution,status(thm),[c324, reflexivity])).
cnf(c47,negated_conjecture,shake_beverage(skolem0001,skolem0004),inference(split_conjunct,status(thm),[c41])).
fof(ax27,axiom,(![U]:(![V]:(shake_beverage(U,V)=>beverage(U,V)))),input).
fof(c112,axiom,(![U]:(![V]:(~shake_beverage(U,V)|beverage(U,V)))),inference(fof_nnf,status(thm),[ax27])).
fof(c113,axiom,(![X45]:(![X46]:(~shake_beverage(X45,X46)|beverage(X45,X46)))),inference(variable_rename,status(thm),[c112])).
cnf(c114,axiom,~shake_beverage(X156,X157)|beverage(X156,X157),inference(split_conjunct,status(thm),[c113])).
cnf(c206,plain,beverage(skolem0001,skolem0004),inference(resolution,status(thm),[c114, c47])).
fof(ax26,axiom,(![U]:(![V]:(beverage(U,V)=>food(U,V)))),input).
fof(c115,axiom,(![U]:(![V]:(~beverage(U,V)|food(U,V)))),inference(fof_nnf,status(thm),[ax26])).
fof(c116,axiom,(![X47]:(![X48]:(~beverage(X47,X48)|food(X47,X48)))),inference(variable_rename,status(thm),[c115])).
cnf(c117,axiom,~beverage(X162,X163)|food(X162,X163),inference(split_conjunct,status(thm),[c116])).
cnf(c207,plain,food(skolem0001,skolem0004),inference(resolution,status(thm),[c117, c206])).
fof(ax25,axiom,(![U]:(![V]:(food(U,V)=>substance_matter(U,V)))),input).
fof(c118,axiom,(![U]:(![V]:(~food(U,V)|substance_matter(U,V)))),inference(fof_nnf,status(thm),[ax25])).
fof(c119,axiom,(![X49]:(![X50]:(~food(X49,X50)|substance_matter(X49,X50)))),inference(variable_rename,status(thm),[c118])).
cnf(c120,axiom,~food(X164,X165)|substance_matter(X164,X165),inference(split_conjunct,status(thm),[c119])).
cnf(c208,plain,substance_matter(skolem0001,skolem0004),inference(resolution,status(thm),[c120, c207])).
fof(ax24,axiom,(![U]:(![V]:(substance_matter(U,V)=>object(U,V)))),input).
fof(c121,axiom,(![U]:(![V]:(~substance_matter(U,V)|object(U,V)))),inference(fof_nnf,status(thm),[ax24])).
fof(c122,axiom,(![X51]:(![X52]:(~substance_matter(X51,X52)|object(X51,X52)))),inference(variable_rename,status(thm),[c121])).
cnf(c123,axiom,~substance_matter(X170,X171)|object(X170,X171),inference(split_conjunct,status(thm),[c122])).
cnf(c209,plain,object(skolem0001,skolem0004),inference(resolution,status(thm),[c123, c208])).
fof(ax23,axiom,(![U]:(![V]:(object(U,V)=>entity(U,V)))),input).
fof(c124,axiom,(![U]:(![V]:(~object(U,V)|entity(U,V)))),inference(fof_nnf,status(thm),[ax23])).
fof(c125,axiom,(![X53]:(![X54]:(~object(X53,X54)|entity(X53,X54)))),inference(variable_rename,status(thm),[c124])).
cnf(c126,axiom,~object(X172,X173)|entity(X172,X173),inference(split_conjunct,status(thm),[c125])).
cnf(c210,plain,entity(skolem0001,skolem0004),inference(resolution,status(thm),[c126, c209])).
cnf(c211,plain,thing(skolem0001,skolem0004),inference(resolution,status(thm),[c129, c210])).
cnf(c212,plain,singleton(skolem0001,skolem0004),inference(resolution,status(thm),[c211, c99])).
cnf(c323,plain,skolem0001!=X477|skolem0004!=X478|singleton(X477,X478),inference(resolution,status(thm),[c30, c212])).
cnf(c376,plain,skolem0001!=X481|singleton(X481,skolem0004),inference(resolution,status(thm),[c323, reflexivity])).
fof(ax30,axiom,(![U]:(![V]:(eventuality(U,V)=>nonexistent(U,V)))),input).
fof(c103,axiom,(![U]:(![V]:(~eventuality(U,V)|nonexistent(U,V)))),inference(fof_nnf,status(thm),[ax30])).
fof(c104,axiom,(![X39]:(![X40]:(~eventuality(X39,X40)|nonexistent(X39,X40)))),inference(variable_rename,status(thm),[c103])).
cnf(c105,axiom,~eventuality(X146,X147)|nonexistent(X146,X147),inference(split_conjunct,status(thm),[c104])).
cnf(c202,plain,nonexistent(skolem0001,skolem0005),inference(resolution,status(thm),[c105, c198])).
cnf(c29,plain,X366!=X368|X367!=X365|~nonexistent(X366,X367)|nonexistent(X368,X365),eq_axiom).
cnf(c319,plain,skolem0001!=X473|skolem0005!=X474|nonexistent(X473,X474),inference(resolution,status(thm),[c29, c202])).
cnf(c373,plain,skolem0001!=X476|nonexistent(X476,skolem0005),inference(resolution,status(thm),[c319, reflexivity])).
cnf(c28,plain,X356!=X358|X357!=X355|~eventuality(X356,X357)|eventuality(X358,X355),eq_axiom).
cnf(c314,plain,skolem0001!=X472|skolem0005!=X471|eventuality(X472,X471),inference(resolution,status(thm),[c28, c198])).
cnf(c372,plain,skolem0001!=X475|eventuality(X475,skolem0005),inference(resolution,status(thm),[c314, reflexivity])).
cnf(c27,plain,X348!=X350|X349!=X347|~event(X348,X349)|event(X350,X347),eq_axiom).
cnf(c310,plain,skolem0001!=X467|skolem0005!=X468|event(X467,X468),inference(resolution,status(thm),[c27, c48])).
cnf(c369,plain,skolem0001!=X470|event(X470,skolem0005),inference(resolution,status(thm),[c310, reflexivity])).
cnf(c26,plain,X339!=X341|X340!=X338|~order(X339,X340)|order(X341,X338),eq_axiom).
cnf(c306,plain,skolem0001!=X466|skolem0005!=X465|order(X466,X465),inference(resolution,status(thm),[c26, c53])).
cnf(c368,plain,skolem0001!=X469|order(X469,skolem0005),inference(resolution,status(thm),[c306, reflexivity])).
cnf(c25,plain,X329!=X331|X330!=X328|~shake_beverage(X329,X330)|shake_beverage(X331,X328),eq_axiom).
cnf(c301,plain,skolem0001!=X462|skolem0004!=X461|shake_beverage(X462,X461),inference(resolution,status(thm),[c25, c47])).
cnf(c365,plain,skolem0001!=X464|shake_beverage(X464,skolem0004),inference(resolution,status(thm),[c301, reflexivity])).
cnf(c24,plain,X321!=X323|X322!=X320|~beverage(X321,X322)|beverage(X323,X320),eq_axiom).
cnf(c297,plain,skolem0001!=X460|skolem0004!=X459|beverage(X460,X459),inference(resolution,status(thm),[c24, c206])).
cnf(c364,plain,skolem0001!=X463|beverage(X463,skolem0004),inference(resolution,status(thm),[c297, reflexivity])).
cnf(c23,plain,X312!=X314|X313!=X311|~food(X312,X313)|food(X314,X311),eq_axiom).
cnf(c293,plain,skolem0001!=X457|skolem0004!=X456|food(X457,X456),inference(resolution,status(thm),[c23, c207])).
cnf(c362,plain,skolem0001!=X458|food(X458,skolem0004),inference(resolution,status(thm),[c293, reflexivity])).
cnf(c22,plain,X302!=X304|X303!=X301|~substance_matter(X302,X303)|substance_matter(X304,X301),eq_axiom).
cnf(c288,plain,skolem0001!=X449|skolem0004!=X450|substance_matter(X449,X450),inference(resolution,status(thm),[c22, c208])).
cnf(c359,plain,skolem0001!=X451|substance_matter(X451,skolem0004),inference(resolution,status(thm),[c288, reflexivity])).
fof(ax21,axiom,(![U]:(![V]:(entity(U,V)=>specific(U,V)))),input).
fof(c130,axiom,(![U]:(![V]:(~entity(U,V)|specific(U,V)))),inference(fof_nnf,status(thm),[ax21])).
fof(c131,axiom,(![X57]:(![X58]:(~entity(X57,X58)|specific(X57,X58)))),inference(variable_rename,status(thm),[c130])).
cnf(c132,axiom,~entity(X180,X181)|specific(X180,X181),inference(split_conjunct,status(thm),[c131])).
cnf(c247,plain,specific(skolem0001,skolem0002),inference(resolution,status(thm),[c243, c132])).
cnf(c21,plain,X294!=X296|X295!=X293|~specific(X294,X295)|specific(X296,X293),eq_axiom).
cnf(c284,plain,skolem0001!=X446|skolem0002!=X447|specific(X446,X447),inference(resolution,status(thm),[c21, c247])).
cnf(c357,plain,skolem0001!=X448|specific(X448,skolem0002),inference(resolution,status(thm),[c284, reflexivity])).
fof(ax31,axiom,(![U]:(![V]:(eventuality(U,V)=>specific(U,V)))),input).
fof(c100,axiom,(![U]:(![V]:(~eventuality(U,V)|specific(U,V)))),inference(fof_nnf,status(thm),[ax31])).
fof(c101,axiom,(![X37]:(![X38]:(~eventuality(X37,X38)|specific(X37,X38)))),inference(variable_rename,status(thm),[c100])).
cnf(c102,axiom,~eventuality(X145,X144)|specific(X145,X144),inference(split_conjunct,status(thm),[c101])).
cnf(c201,plain,specific(skolem0001,skolem0005),inference(resolution,status(thm),[c102, c198])).
cnf(c283,plain,skolem0001!=X439|skolem0005!=X440|specific(X439,X440),inference(resolution,status(thm),[c21, c201])).
cnf(c354,plain,skolem0001!=X441|specific(X441,skolem0005),inference(resolution,status(thm),[c283, reflexivity])).
cnf(c213,plain,specific(skolem0001,skolem0004),inference(resolution,status(thm),[c132, c210])).
cnf(c282,plain,skolem0001!=X432|skolem0004!=X433|specific(X432,X433),inference(resolution,status(thm),[c21, c213])).
cnf(c351,plain,skolem0001!=X438|specific(X438,skolem0004),inference(resolution,status(thm),[c282, reflexivity])).
fof(ax20,axiom,(![U]:(![V]:(entity(U,V)=>existent(U,V)))),input).
fof(c133,axiom,(![U]:(![V]:(~entity(U,V)|existent(U,V)))),inference(fof_nnf,status(thm),[ax20])).
fof(c134,axiom,(![X59]:(![X60]:(~entity(X59,X60)|existent(X59,X60)))),inference(variable_rename,status(thm),[c133])).
cnf(c135,axiom,~entity(X183,X182)|existent(X183,X182),inference(split_conjunct,status(thm),[c134])).
cnf(c214,plain,existent(skolem0001,skolem0004),inference(resolution,status(thm),[c135, c210])).
cnf(c20,plain,X285!=X287|X286!=X284|~existent(X285,X286)|existent(X287,X284),eq_axiom).
cnf(c278,plain,skolem0001!=X429|skolem0004!=X430|existent(X429,X430),inference(resolution,status(thm),[c20, c214])).
cnf(c349,plain,skolem0001!=X431|existent(X431,skolem0004),inference(resolution,status(thm),[c278, reflexivity])).
cnf(c244,plain,existent(skolem0001,skolem0002),inference(resolution,status(thm),[c243, c135])).
cnf(c277,plain,skolem0001!=X420|skolem0002!=X421|existent(X420,X421),inference(resolution,status(thm),[c20, c244])).
cnf(c346,plain,skolem0001!=X422|existent(X422,skolem0002),inference(resolution,status(thm),[c277, reflexivity])).
fof(ax19,axiom,(![U]:(![V]:(object(U,V)=>nonliving(U,V)))),input).
fof(c136,axiom,(![U]:(![V]:(~object(U,V)|nonliving(U,V)))),inference(fof_nnf,status(thm),[ax19])).
fof(c137,axiom,(![X61]:(![X62]:(~object(X61,X62)|nonliving(X61,X62)))),inference(variable_rename,status(thm),[c136])).
cnf(c138,axiom,~object(X189,X188)|nonliving(X189,X188),inference(split_conjunct,status(thm),[c137])).
cnf(c216,plain,nonliving(skolem0001,skolem0004),inference(resolution,status(thm),[c138, c209])).
cnf(c19,plain,X275!=X277|X276!=X274|~nonliving(X275,X276)|nonliving(X277,X274),eq_axiom).
cnf(c272,plain,skolem0001!=X418|skolem0004!=X417|nonliving(X418,X417),inference(resolution,status(thm),[c19, c216])).
cnf(c344,plain,skolem0001!=X419|nonliving(X419,skolem0004),inference(resolution,status(thm),[c272, reflexivity])).
cnf(c18,plain,X265!=X267|X266!=X264|~object(X265,X266)|object(X267,X264),eq_axiom).
cnf(c268,plain,skolem0001!=X409|skolem0004!=X408|object(X409,X408),inference(resolution,status(thm),[c18, c209])).
cnf(c341,plain,skolem0001!=X410|object(X410,skolem0004),inference(resolution,status(thm),[c268, reflexivity])).
cnf(c1,plain,X123!=X125|X124!=X122|~female(X123,X124)|female(X125,X122),eq_axiom).
fof(ax1,axiom,(![U]:(![V]:(woman(U,V)=>female(U,V)))),input).
fof(c190,axiom,(![U]:(![V]:(~woman(U,V)|female(U,V)))),inference(fof_nnf,status(thm),[ax1])).
fof(c191,axiom,(![X97]:(![X98]:(~woman(X97,X98)|female(X97,X98)))),inference(variable_rename,status(thm),[c190])).
cnf(c192,axiom,~woman(X261,X260)|female(X261,X260),inference(split_conjunct,status(thm),[c191])).
cnf(c265,plain,female(skolem0001,skolem0002),inference(resolution,status(thm),[c192, c44])).
cnf(c267,plain,skolem0001!=X402|skolem0002!=X401|female(X402,X401),inference(resolution,status(thm),[c265, c1])).
cnf(c338,plain,skolem0001!=X407|female(X407,skolem0002),inference(resolution,status(thm),[c267, reflexivity])).
cnf(c3,plain,X141!=X143|X142!=X140|~animate(X141,X142)|animate(X143,X140),eq_axiom).
fof(ax2,axiom,(![U]:(![V]:(human_person(U,V)=>animate(U,V)))),input).
fof(c187,axiom,(![U]:(![V]:(~human_person(U,V)|animate(U,V)))),inference(fof_nnf,status(thm),[ax2])).
fof(c188,axiom,(![X95]:(![X96]:(~human_person(X95,X96)|animate(X95,X96)))),inference(variable_rename,status(thm),[c187])).
cnf(c189,axiom,~human_person(X254,X255)|animate(X254,X255),inference(split_conjunct,status(thm),[c188])).
cnf(c262,plain,animate(skolem0001,skolem0002),inference(resolution,status(thm),[c189, c238])).
cnf(c264,plain,skolem0001!=X398|skolem0002!=X399|animate(X398,X399),inference(resolution,status(thm),[c262, c3])).
cnf(c336,plain,skolem0001!=X400|animate(X400,skolem0002),inference(resolution,status(thm),[c264, reflexivity])).
cnf(c17,plain,X257!=X259|X258!=X256|~relname(X257,X258)|relname(X259,X256),eq_axiom).
cnf(c263,plain,skolem0001!=X390|skolem0003!=X389|relname(X390,X389),inference(resolution,status(thm),[c17, c222])).
cnf(c333,plain,skolem0001!=X391|relname(X391,skolem0003),inference(resolution,status(thm),[c263, reflexivity])).
cnf(c4,plain,X149!=X151|X150!=X148|~human(X149,X150)|human(X151,X148),eq_axiom).
fof(ax3,axiom,(![U]:(![V]:(human_person(U,V)=>human(U,V)))),input).
fof(c184,axiom,(![U]:(![V]:(~human_person(U,V)|human(U,V)))),inference(fof_nnf,status(thm),[ax3])).
fof(c185,axiom,(![X93]:(![X94]:(~human_person(X93,X94)|human(X93,X94)))),inference(variable_rename,status(thm),[c184])).
cnf(c186,axiom,~human_person(X252,X253)|human(X252,X253),inference(split_conjunct,status(thm),[c185])).
cnf(c259,plain,human(skolem0001,skolem0002),inference(resolution,status(thm),[c186, c238])).
cnf(c260,plain,skolem0001!=X387|skolem0002!=X386|human(X387,X386),inference(resolution,status(thm),[c259, c4])).
cnf(c331,plain,skolem0001!=X388|human(X388,skolem0002),inference(resolution,status(thm),[c260, reflexivity])).
cnf(c16,plain,X249!=X251|X250!=X248|~relation(X249,X250)|relation(X251,X248),eq_axiom).
cnf(c258,plain,skolem0001!=X380|skolem0003!=X379|relation(X380,X379),inference(resolution,status(thm),[c16, c224])).
cnf(c328,plain,skolem0001!=X381|relation(X381,skolem0003),inference(resolution,status(thm),[c258, reflexivity])).
cnf(c6,plain,X167!=X169|X168!=X166|~living(X167,X168)|living(X169,X166),eq_axiom).
fof(ax4,axiom,(![U]:(![V]:(organism(U,V)=>living(U,V)))),input).
fof(c181,axiom,(![U]:(![V]:(~organism(U,V)|living(U,V)))),inference(fof_nnf,status(thm),[ax4])).
fof(c182,axiom,(![X91]:(![X92]:(~organism(X91,X92)|living(X91,X92)))),inference(variable_rename,status(thm),[c181])).
cnf(c183,axiom,~organism(X246,X247)|living(X246,X247),inference(split_conjunct,status(thm),[c182])).
cnf(c255,plain,living(skolem0001,skolem0002),inference(resolution,status(thm),[c183, c240])).
cnf(c256,plain,skolem0001!=X372|skolem0002!=X373|living(X372,X373),inference(resolution,status(thm),[c255, c6])).
cnf(c322,plain,skolem0001!=X378|living(X378,skolem0002),inference(resolution,status(thm),[c256, reflexivity])).
cnf(c7,plain,X177!=X179|X178!=X176|~impartial(X177,X178)|impartial(X179,X176),eq_axiom).
fof(ax5,axiom,(![U]:(![V]:(organism(U,V)=>impartial(U,V)))),input).
fof(c178,axiom,(![U]:(![V]:(~organism(U,V)|impartial(U,V)))),inference(fof_nnf,status(thm),[ax5])).
fof(c179,axiom,(![X89]:(![X90]:(~organism(X89,X90)|impartial(X89,X90)))),inference(variable_rename,status(thm),[c178])).
cnf(c180,axiom,~organism(X245,X244)|impartial(X245,X244),inference(split_conjunct,status(thm),[c179])).
cnf(c253,plain,impartial(skolem0001,skolem0002),inference(resolution,status(thm),[c180, c240])).
cnf(c254,plain,skolem0001!=X370|skolem0002!=X369|impartial(X370,X369),inference(resolution,status(thm),[c253, c7])).
cnf(c320,plain,skolem0001!=X371|impartial(X371,skolem0002),inference(resolution,status(thm),[c254, reflexivity])).
cnf(c15,plain,X241!=X243|X242!=X240|~thing(X241,X242)|thing(X243,X240),eq_axiom).
cnf(c252,plain,skolem0001!=X362|skolem0004!=X363|thing(X362,X363),inference(resolution,status(thm),[c15, c211])).
cnf(c317,plain,skolem0001!=X364|thing(X364,skolem0004),inference(resolution,status(thm),[c252, reflexivity])).
cnf(c251,plain,skolem0001!=X359|skolem0002!=X360|thing(X359,X360),inference(resolution,status(thm),[c15, c245])).
cnf(c315,plain,skolem0001!=X361|thing(X361,skolem0002),inference(resolution,status(thm),[c251, reflexivity])).
cnf(c250,plain,skolem0001!=X352|skolem0003!=X353|thing(X352,X353),inference(resolution,status(thm),[c15, c226])).
cnf(c312,plain,skolem0001!=X354|thing(X354,skolem0003),inference(resolution,status(thm),[c250, reflexivity])).
cnf(c249,plain,skolem0001!=X345|skolem0005!=X346|thing(X345,X346),inference(resolution,status(thm),[c15, c199])).
cnf(c309,plain,skolem0001!=X351|thing(X351,skolem0005),inference(resolution,status(thm),[c249, reflexivity])).
cnf(c8,plain,X185!=X187|X186!=X184|~entity(X185,X186)|entity(X187,X184),eq_axiom).
cnf(c246,plain,skolem0001!=X342|skolem0002!=X343|entity(X342,X343),inference(resolution,status(thm),[c243, c8])).
cnf(c307,plain,skolem0001!=X344|entity(X344,skolem0002),inference(resolution,status(thm),[c246, reflexivity])).
fof(ax12,axiom,(![U]:(![V]:(abstraction(U,V)=>nonhuman(U,V)))),input).
fof(c157,axiom,(![U]:(![V]:(~abstraction(U,V)|nonhuman(U,V)))),inference(fof_nnf,status(thm),[ax12])).
fof(c158,axiom,(![X75]:(![X76]:(~abstraction(X75,X76)|nonhuman(X75,X76)))),inference(variable_rename,status(thm),[c157])).
cnf(c159,axiom,~abstraction(X215,X214)|nonhuman(X215,X214),inference(split_conjunct,status(thm),[c158])).
cnf(c229,plain,nonhuman(skolem0001,skolem0003),inference(resolution,status(thm),[c159, c225])).
cnf(c14,plain,X235!=X237|X236!=X234|~nonhuman(X235,X236)|nonhuman(X237,X234),eq_axiom).
cnf(c242,plain,skolem0001!=X335|skolem0003!=X336|nonhuman(X335,X336),inference(resolution,status(thm),[c14, c229])).
cnf(c304,plain,skolem0001!=X337|nonhuman(X337,skolem0003),inference(resolution,status(thm),[c242, reflexivity])).
cnf(c5,plain,X159!=X161|X160!=X158|~organism(X159,X160)|organism(X161,X158),eq_axiom).
cnf(c241,plain,skolem0001!=X333|skolem0002!=X332|organism(X333,X332),inference(resolution,status(thm),[c240, c5])).
cnf(c302,plain,skolem0001!=X334|organism(X334,skolem0002),inference(resolution,status(thm),[c241, reflexivity])).
cnf(c2,plain,X133!=X135|X134!=X132|~human_person(X133,X134)|human_person(X135,X132),eq_axiom).
cnf(c239,plain,skolem0001!=X325|skolem0002!=X326|human_person(X325,X326),inference(resolution,status(thm),[c238, c2])).
cnf(c299,plain,skolem0001!=X327|human_person(X327,skolem0002),inference(resolution,status(thm),[c239, reflexivity])).
fof(ax11,axiom,(![U]:(![V]:(abstraction(U,V)=>general(U,V)))),input).
fof(c160,axiom,(![U]:(![V]:(~abstraction(U,V)|general(U,V)))),inference(fof_nnf,status(thm),[ax11])).
fof(c161,axiom,(![X77]:(![X78]:(~abstraction(X77,X78)|general(X77,X78)))),inference(variable_rename,status(thm),[c160])).
cnf(c162,axiom,~abstraction(X216,X217)|general(X216,X217),inference(split_conjunct,status(thm),[c161])).
cnf(c230,plain,general(skolem0001,skolem0003),inference(resolution,status(thm),[c162, c225])).
cnf(c13,plain,X227!=X229|X228!=X226|~general(X227,X228)|general(X229,X226),eq_axiom).
cnf(c237,plain,skolem0001!=X319|skolem0003!=X318|general(X319,X318),inference(resolution,status(thm),[c13, c230])).
cnf(c296,plain,skolem0001!=X324|general(X324,skolem0003),inference(resolution,status(thm),[c237, reflexivity])).
cnf(c12,plain,X219!=X221|X220!=X218|~unisex(X219,X220)|unisex(X221,X218),eq_axiom).
fof(ax10,axiom,(![U]:(![V]:(abstraction(U,V)=>unisex(U,V)))),input).
fof(c163,axiom,(![U]:(![V]:(~abstraction(U,V)|unisex(U,V)))),inference(fof_nnf,status(thm),[ax10])).
fof(c164,axiom,(![X79]:(![X80]:(~abstraction(X79,X80)|unisex(X79,X80)))),inference(variable_rename,status(thm),[c163])).
cnf(c165,axiom,~abstraction(X223,X222)|unisex(X223,X222),inference(split_conjunct,status(thm),[c164])).
cnf(c234,plain,unisex(skolem0001,skolem0003),inference(resolution,status(thm),[c165, c225])).
cnf(c235,plain,skolem0001!=X315|skolem0003!=X316|unisex(X315,X316),inference(resolution,status(thm),[c234, c12])).
cnf(c294,plain,skolem0001!=X317|unisex(X317,skolem0003),inference(resolution,status(thm),[c235, reflexivity])).
fof(ax17,axiom,(![U]:(![V]:(object(U,V)=>unisex(U,V)))),input).
fof(c142,axiom,(![U]:(![V]:(~object(U,V)|unisex(U,V)))),inference(fof_nnf,status(thm),[ax17])).
fof(c143,axiom,(![X65]:(![X66]:(~object(X65,X66)|unisex(X65,X66)))),inference(variable_rename,status(thm),[c142])).
cnf(c144,axiom,~object(X196,X197)|unisex(X196,X197),inference(split_conjunct,status(thm),[c143])).
cnf(c221,plain,unisex(skolem0001,skolem0004),inference(resolution,status(thm),[c144, c209])).
cnf(c232,plain,skolem0001!=X308|skolem0004!=X309|unisex(X308,X309),inference(resolution,status(thm),[c12, c221])).
cnf(c291,plain,skolem0001!=X310|unisex(X310,skolem0004),inference(resolution,status(thm),[c232, reflexivity])).
fof(ax29,axiom,(![U]:(![V]:(eventuality(U,V)=>unisex(U,V)))),input).
fof(c106,axiom,(![U]:(![V]:(~eventuality(U,V)|unisex(U,V)))),inference(fof_nnf,status(thm),[ax29])).
fof(c107,axiom,(![X41]:(![X42]:(~eventuality(X41,X42)|unisex(X41,X42)))),inference(variable_rename,status(thm),[c106])).
cnf(c108,axiom,~eventuality(X152,X153)|unisex(X152,X153),inference(split_conjunct,status(thm),[c107])).
cnf(c204,plain,unisex(skolem0001,skolem0005),inference(resolution,status(thm),[c108, c198])).
cnf(c231,plain,skolem0001!=X305|skolem0005!=X306|unisex(X305,X306),inference(resolution,status(thm),[c12, c204])).
cnf(c289,plain,skolem0001!=X307|unisex(X307,skolem0005),inference(resolution,status(thm),[c231, reflexivity])).
cnf(c11,plain,X211!=X213|X212!=X210|~abstraction(X211,X212)|abstraction(X213,X210),eq_axiom).
cnf(c227,plain,skolem0001!=X298|skolem0003!=X299|abstraction(X298,X299),inference(resolution,status(thm),[c11, c225])).
cnf(c286,plain,skolem0001!=X300|abstraction(X300,skolem0003),inference(resolution,status(thm),[c227, reflexivity])).
cnf(c10,plain,X201!=X203|X202!=X200|~forename(X201,X202)|forename(X203,X200),eq_axiom).
cnf(c223,plain,skolem0001!=X292|skolem0003!=X291|forename(X292,X291),inference(resolution,status(thm),[c10, c46])).
cnf(c281,plain,skolem0001!=X297|forename(X297,skolem0003),inference(resolution,status(thm),[c223, reflexivity])).
fof(ax18,axiom,(![U]:(![V]:(object(U,V)=>impartial(U,V)))),input).
fof(c139,axiom,(![U]:(![V]:(~object(U,V)|impartial(U,V)))),inference(fof_nnf,status(thm),[ax18])).
fof(c140,axiom,(![X63]:(![X64]:(~object(X63,X64)|impartial(X63,X64)))),inference(variable_rename,status(thm),[c139])).
cnf(c141,axiom,~object(X191,X190)|impartial(X191,X190),inference(split_conjunct,status(thm),[c140])).
cnf(c218,plain,impartial(skolem0001,skolem0004),inference(resolution,status(thm),[c141, c209])).
cnf(c220,plain,skolem0001!=X289|skolem0004!=X288|impartial(X289,X288),inference(resolution,status(thm),[c218, c7])).
cnf(c279,plain,skolem0001!=X290|impartial(X290,skolem0004),inference(resolution,status(thm),[c220, reflexivity])).
cnf(c45,negated_conjecture,mia_forename(skolem0001,skolem0003),inference(split_conjunct,status(thm),[c41])).
cnf(c9,plain,X193!=X195|X194!=X192|~mia_forename(X193,X194)|mia_forename(X195,X192),eq_axiom).
cnf(c219,plain,skolem0001!=X281|skolem0003!=X282|mia_forename(X281,X282),inference(resolution,status(thm),[c9, c45])).
cnf(c275,plain,skolem0001!=X283|mia_forename(X283,skolem0003),inference(resolution,status(thm),[c219, reflexivity])).
cnf(c215,plain,skolem0001!=X278|skolem0004!=X279|entity(X278,X279),inference(resolution,status(thm),[c8, c210])).
cnf(c273,plain,skolem0001!=X280|entity(X280,skolem0004),inference(resolution,status(thm),[c215, reflexivity])).
cnf(c0,plain,X109!=X111|X110!=X108|~woman(X109,X110)|woman(X111,X108),eq_axiom).
cnf(c195,plain,skolem0001!=X272|skolem0002!=X271|woman(X272,X271),inference(resolution,status(thm),[c0, c44])).
cnf(c270,plain,skolem0001!=X273|woman(X273,skolem0002),inference(resolution,status(thm),[c195, reflexivity])).
cnf(c36,plain,X268!=X269|~actual_world(X268)|actual_world(X269),eq_axiom).
fof(ax42,axiom,(![U]:(![V]:(unisex(U,V)=>(~female(U,V))))),input).
fof(c61,axiom,(![U]:(![V]:(unisex(U,V)=>~female(U,V)))),inference(fof_simplification,status(thm),[ax42])).
fof(c62,axiom,(![U]:(![V]:(~unisex(U,V)|~female(U,V)))),inference(fof_nnf,status(thm),[c61])).
fof(c63,axiom,(![X15]:(![X16]:(~unisex(X15,X16)|~female(X15,X16)))),inference(variable_rename,status(thm),[c62])).
cnf(c64,axiom,~unisex(X107,X106)|~female(X107,X106),inference(split_conjunct,status(thm),[c63])).
cnf(c266,plain,~unisex(skolem0001,skolem0002),inference(resolution,status(thm),[c265, c64])).
fof(ax39,axiom,(![U]:(![V]:(nonhuman(U,V)=>(~human(U,V))))),input).
fof(c73,axiom,(![U]:(![V]:(nonhuman(U,V)=>~human(U,V)))),inference(fof_simplification,status(thm),[ax39])).
fof(c74,axiom,(![U]:(![V]:(~nonhuman(U,V)|~human(U,V)))),inference(fof_nnf,status(thm),[c73])).
fof(c75,axiom,(![X21]:(![X22]:(~nonhuman(X21,X22)|~human(X21,X22)))),inference(variable_rename,status(thm),[c74])).
cnf(c76,axiom,~nonhuman(X117,X116)|~human(X117,X116),inference(split_conjunct,status(thm),[c75])).
cnf(c261,plain,~nonhuman(skolem0001,skolem0002),inference(resolution,status(thm),[c259, c76])).
fof(ax40,axiom,(![U]:(![V]:(nonliving(U,V)=>(~living(U,V))))),input).
fof(c69,axiom,(![U]:(![V]:(nonliving(U,V)=>~living(U,V)))),inference(fof_simplification,status(thm),[ax40])).
fof(c70,axiom,(![U]:(![V]:(~nonliving(U,V)|~living(U,V)))),inference(fof_nnf,status(thm),[c69])).
fof(c71,axiom,(![X19]:(![X20]:(~nonliving(X19,X20)|~living(X19,X20)))),inference(variable_rename,status(thm),[c70])).
cnf(c72,axiom,~nonliving(X115,X114)|~living(X115,X114),inference(split_conjunct,status(thm),[c71])).
cnf(c257,plain,~nonliving(skolem0001,skolem0002),inference(resolution,status(thm),[c255, c72])).
fof(ax9,axiom,(![U]:(![V]:(mia_forename(U,V)=>forename(U,V)))),input).
fof(c166,axiom,(![U]:(![V]:(~mia_forename(U,V)|forename(U,V)))),inference(fof_nnf,status(thm),[ax9])).
fof(c167,axiom,(![X81]:(![X82]:(~mia_forename(X81,X82)|forename(X81,X82)))),inference(variable_rename,status(thm),[c166])).
cnf(c168,axiom,~mia_forename(X225,X224)|forename(X225,X224),inference(split_conjunct,status(thm),[c167])).
fof(ax41,axiom,(![U]:(![V]:(specific(U,V)=>(~general(U,V))))),input).
fof(c65,axiom,(![U]:(![V]:(specific(U,V)=>~general(U,V)))),inference(fof_simplification,status(thm),[ax41])).
fof(c66,axiom,(![U]:(![V]:(~specific(U,V)|~general(U,V)))),inference(fof_nnf,status(thm),[c65])).
fof(c67,axiom,(![X17]:(![X18]:(~specific(X17,X18)|~general(X17,X18)))),inference(variable_rename,status(thm),[c66])).
cnf(c68,axiom,~specific(X113,X112)|~general(X113,X112),inference(split_conjunct,status(thm),[c67])).
cnf(c233,plain,~specific(skolem0001,skolem0003),inference(resolution,status(thm),[c230, c68])).
fof(ax37,axiom,(![U]:(![V]:(animate(U,V)=>(~nonliving(U,V))))),input).
fof(c81,axiom,(![U]:(![V]:(animate(U,V)=>~nonliving(U,V)))),inference(fof_simplification,status(thm),[ax37])).
fof(c82,axiom,(![U]:(![V]:(~animate(U,V)|~nonliving(U,V)))),inference(fof_nnf,status(thm),[c81])).
fof(c83,axiom,(![X25]:(![X26]:(~animate(X25,X26)|~nonliving(X25,X26)))),inference(variable_rename,status(thm),[c82])).
cnf(c84,axiom,~animate(X120,X121)|~nonliving(X120,X121),inference(split_conjunct,status(thm),[c83])).
cnf(c217,plain,~animate(skolem0001,skolem0004),inference(resolution,status(thm),[c216, c84])).
fof(ax28,axiom,(![U]:(![V]:(order(U,V)=>event(U,V)))),input).
fof(c109,axiom,(![U]:(![V]:(~order(U,V)|event(U,V)))),inference(fof_nnf,status(thm),[ax28])).
fof(c110,axiom,(![X43]:(![X44]:(~order(X43,X44)|event(X43,X44)))),inference(variable_rename,status(thm),[c109])).
cnf(c111,axiom,~order(X154,X155)|event(X154,X155),inference(split_conjunct,status(thm),[c110])).
fof(ax38,axiom,(![U]:(![V]:(existent(U,V)=>(~nonexistent(U,V))))),input).
fof(c77,axiom,(![U]:(![V]:(existent(U,V)=>~nonexistent(U,V)))),inference(fof_simplification,status(thm),[ax38])).
fof(c78,axiom,(![U]:(![V]:(~existent(U,V)|~nonexistent(U,V)))),inference(fof_nnf,status(thm),[c77])).
fof(c79,axiom,(![X23]:(![X24]:(~existent(X23,X24)|~nonexistent(X23,X24)))),inference(variable_rename,status(thm),[c78])).
cnf(c80,axiom,~existent(X119,X118)|~nonexistent(X119,X118),inference(split_conjunct,status(thm),[c79])).
cnf(c203,plain,~existent(skolem0001,skolem0005),inference(resolution,status(thm),[c202, c80])).
fof(ax35,axiom,(![U]:(![V]:(act(U,V)=>event(U,V)))),input).
fof(c88,axiom,(![U]:(![V]:(~act(U,V)|event(U,V)))),inference(fof_nnf,status(thm),[ax35])).
fof(c89,axiom,(![X29]:(![X30]:(~act(X29,X30)|event(X29,X30)))),inference(variable_rename,status(thm),[c88])).
cnf(c90,axiom,~act(X128,X129)|event(X128,X129),inference(split_conjunct,status(thm),[c89])).
cnf(transitivity,axiom,X105!=X103|X103!=X104|X105=X104,eq_axiom).
cnf(symmetry,axiom,X101!=X100|X100=X101,eq_axiom).
cnf(c42,negated_conjecture,actual_world(skolem0001),inference(split_conjunct,status(thm),[c41])).
# SZS output end Saturation
```

### Sample solution for SWV017+1

```Timeout
```

## Satallax 3.4

Michael Färber
Universität Innsbruck, Austria

### Sample solution for SET014^4

```% SZS output start Proof
thf(ty_eigen__2, type, eigen__2 : (\$i>\$o)).
thf(ty_eigen__1, type, eigen__1 : (\$i>\$o)).
thf(ty_eigen__0, type, eigen__0 : (\$i>\$o)).
thf(ty_eigen__3, type, eigen__3 : \$i).
thf(sP1,plain,sP1 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
thf(sP2,plain,sP2 <=> (sP1 => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP2])])).
thf(sP3,plain,sP3 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
thf(sP4,plain,sP4 <=> (sP3 => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP4])])).
thf(sP5,plain,sP5 <=> (![X1:\$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP5])])).
thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP6])])).
thf(sP7,plain,sP7 <=> (![X1:\$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
thf(def_in,definition,(in = (^[X1:\$i]:(^[X2:\$i>\$o]:(X2 @ X1))))).
thf(def_is_a,definition,(is_a = (^[X1:\$i]:(^[X2:\$i>\$o]:(X2 @ X1))))).
thf(def_emptyset,definition,(emptyset = (^[X1:\$i]:\$false))).
thf(def_unord_pair,definition,(unord_pair = (^[X1:\$i]:(^[X2:\$i]:(^[X3:\$i]:((~((X3 = X1))) => (X3 = X2))))))).
thf(def_singleton,definition,(singleton = (^[X1:\$i]:(^[X2:\$i]:(X2 = X1))))).
thf(def_union,definition,(union = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
thf(def_excl_union,definition,(excl_union = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))).
thf(def_intersection,definition,(intersection = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_setminus,definition,(setminus = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(~(((X1 @ X3) => (X2 @ X3))))))))).
thf(def_complement,definition,(complement = (^[X1:\$i>\$o]:(^[X2:\$i]:(~((X1 @ X2))))))).
thf(def_disjoint,definition,(disjoint = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(((intersection @ X1) @ X2) = emptyset))))).
thf(def_subset,definition,(subset = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(![X3:\$i]:((X1 @ X3) => (X2 @ X3))))))).
thf(def_meets,definition,(meets = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(~((![X3:\$i]:((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_misses,definition,(misses = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(![X3:\$i]:((X1 @ X3) => (~((X2 @ X3))))))))).
thf(thm,conjecture,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:((~(((![X3:\$i]:((eigen__0 @ X3) => (X2 @ X3))) => (~((![X3:\$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:\$i]:(((~((eigen__0 @ X3))) => (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:\$i>\$o]:((~(((![X2:\$i]:((eigen__0 @ X2) => (X1 @ X2))) => (~((![X2:\$i]:((eigen__1 @ X2) => (X1 @ X2)))))))) => (![X2:\$i]:(((~((eigen__0 @ X2))) => (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~(((~((sP7 => (~(sP5))))) => (![X1:\$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,(~((sP7 => (~(sP5))))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:\$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,sP7,introduced(assumption,[])).
thf(h7,assumption,sP5,introduced(assumption,[])).
thf(h8,assumption,(~((((~(sP1)) => sP3) => sP6))),introduced(assumption,[])).
thf(h9,assumption,((~(sP1)) => sP3),introduced(assumption,[])).
thf(h10,assumption,(~(sP6)),introduced(assumption,[])).
thf(h11,assumption,sP1,introduced(assumption,[])).
thf(h12,assumption,sP3,introduced(assumption,[])).
thf(1,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])).
thf(2,plain,((~(sP2) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(3,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,h6,h11,h10])).
thf(4,plain,(~(sP5) | sP4),inference(all_rule,[status(thm)],[])).
thf(5,plain,((~(sP4) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(6,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[4,5,h7,h12,h10])).
thf(7,plain,\$false,inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,3,6,h11,h12])).
thf(8,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10])).
thf(9,plain,\$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,8,h8])).
thf(10,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,9,h6,h7])).
thf(11,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5])).
thf(12,plain,\$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3])).
thf(13,plain,\$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])).
thf(14,plain,\$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])).
thf(0,theorem,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])).
% SZS output end Proof
```

## Satallax 3.5

Michael Färber
Inria, LSV, ENS Paris-Saclay, France

### Sample solution for SET014^4

```% SZS output start Proof
thf(ty_eigen__2, type, eigen__2 : (\$i>\$o)).
thf(ty_eigen__1, type, eigen__1 : (\$i>\$o)).
thf(ty_eigen__0, type, eigen__0 : (\$i>\$o)).
thf(ty_eigen__3, type, eigen__3 : \$i).
thf(sP1,plain,sP1 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
thf(sP2,plain,sP2 <=> (sP1 => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP2])])).
thf(sP3,plain,sP3 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
thf(sP4,plain,sP4 <=> (sP3 => (eigen__2 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP4])])).
thf(sP5,plain,sP5 <=> (![X1:\$i]:((eigen__1 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP5])])).
thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP6])])).
thf(sP7,plain,sP7 <=> (![X1:\$i]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
thf(def_in,definition,(in = (^[X1:\$i]:(^[X2:\$i>\$o]:(X2 @ X1))))).
thf(def_is_a,definition,(is_a = (^[X1:\$i]:(^[X2:\$i>\$o]:(X2 @ X1))))).
thf(def_emptyset,definition,(emptyset = (^[X1:\$i]:\$false))).
thf(def_unord_pair,definition,(unord_pair = (^[X1:\$i]:(^[X2:\$i]:(^[X3:\$i]:((~((X3 = X1))) => (X3 = X2))))))).
thf(def_singleton,definition,(singleton = (^[X1:\$i]:(^[X2:\$i]:(X2 = X1))))).
thf(def_union,definition,(union = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
thf(def_excl_union,definition,(excl_union = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))).
thf(def_intersection,definition,(intersection = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_setminus,definition,(setminus = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(^[X3:\$i]:(~(((X1 @ X3) => (X2 @ X3))))))))).
thf(def_complement,definition,(complement = (^[X1:\$i>\$o]:(^[X2:\$i]:(~((X1 @ X2))))))).
thf(def_disjoint,definition,(disjoint = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(((intersection @ X1) @ X2) = emptyset))))).
thf(def_subset,definition,(subset = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(![X3:\$i]:((X1 @ X3) => (X2 @ X3))))))).
thf(def_meets,definition,(meets = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(~((![X3:\$i]:((X1 @ X3) => (~((X2 @ X3))))))))))).
thf(def_misses,definition,(misses = (^[X1:\$i>\$o]:(^[X2:\$i>\$o]:(![X3:\$i]:((X1 @ X3) => (~((X2 @ X3))))))))).
thf(thm,conjecture,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4)))))))).
thf(h0,negated_conjecture,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))))),inference(assume_negation,[status(cth)],[thm])).
thf(h1,assumption,(~((![X1:\$i>\$o]:(![X2:\$i>\$o]:((~(((![X3:\$i]:((eigen__0 @ X3) => (X2 @ X3))) => (~((![X3:\$i]:((X1 @ X3) => (X2 @ X3)))))))) => (![X3:\$i]:(((~((eigen__0 @ X3))) => (X1 @ X3)) => (X2 @ X3)))))))),introduced(assumption,[])).
thf(h2,assumption,(~((![X1:\$i>\$o]:((~(((![X2:\$i]:((eigen__0 @ X2) => (X1 @ X2))) => (~((![X2:\$i]:((eigen__1 @ X2) => (X1 @ X2)))))))) => (![X2:\$i]:(((~((eigen__0 @ X2))) => (eigen__1 @ X2)) => (X1 @ X2))))))),introduced(assumption,[])).
thf(h3,assumption,(~(((~((sP7 => (~(sP5))))) => (![X1:\$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1)))))),introduced(assumption,[])).
thf(h4,assumption,(~((sP7 => (~(sP5))))),introduced(assumption,[])).
thf(h5,assumption,(~((![X1:\$i]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (eigen__2 @ X1))))),introduced(assumption,[])).
thf(h6,assumption,sP7,introduced(assumption,[])).
thf(h7,assumption,sP5,introduced(assumption,[])).
thf(h8,assumption,(~((((~(sP1)) => sP3) => sP6))),introduced(assumption,[])).
thf(h9,assumption,((~(sP1)) => sP3),introduced(assumption,[])).
thf(h10,assumption,(~(sP6)),introduced(assumption,[])).
thf(h11,assumption,sP1,introduced(assumption,[])).
thf(h12,assumption,sP3,introduced(assumption,[])).
thf(1,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])).
thf(2,plain,((~(sP2) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(3,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,h6,h11,h10])).
thf(4,plain,(~(sP5) | sP4),inference(all_rule,[status(thm)],[])).
thf(5,plain,((~(sP4) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(6,plain,\$false,inference(prop_unsat,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[4,5,h7,h12,h10])).
thf(7,plain,\$false,inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,3,6,h11,h12])).
thf(8,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10])).
thf(9,plain,\$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,8,h8])).
thf(10,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,9,h6,h7])).
thf(11,plain,\$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5])).
thf(12,plain,\$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3])).
thf(13,plain,\$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])).
thf(14,plain,\$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])).
thf(0,theorem,(![X1:\$i>\$o]:(![X2:\$i>\$o]:(![X3:\$i>\$o]:((~(((![X4:\$i]:((X1 @ X4) => (X3 @ X4))) => (~((![X4:\$i]:((X2 @ X4) => (X3 @ X4)))))))) => (![X4:\$i]:(((~((X1 @ X4))) => (X2 @ X4)) => (X3 @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])).
% SZS output end Proof
```

## Twee 2.2.1

Nick Smallbone
Chalmers University of Technology, Sweden

### Sample proof for SEU140+2

```% SZS output start Proof
Take the following subset of the input axioms:
fof(commutativity_k3_xboole_0, axiom, ![A, B]: set_intersection2(A, B)=set_intersection2(B, A)).
fof(d10_xboole_0, axiom, ![A, B]: (A=B <=> (subset(A, B) & subset(B, A)))).
fof(d7_xboole_0, axiom, ![A, B]: (disjoint(A, B) <=> set_intersection2(A, B)=empty_set)).
fof(symmetry_r1_xboole_0, axiom, ![A, B]: (disjoint(A, B) => disjoint(B, A))).
fof(t26_xboole_1, lemma, ![A, B, C]: (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C)))).
fof(t2_xboole_1, lemma, ![A]: subset(empty_set, A)).
fof(t63_xboole_1, conjecture, ![A, B, C]: ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))).

Now clausify the problem and encode Horn clauses using encoding 3 of
http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
We repeatedly replace C & s=t => u=v by the two clauses:
fresh(y, y, x1...xn) = u
C => fresh(s, t, x1...xn) = v
where fresh is a fresh function symbol and x1..xn are the free
variables of u and v.
A predicate p(X) is encoded as p(X)=true (this is sound, because the
input problem has no model of domain size 1).

The encoding turns the above axioms into the following unit equations and goals:

Axiom 1 (d10_xboole_0_1): fresh12(X, X, Y, Z) = Y.
Axiom 2 (d10_xboole_0_1): fresh11(X, X, Y, Z) = Z.
Axiom 3 (d7_xboole_0): fresh32(X, X, Y, Z) = true2.
Axiom 4 (d7_xboole_0_1): fresh31(X, X, Y, Z) = empty_set.
Axiom 5 (symmetry_r1_xboole_0): fresh25(X, X, Y, Z) = true2.
Axiom 6 (t26_xboole_1): fresh20(X, X, Y, Z, W) = true2.
Axiom 7 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
Axiom 8 (d10_xboole_0_1): fresh12(subset(X, Y), true2, Y, X) = fresh11(subset(Y, X), true2, Y, X).
Axiom 9 (d7_xboole_0_1): fresh31(disjoint(X, Y), true2, X, Y) = set_intersection2(X, Y).
Axiom 10 (d7_xboole_0): fresh32(set_intersection2(X, Y), empty_set, X, Y) = disjoint(X, Y).
Axiom 11 (symmetry_r1_xboole_0): fresh25(disjoint(X, Y), true2, X, Y) = disjoint(Y, X).
Axiom 12 (t26_xboole_1): fresh20(subset(X, Y), true2, X, Y, Z) = subset(set_intersection2(X, Z), set_intersection2(Y, Z)).
Axiom 13 (t2_xboole_1): subset(empty_set, X) = true2.
Axiom 14 (t63_xboole_1): subset(sK1_t63_xboole_1_A, sK3_t63_xboole_1_B) = true2.
Axiom 15 (t63_xboole_1_1): disjoint(sK3_t63_xboole_1_B, sK2_t63_xboole_1_C) = true2.

Goal 1 (t63_xboole_1_2): disjoint(sK1_t63_xboole_1_A, sK2_t63_xboole_1_C) = true2.
Proof:
disjoint(sK1_t63_xboole_1_A, sK2_t63_xboole_1_C)
= { by axiom 11 (symmetry_r1_xboole_0) }
fresh25(disjoint(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 10 (d7_xboole_0) }
fresh25(fresh32(set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 1 (d10_xboole_0_1) }
fresh25(fresh32(fresh12(true2, true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 13 (t2_xboole_1) }
fresh25(fresh32(fresh12(subset(empty_set, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 8 (d10_xboole_0_1) }
fresh25(fresh32(fresh11(subset(set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 7 (commutativity_k3_xboole_0) }
fresh25(fresh32(fresh11(subset(set_intersection2(sK1_t63_xboole_1_A, sK2_t63_xboole_1_C), empty_set), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 4 (d7_xboole_0_1) }
fresh25(fresh32(fresh11(subset(set_intersection2(sK1_t63_xboole_1_A, sK2_t63_xboole_1_C), fresh31(true2, true2, sK3_t63_xboole_1_B, sK2_t63_xboole_1_C)), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 15 (t63_xboole_1_1) }
fresh25(fresh32(fresh11(subset(set_intersection2(sK1_t63_xboole_1_A, sK2_t63_xboole_1_C), fresh31(disjoint(sK3_t63_xboole_1_B, sK2_t63_xboole_1_C), true2, sK3_t63_xboole_1_B, sK2_t63_xboole_1_C)), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 9 (d7_xboole_0_1) }
fresh25(fresh32(fresh11(subset(set_intersection2(sK1_t63_xboole_1_A, sK2_t63_xboole_1_C), set_intersection2(sK3_t63_xboole_1_B, sK2_t63_xboole_1_C)), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 12 (t26_xboole_1) }
fresh25(fresh32(fresh11(fresh20(subset(sK1_t63_xboole_1_A, sK3_t63_xboole_1_B), true2, sK1_t63_xboole_1_A, sK3_t63_xboole_1_B, sK2_t63_xboole_1_C), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 14 (t63_xboole_1) }
fresh25(fresh32(fresh11(fresh20(true2, true2, sK1_t63_xboole_1_A, sK3_t63_xboole_1_B, sK2_t63_xboole_1_C), true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 6 (t26_xboole_1) }
fresh25(fresh32(fresh11(true2, true2, set_intersection2(sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), empty_set), empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 2 (d10_xboole_0_1) }
fresh25(fresh32(empty_set, empty_set, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A), true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 3 (d7_xboole_0) }
fresh25(true2, true2, sK2_t63_xboole_1_C, sK1_t63_xboole_1_A)
= { by axiom 5 (symmetry_r1_xboole_0) }
true2
% SZS output end Proof
```

### Sample proof for BOO001-1

```% SZS output start CNFRefutation
cnf(c1, negated_conjecture, inverse(inverse(a))!=a, file('BOO001-1.p', prove_inverse_is_self_cancelling)).
fof(c2, axiom, ![X2, Y2]: multiply(X2, Y2, inverse(Y2))=X2, file('BOO001-1.p', skolemised)).
cnf(c3, plain, multiply(X, Y, inverse(Y))=X, inference(clausify, [status(thm)], [c2])).
cnf(c4, plain, multiply(a, inverse(a), inverse(inverse(a)))=a, inference(rw, [status(thm)], [c3])).
cnf(c5, plain, multiply(a, inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))=a, inference(rw, [status(thm)], [c4, c3])).
fof(c6, axiom, ![X2, Y2]: multiply(Y2, X2, X2)=X2, file('BOO001-1.p', skolemised)).
cnf(c7, plain, multiply(Y2, X2, X2)=X2, inference(clausify, [status(thm)], [c6])).
cnf(c8, plain, multiply(multiply(inverse(inverse(a)), a, a), inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))=a, inference(rw, [status(thm)], [c5, c7])).
fof(c9, axiom, ![X2, Y2, V2, W2, Z2]: multiply(multiply(V2, W2, X2), Y2, multiply(V2, W2, Z2))=multiply(V2, W2, multiply(X2, Y2, Z2)), file('BOO001-1.p', skolemised)).
cnf(c10, plain, multiply(multiply(V, W, X2), Y2, multiply(V, W, Z))=multiply(V, W, multiply(X2, Y2, Z)), inference(clausify, [status(thm)], [c9])).
cnf(c11, plain, multiply(inverse(inverse(a)), a, multiply(a, inverse(a), inverse(a)))=a, inference(rw, [status(thm)], [c8, c10])).
cnf(c12, plain, multiply(inverse(inverse(a)), a, inverse(a))=a, inference(rw, [status(thm)], [c11, c7])).
cnf(c13, plain, inverse(inverse(a))=a, inference(rw, [status(thm)], [c12, c3])).
cnf(c14, plain, \$false, inference(resolution, [status(thm)], [c1, c13])).
% SZS output end CNFRefutation
```

## Vampire 4.4

Giles Reger
University of Manchester, United Kingdom

### Sample proof for DAT013=1

```% SZS output start Proof for DAT013=1
tff(type_def_5, type, array: \$tType).
tff(func_def_0, type, read: (array * \$int) > \$int).
tff(func_def_1, type, write: (array * \$int * \$int) > array).
tff(func_def_5, type, sK0: array).
tff(func_def_6, type, sK1: \$int).
tff(func_def_7, type, sK2: \$int).
tff(func_def_8, type, sK3: \$int).
tff(f3,conjecture,(
! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/DAT/DAT013=1.p',co1)).
tff(f4,negated_conjecture,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
inference(negated_conjecture,[],[f3])).
tff(f5,plain,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((~\$less(X2,X3) & ~\$less(X3,X1)) => \$less(0,read(X0,X3))) => ! [X4 : \$int] : ((~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) => \$less(0,read(X0,X4))))),
inference(evaluation,[],[f4])).
tff(f7,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & (~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3)))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | (\$less(X2,X3) | \$less(X3,X1))))),
inference(ennf_transformation,[],[f5])).
tff(f8,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & ~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | \$less(X2,X3) | \$less(X3,X1)))),
inference(flattening,[],[f7])).
tff(f9,plain,(
~\$less(sK3,\$sum(sK1,3))),
inference(cnf_transformation,[],[f8])).
tff(f10,plain,(
~\$less(sK2,sK3)),
inference(cnf_transformation,[],[f8])).
tff(f11,plain,(
inference(cnf_transformation,[],[f8])).
tff(f12,plain,(
( ! [X3:\$int] : (\$less(0,read(sK0,X3)) | \$less(sK2,X3) | \$less(X3,sK1)) )),
inference(cnf_transformation,[],[f8])).
tff(f19,plain,(
introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
tff(f20,plain,(
inference(avatar_component_clause,[],[f19])).
tff(f21,plain,(
~spl4_1),
inference(avatar_split_clause,[],[f11,f19])).
tff(f23,plain,(
spl4_2 <=> \$less(sK2,sK3)),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
tff(f26,plain,(
spl4_3 <=> ~\$less(sK2,sK3)),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])])).
tff(f28,plain,(
~spl4_3),
inference(avatar_split_clause,[],[f10,f26])).
tff(f33,plain,(
spl4_5 <=> ~\$less(sK3,\$sum(sK1,3))),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])])).
tff(f35,plain,(
~spl4_5),
inference(avatar_split_clause,[],[f9,f33])).
tff(f36,plain,(
\$less(sK2,sK3) | \$less(sK3,sK1) | ~spl4_1),
inference(resolution,[],[f12,f20])).
tff(f41,plain,(
spl4_6 <=> \$less(sK3,sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])])).
tff(f43,plain,(
spl4_6 | spl4_2 | spl4_1),
inference(avatar_split_clause,[],[f36,f19,f23,f41])).
tff(f44,plain,(
\$false),
inference(avatar_sat_refutation,[],[f21,f28,f35,f43])).
% SZS output end Proof for DAT013=1
```

### Sample proof for SEU140+2

```% SZS output start Proof for SEU140+2
fof(f3,axiom,(
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',commutativity_k2_xboole_0)).
fof(f4,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',commutativity_k3_xboole_0)).
fof(f5,axiom,(
! [X0,X1] : (X0 = X1 <=> (subset(X1,X0) & subset(X0,X1)))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',d10_xboole_0)).
fof(f10,axiom,(
! [X0,X1,X2] : (set_difference(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (~in(X3,X1) & in(X3,X0))))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',d4_xboole_0)).
fof(f11,axiom,(
! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',d7_xboole_0)).
fof(f28,axiom,(
! [X0,X1] : (subset(X0,X1) => set_union2(X0,X1) = X1)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t12_xboole_1)).
fof(f39,axiom,(
! [X0,X1] : subset(set_difference(X0,X1),X0)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t36_xboole_1)).
fof(f40,axiom,(
! [X0,X1] : (empty_set = set_difference(X0,X1) <=> subset(X0,X1))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t37_xboole_1)).
fof(f41,axiom,(
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t39_xboole_1)).
fof(f42,axiom,(
! [X0] : set_difference(X0,empty_set) = X0),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t3_boole)).
fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f45,axiom,(
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t40_xboole_1)).
fof(f47,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t48_xboole_1)).
fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f55,axiom,(
! [X0,X1] : subset(X0,set_union2(X0,X1))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SEU/SEU140+2.p',t7_xboole_1)).
fof(f59,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f65,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).
fof(f66,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f65])).
fof(f69,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f59])).
fof(f71,plain,(
! [X0,X1] : (set_union2(X0,X1) = X1 | ~subset(X0,X1))),
inference(ennf_transformation,[],[f28])).
fof(f94,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK0,sK2) & disjoint(sK1,sK2) & subset(sK0,sK1))),
introduced(choice_axiom,[])).
fof(f95,plain,(
~disjoint(sK0,sK2) & disjoint(sK1,sK2) & subset(sK0,sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f66,f94])).
fof(f98,plain,(
! [X1,X0] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK4(X0,X1),X1) & in(sK4(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f99,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK4(X0,X1),X1) & in(sK4(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f69,f98])).
fof(f100,plain,(
! [X0,X1] : ((empty_set = set_difference(X0,X1) | ~subset(X0,X1)) & (subset(X0,X1) | empty_set != set_difference(X0,X1)))),
inference(nnf_transformation,[],[f40])).
fof(f109,plain,(
! [X0,X1] : ((X0 = X1 | (~subset(X1,X0) | ~subset(X0,X1))) & ((subset(X1,X0) & subset(X0,X1)) | X0 != X1))),
inference(nnf_transformation,[],[f5])).
fof(f110,plain,(
! [X0,X1] : ((X0 = X1 | ~subset(X1,X0) | ~subset(X0,X1)) & ((subset(X1,X0) & subset(X0,X1)) | X0 != X1))),
inference(flattening,[],[f109])).
fof(f111,plain,(
! [X0,X1] : ((disjoint(X0,X1) | set_intersection2(X0,X1) != empty_set) & (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)))),
inference(nnf_transformation,[],[f11])).
fof(f116,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : (((in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (in(X3,X1) | ~in(X3,X0))) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(nnf_transformation,[],[f10])).
fof(f117,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | in(X3,X1) | ~in(X3,X0)) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(flattening,[],[f116])).
fof(f118,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(rectify,[],[f117])).
fof(f119,plain,(
! [X2,X1,X0] : (? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((in(sK8(X0,X1,X2),X1) | ~in(sK8(X0,X1,X2),X0) | ~in(sK8(X0,X1,X2),X2)) & ((~in(sK8(X0,X1,X2),X1) & in(sK8(X0,X1,X2),X0)) | in(sK8(X0,X1,X2),X2))))),
introduced(choice_axiom,[])).
fof(f120,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ((in(sK8(X0,X1,X2),X1) | ~in(sK8(X0,X1,X2),X0) | ~in(sK8(X0,X1,X2),X2)) & ((~in(sK8(X0,X1,X2),X1) & in(sK8(X0,X1,X2),X0)) | in(sK8(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f118,f119])).
fof(f135,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f95])).
fof(f136,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f95])).
fof(f137,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f95])).
fof(f140,plain,(
( ! [X0,X1] : (subset(X0,set_union2(X0,X1))) )),
inference(cnf_transformation,[],[f55])).
fof(f142,plain,(
( ! [X0,X1] : (subset(set_difference(X0,X1),X0)) )),
inference(cnf_transformation,[],[f39])).
fof(f143,plain,(
( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))) )),
inference(cnf_transformation,[],[f41])).
fof(f144,plain,(
( ! [X0,X1] : (set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)) )),
inference(cnf_transformation,[],[f45])).
fof(f145,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
inference(cnf_transformation,[],[f47])).
fof(f148,plain,(
( ! [X0,X1] : (in(sK4(X0,X1),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f99])).
fof(f149,plain,(
( ! [X0,X1] : (in(sK4(X0,X1),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f99])).
fof(f152,plain,(
( ! [X0,X1] : (~subset(X0,X1) | set_union2(X0,X1) = X1) )),
inference(cnf_transformation,[],[f71])).
fof(f155,plain,(
( ! [X0,X1] : (~subset(X0,X1) | empty_set = set_difference(X0,X1)) )),
inference(cnf_transformation,[],[f100])).
fof(f165,plain,(
( ! [X0] : (set_difference(X0,empty_set) = X0) )),
inference(cnf_transformation,[],[f42])).
fof(f176,plain,(
( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X1,X0)) )),
inference(cnf_transformation,[],[f3])).
fof(f177,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_intersection2(X1,X0)) )),
inference(cnf_transformation,[],[f4])).
fof(f187,plain,(
( ! [X0,X1] : (~subset(X0,X1) | ~subset(X1,X0) | X0 = X1) )),
inference(cnf_transformation,[],[f110])).
fof(f189,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f111])).
fof(f196,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X0) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f120])).
fof(f197,plain,(
( ! [X4,X2,X0,X1] : (~in(X4,X1) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f120])).
fof(f224,plain,(
( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0))) )),
inference(definition_unfolding,[],[f177,f145,f145])).
fof(f226,plain,(
( ! [X0,X1] : (~disjoint(X0,X1) | empty_set = set_difference(X0,set_difference(X0,X1))) )),
inference(definition_unfolding,[],[f189,f145])).
fof(f237,plain,(
( ! [X4,X0,X1] : (~in(X4,X1) | ~in(X4,set_difference(X0,X1))) )),
inference(equality_resolution,[],[f197])).
fof(f238,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,X1)) | in(X4,X0)) )),
inference(equality_resolution,[],[f196])).
fof(f291,plain,(
( ! [X2,X1] : (set_union2(X1,X2) = set_union2(X1,set_union2(X1,X2))) )),
inference(resolution,[],[f152,f140])).
fof(f295,plain,(
set_union2(sK0,sK1) = sK1),
inference(resolution,[],[f152,f135])).
fof(f316,plain,(
( ! [X2,X1] : (empty_set = set_difference(X1,set_union2(X1,X2))) )),
inference(resolution,[],[f155,f140])).
fof(f333,plain,(
( ! [X10,X8,X9] : (~in(sK4(X8,X9),set_difference(X10,X9)) | disjoint(X8,X9)) )),
inference(resolution,[],[f237,f149])).
fof(f343,plain,(
( ! [X4,X2,X3] : (in(sK4(set_difference(X2,X3),X4),X2) | disjoint(set_difference(X2,X3),X4)) )),
inference(resolution,[],[f238,f148])).
fof(f371,plain,(
( ! [X2,X1] : (set_difference(X1,X2) = set_difference(set_union2(X2,X1),X2)) )),
inference(superposition,[],[f144,f176])).
fof(f373,plain,(
( ! [X6,X7] : (set_difference(X6,set_difference(X7,X6)) = set_difference(set_union2(X6,X7),set_difference(X7,X6))) )),
inference(superposition,[],[f144,f143])).
fof(f561,plain,(
( ! [X12,X11] : (subset(set_difference(X12,set_difference(X12,X11)),X11)) )),
inference(superposition,[],[f142,f224])).
fof(f1382,plain,(
spl13_24 <=> set_difference(sK1,sK2) = sK1),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])])).
fof(f1383,plain,(
set_difference(sK1,sK2) = sK1 | ~spl13_24),
inference(avatar_component_clause,[],[f1382])).
fof(f1905,plain,(
empty_set = set_difference(sK1,set_difference(sK1,sK2))),
inference(resolution,[],[f136,f226])).
fof(f1956,plain,(
subset(set_difference(sK1,empty_set),set_difference(sK1,sK2))),
inference(superposition,[],[f561,f1905])).
fof(f1963,plain,(
subset(sK1,set_difference(sK1,sK2))),
inference(forward_demodulation,[],[f1956,f165])).
fof(f1989,plain,(
~subset(set_difference(sK1,sK2),sK1) | set_difference(sK1,sK2) = sK1),
inference(resolution,[],[f1963,f187])).
fof(f1996,plain,(
set_difference(sK1,sK2) = sK1),
inference(subsumption_resolution,[],[f1989,f142])).
fof(f1997,plain,(
spl13_24),
inference(avatar_split_clause,[],[f1996,f1382])).
fof(f2849,plain,(
( ! [X2,X0,X1] : (disjoint(set_difference(set_difference(X0,X1),X2),X1) | disjoint(set_difference(set_difference(X0,X1),X2),X1)) )),
inference(resolution,[],[f343,f333])).
fof(f2875,plain,(
( ! [X2,X0,X1] : (disjoint(set_difference(set_difference(X0,X1),X2),X1)) )),
inference(duplicate_literal_removal,[],[f2849])).
fof(f3339,plain,(
( ! [X6,X5] : (set_difference(X5,set_difference(set_union2(X5,X6),X5)) = set_difference(set_union2(X5,X6),set_difference(set_union2(X5,X6),X5))) )),
inference(superposition,[],[f373,f291])).
fof(f3392,plain,(
( ! [X6,X5] : (set_difference(X5,set_difference(X5,set_union2(X5,X6))) = set_difference(X5,set_difference(set_union2(X5,X6),X5))) )),
inference(forward_demodulation,[],[f3339,f224])).
fof(f3393,plain,(
( ! [X6,X5] : (set_difference(X5,set_difference(X6,X5)) = set_difference(X5,set_difference(X5,set_union2(X5,X6)))) )),
inference(forward_demodulation,[],[f3392,f371])).
fof(f3394,plain,(
( ! [X6,X5] : (set_difference(X5,empty_set) = set_difference(X5,set_difference(X6,X5))) )),
inference(forward_demodulation,[],[f3393,f316])).
fof(f3395,plain,(
( ! [X6,X5] : (set_difference(X5,set_difference(X6,X5)) = X5) )),
inference(forward_demodulation,[],[f3394,f165])).
fof(f8484,plain,(
( ! [X35] : (disjoint(set_difference(sK1,X35),sK2)) ) | ~spl13_24),
inference(superposition,[],[f2875,f1383])).
fof(f8869,plain,(
( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X7,X6)) = X6) )),
inference(backward_demodulation,[],[f3395,f373])).
fof(f9076,plain,(
set_difference(sK1,set_difference(sK1,sK0)) = sK0),
inference(superposition,[],[f8869,f295])).
fof(f9268,plain,(
disjoint(sK0,sK2) | ~spl13_24),
inference(superposition,[],[f8484,f9076])).
fof(f9375,plain,(
\$false | ~spl13_24),
inference(subsumption_resolution,[],[f9268,f137])).
fof(f9376,plain,(
~spl13_24),
fof(f9532,plain,(
\$false),
inference(avatar_sat_refutation,[],[f1997,f9376])).
% SZS output end Proof for SEU140+2
```

### Sample proof for NLP042+1

```% # SZS output start Saturation.
tff(u313,negated_conjecture,
~woman(sK0,sK3)).

tff(u312,negated_conjecture,
~woman(sK0,sK4)).

tff(u311,negated_conjecture,
~woman(sK0,sK2)).

tff(u310,axiom,
(![X1, X0] : ((~woman(X0,X1) | ~forename(X0,X1))))).

tff(u309,axiom,
(![X1, X0] : ((~woman(X0,X1) | ~unisex(X0,X1))))).

tff(u308,negated_conjecture,
woman(sK0,sK1)).

tff(u307,axiom,
(![X1, X0] : ((~female(X0,X1) | ~unisex(X0,X1))))).

tff(u306,axiom,
(![X1, X0] : ((female(X0,X1) | ~woman(X0,X1))))).

tff(u305,negated_conjecture,
~human_person(sK0,sK3)).

tff(u304,negated_conjecture,
~human_person(sK0,sK4)).

tff(u303,negated_conjecture,
~human_person(sK0,sK2)).

tff(u302,axiom,
(![X1, X0] : ((~human_person(X0,X1) | ~forename(X0,X1))))).

tff(u301,axiom,
(![X1, X0] : ((human_person(X0,X1) | ~woman(X0,X1))))).

tff(u300,negated_conjecture,
~animate(sK0,sK3)).

tff(u299,axiom,
(![X1, X0] : ((animate(X0,X1) | ~human_person(X0,X1))))).

tff(u298,axiom,
(![X1, X0] : ((~human(X0,X1) | ~forename(X0,X1))))).

tff(u297,axiom,
(![X1, X0] : ((human(X0,X1) | ~human_person(X0,X1))))).

tff(u296,negated_conjecture,
~organism(sK0,sK3)).

tff(u295,negated_conjecture,
~organism(sK0,sK4)).

tff(u294,negated_conjecture,
~organism(sK0,sK2)).

tff(u293,axiom,
(![X1, X0] : ((organism(X0,X1) | ~human_person(X0,X1))))).

tff(u292,negated_conjecture,
~living(sK0,sK3)).

tff(u291,axiom,
(![X1, X0] : ((living(X0,X1) | ~organism(X0,X1))))).

tff(u290,negated_conjecture,
~entity(sK0,sK4)).

tff(u289,negated_conjecture,
~entity(sK0,sK2)).

tff(u288,axiom,
(![X1, X0] : ((entity(X0,X1) | ~organism(X0,X1))))).

tff(u287,negated_conjecture,
entity(sK0,sK3)).

tff(u286,negated_conjecture,
((~entity(sK0,sK1)) | entity(sK0,sK1))).

tff(u285,axiom,
(![X1, X0] : ((~mia_forename(X0,X1) | ~entity(X0,X1))))).

tff(u284,negated_conjecture,
~mia_forename(sK0,sK1)).

tff(u283,negated_conjecture,
~mia_forename(sK0,sK4)).

tff(u282,negated_conjecture,
mia_forename(sK0,sK2)).

tff(u281,negated_conjecture,
~forename(sK0,sK1)).

tff(u280,negated_conjecture,
~forename(sK0,sK4)).

tff(u279,axiom,
(![X1, X0] : ((~forename(X0,X1) | ~entity(X0,X1))))).

tff(u278,negated_conjecture,
forename(sK0,sK2)).

tff(u277,axiom,
(![X1, X0] : ((forename(X0,X1) | ~mia_forename(X0,X1))))).

tff(u276,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | ~entity(X0,X1))))).

tff(u275,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1))))).

tff(u274,negated_conjecture,
~abstraction(sK0,sK1)).

tff(u273,negated_conjecture,
~abstraction(sK0,sK4)).

tff(u272,axiom,
(![X1, X0] : ((abstraction(X0,X1) | ~forename(X0,X1))))).

tff(u271,negated_conjecture,
~unisex(sK0,sK1)).

tff(u270,axiom,
(![X1, X0] : ((unisex(X0,X1) | ~abstraction(X0,X1))))).

tff(u269,negated_conjecture,
unisex(sK0,sK3)).

tff(u268,negated_conjecture,
unisex(sK0,sK4)).

tff(u267,axiom,
(![X1, X0] : ((~general(X0,X1) | ~entity(X0,X1))))).

tff(u266,negated_conjecture,
~general(sK0,sK4)).

tff(u265,axiom,
(![X1, X0] : ((general(X0,X1) | ~abstraction(X0,X1))))).

tff(u264,axiom,
(![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1))))).

tff(u263,axiom,
(![X1, X0] : ((nonhuman(X0,X1) | ~forename(X0,X1))))).

tff(u262,axiom,
(![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1))))).

tff(u261,axiom,
(![X1, X0] : ((relation(X0,X1) | ~forename(X0,X1))))).

tff(u260,axiom,
(![X1, X0] : ((~relname(X0,X1) | relation(X0,X1))))).

tff(u259,axiom,
(![X1, X0] : ((relname(X0,X1) | ~forename(X0,X1))))).

tff(u258,axiom,
(![X1, X0] : ((~object(X0,X1) | unisex(X0,X1))))).

tff(u257,axiom,
(![X1, X0] : ((~object(X0,X1) | entity(X0,X1))))).

tff(u256,axiom,
(![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1))))).

tff(u255,negated_conjecture,
object(sK0,sK3)).

tff(u254,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1))))).

tff(u253,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1))))).

tff(u252,negated_conjecture,
nonliving(sK0,sK3)).

tff(u251,negated_conjecture,
~existent(sK0,sK4)).

tff(u250,axiom,
(![X1, X0] : ((existent(X0,X1) | ~entity(X0,X1))))).

tff(u249,axiom,
(![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1))))).

tff(u248,axiom,
(![X1, X0] : ((specific(X0,X1) | ~entity(X0,X1))))).

tff(u247,negated_conjecture,
specific(sK0,sK4)).

tff(u246,axiom,
(![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1))))).

tff(u245,negated_conjecture,
substance_matter(sK0,sK3)).

tff(u244,axiom,
(![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1))))).

tff(u243,negated_conjecture,
food(sK0,sK3)).

tff(u242,axiom,
(![X1, X0] : ((~beverage(X0,X1) | food(X0,X1))))).

tff(u241,negated_conjecture,
beverage(sK0,sK3)).

tff(u240,axiom,
(![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1))))).

tff(u239,negated_conjecture,
shake_beverage(sK0,sK3)).

tff(u238,axiom,
(![X1, X0] : ((~order(X0,X1) | eventuality(X0,X1))))).

tff(u237,negated_conjecture,
order(sK0,sK4)).

tff(u236,axiom,
(![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1))))).

tff(u235,negated_conjecture,
event(sK0,sK4)).

tff(u234,axiom,
(![X1, X0] : ((event(X0,X1) | ~order(X0,X1))))).

tff(u233,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1))))).

tff(u232,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1))))).

tff(u231,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1))))).

tff(u230,negated_conjecture,
eventuality(sK0,sK4)).

tff(u229,axiom,
(![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1))))).

tff(u228,negated_conjecture,
nonexistent(sK0,sK4)).

tff(u227,axiom,
(![X1, X0] : ((~act(X0,X1) | event(X0,X1))))).

tff(u226,axiom,
(![X1, X0] : ((act(X0,X1) | ~order(X0,X1))))).

tff(u225,axiom,
(![X1, X3, X0, X2] : ((~of(X0,X2,X1) | (X2 = X3) | ~forename(X0,X3) | ~of(X0,X3,X1) | ~forename(X0,X2) | ~entity(X0,X1))))).

tff(u224,negated_conjecture,
((~(![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0))))) | (![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0)))))).

tff(u223,negated_conjecture,
of(sK0,sK2,sK1)).

tff(u222,axiom,
(![X1, X3, X0] : ((~nonreflexive(X0,X1) | ~agent(X0,X1,X3) | ~patient(X0,X1,X3))))).

tff(u221,negated_conjecture,
nonreflexive(sK0,sK4)).

tff(u220,negated_conjecture,
~agent(sK0,sK4,sK3)).

tff(u219,negated_conjecture,
agent(sK0,sK4,sK1)).

tff(u218,negated_conjecture,
(![X0] : ((~patient(sK0,sK4,X0) | ~agent(sK0,sK4,X0))))).

tff(u217,negated_conjecture,
patient(sK0,sK4,sK3)).

% # SZS output end Saturation.
```

### Sample proof for SWV017+1

```% SZS output start FiniteModel for SWV017+1
tff(declare_\$i,type,\$i:\$tType).
tff(declare_\$i1,type,at:\$i).
tff(declare_\$i2,type,an_a_nonce:\$i).
tff(finite_domain,axiom,
! [X:\$i] : (
X = at | X = an_a_nonce
) ).

tff(distinct_domain,axiom,
at != an_a_nonce
).

tff(declare_t,type,t:\$i).
tff(t_definition,axiom,t = at).
tff(declare_a,type,a:\$i).
tff(a_definition,axiom,a = at).
tff(declare_b,type,b:\$i).
tff(b_definition,axiom,b = at).
tff(declare_bt,type,bt:\$i).
tff(bt_definition,axiom,bt = an_a_nonce).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:\$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = an_a_nonce).
tff(declare_key,type,key: \$i * \$i > \$i).
tff(function_key,axiom,
key(at,at) = at
& key(at,an_a_nonce) = at
& key(an_a_nonce,at) = at
& key(an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_pair,type,pair: \$i * \$i > \$i).
tff(function_pair,axiom,
pair(at,at) = at
& pair(at,an_a_nonce) = an_a_nonce
& pair(an_a_nonce,at) = at
& pair(an_a_nonce,an_a_nonce) = at

).

tff(declare_sent,type,sent: \$i * \$i * \$i > \$i).
tff(function_sent,axiom,
sent(at,at,at) = at
& sent(at,at,an_a_nonce) = at
& sent(at,an_a_nonce,at) = at
& sent(at,an_a_nonce,an_a_nonce) = an_a_nonce
& sent(an_a_nonce,at,at) = at
& sent(an_a_nonce,at,an_a_nonce) = at
& sent(an_a_nonce,an_a_nonce,at) = at
& sent(an_a_nonce,an_a_nonce,an_a_nonce) = at

).

).

tff(declare_encrypt,type,encrypt: \$i * \$i > \$i).
tff(function_encrypt,axiom,
encrypt(at,at) = an_a_nonce
& encrypt(at,an_a_nonce) = an_a_nonce
& encrypt(an_a_nonce,at) = at
& encrypt(an_a_nonce,an_a_nonce) = at

).

tff(declare_triple,type,triple: \$i * \$i * \$i > \$i).
tff(function_triple,axiom,
triple(at,at,at) = at
& triple(at,at,an_a_nonce) = an_a_nonce
& triple(at,an_a_nonce,at) = at
& triple(at,an_a_nonce,an_a_nonce) = at
& triple(an_a_nonce,at,at) = at
& triple(an_a_nonce,at,an_a_nonce) = an_a_nonce
& triple(an_a_nonce,an_a_nonce,at) = at
& triple(an_a_nonce,an_a_nonce,an_a_nonce) = an_a_nonce

).

tff(declare_generate_b_nonce,type,generate_b_nonce: \$i > \$i).
tff(function_generate_b_nonce,axiom,
generate_b_nonce(at) = an_a_nonce
& generate_b_nonce(an_a_nonce) = an_a_nonce

).

tff(declare_generate_expiration_time,type,generate_expiration_time: \$i > \$i).
tff(function_generate_expiration_time,axiom,
generate_expiration_time(at) = an_a_nonce
& generate_expiration_time(an_a_nonce) = an_a_nonce

).

tff(declare_generate_key,type,generate_key: \$i > \$i).
tff(function_generate_key,axiom,
generate_key(at) = at
& generate_key(an_a_nonce) = at

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: \$i > \$i).
tff(function_generate_intruder_nonce,axiom,
generate_intruder_nonce(at) = at
& generate_intruder_nonce(an_a_nonce) = an_a_nonce

).

tff(declare_a_holds,type,a_holds: \$i > \$o ).
tff(predicate_a_holds,axiom,
a_holds(at)
& a_holds(an_a_nonce)

).

tff(declare_party_of_protocol,type,party_of_protocol: \$i > \$o ).
tff(predicate_party_of_protocol,axiom,
party_of_protocol(at)
& party_of_protocol(an_a_nonce)

).

tff(declare_message,type,message: \$i > \$o ).
tff(predicate_message,axiom,
message(at)
& message(an_a_nonce)

).

tff(declare_a_stored,type,a_stored: \$i > \$o ).
tff(predicate_a_stored,axiom,
~a_stored(at)
& a_stored(an_a_nonce)

).

tff(declare_b_holds,type,b_holds: \$i > \$o ).
tff(predicate_b_holds,axiom,
b_holds(at)
& b_holds(an_a_nonce)

).

tff(declare_fresh_to_b,type,fresh_to_b: \$i > \$o ).
tff(predicate_fresh_to_b,axiom,
fresh_to_b(at)
& fresh_to_b(an_a_nonce)

).

tff(declare_b_stored,type,b_stored: \$i > \$o ).
tff(predicate_b_stored,axiom,
b_stored(at)
& b_stored(an_a_nonce)

).

tff(declare_a_key,type,a_key: \$i > \$o ).
tff(predicate_a_key,axiom,
a_key(at)
& ~a_key(an_a_nonce)

).

tff(declare_t_holds,type,t_holds: \$i > \$o ).
tff(predicate_t_holds,axiom,
t_holds(at)
& ~t_holds(an_a_nonce)

).

tff(declare_a_nonce,type,a_nonce: \$i > \$o ).
tff(predicate_a_nonce,axiom,
~a_nonce(at)
& a_nonce(an_a_nonce)

).

tff(declare_intruder_message,type,intruder_message: \$i > \$o ).
tff(predicate_intruder_message,axiom,
intruder_message(at)
& intruder_message(an_a_nonce)

).

tff(declare_intruder_holds,type,intruder_holds: \$i > \$o ).
tff(predicate_intruder_holds,axiom,
intruder_holds(at)
& intruder_holds(an_a_nonce)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: \$i > \$o ).
tff(predicate_fresh_intruder_nonce,axiom,
~fresh_intruder_nonce(at)
& fresh_intruder_nonce(an_a_nonce)

).

% SZS output end FiniteModel for SWV017+1
```

## Vampire 4.5

Giles Reger
University of Manchester, United Kingdom

### Sample solution for SET014^4

```% SZS output start Proof for SET014^4
tff(func_def_3, type, ->: ('\$tType' * '\$tType') > '\$tType').
tff(func_def_4, type, in: '\$i' -> ('\$i' -> '\$o') -> '\$o').
tff(func_def_5, type, vAPP: !>[X0: \$ttype, X1: \$ttype]:(X0 -> X1 * X0) > X1).
tff(func_def_6, type, is_a: '\$i' -> ('\$i' -> '\$o') -> '\$o').
tff(func_def_7, type, emptyset: '\$i' -> '\$o').
tff(func_def_8, type, unord_pair: '\$i' -> '\$i' -> '\$i' -> '\$o').
tff(func_def_9, type, singleton: '\$i' -> '\$i' -> '\$o').
tff(func_def_10, type, union: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$i' -> '\$o').
tff(func_def_11, type, excl_union: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$i' -> '\$o').
tff(func_def_12, type, intersection: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$i' -> '\$o').
tff(func_def_13, type, setminus: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$i' -> '\$o').
tff(func_def_14, type, complement: ('\$i' -> '\$o') -> '\$i' -> '\$o').
tff(func_def_15, type, disjoint: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$o').
tff(func_def_16, type, subset: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$o').
tff(func_def_17, type, meets: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$o').
tff(func_def_18, type, misses: ('\$i' -> '\$o') -> ('\$i' -> '\$o') -> '\$o').
tff(func_def_21, type, iCOMB: !>[X2: \$ttype]:X2 -> X2).
tff(func_def_22, type, cCOMB: !>[X0: \$ttype, X1: \$ttype, X2: \$ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2).
tff(func_def_23, type, vEQ: !>[X0: \$ttype]:X0 -> X0 -> '\$o').
tff(func_def_24, type, bCOMB: !>[X0: \$ttype, X1: \$ttype, X2: \$ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
tff(func_def_25, type, vNOT: '\$o' -> '\$o').
tff(func_def_26, type, vAND: '\$o' -> '\$o' -> '\$o').
tff(func_def_27, type, vSIGMA: !>[X0: \$ttype]:(X0 -> '\$o') -> '\$o').
tff(func_def_28, type, sCOMB: !>[X0: \$ttype, X1: \$ttype, X2: \$ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
tff(func_def_29, type, vOR: '\$o' -> '\$o' -> '\$o').
tff(func_def_30, type, kCOMB: !>[X1: \$ttype, X2: \$ttype]:X1 -> X2 -> X1).
tff(func_def_31, type, vIMP: '\$o' -> '\$o' -> '\$o').
tff(func_def_32, type, vPI: !>[X0: \$ttype]:(X0 -> '\$o') -> '\$o').
tff(func_def_33, type, sK0: '\$i' -> '\$o').
tff(func_def_34, type, sK1: '\$i' -> '\$o').
tff(func_def_35, type, sK2: '\$i' -> '\$o').
tff(f6,axiom,(
union = (^[X0 : '\$i' -> '\$o', X2 : '\$i' -> '\$o', X3 : '\$i'] : X2 @ X3 | X0 @ X3)),
file('Problems/SET/SET014^4.p',unknown)).
tff(f12,axiom,(
subset = (^[X0 : '\$i' -> '\$o', X2 : '\$i' -> '\$o'] : ! [X3] : (X0 @ X3 => X2 @ X3))),
file('Problems/SET/SET014^4.p',unknown)).
tff(f15,conjecture,(
! [X0 : '\$i' -> '\$o',X2 : '\$i' -> '\$o',X4 : '\$i' -> '\$o'] : ((subset @ X2 @ X4 & subset @ X0 @ X4) => subset @ (union @ X0 @ X2) @ X4)),
file('Problems/SET/SET014^4.p',unknown)).
tff(f16,negated_conjecture,(
~! [X0 : '\$i' -> '\$o',X2 : '\$i' -> '\$o',X4 : '\$i' -> '\$o'] : ((subset @ X2 @ X4 & subset @ X0 @ X4) => subset @ (union @ X0 @ X2) @ X4)),
inference(negated_conjecture,[],[f15])).
tff(f17,plain,(
~! [X0 : '\$i' -> '\$o',X1 : '\$i' -> '\$o',X2 : '\$i' -> '\$o'] : ((subset @ X1 @ X2 & subset @ X0 @ X2) => subset @ (union @ X0 @ X1) @ X2)),
inference(rectify,[],[f16])).
tff(f18,plain,(
~! [X0 : '\$i' -> '\$o',X1 : '\$i' -> '\$o',X2 : '\$i' -> '\$o'] : (((subset @ X1 @ X2 = \$true) & (subset @ X0 @ X2 = \$true)) => (subset @ (union @ X0 @ X1) @ X2 = \$true))),
inference(fool_elimination,[],[f17])).
tff(f40,plain,(
union = (^[X0 : '\$i' -> '\$o', X1 : '\$i' -> '\$o', X2 : '\$i'] : X1 @ X2 | X0 @ X2)),
inference(rectify,[],[f6])).
tff(f41,plain,(
bCOMB @ sCOMB @ (bCOMB @ vOR) = union),
inference(fool_elimination,[],[f40])).
tff(f42,plain,(
subset = (^[X0 : '\$i' -> '\$o', X1 : '\$i' -> '\$o'] : ! [X2] : (X0 @ X2 => X1 @ X2))),
inference(rectify,[],[f12])).
tff(f43,plain,(
bCOMB @ (bCOMB @ vPI('\$i')) @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) = subset),
inference(fool_elimination,[],[f42])).
tff(f44,plain,(
? [X0 : '\$i' -> '\$o',X1 : '\$i' -> '\$o',X2 : '\$i' -> '\$o'] : ((subset @ (union @ X0 @ X1) @ X2 != \$true) & ((subset @ X1 @ X2 = \$true) & (subset @ X0 @ X2 = \$true)))),
inference(ennf_transformation,[],[f18])).
tff(f45,plain,(
? [X0 : '\$i' -> '\$o',X1 : '\$i' -> '\$o',X2 : '\$i' -> '\$o'] : ((subset @ (union @ X0 @ X1) @ X2 != \$true) & (subset @ X1 @ X2 = \$true) & (subset @ X0 @ X2 = \$true))),
inference(flattening,[],[f44])).
tff(f46,plain,(
? [X0 : '\$i' -> '\$o',X1 : '\$i' -> '\$o',X2 : '\$i' -> '\$o'] : ((subset @ (union @ X0 @ X1) @ X2 != \$true) & (subset @ X1 @ X2 = \$true) & (subset @ X0 @ X2 = \$true)) => ((subset @ (union @ sK0 @ sK1) @ sK2 != \$true) & (subset @ sK1 @ sK2 = \$true) & (subset @ sK0 @ sK2 = \$true))),
introduced(choice_axiom,[])).
tff(f47,plain,(
(subset @ (union @ sK0 @ sK1) @ sK2 != \$true) & (subset @ sK1 @ sK2 = \$true) & (subset @ sK0 @ sK2 = \$true)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f45,f46])).
tff(f48,plain,(
(subset @ sK0 @ sK2 = \$true)),
inference(cnf_transformation,[],[f47])).
tff(f49,plain,(
(subset @ sK1 @ sK2 = \$true)),
inference(cnf_transformation,[],[f47])).
tff(f50,plain,(
(subset @ (union @ sK0 @ sK1) @ sK2 != \$true)),
inference(cnf_transformation,[],[f47])).
tff(f63,plain,(
bCOMB @ sCOMB @ (bCOMB @ vOR) = union),
inference(cnf_transformation,[],[f41])).
tff(f64,plain,(
bCOMB @ (bCOMB @ vPI('\$i')) @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) = subset),
inference(cnf_transformation,[],[f43])).
tff(f66,plain,(
(bCOMB @ (bCOMB @ vPI('\$i')) @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ sCOMB @ (bCOMB @ vOR) @ sK0 @ sK1) @ sK2 != \$true)),
inference(definition_unfolding,[],[f50,f64,f63])).
tff(f67,plain,(
(bCOMB @ (bCOMB @ vPI('\$i')) @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ sK1 @ sK2 = \$true)),
inference(definition_unfolding,[],[f49,f64])).
tff(f68,plain,(
(bCOMB @ (bCOMB @ vPI('\$i')) @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ sK0 @ sK2 = \$true)),
inference(definition_unfolding,[],[f48,f64])).
tff(f69,plain,(
(vPI('\$i') @ (sCOMB @ (bCOMB @ vIMP @ sK0) @ sK2) = \$true)),
inference(combinator_demodulation,[],[f68])).
tff(f70,plain,(
( ! [X1] : ((sCOMB @ (bCOMB @ vIMP @ sK0) @ sK2 @ X1 = \$true)) )),
inference(pi_clausification,[],[f69])).
tff(f71,plain,(
( ! [X1] : ((vIMP @ (sK0 @ X1) @ (sK2 @ X1) = \$true)) )),
inference(combinator_demodulation,[],[f70])).
tff(f72,plain,(
( ! [X1] : ((sK2 @ X1 = \$true) | (sK0 @ X1 = \$false)) )),
inference(binary_proxy_clausification,[],[f71])).
tff(f73,plain,(
(vPI('\$i') @ (sCOMB @ (bCOMB @ vIMP @ sK1) @ sK2) = \$true)),
inference(combinator_demodulation,[],[f67])).
tff(f74,plain,(
( ! [X1] : ((sCOMB @ (bCOMB @ vIMP @ sK1) @ sK2 @ X1 = \$true)) )),
inference(pi_clausification,[],[f73])).
tff(f75,plain,(
( ! [X1] : ((vIMP @ (sK1 @ X1) @ (sK2 @ X1) = \$true)) )),
inference(combinator_demodulation,[],[f74])).
tff(f76,plain,(
( ! [X1] : ((sK2 @ X1 = \$true) | (sK1 @ X1 = \$false)) )),
inference(binary_proxy_clausification,[],[f75])).
tff(f77,plain,(
(vPI('\$i') @ (sCOMB @ (bCOMB @ vIMP @ (sCOMB @ (bCOMB @ vOR @ sK0) @ sK1)) @ sK2) != \$true)),
inference(combinator_demodulation,[],[f66])).
tff(f78,plain,(
(sCOMB @ (bCOMB @ vIMP @ (sCOMB @ (bCOMB @ vOR @ sK0) @ sK1)) @ sK2 @ sK3 = \$false)),
inference(sigma_clausification,[],[f77])).
tff(f79,plain,(
(vIMP @ (vOR @ (sK0 @ sK3) @ (sK1 @ sK3)) @ (sK2 @ sK3) = \$false)),
inference(combinator_demodulation,[],[f78])).
tff(f80,plain,(
(vOR @ (sK0 @ sK3) @ (sK1 @ sK3) = \$true)),
inference(binary_proxy_clausification,[],[f79])).
tff(f81,plain,(
(sK2 @ sK3 = \$false)),
inference(binary_proxy_clausification,[],[f79])).
tff(f82,plain,(
(sK0 @ sK3 = \$true) | (sK1 @ sK3 = \$true)),
inference(binary_proxy_clausification,[],[f80])).
tff(f83,plain,(
(\$false = \$true) | (sK0 @ sK3 = \$false)),
inference(superposition,[],[f72,f81])).
tff(f86,plain,(
(sK0 @ sK3 = \$false)),
inference(trivial_inequality_removal,[],[f83])).
tff(f87,plain,(
(\$false = \$true) | (sK1 @ sK3 = \$true)),
inference(backward_demodulation,[],[f86,f82])).
tff(f88,plain,(
(sK1 @ sK3 = \$true)),
inference(trivial_inequality_removal,[],[f87])).
tff(f89,plain,(
(\$false = \$true) | (sK1 @ sK3 = \$false)),
inference(superposition,[],[f76,f81])).
tff(f92,plain,(
(sK1 @ sK3 = \$false)),
inference(trivial_inequality_removal,[],[f89])).
tff(f93,plain,(
(\$false = \$true)),
inference(backward_demodulation,[],[f92,f88])).
tff(f94,plain,(
\$false),
inference(trivial_inequality_removal,[],[f93])).
% SZS output end Proof for SET014^4
```

### Sample proof for DAT013=1

```% SZS output start Proof for DAT013=1
tff(type_def_5, type, array: \$tType).
tff(func_def_0, type, read: (array * \$int) > \$int).
tff(func_def_1, type, write: (array * \$int * \$int) > array).
tff(func_def_7, type, sK0: array).
tff(func_def_8, type, sK1: \$int).
tff(func_def_9, type, sK2: \$int).
tff(func_def_10, type, sK3: \$int).
tff(f2323,plain,(
\$false),
inference(subsumption_resolution,[],[f2316,f143])).
tff(f143,plain,(
\$less(sK3,sK1)),
inference(subsumption_resolution,[],[f140,f29])).
tff(f29,plain,(
~\$less(sK2,sK3)),
inference(cnf_transformation,[],[f24])).
tff(f24,plain,(
(~\$less(0,read(sK0,sK3)) & ~\$less(sK2,sK3) & ~\$less(sK3,\$sum(sK1,3))) & ! [X4 : \$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22])).
tff(f22,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) & ! [X4 : \$int] : (\$less(0,read(X0,X4)) | \$less(X2,X4) | \$less(X4,X1))) => (? [X3 : \$int] : (~\$less(0,read(sK0,X3)) & ~\$less(sK2,X3) & ~\$less(X3,\$sum(sK1,3))) & ! [X4 : \$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1)))),
introduced(choice_axiom,[])).
tff(f23,plain,(
? [X3 : \$int] : (~\$less(0,read(sK0,X3)) & ~\$less(sK2,X3) & ~\$less(X3,\$sum(sK1,3))) => (~\$less(0,read(sK0,sK3)) & ~\$less(sK2,sK3) & ~\$less(sK3,\$sum(sK1,3)))),
introduced(choice_axiom,[])).
tff(f21,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X3 : \$int] : (~\$less(0,read(X0,X3)) & ~\$less(X2,X3) & ~\$less(X3,\$sum(X1,3))) & ! [X4 : \$int] : (\$less(0,read(X0,X4)) | \$less(X2,X4) | \$less(X4,X1)))),
inference(rectify,[],[f20])).
tff(f20,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & ~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | \$less(X2,X3) | \$less(X3,X1)))),
inference(flattening,[],[f19])).
tff(f19,plain,(
? [X0 : array,X1 : \$int,X2 : \$int] : (? [X4 : \$int] : (~\$less(0,read(X0,X4)) & (~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3)))) & ! [X3 : \$int] : (\$less(0,read(X0,X3)) | (\$less(X2,X3) | \$less(X3,X1))))),
inference(ennf_transformation,[],[f5])).
tff(f5,plain,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((~\$less(X2,X3) & ~\$less(X3,X1)) => \$less(0,read(X0,X3))) => ! [X4 : \$int] : ((~\$less(X2,X4) & ~\$less(X4,\$sum(X1,3))) => \$less(0,read(X0,X4))))),
inference(theory_normalization,[],[f4])).
tff(f4,negated_conjecture,(
~! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
inference(negated_conjecture,[],[f3])).
tff(f3,conjecture,(
! [X0 : array,X1 : \$int,X2 : \$int] : (! [X3 : \$int] : ((\$lesseq(X3,X2) & \$lesseq(X1,X3)) => \$greater(read(X0,X3),0)) => ! [X4 : \$int] : ((\$lesseq(X4,X2) & \$lesseq(\$sum(X1,3),X4)) => \$greater(read(X0,X4),0)))),
file('Problems/DAT/DAT013=1.p',unknown)).
tff(f140,plain,(
\$less(sK2,sK3) | \$less(sK3,sK1)),
inference(resolution,[],[f27,f30])).
tff(f30,plain,(
inference(cnf_transformation,[],[f24])).
tff(f27,plain,(
( ! [X4:\$int] : (\$less(0,read(sK0,X4)) | \$less(sK2,X4) | \$less(X4,sK1)) )),
inference(cnf_transformation,[],[f24])).
tff(f2316,plain,(
~\$less(sK3,sK1)),
inference(backward_demodulation,[],[f31,f2315])).
tff(f2315,plain,(
sK1 = \$sum(3,sK1)),
inference(subsumption_resolution,[],[f2282,f1467])).
tff(f1467,plain,(
( ! [X3:\$int] : (~\$less(\$sum(3,X3),X3)) )),
inference(resolution,[],[f1229,f125])).
tff(f125,plain,(
( ! [X6:\$int,X4:\$int,X5:\$int] : (\$less(\$sum(X6,X5),\$sum(X5,X4)) | ~\$less(X6,X4)) )),
inference(superposition,[],[f14,f6])).
tff(f6,plain,(
( ! [X0:\$int,X1:\$int] : (\$sum(X0,X1) = \$sum(X1,X0)) )),
introduced(theory_axiom,[])).
tff(f14,plain,(
( ! [X2:\$int,X0:\$int,X1:\$int] : (\$less(\$sum(X0,X2),\$sum(X1,X2)) | ~\$less(X0,X1)) )),
introduced(theory_axiom,[])).
tff(f1229,plain,(
( ! [X8:\$int] : (~\$less(\$sum(X8,3),X8)) )),
inference(evaluation,[],[f1219])).
tff(f1219,plain,(
( ! [X8:\$int] : (~\$less(\$sum(\$sum(X8,1),2),X8)) )),
inference(resolution,[],[f1070,f73])).
tff(f73,plain,(
( ! [X4:\$int,X3:\$int] : (\$less(X3,\$sum(X4,1)) | ~\$less(X3,X4)) )),
inference(resolution,[],[f12,f43])).
tff(f43,plain,(
( ! [X0:\$int] : (\$less(X0,\$sum(X0,1))) )),
inference(resolution,[],[f15,f11])).
tff(f11,plain,(
( ! [X0:\$int] : (~\$less(X0,X0)) )),
introduced(theory_axiom,[])).
tff(f15,plain,(
( ! [X0:\$int,X1:\$int] : (\$less(X1,\$sum(X0,1)) | \$less(X0,X1)) )),
introduced(theory_axiom,[])).
tff(f12,plain,(
( ! [X2:\$int,X0:\$int,X1:\$int] : (~\$less(X1,X2) | ~\$less(X0,X1) | \$less(X0,X2)) )),
introduced(theory_axiom,[])).
tff(f1070,plain,(
( ! [X8:\$int] : (~\$less(\$sum(X8,2),X8)) )),
inference(evaluation,[],[f1060])).
tff(f1060,plain,(
( ! [X8:\$int] : (~\$less(\$sum(\$sum(X8,1),1),X8)) )),
inference(resolution,[],[f986,f73])).
tff(f986,plain,(
( ! [X6:\$int] : (~\$less(\$sum(X6,1),X6)) )),
inference(resolution,[],[f73,f11])).
tff(f2282,plain,(
\$less(\$sum(3,sK1),sK1) | sK1 = \$sum(3,sK1)),
inference(resolution,[],[f742,f31])).
tff(f742,plain,(
( ! [X56:\$int] : (\$less(sK3,X56) | \$less(X56,sK1) | sK1 = X56) )),
inference(resolution,[],[f84,f143])).
tff(f84,plain,(
( ! [X4:\$int,X5:\$int,X3:\$int] : (~\$less(X5,X4) | X3 = X4 | \$less(X3,X4) | \$less(X5,X3)) )),
inference(resolution,[],[f13,f12])).
tff(f13,plain,(
( ! [X0:\$int,X1:\$int] : (\$less(X1,X0) | \$less(X0,X1) | X0 = X1) )),
introduced(theory_axiom,[])).
tff(f31,plain,(
~\$less(sK3,\$sum(3,sK1))),
inference(forward_demodulation,[],[f28,f6])).
tff(f28,plain,(
~\$less(sK3,\$sum(sK1,3))),
inference(cnf_transformation,[],[f24])).
% SZS output end Proof for DAT013=1
```

### Sample proof for SEU140+2

```% SZS output start Proof for SEU140+2
fof(f4471,plain,(
\$false),
inference(subsumption_resolution,[],[f4465,f210])).
fof(f210,plain,(
~disjoint(sK10,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f134,plain,(
~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f88,f133])).
fof(f133,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1)) => (~disjoint(sK10,sK12) & disjoint(sK11,sK12) & subset(sK10,sK11))),
introduced(choice_axiom,[])).
fof(f88,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & disjoint(X1,X2) & subset(X0,X1))),
inference(flattening,[],[f87])).
fof(f87,plain,(
? [X0,X1,X2] : (~disjoint(X0,X2) & (disjoint(X1,X2) & subset(X0,X1)))),
inference(ennf_transformation,[],[f52])).
fof(f52,negated_conjecture,(
~! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
inference(negated_conjecture,[],[f51])).
fof(f51,conjecture,(
! [X0,X1,X2] : ((disjoint(X1,X2) & subset(X0,X1)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f4465,plain,(
disjoint(sK10,sK12)),
inference(superposition,[],[f4351,f2135])).
fof(f2135,plain,(
sK12 = set_difference(set_union2(sK11,sK12),sK11)),
inference(superposition,[],[f741,f931])).
fof(f931,plain,(
sK11 = set_difference(sK11,sK12)),
inference(forward_demodulation,[],[f930,f338])).
fof(f338,plain,(
( ! [X6,X7] : (set_union2(set_difference(X6,X7),X6) = X6) )),
inference(resolution,[],[f180,f192])).
fof(f192,plain,(
( ! [X0,X1] : (subset(set_difference(X0,X1),X0)) )),
inference(cnf_transformation,[],[f39])).
fof(f39,axiom,(
! [X0,X1] : subset(set_difference(X0,X1),X0)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f180,plain,(
( ! [X0,X1] : (~subset(X0,X1) | set_union2(X0,X1) = X1) )),
inference(cnf_transformation,[],[f73])).
fof(f73,plain,(
! [X0,X1] : (set_union2(X0,X1) = X1 | ~subset(X0,X1))),
inference(ennf_transformation,[],[f28])).
fof(f28,axiom,(
! [X0,X1] : (subset(X0,X1) => set_union2(X0,X1) = X1)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f930,plain,(
set_difference(sK11,sK12) = set_union2(set_difference(sK11,sK12),sK11)),
inference(forward_demodulation,[],[f929,f281])).
fof(f281,plain,(
( ! [X1] : (set_union2(empty_set,X1) = X1) )),
inference(superposition,[],[f137,f183])).
fof(f183,plain,(
( ! [X0] : (set_union2(X0,empty_set) = X0) )),
inference(cnf_transformation,[],[f31])).
fof(f31,axiom,(
! [X0] : set_union2(X0,empty_set) = X0),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f137,plain,(
( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X1,X0)) )),
inference(cnf_transformation,[],[f3])).
fof(f3,axiom,(
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f929,plain,(
set_union2(set_difference(sK11,sK12),sK11) = set_union2(empty_set,set_difference(sK11,sK12))),
inference(forward_demodulation,[],[f914,f137])).
fof(f914,plain,(
set_union2(set_difference(sK11,sK12),sK11) = set_union2(set_difference(sK11,sK12),empty_set)),
inference(superposition,[],[f195,f587])).
fof(f587,plain,(
empty_set = set_difference(sK11,set_difference(sK11,sK12))),
inference(resolution,[],[f224,f209])).
fof(f209,plain,(
disjoint(sK11,sK12)),
inference(cnf_transformation,[],[f134])).
fof(f224,plain,(
( ! [X0,X1] : (~disjoint(X0,X1) | empty_set = set_difference(X0,set_difference(X0,X1))) )),
inference(definition_unfolding,[],[f165,f203])).
fof(f203,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))) )),
inference(cnf_transformation,[],[f47])).
fof(f47,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f165,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f119])).
fof(f119,plain,(
! [X0,X1] : ((disjoint(X0,X1) | set_intersection2(X0,X1) != empty_set) & (set_intersection2(X0,X1) = empty_set | ~disjoint(X0,X1)))),
inference(nnf_transformation,[],[f11])).
fof(f11,axiom,(
! [X0,X1] : (disjoint(X0,X1) <=> set_intersection2(X0,X1) = empty_set)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f195,plain,(
( ! [X0,X1] : (set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))) )),
inference(cnf_transformation,[],[f41])).
fof(f41,axiom,(
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f741,plain,(
( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = X7) )),
inference(forward_demodulation,[],[f740,f196])).
fof(f196,plain,(
( ! [X0] : (set_difference(X0,empty_set) = X0) )),
inference(cnf_transformation,[],[f42])).
fof(f42,axiom,(
! [X0] : set_difference(X0,empty_set) = X0),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f740,plain,(
( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = set_difference(X7,empty_set)) )),
inference(forward_demodulation,[],[f690,f324])).
fof(f324,plain,(
( ! [X4,X3] : (empty_set = set_difference(X3,set_union2(X4,X3))) )),
inference(resolution,[],[f175,f286])).
fof(f286,plain,(
( ! [X6,X7] : (subset(X6,set_union2(X7,X6))) )),
inference(superposition,[],[f213,f137])).
fof(f213,plain,(
( ! [X0,X1] : (subset(X0,set_union2(X0,X1))) )),
inference(cnf_transformation,[],[f55])).
fof(f55,axiom,(
! [X0,X1] : subset(X0,set_union2(X0,X1))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f175,plain,(
( ! [X0,X1] : (~subset(X0,X1) | empty_set = set_difference(X0,X1)) )),
inference(cnf_transformation,[],[f120])).
fof(f120,plain,(
! [X0,X1] : ((empty_set = set_difference(X0,X1) | ~subset(X0,X1)) & (subset(X0,X1) | empty_set != set_difference(X0,X1)))),
inference(nnf_transformation,[],[f23])).
fof(f23,axiom,(
! [X0,X1] : (empty_set = set_difference(X0,X1) <=> subset(X0,X1))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f690,plain,(
( ! [X6,X7] : (set_difference(set_union2(X6,X7),set_difference(X6,X7)) = set_difference(X7,set_difference(X7,set_union2(X6,X7)))) )),
inference(superposition,[],[f216,f201])).
fof(f201,plain,(
( ! [X0,X1] : (set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)) )),
inference(cnf_transformation,[],[f45])).
fof(f45,axiom,(
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f216,plain,(
( ! [X0,X1] : (set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0))) )),
inference(definition_unfolding,[],[f138,f203,f203])).
fof(f138,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = set_intersection2(X1,X0)) )),
inference(cnf_transformation,[],[f4])).
fof(f4,axiom,(
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f4351,plain,(
( ! [X41] : (disjoint(sK10,set_difference(X41,sK11))) )),
inference(superposition,[],[f4323,f2122])).
fof(f2122,plain,(
sK10 = set_difference(sK11,set_difference(sK11,sK10))),
inference(superposition,[],[f741,f434])).
fof(f434,plain,(
sK11 = set_union2(sK11,sK10)),
inference(forward_demodulation,[],[f433,f281])).
fof(f433,plain,(
set_union2(sK11,sK10) = set_union2(empty_set,sK11)),
inference(forward_demodulation,[],[f421,f137])).
fof(f421,plain,(
set_union2(sK11,sK10) = set_union2(sK11,empty_set)),
inference(superposition,[],[f195,f328])).
fof(f328,plain,(
empty_set = set_difference(sK10,sK11)),
inference(resolution,[],[f175,f208])).
fof(f208,plain,(
subset(sK10,sK11)),
inference(cnf_transformation,[],[f134])).
fof(f4323,plain,(
( ! [X4,X2,X3] : (disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
inference(duplicate_literal_removal,[],[f4288])).
fof(f4288,plain,(
( ! [X4,X2,X3] : (disjoint(set_difference(X2,X3),set_difference(X4,X2)) | disjoint(set_difference(X2,X3),set_difference(X4,X2))) )),
inference(resolution,[],[f401,f395])).
fof(f395,plain,(
( ! [X10,X8,X9] : (~in(sK8(X8,set_difference(X9,X10)),X10) | disjoint(X8,set_difference(X9,X10))) )),
inference(resolution,[],[f243,f198])).
fof(f198,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f130,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & ((in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)) | disjoint(X0,X1)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f82,f129])).
fof(f129,plain,(
! [X1,X0] : (? [X3] : (in(X3,X1) & in(X3,X0)) => (in(sK8(X0,X1),X1) & in(sK8(X0,X1),X0)))),
introduced(choice_axiom,[])).
fof(f82,plain,(
! [X0,X1] : ((~disjoint(X0,X1) | ! [X2] : (~in(X2,X1) | ~in(X2,X0))) & (? [X3] : (in(X3,X1) & in(X3,X0)) | disjoint(X0,X1)))),
inference(ennf_transformation,[],[f62])).
fof(f62,plain,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X3] : ~(in(X3,X1) & in(X3,X0)) & ~disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(disjoint(X0,X1) & ? [X2] : (in(X2,X1) & in(X2,X0))) & ~(! [X2] : ~(in(X2,X1) & in(X2,X0)) & ~disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f243,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,X1)) | ~in(X4,X1)) )),
inference(equality_resolution,[],[f160])).
fof(f160,plain,(
( ! [X4,X2,X0,X1] : (~in(X4,X1) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f118])).
fof(f118,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f116,f117])).
fof(f117,plain,(
! [X2,X1,X0] : (? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2))) => ((in(sK4(X0,X1,X2),X1) | ~in(sK4(X0,X1,X2),X0) | ~in(sK4(X0,X1,X2),X2)) & ((~in(sK4(X0,X1,X2),X1) & in(sK4(X0,X1,X2),X0)) | in(sK4(X0,X1,X2),X2))))),
introduced(choice_axiom,[])).
fof(f116,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X4] : ((in(X4,X2) | in(X4,X1) | ~in(X4,X0)) & ((~in(X4,X1) & in(X4,X0)) | ~in(X4,X2))) | set_difference(X0,X1) != X2))),
inference(rectify,[],[f115])).
fof(f115,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : ((in(X3,X1) | ~in(X3,X0) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | in(X3,X1) | ~in(X3,X0)) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(flattening,[],[f114])).
fof(f114,plain,(
! [X0,X1,X2] : ((set_difference(X0,X1) = X2 | ? [X3] : (((in(X3,X1) | ~in(X3,X0)) | ~in(X3,X2)) & ((~in(X3,X1) & in(X3,X0)) | in(X3,X2)))) & (! [X3] : ((in(X3,X2) | (in(X3,X1) | ~in(X3,X0))) & ((~in(X3,X1) & in(X3,X0)) | ~in(X3,X2))) | set_difference(X0,X1) != X2))),
inference(nnf_transformation,[],[f10])).
fof(f10,axiom,(
! [X0,X1,X2] : (set_difference(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (~in(X3,X1) & in(X3,X0))))),
file('Problems/SEU/SEU140+2.p',unknown)).
fof(f401,plain,(
( ! [X4,X2,X3] : (in(sK8(set_difference(X2,X3),X4),X2) | disjoint(set_difference(X2,X3),X4)) )),
inference(resolution,[],[f244,f197])).
fof(f197,plain,(
( ! [X0,X1] : (in(sK8(X0,X1),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f130])).
fof(f244,plain,(
( ! [X4,X0,X1] : (~in(X4,set_difference(X0,X1)) | in(X4,X0)) )),
inference(equality_resolution,[],[f159])).
fof(f159,plain,(
( ! [X4,X2,X0,X1] : (in(X4,X0) | ~in(X4,X2) | set_difference(X0,X1) != X2) )),
inference(cnf_transformation,[],[f118])).
% SZS output end Proof for SEU140+2
```

### Sample proof for NLP042+1

```% # SZS output start Saturation.
tff(u283,axiom,
(![X1, X0] : ((~woman(X0,X1) | human_person(X0,X1))))).

tff(u282,axiom,
(![X1, X0] : ((~woman(X0,X1) | female(X0,X1))))).

tff(u281,negated_conjecture,
woman(sK0,sK1)).

tff(u280,negated_conjecture,
~female(sK0,sK4)).

tff(u279,negated_conjecture,
~female(sK0,sK2)).

tff(u278,negated_conjecture,
~female(sK0,sK3)).

tff(u277,negated_conjecture,
female(sK0,sK1)).

tff(u276,axiom,
(![X1, X0] : ((~human_person(X0,X1) | organism(X0,X1))))).

tff(u275,axiom,
(![X1, X0] : ((~human_person(X0,X1) | human(X0,X1))))).

tff(u274,axiom,
(![X1, X0] : ((~human_person(X0,X1) | animate(X0,X1))))).

tff(u273,negated_conjecture,
human_person(sK0,sK1)).

tff(u272,negated_conjecture,
~animate(sK0,sK3)).

tff(u271,negated_conjecture,
animate(sK0,sK1)).

tff(u270,negated_conjecture,
~human(sK0,sK2)).

tff(u269,negated_conjecture,
human(sK0,sK1)).

tff(u268,axiom,
(![X1, X0] : ((~organism(X0,X1) | entity(X0,X1))))).

tff(u267,axiom,
(![X1, X0] : ((~organism(X0,X1) | living(X0,X1))))).

tff(u266,negated_conjecture,
organism(sK0,sK1)).

tff(u265,negated_conjecture,
~living(sK0,sK3)).

tff(u264,negated_conjecture,
living(sK0,sK1)).

tff(u263,axiom,
(![X1, X0] : ((~entity(X0,X1) | specific(X0,X1))))).

tff(u262,axiom,
(![X1, X0] : ((~entity(X0,X1) | existent(X0,X1))))).

tff(u261,negated_conjecture,
entity(sK0,sK1)).

tff(u260,negated_conjecture,
entity(sK0,sK3)).

tff(u259,axiom,
(![X1, X0] : ((~mia_forename(X0,X1) | forename(X0,X1))))).

tff(u258,negated_conjecture,
mia_forename(sK0,sK2)).

tff(u257,axiom,
(![X1, X0] : ((~forename(X0,X1) | relname(X0,X1))))).

tff(u256,negated_conjecture,
forename(sK0,sK2)).

tff(u255,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | nonhuman(X0,X1))))).

tff(u254,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | general(X0,X1))))).

tff(u253,axiom,
(![X1, X0] : ((~abstraction(X0,X1) | unisex(X0,X1))))).

tff(u252,negated_conjecture,
abstraction(sK0,sK2)).

tff(u251,axiom,
(![X1, X0] : ((~unisex(X0,X1) | ~female(X0,X1))))).

tff(u250,negated_conjecture,
unisex(sK0,sK2)).

tff(u249,negated_conjecture,
unisex(sK0,sK4)).

tff(u248,negated_conjecture,
unisex(sK0,sK3)).

tff(u247,negated_conjecture,
~general(sK0,sK4)).

tff(u246,negated_conjecture,
~general(sK0,sK1)).

tff(u245,negated_conjecture,
~general(sK0,sK3)).

tff(u244,negated_conjecture,
general(sK0,sK2)).

tff(u243,axiom,
(![X1, X0] : ((~nonhuman(X0,X1) | ~human(X0,X1))))).

tff(u242,negated_conjecture,
nonhuman(sK0,sK2)).

tff(u241,axiom,
(![X1, X0] : ((~relation(X0,X1) | abstraction(X0,X1))))).

tff(u240,negated_conjecture,
relation(sK0,sK2)).

tff(u239,axiom,
(![X1, X0] : ((~relname(X0,X1) | relation(X0,X1))))).

tff(u238,negated_conjecture,
relname(sK0,sK2)).

tff(u237,axiom,
(![X1, X0] : ((~object(X0,X1) | entity(X0,X1))))).

tff(u236,axiom,
(![X1, X0] : ((~object(X0,X1) | nonliving(X0,X1))))).

tff(u235,axiom,
(![X1, X0] : ((~object(X0,X1) | unisex(X0,X1))))).

tff(u234,negated_conjecture,
object(sK0,sK3)).

tff(u233,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~living(X0,X1))))).

tff(u232,axiom,
(![X1, X0] : ((~nonliving(X0,X1) | ~animate(X0,X1))))).

tff(u231,negated_conjecture,
nonliving(sK0,sK3)).

tff(u230,negated_conjecture,
~existent(sK0,sK4)).

tff(u229,negated_conjecture,
existent(sK0,sK1)).

tff(u228,negated_conjecture,
existent(sK0,sK3)).

tff(u227,axiom,
(![X1, X0] : ((~specific(X0,X1) | ~general(X0,X1))))).

tff(u226,negated_conjecture,
specific(sK0,sK1)).

tff(u225,negated_conjecture,
specific(sK0,sK4)).

tff(u224,negated_conjecture,
specific(sK0,sK3)).

tff(u223,axiom,
(![X1, X0] : ((~substance_matter(X0,X1) | object(X0,X1))))).

tff(u222,negated_conjecture,
substance_matter(sK0,sK3)).

tff(u221,axiom,
(![X1, X0] : ((~food(X0,X1) | substance_matter(X0,X1))))).

tff(u220,negated_conjecture,
food(sK0,sK3)).

tff(u219,axiom,
(![X1, X0] : ((~beverage(X0,X1) | food(X0,X1))))).

tff(u218,negated_conjecture,
beverage(sK0,sK3)).

tff(u217,axiom,
(![X1, X0] : ((~shake_beverage(X0,X1) | beverage(X0,X1))))).

tff(u216,negated_conjecture,
shake_beverage(sK0,sK3)).

tff(u215,axiom,
(![X1, X0] : ((~order(X0,X1) | act(X0,X1))))).

tff(u214,axiom,
(![X1, X0] : ((~order(X0,X1) | event(X0,X1))))).

tff(u213,negated_conjecture,
order(sK0,sK4)).

tff(u212,axiom,
(![X1, X0] : ((~event(X0,X1) | eventuality(X0,X1))))).

tff(u211,negated_conjecture,
event(sK0,sK4)).

tff(u210,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | specific(X0,X1))))).

tff(u209,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | nonexistent(X0,X1))))).

tff(u208,axiom,
(![X1, X0] : ((~eventuality(X0,X1) | unisex(X0,X1))))).

tff(u207,negated_conjecture,
eventuality(sK0,sK4)).

tff(u206,axiom,
(![X1, X0] : ((~nonexistent(X0,X1) | ~existent(X0,X1))))).

tff(u205,negated_conjecture,
nonexistent(sK0,sK4)).

tff(u204,axiom,
(![X1, X0] : ((~act(X0,X1) | event(X0,X1))))).

tff(u203,negated_conjecture,
act(sK0,sK4)).

tff(u202,axiom,
(![X1, X3, X0, X2] : ((~of(X0,X3,X1) | (X2 = X3) | ~forename(X0,X3) | ~of(X0,X2,X1) | ~forename(X0,X2) | ~entity(X0,X1))))).

tff(u201,negated_conjecture,
(![X0] : ((~of(sK0,X0,sK1) | (sK2 = X0) | ~forename(sK0,X0))))).

tff(u200,negated_conjecture,
of(sK0,sK2,sK1)).

tff(u199,negated_conjecture,
nonreflexive(sK0,sK4)).

tff(u198,negated_conjecture,
~agent(sK0,sK4,sK3)).

tff(u197,negated_conjecture,
agent(sK0,sK4,sK1)).

tff(u196,axiom,
(![X1, X3, X0] : ((~patient(X0,X1,X3) | ~agent(X0,X1,X3) | ~nonreflexive(X0,X1))))).

tff(u195,negated_conjecture,
patient(sK0,sK4,sK3)).

% # SZS output end Saturation.
```

### Sample proof for SWV017+1

```% SZS output start FiniteModel for SWV017+1
tff(declare_\$i,type,\$i:\$tType).
tff(declare_\$i1,type,at:\$i).
tff(declare_\$i2,type,t:\$i).
tff(finite_domain,axiom,
! [X:\$i] : (
X = at | X = t
) ).

tff(distinct_domain,axiom,
at != t
).

tff(declare_a,type,a:\$i).
tff(a_definition,axiom,a = at).
tff(declare_b,type,b:\$i).
tff(b_definition,axiom,b = at).
tff(declare_an_a_nonce,type,an_a_nonce:\$i).
tff(an_a_nonce_definition,axiom,an_a_nonce = t).
tff(declare_bt,type,bt:\$i).
tff(bt_definition,axiom,bt = at).
tff(declare_an_intruder_nonce,type,an_intruder_nonce:\$i).
tff(an_intruder_nonce_definition,axiom,an_intruder_nonce = at).
tff(declare_key,type,key: \$i * \$i > \$i).
tff(function_key,axiom,
key(at,at) = at
& key(at,t) = t
& key(t,at) = t
& key(t,t) = t

).

tff(declare_pair,type,pair: \$i * \$i > \$i).
tff(function_pair,axiom,
pair(at,at) = at
& pair(at,t) = t
& pair(t,at) = at
& pair(t,t) = at

).

tff(declare_sent,type,sent: \$i * \$i * \$i > \$i).
tff(function_sent,axiom,
sent(at,at,at) = at
& sent(at,at,t) = at
& sent(at,t,at) = at
& sent(at,t,t) = at
& sent(t,at,at) = at
& sent(t,at,t) = at
& sent(t,t,at) = at
& sent(t,t,t) = at

).

).

tff(declare_encrypt,type,encrypt: \$i * \$i > \$i).
tff(function_encrypt,axiom,
encrypt(at,at) = at
& encrypt(at,t) = at
& encrypt(t,at) = at
& encrypt(t,t) = t

).

tff(declare_triple,type,triple: \$i * \$i * \$i > \$i).
tff(function_triple,axiom,
triple(at,at,at) = t
& triple(at,at,t) = at
& triple(at,t,at) = at
& triple(at,t,t) = at
& triple(t,at,at) = t
& triple(t,at,t) = t
& triple(t,t,at) = at
& triple(t,t,t) = at

).

tff(declare_generate_b_nonce,type,generate_b_nonce: \$i > \$i).
tff(function_generate_b_nonce,axiom,
generate_b_nonce(at) = t
& generate_b_nonce(t) = t

).

tff(declare_generate_expiration_time,type,generate_expiration_time: \$i > \$i).
tff(function_generate_expiration_time,axiom,
generate_expiration_time(at) = t
& generate_expiration_time(t) = t

).

tff(declare_generate_key,type,generate_key: \$i > \$i).
tff(function_generate_key,axiom,
generate_key(at) = at
& generate_key(t) = at

).

tff(declare_generate_intruder_nonce,type,generate_intruder_nonce: \$i > \$i).
tff(function_generate_intruder_nonce,axiom,
generate_intruder_nonce(at) = at
& generate_intruder_nonce(t) = t

).

tff(declare_a_holds,type,a_holds: \$i > \$o ).
tff(predicate_a_holds,axiom,
%         a_holds(at) undefined in model
%         a_holds(t) undefined in model

).

tff(declare_party_of_protocol,type,party_of_protocol: \$i > \$o ).
tff(predicate_party_of_protocol,axiom,
party_of_protocol(at)
& party_of_protocol(t)

).

tff(declare_message,type,message: \$i > \$o ).
tff(predicate_message,axiom,
message(at)
& ~message(t)

).

tff(declare_a_stored,type,a_stored: \$i > \$o ).
tff(predicate_a_stored,axiom,
~a_stored(at)
& a_stored(t)

).

tff(declare_b_holds,type,b_holds: \$i > \$o ).
tff(predicate_b_holds,axiom,
%         b_holds(at) undefined in model
%         b_holds(t) undefined in model

).

tff(declare_fresh_to_b,type,fresh_to_b: \$i > \$o ).
tff(predicate_fresh_to_b,axiom,
fresh_to_b(at)
& fresh_to_b(t)

).

tff(declare_b_stored,type,b_stored: \$i > \$o ).
tff(predicate_b_stored,axiom,
%         b_stored(at) undefined in model
%         b_stored(t) undefined in model

).

tff(declare_a_key,type,a_key: \$i > \$o ).
tff(predicate_a_key,axiom,
a_key(at)
& ~a_key(t)

).

tff(declare_t_holds,type,t_holds: \$i > \$o ).
tff(predicate_t_holds,axiom,
t_holds(at)
& ~t_holds(t)

).

tff(declare_a_nonce,type,a_nonce: \$i > \$o ).
tff(predicate_a_nonce,axiom,
~a_nonce(at)
& a_nonce(t)

).

tff(declare_intruder_message,type,intruder_message: \$i > \$o ).
tff(predicate_intruder_message,axiom,
intruder_message(at)
& intruder_message(t)

).

tff(declare_intruder_holds,type,intruder_holds: \$i > \$o ).
tff(predicate_intruder_holds,axiom,
intruder_holds(at)
& intruder_holds(t)

).

tff(declare_fresh_intruder_nonce,type,fresh_intruder_nonce: \$i > \$o ).
tff(predicate_fresh_intruder_nonce,axiom,
fresh_intruder_nonce(at)
& ~fresh_intruder_nonce(t)

).

% SZS output end FiniteModel for SWV017+1
```

### Sample solution for BOO001-1

```% SZS output start Proof for BOO001-1
fof(f263,plain,(
\$false),
inference(trivial_inequality_removal,[],[f258])).
fof(f258,plain,(
a != a),
inference(superposition,[],[f6,f186])).
fof(f186,plain,(
( ! [X24] : (inverse(inverse(X24)) = X24) )),
inference(superposition,[],[f132,f5])).
fof(f5,axiom,(
( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f132,plain,(
( ! [X31,X32] : (multiply(X32,inverse(X32),X31) = X31) )),
inference(superposition,[],[f32,f5])).
fof(f32,plain,(
( ! [X4,X5,X3] : (multiply(X5,X3,X4) = multiply(X3,X4,multiply(X5,X3,X4))) )),
inference(superposition,[],[f7,f2])).
fof(f2,axiom,(
( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f7,plain,(
( ! [X2,X0,X3,X1] : (multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3))) )),
inference(superposition,[],[f1,f2])).
fof(f1,axiom,(
( ! [X4,X2,X0,X3,X1] : (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4))) )),
file('Problems/BOO/BOO001-1.p',unknown)).
fof(f6,axiom,(
a != inverse(inverse(a))),
file('Problems/BOO/BOO001-1.p',unknown)).
% SZS output end Proof for BOO001-1
```

## Zipperposition 2.0

Petar Vukmirović
Vrije Universiteit Amsterdam, The Netherlands

### Sample solution for SET014^4

```% SZS output start Refutation
tff(subset, axiom, subset() =
^[X:((\$i > \$o)),Y:((\$i > \$o))]: (![U]: (X(U) => Y(U)))).
tff('0', plain,
subset = (^[X:((\$i > \$o)),Y:((\$i > \$o))]: (![U]: (X(U) => Y(U)))),
inference('simplify_rw_rule', [status(thm)], [subset])).
tff('1', plain,
subset =
(^[V_1:((\$i > \$o)),V_2:((\$i > \$o))]: (![X4]: (V_1(X4) => V_2(X4)))),
define([status(thm)])).
tff(union, axiom, union() = ^[X:((\$i > \$o)),Y:((\$i > \$o)),U]: (X(U) | Y(U))).
tff('2', plain, union = (^[X:((\$i > \$o)),Y:((\$i > \$o)),U]: (X(U) | Y(U))),
inference('simplify_rw_rule', [status(thm)], [union])).
tff('3', plain,
union = (^[V_1:((\$i > \$o)),V_2:((\$i > \$o)),V_3]: (V_1(V_3) | V_2(V_3))),
define([status(thm)])).
tff(thm, conjecture,
(![X:((\$i > \$o)),Y:((\$i > \$o)),A:((\$i > \$o))]:
((subset(X,A) & subset(Y,A)) => subset(union(X,Y),A)))).
tff(zf_stmt_0, conjecture,
(![X4:((\$i > \$o)),X6:((\$i > \$o)),X8:((\$i > \$o))]:
(((![X12]: (X6(X12) => X8(X12))) & (![X10]: (X4(X10) => X8(X10)))) =>
(![X14]: ((X6(X14) | X4(X14)) => X8(X14)))))).
tff(zf_stmt_1, negated_conjecture,
(~
(![X4:((\$i > \$o)),X6:((\$i > \$o)),X8:((\$i > \$o))]:
(((![X12]: (X6(X12) => X8(X12))) & (![X10]: (X4(X10) => X8(X10)))) =>
(![X14]: ((X6(X14) | X4(X14)) => X8(X14))))))).
tff('4', plain,
~ (!!((^[Y0 : \$i > \$o]:
(!!((^[Y1 : \$i > \$o]:
(!!((^[Y2 : \$i > \$o]:
(((!!((^[Y3 : \$i]: (Y1(Y3) => Y2(Y3))))) &
(!!((^[Y3 : \$i]: (Y0(Y3) => Y2(Y3)))))) =>
(!!((^[Y3 : \$i]: ((Y1(Y3) | Y0(Y3)) => Y2(Y3))))))))))))))),
inference('cnf', [status(esa)], [zf_stmt_1])).
tff('5', plain,
~ (!!((^[Y0 : \$i > \$o]:
(!!((^[Y1 : \$i > \$o]:
(((!!((^[Y2 : \$i]: (Y0(Y2) => Y1(Y2))))) &
(!!((^[Y2 : \$i]: ('#sk1'(Y2) => Y1(Y2)))))) =>
(!!((^[Y2 : \$i]: ((Y0(Y2) | '#sk1'(Y2)) => Y1(Y2)))))))))))),
inference('lazy_cnf_exists', [status(thm)], ['4'])).
tff('6', plain,
~ (!!((^[Y0 : \$i > \$o]:
(((!!((^[Y1 : \$i]: ('#sk2'(Y1) => Y0(Y1))))) &
(!!((^[Y1 : \$i]: ('#sk1'(Y1) => Y0(Y1)))))) =>
(!!((^[Y1 : \$i]: (('#sk2'(Y1) | '#sk1'(Y1)) => Y0(Y1))))))))),
inference('lazy_cnf_exists', [status(thm)], ['5'])).
tff('7', plain,
~ (((!!((^[Y0 : \$i]: ('#sk2'(Y0) => '#sk3'(Y0))))) &
(!!((^[Y0 : \$i]: ('#sk1'(Y0) => '#sk3'(Y0)))))) =>
(!!((^[Y0 : \$i]: (('#sk2'(Y0) | '#sk1'(Y0)) => '#sk3'(Y0)))))),
inference('lazy_cnf_exists', [status(thm)], ['6'])).
tff('8', plain,
~ (!!((^[Y0 : \$i]: (('#sk2'(Y0) | '#sk1'(Y0)) => '#sk3'(Y0))))),
inference('lazy_cnf_imply', [status(thm)], ['7'])).
tff('9', plain, ~ (('#sk2'('#sk4') | '#sk1'('#sk4')) => '#sk3'('#sk4')),
inference('lazy_cnf_exists', [status(thm)], ['8'])).
tff('10', plain, ~ '#sk3'('#sk4'),
inference('lazy_cnf_imply', [status(thm)], ['9'])).
tff('11', plain,  ('#sk2'('#sk4') | '#sk1'('#sk4')),
inference('lazy_cnf_imply', [status(thm)], ['9'])).
tff('12', plain, ( '#sk2'('#sk4') |  '#sk1'('#sk4')),
inference('lazy_cnf_or', [status(thm)], ['11'])).
tff('13', plain,
((!!((^[Y0 : \$i]: ('#sk2'(Y0) => '#sk3'(Y0))))) &
(!!((^[Y0 : \$i]: ('#sk1'(Y0) => '#sk3'(Y0)))))),
inference('lazy_cnf_imply', [status(thm)], ['7'])).
tff('14', plain,  (!!((^[Y0 : \$i]: ('#sk2'(Y0) => '#sk3'(Y0))))),
inference('lazy_cnf_and', [status(thm)], ['13'])).
tff('15', plain, ![X1]:  ('#sk2'(X1) => '#sk3'(X1)),
inference('lazy_cnf_forall', [status(thm)], ['14'])).
tff('16', plain, ![X1]: (~ '#sk2'(X1) |  '#sk3'(X1)),
inference('lazy_cnf_imply', [status(thm)], ['15'])).
tff('17', plain, ( '#sk1'('#sk4') |  '#sk3'('#sk4')),
inference('sup-', [status(thm)], ['12', '16'])).
tff('18', plain,  (!!((^[Y0 : \$i]: ('#sk1'(Y0) => '#sk3'(Y0))))),
inference('lazy_cnf_and', [status(thm)], ['13'])).
tff('19', plain, ![X1]:  ('#sk1'(X1) => '#sk3'(X1)),
inference('lazy_cnf_forall', [status(thm)], ['18'])).
tff('20', plain, ![X1]: (~ '#sk1'(X1) |  '#sk3'(X1)),
inference('lazy_cnf_imply', [status(thm)], ['19'])).
tff('21', plain,  '#sk3'('#sk4'),
inference('clc', [status(thm)], ['17', '20'])).
tff('22', plain, \$false, inference('demod', [status(thm)], ['10', '21'])).

% SZS output end Refutation
```

### Sample solution for SEU140+2

```% SZS output start Refutation
tff(t63_xboole_1, conjecture,
(![A,B,C]: ((subset(A,B) & disjoint(B,C)) => disjoint(A,C)))).
tff(zf_stmt_0, negated_conjecture,
(~(![A,B,C]: ((subset(A,B) & disjoint(B,C)) => disjoint(A,C))))).
tff('0', plain, ~ disjoint(sk_A_2, sk_C_4),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff('1', plain,  disjoint(sk_B_1, sk_C_4),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(d7_xboole_0, axiom,
(![A,B]: (disjoint(A,B) <=> (set_intersection2(A,B) = empty_set)))).
tff('2', plain,
![X36, X37]:
(set_intersection2(X36, X37) = empty_set | ~ disjoint(X36, X37)),
inference('cnf', [status(esa)], [d7_xboole_0])).
tff('3', plain, set_intersection2(sk_B_1, sk_C_4) = empty_set,
inference('sup-', [status(thm)], ['1', '2'])).
tff('4', plain,  subset(sk_A_2, sk_B_1),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(t26_xboole_1, axiom,
(![A,B,C]:
(subset(A,B) => subset(set_intersection2(A,C),set_intersection2(B,C))))).
tff('5', plain,
![X66, X67, X68]:
(~ subset(X66, X67)
|  subset(set_intersection2(X66, X68), set_intersection2(X67, X68))),
inference('cnf', [status(esa)], [t26_xboole_1])).
tff('6', plain,
![X0]:
subset(set_intersection2(sk_A_2, X0), set_intersection2(sk_B_1, X0)),
inference('sup-', [status(thm)], ['4', '5'])).
tff('7', plain,  subset(set_intersection2(sk_A_2, sk_C_4), empty_set),
inference('sup+', [status(thm)], ['3', '6'])).
tff(t3_xboole_1, axiom, (![A]: (subset(A,empty_set) => (A = empty_set)))).
tff('8', plain, ![X90]: (X90 = empty_set | ~ subset(X90, empty_set)),
inference('cnf', [status(esa)], [t3_xboole_1])).
tff('9', plain, set_intersection2(sk_A_2, sk_C_4) = empty_set,
inference('sup-', [status(thm)], ['7', '8'])).
tff('10', plain,
![X36, X38]:
( disjoint(X36, X38) | set_intersection2(X36, X38) != empty_set),
inference('cnf', [status(esa)], [d7_xboole_0])).
tff('11', plain, (empty_set != empty_set |  disjoint(sk_A_2, sk_C_4)),
inference('sup-', [status(thm)], ['9', '10'])).
tff('12', plain,  disjoint(sk_A_2, sk_C_4),
inference('simplify', [status(thm)], ['11'])).
tff('13', plain, \$false, inference('demod', [status(thm)], ['0', '12'])).

% SZS output end Refutation
```

### Sample solution for HL400001^7

```% SZS output start Refutation
tff(thm_2Ebool_2ETRUTH, conjecture, (c_2Ebool_2ET)).
tff(zf_stmt_0, negated_conjecture, (~c_2Ebool_2ET)).
tff('0', plain, ~ c_2Ebool_2ET, inference('cnf', [status(esa)], [zf_stmt_0])).
tff(thm_2Ebool_2ET__DEF, axiom, (c_2Ebool_2ET <=> (![V1x:\$o]: \$true))).
tff('1', plain,  c_2Ebool_2ET,
inference('cnf', [status(esa)], [thm_2Ebool_2ET__DEF])).
tff('2', plain, \$false, inference('demod', [status(thm)], ['0', '1'])).

% SZS output end Refutation
```

### Sample solution for HL400001^5

```% SZS output start Refutation
tff(conj_thm_2Ebool_2ETRUTH, conjecture, (\$true)).
tff(zf_stmt_0, negated_conjecture, (\$false)).
tff('0', plain, \$false, inference('cnf', [status(esa)], [zf_stmt_0])).

% SZS output end Refutation
```

### Sample solution for HL400001^4

```% SZS output start Refutation
tff(thm_2Ebool_2ETRUTH, conjecture, (mono_2Ec_2Ebool_2ET)).
tff(zf_stmt_0, negated_conjecture, (~mono_2Ec_2Ebool_2ET)).
tff('0', plain, ~ mono_2Ec_2Ebool_2ET,
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(thm_2Ebool_2ET__DEF, axiom, (mono_2Ec_2Ebool_2ET <=> (![V0x:\$o]: \$true))).
tff('1', plain,  mono_2Ec_2Ebool_2ET,
inference('cnf', [status(esa)], [thm_2Ebool_2ET__DEF])).
tff('2', plain, \$false, inference('demod', [status(thm)], ['0', '1'])).

% SZS output end Refutation
```

### Sample solution for HL400001_7

```% SZS output start Refutation
tff(thm_2Ebool_2ETRUTH, conjecture, (p(c_2Ebool_2ET_2E0))).
tff(zf_stmt_0, negated_conjecture, (~p(c_2Ebool_2ET_2E0))).
tff('0', plain, ~ p(c_2Ebool_2ET_2E0),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(thm_2Eextra_2Dho_2Etruth, axiom, (p(c_2Ebool_2ET_2E0))).
tff('1', plain,  p(c_2Ebool_2ET_2E0),
inference('cnf', [status(esa)], [thm_2Eextra_2Dho_2Etruth])).
tff('2', plain, \$false, inference('demod', [status(thm)], ['0', '1'])).

% SZS output end Refutation
```

### Sample solution for HL400001_5

```% SZS output start Refutation
tff(conj_thm_2Ebool_2ETRUTH, conjecture, (\$true)).
tff(zf_stmt_0, negated_conjecture, (\$false)).
tff('0', plain, \$false, inference('cnf', [status(esa)], [zf_stmt_0])).

% SZS output end Refutation
```

### Sample solution for HL400001_4

```% SZS output start Refutation
tff(thm_2Ebool_2ETRUTH, conjecture, (p(mono_2Ec_2Ebool_2ET_2E0))).
tff(zf_stmt_0, negated_conjecture, (~p(mono_2Ec_2Ebool_2ET_2E0))).
tff('0', plain, ~ p(mono_2Ec_2Ebool_2ET_2E0),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(reserved_2Eho_2Etruth, axiom, (p(mono_2Ec_2Ebool_2ET_2E0))).
tff('1', plain,  p(mono_2Ec_2Ebool_2ET_2E0),
inference('cnf', [status(esa)], [reserved_2Eho_2Etruth])).
tff('2', plain, \$false, inference('demod', [status(thm)], ['0', '1'])).

% SZS output end Refutation
```

### Sample solution for HL400001+5

```% SZS output start Refutation
tff(conj_thm_2Ebool_2ETRUTH, conjecture, (\$true)).
tff(zf_stmt_0, negated_conjecture, (\$false)).
tff('0', plain, \$false, inference('cnf', [status(esa)], [zf_stmt_0])).

% SZS output end Refutation
```

### Sample solution for HL400001+4

```% SZS output start Refutation
tff(thm_2Ebool_2ETRUTH, conjecture,
(p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))).
tff(zf_stmt_0, negated_conjecture,
(~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))).
tff('0', plain, ~ p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(reserved_2Eho_2Etruth, axiom, (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))).
tff('1', plain,  p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)),
inference('cnf', [status(esa)], [reserved_2Eho_2Etruth])).
tff('2', plain, \$false, inference('demod', [status(thm)], ['0', '1'])).

% SZS output end Refutation
```