# Entrants' Sample Solutions

## CSE 1.2

Feng Cao
Southwest Jiaotong University, China

### Sample proof 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(x111
1,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(x11
22,x1123,x1121),x1122)+E(x1121,f16(x1122,x1123))

[115]P5(f10(x1152,x1153,x1151),x1153)+~P5(f10(x1152,x1153,x1151),x1151)+~P5(f1
0(x1152,x1153,x1151),x1152)+E(x1151,f12(x1152,x1153))
[116]~P5(f11(x1162,x1163,x1161),x1161)+~P5(f11(x1162,x1163,x1161),x1163)+~P5(f
11(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(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(131,plain,
(~P5(x1311,a1)),
inference(rename_variables,[],[118])).
cnf(134,plain,
(~P5(x1341,a1)),
inference(rename_variables,[],[118])).
cnf(137,plain,
(E(f16(x1371,x1371),x1371)),
inference(rename_variables,[],[44])).
cnf(160,plain,
(~E(a5,a3)),
inference(scs_inference,[],[37,38,55,118,131,134,47,48,36,44,137,46,71,81,82,6
3,64,69,80,2,65,122,126,77,84,29,30,31])).
cnf(163,plain,
(E(f16(x1631,x1631),x1631)),
inference(rename_variables,[],[44])).
cnf(165,plain,
(E(f16(x1651,x1651),x1651)),
inference(rename_variables,[],[44])).
cnf(169,plain,
(E(f16(x1691,x1691),x1691)),
inference(rename_variables,[],[44])).
cnf(172,plain,
(~P5(x1721,a1)),
inference(rename_variables,[],[118])).
cnf(180,plain,
(E(f16(x1801,x1801),x1801)),
inference(rename_variables,[],[44])).
cnf(194,plain,
(~E(f12(a3,f12(a3,a6)),a1)),
inference(scs_inference,[],[37,38,55,118,131,134,172,47,48,35,36,54,44,137,163
,165,169,41,46,71,81,82,63,64,69,80,2,65,122,126,77,84,29,30,31,32,3,26,58,87,
97,100,125,94,76,67,72,88,89,90,95])).
cnf(198,plain,
(P5(f4(a3,a6),f12(a3,f12(a3,a6)))),
inference(scs_inference,[],[37,38,55,118,131,134,172,47,48,35,36,54,44,137,163

,165,169,41,46,71,81,82,63,64,69,80,2,65,122,126,77,84,29,30,31,32,3,26,58,87,
97,100,125,94,76,67,72,88,89,90,95,99,104])).
cnf(200,plain,
(~P5(x2001,f12(a5,f12(a5,a6)))),
inference(scs_inference,[],[37,38,55,118,131,134,172,47,48,35,36,54,44,137,163
,165,169,41,46,71,81,82,63,64,69,80,2,65,122,126,77,84,29,30,31,32,3,26,58,87,
97,100,125,94,76,67,72,88,89,90,95,99,104,106])).
cnf(202,plain,
(P3(f12(a3,f12(a3,x2021)),f12(a5,f12(a5,x2021)))),
inference(scs_inference,[],[37,38,55,118,131,134,172,47,48,35,36,54,44,137,163
,165,169,41,46,71,81,82,63,64,69,80,2,65,122,126,77,84,29,30,31,32,3,26,58,87,
97,100,125,94,76,67,72,88,89,90,95,99,104,106,107])).
cnf(240,plain,
(~P3(a5,a3)),
inference(scs_inference,[],[37,38,55,118,131,134,172,47,48,35,36,54,44,137,163
,165,169,180,41,46,71,81,82,63,64,69,80,2,65,122,126,77,84,29,30,31,32,3,26,58
,87,97,100,125,94,76,67,72,88,89,90,95,99,104,106,107,60,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,57,62,74,78,79,123,73])).
cnf(322,plain,
(\$false),
inference(scs_inference,[],[38,55,160,240,200,202,198,194,96,120,121,67,74,69,
80,122,65,71,81,82,60,2,57,123,126,63,108,83]),
['proof']).
% SZS output end Proof
```

## CSE_E 1.1

Feng Cao
Southwest Jiaotong University, China

### Sample proof for SEU140+2

```% 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/sample_CASC2019/SEU140+2.p', t63_xboole_1)).
fof(symmetry_r1_xboole_0, axiom, ![X1, X2]:(disjoint(X1,X2)=>disjoint(X2,X1)),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', symmetry_r1_xboole_0)).
fof(t1_xboole_1, lemma, ![X1, X2,
X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3)),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t1_xboole_1)).
fof(t40_xboole_1, lemma, ![X1,
X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t40_xboole_1)).
fof(commutativity_k2_xboole_0, axiom, ![X1,
X2]:set_union2(X1,X2)=set_union2(X2,X1),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p',
commutativity_k2_xboole_0)).
fof(t2_boole, axiom, ![X1]:set_intersection2(X1,empty_set)=empty_set,
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t2_boole)).
fof(t48_xboole_1, lemma, ![X1,
X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t48_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/sample_CASC2019/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/sample_CASC2019/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/sample_CASC2019/SEU140+2.p', l32_xboole_1)).
fof(d7_xboole_0, axiom, ![X1,
X2]:(disjoint(X1,X2)<=>set_intersection2(X1,X2)=empty_set),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', d7_xboole_0)).
fof(t39_xboole_1, lemma, ![X1,
X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t39_xboole_1)).

fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1,
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t3_boole)).
fof(commutativity_k3_xboole_0, axiom, ![X1,
X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p',
commutativity_k3_xboole_0)).
fof(t36_xboole_1, lemma, ![X1, X2]:subset(set_difference(X1,X2),X1),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t36_xboole_1)).
fof(t12_xboole_1, lemma, ![X1, X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2),
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t12_xboole_1)).
fof(t1_boole, axiom, ![X1]:set_union2(X1,empty_set)=X1,
file('/home/ars01/Desktop/sample_CASC2019/SEU140+2.p', t1_boole)).
fof(c_0_17, 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_18, plain, ![X57, X58]:(~disjoint(X57,X58)|disjoint(X58,X57)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symm
etry_r1_xboole_0])])).
fof(c_0_19, 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)],[in
ference(fof_nnf,[status(thm)],[c_0_17])])])).
fof(c_0_20, lemma, ![X67, X68,
X69]:(~subset(X67,X68)|~subset(X68,X69)|subset(X67,X69)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_x
boole_1])])).
fof(c_0_21, lemma, ![X95,
X96]:set_difference(set_union2(X95,X96),X96)=set_difference(X95,X96),
inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_22, plain, ![X9, X10]:set_union2(X9,X10)=set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_23, plain, ![X75]:set_intersection2(X75,empty_set)=empty_set,
inference(variable_rename,[status(thm)],[t2_boole])).
fof(c_0_24, lemma, ![X99,
X100]:set_difference(X99,set_difference(X99,X100))=set_intersection2(X99,X100)
, inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_25, lemma, ![X90, X91, X90, X91,
X93]:(((in(esk9_2(X90,X91),X90)|disjoint(X90,X91))&(in(esk9_2(X90,X91),X91)|di
sjoint(X90,X91)))&(~in(X93,X90)|~in(X93,X91)|~disjoint(X90,X91))),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[in
ference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[infer
ence(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[in
ference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_
xboole_0])])])])])])])])).
cnf(c_0_26, plain, (disjoint(X2,X1)|~disjoint(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_27, negated_conjecture, (disjoint(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_28, plain, ![X32, X33, X34, X35, X35, X32, X33,
X34]:((((in(X35,X32)|~in(X35,X34)|X34!=set_difference(X32,X33))&(~in(X35,X33)|

~in(X35,X34)|X34!=set_difference(X32,X33)))&(~in(X35,X32)|in(X35,X33)|in(X35,X
34)|X34!=set_difference(X32,X33)))&((~in(esk5_3(X32,X33,X34),X34)|(~in(esk5_3(
X32,X33,X34),X32)|in(esk5_3(X32,X33,X34),X33))|X34=set_difference(X32,X33))&((
in(esk5_3(X32,X33,X34),X32)|in(esk5_3(X32,X33,X34),X34)|X34=set_difference(X32
,X33))&(~in(esk5_3(X32,X33,X34),X33)|in(esk5_3(X32,X33,X34),X34)|X34=set_diffe
rence(X32,X33))))),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[in
ference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[infer
ence(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[in
ference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_
xboole_0])])])])])])])])).
fof(c_0_29, lemma, ![X51, X52, X51,
X52]:((set_difference(X51,X52)!=empty_set|subset(X51,X52))&(~subset(X51,X52)|s
et_difference(X51,X52)=empty_set)),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)]
,[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3
2_xboole_1])])])])).
cnf(c_0_30, lemma, (subset(X1,X3)|~subset(X1,X2)|~subset(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_31, negated_conjecture, (subset(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_32, plain, ![X37, X38, X37,
X38]:((~disjoint(X37,X38)|set_intersection2(X37,X38)=empty_set)&(set_intersect
ion2(X37,X38)!=empty_set|disjoint(X37,X38))),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)]
,[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7
_xboole_0])])])])).
cnf(c_0_33, lemma,
(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_34, plain, (set_union2(X1,X2)=set_union2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_35, lemma, ![X87,
X88]:set_union2(X87,set_difference(X88,X87))=set_union2(X87,X88),
inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_36, plain, (set_intersection2(X1,empty_set)=empty_set),
inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_37, lemma,
(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_24])).
fof(c_0_38, plain, ![X89]:set_difference(X89,empty_set)=X89,
inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_39, lemma, (~in(X1,X2)|~in(X1,X3)|~disjoint(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_40, negated_conjecture, (disjoint(esk13_0,esk12_0)),
inference(spm,[status(thm)],[c_0_26, c_0_27])).
cnf(c_0_41, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_difference(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_28])).
fof(c_0_42, plain, ![X11,
X12]:set_intersection2(X11,X12)=set_intersection2(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).

cnf(c_0_43, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_44, negated_conjecture, (subset(X1,esk12_0)|~subset(X1,esk11_0)),
inference(spm,[status(thm)],[c_0_30, c_0_31])).
fof(c_0_45, lemma, ![X83, X84]:subset(set_difference(X83,X84),X83),
inference(variable_rename,[status(thm)],[t36_xboole_1])).
fof(c_0_46, lemma, ![X59, X60]:(~subset(X59,X60)|set_union2(X59,X60)=X60),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_
xboole_1])])).
cnf(c_0_47, plain, (disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set),
inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_48, lemma,
(set_difference(set_union2(X1,X2),X1)=set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_33, c_0_34])).
cnf(c_0_49, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_35])).
cnf(c_0_50, plain,
(set_difference(X1,set_difference(X1,empty_set))=empty_set),
inference(rw,[status(thm)],[c_0_36, c_0_37])).
cnf(c_0_51, plain, (set_difference(X1,empty_set)=X1),
inference(split_conjunct,[status(thm)],[c_0_38])).
cnf(c_0_52, negated_conjecture, (~in(X1,esk12_0)|~in(X1,esk13_0)),
inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_53, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_54, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3))),
inference(er,[status(thm)],[c_0_41])).
cnf(c_0_55, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_56, plain, (set_intersection2(X1,X2)=set_intersection2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_57, lemma, (set_difference(X1,esk12_0)=empty_set|~subset(X1,esk11_0)),
inference(spm,[status(thm)],[c_0_43, c_0_44])).
cnf(c_0_58, lemma, (subset(set_difference(X1,X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_59, plain, (set_intersection2(X1,X2)=empty_set|~disjoint(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_32])).
fof(c_0_60, plain, ![X66]:set_union2(X66,empty_set)=X66,
inference(variable_rename,[status(thm)],[t1_boole])).
cnf(c_0_61, lemma, (set_union2(X1,X2)=X2|~subset(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_62, plain,
(disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set),
inference(rw,[status(thm)],[c_0_47, c_0_37])).
cnf(c_0_63, lemma,
(set_difference(set_difference(X1,X2),X2)=set_difference(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]),
c_0_48])).
cnf(c_0_64, plain, (set_difference(X1,X1)=empty_set),
inference(rw,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_65, lemma, (disjoint(X1,esk13_0)|~in(esk9_2(X1,esk13_0),esk12_0)),

inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_66, lemma,
(disjoint(set_difference(X1,X2),X3)|in(esk9_2(set_difference(X1,X2),X3),X1)),
inference(spm,[status(thm)],[c_0_54, c_0_55])).
cnf(c_0_67, 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_56,
c_0_37]), c_0_37])).
cnf(c_0_68, lemma,
(set_difference(set_difference(esk11_0,X1),esk12_0)=empty_set),
inference(spm,[status(thm)],[c_0_57, c_0_58])).
cnf(c_0_69, plain,
(set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2)),
inference(rw,[status(thm)],[c_0_59, c_0_37])).
cnf(c_0_70, plain, (set_union2(X1,empty_set)=X1),
inference(split_conjunct,[status(thm)],[c_0_60])).
cnf(c_0_71, lemma, (set_union2(X1,set_difference(X1,X2))=X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_58]),
c_0_34])).
cnf(c_0_72, lemma, (disjoint(set_difference(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(
thm)],[c_0_62, c_0_63]), c_0_64])])).
cnf(c_0_73, lemma, (disjoint(set_difference(esk12_0,X1),esk13_0)),
inference(spm,[status(thm)],[c_0_65, c_0_66])).
cnf(c_0_74, lemma,
(set_difference(esk12_0,set_difference(esk12_0,set_difference(esk11_0,X1)))=se
t_difference(esk11_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]),
c_0_51])).
cnf(c_0_75, lemma, (set_difference(X1,X2)=X1|~disjoint(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(t
hm)],[inference(spm,[status(thm)],[c_0_49, c_0_69]), c_0_70]), c_0_34]),
c_0_71])).
cnf(c_0_76, lemma, (disjoint(X1,set_difference(X2,X1))),
inference(spm,[status(thm)],[c_0_26, c_0_72])).
cnf(c_0_77, lemma, (disjoint(set_difference(esk11_0,X1),esk13_0)),
inference(spm,[status(thm)],[c_0_73, c_0_74])).
cnf(c_0_78, lemma, (set_difference(X1,set_difference(X2,X1))=X1),
inference(spm,[status(thm)],[c_0_75, c_0_76])).
cnf(c_0_79, negated_conjecture, (~disjoint(esk11_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_80, lemma, (\$false),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]),
c_0_79]), ['proof']).
% SZS output end Proof
```

## CVC4 1.7

Andrew Reynolds
University of Iowa, USA

### Sample proof for SET014^4

```% SZS status Theorem for SET014^4
(skolem (forall ((X (-> \$\$unsorted Bool)) (Y (-> \$\$unsorted Bool)) (A (-> \$\$unsorted Bool)) (BOUND_VARIABLE_665 \$\$unsorted)) (or (not (forall ((BOUND_VARIABLE_612 \$\$unsorted)) (or (not (X BOUND_VARIABLE_612)) (A BOUND_VARIABLE_612)) )) (not (forall ((BOUND_VARIABLE_620 \$\$unsorted)) (or (not (Y BOUND_VARIABLE_620)) (A BOUND_VARIABLE_620)) )) (and (not (X BOUND_VARIABLE_665)) (not (Y BOUND_VARIABLE_665))) (A BOUND_VARIABLE_665)) )
( skv_1 skv_2 skv_3 skv_4 )
)
(instantiation (forall ((BOUND_VARIABLE_612 \$\$unsorted)) (or (not (skv_1 BOUND_VARIABLE_612)) (skv_3 BOUND_VARIABLE_612)) )
( skv_4 )
)
(instantiation (forall ((BOUND_VARIABLE_620 \$\$unsorted)) (or (not (skv_2 BOUND_VARIABLE_620)) (skv_3 BOUND_VARIABLE_620)) )
( skv_4 )
)
```

### Sample proof for DAT013=1

```% SZS status Theorem for DAT013=1
(skolem (forall ((U array) (V Int) (W Int) (BOUND_VARIABLE_392 Int)) (let ((_let_0 (* (- 1) BOUND_VARIABLE_392))) (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_392) 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 )
)
```

### Sample proof for SEU140+2

```% SZS status Theorem 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 )
)
(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)) (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)) (= (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_4, skv_5 )
( skv_5, skv_3 )
)
(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)) (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_4, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (disjoint A B) (not (forall ((C \$\$unsorted)) (or (not (in C A)) (not (in C B))) ))) )
( skv_3, skv_5 )
( skv_5, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (BOUND_VARIABLE_840 \$\$unsorted)) (or (not (disjoint A B)) (not (in BOUND_VARIABLE_840 A)) (not (in BOUND_VARIABLE_840 B))) )
( 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 )
)
(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 ((A \$\$unsorted) (B \$\$unsorted)) (or (disjoint A B) (not (forall ((C \$\$unsorted)) (not (in C (set_intersection2 A B))) ))) )
( skv_3, skv_5 )
( skv_5, skv_3 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted) (BOUND_VARIABLE_882 \$\$unsorted)) (or (not (in BOUND_VARIABLE_882 (set_intersection2 A B))) (not (disjoint A B))) )
( skv_3, skv_4, skv_6 )
)
(instantiation (forall ((A \$\$unsorted) (B \$\$unsorted)) (or (not (subset A B)) (not (proper_subset B A))) )
( skv_3, skv_4 )
)
(instantiation (forall ((A \$\$unsorted)) (or (not (empty A)) (= empty_set A)) )
( 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, skv_1 )
( skv_1, empty_set )
)
(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 )
)
```

### 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_8087 \$\$unsorted) (BOUND_VARIABLE_8088 \$\$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_3 \$x2)) true (ite (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_1 \$x2)) true (and (= @uc_\$\$unsorted_0 \$x1) (= @uc_\$\$unsorted_2 \$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_8087 \$\$unsorted) (BOUND_VARIABLE_8088 \$\$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_8087 \$\$unsorted) (BOUND_VARIABLE_8088 \$\$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_8143 \$\$unsorted) (BOUND_VARIABLE_8144 \$\$unsorted) (BOUND_VARIABLE_8145 \$\$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_8156 \$\$unsorted)) Bool true)
(define-fun past ((BOUND_VARIABLE_8087 \$\$unsorted) (BOUND_VARIABLE_8088 \$\$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 status Theorem for SET014^4 (skolem (forall ((X (-> \$\$unsorted Bool)) (Y (-> \$\$unsorted Bool)) (A (-> \$\$unsorted Bool)) (BOUND_VARIABLE_665 \$\$unsorted)) (or (not (forall ((BOUND_VARIABLE_612 \$\$unsorted)) (or (not (X BOUND_VARIABLE_612)) (A BOUND_VARIABLE_612)) )) (not (forall ((BOUND_VARIABLE_620 \$\$unsorted)) (or (not (Y BOUND_VARIABLE_620)) (A BOUND_VARIABLE_620)) )) (and (not (X BOUND_VARIABLE_665)) (not (Y BOUND_VARIABLE_665))) (A BOUND_VARIABLE_665)) ) ( skv_1 skv_2 skv_3 skv_4 ) ) (instantiation (forall ((BOUND_VARIABLE_612 \$\$unsorted)) (or (not (skv_1 BOUND_VARIABLE_612)) (skv_3 BOUND_VARIABLE_612)) ) ( skv_4 ) ) (instantiation (forall ((BOUND_VARIABLE_620 \$\$unsorted)) (or (not (skv_2 BOUND_VARIABLE_620)) (skv_3 BOUND_VARIABLE_620)) ) ( skv_4 ) )

## E 2.4

Stephan Schulz
DHBW Stuttgart, Germany

### Sample proof for SEU140+2

```# SZS output start CNFRefutation
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t63_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('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', commutativity_k3_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_6.0.0_FLAT/SEU140+2.p', t48_xboole_1)).
fof(t40_xboole_1, lemma, ![X1, X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t40_xboole_1)).
fof(commutativity_k2_xboole_0, axiom, ![X1, X2]:set_union2(X1,X2)=set_union2(X2,X1), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', commutativity_k2_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(t7_xboole_1, lemma, ![X1, X2]:subset(X1,set_union2(X1,X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t7_xboole_1)).
fof(symmetry_r1_xboole_0, axiom, ![X1, X2]:(disjoint(X1,X2)=>disjoint(X2,X1)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', symmetry_r1_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_6.0.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t3_boole)).
fof(t39_xboole_1, lemma, ![X1, X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t39_xboole_1)).
fof(t1_boole, axiom, ![X1]:set_union2(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t1_boole)).
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])).
fof(c_0_14, plain, ![X32, X33, X34, X35, X35, X32, X33, X34]:((((in(X35,X32)|~in(X35,X34)|X34!=set_difference(X32,X33))&(~in(X35,X33)|~in(X35,X34)|X34!=set_difference(X32,X33)))&(~in(X35,X32)|in(X35,X33)|in(X35,X34)|X34!=set_difference(X32,X33)))&((~in(esk5_3(X32,X33,X34),X34)|(~in(esk5_3(X32,X33,X34),X32)|in(esk5_3(X32,X33,X34),X33))|X34=set_difference(X32,X33))&((in(esk5_3(X32,X33,X34),X32)|in(esk5_3(X32,X33,X34),X34)|X34=set_difference(X32,X33))&(~in(esk5_3(X32,X33,X34),X33)|in(esk5_3(X32,X33,X34),X34)|X34=set_difference(X32,X33))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])])).
fof(c_0_15, plain, ![X11, X12]:set_intersection2(X11,X12)=set_intersection2(X12,X11), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).
fof(c_0_16, lemma, ![X99, X100]:set_difference(X99,set_difference(X99,X100))=set_intersection2(X99,X100), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_17, lemma, ![X95, X96]:set_difference(set_union2(X95,X96),X96)=set_difference(X95,X96), inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_18, plain, ![X9, X10]:set_union2(X9,X10)=set_union2(X10,X9), inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_19, lemma, ![X51, X52, X51, X52]:((set_difference(X51,X52)!=empty_set|subset(X51,X52))&(~subset(X51,X52)|set_difference(X51,X52)=empty_set)), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])])])).
fof(c_0_20, lemma, ![X114, X115]:subset(X114,set_union2(X114,X115)), inference(variable_rename,[status(thm)],[t7_xboole_1])).
fof(c_0_21, plain, ![X57, X58]:(~disjoint(X57,X58)|disjoint(X58,X57)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])).
fof(c_0_22, 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_23, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_difference(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_24, lemma, ![X90, X91, X90, X91, X93]:(((in(esk9_2(X90,X91),X90)|disjoint(X90,X91))&(in(esk9_2(X90,X91),X91)|disjoint(X90,X91)))&(~in(X93,X90)|~in(X93,X91)|~disjoint(X90,X91))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])])).
cnf(c_0_25, plain, (set_intersection2(X1,X2)=set_intersection2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
cnf(c_0_26, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_16])).
cnf(c_0_27, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_28, plain, (set_union2(X1,X2)=set_union2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_29, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_30, lemma, (subset(X1,set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_20])).
fof(c_0_31, plain, ![X89]:set_difference(X89,empty_set)=X89, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_32, plain, (disjoint(X2,X1)|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_33, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_34, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3))), inference(er,[status(thm)],[c_0_23])).
cnf(c_0_35, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_36, 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_25, c_0_26]), c_0_26])).
cnf(c_0_37, lemma, (set_difference(set_union2(X1,X2),X1)=set_difference(X2,X1)), inference(spm,[status(thm)],[c_0_27, c_0_28])).
cnf(c_0_38, lemma, (set_difference(X1,set_union2(X1,X2))=empty_set), inference(spm,[status(thm)],[c_0_29, c_0_30])).
cnf(c_0_39, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_31])).
fof(c_0_40, lemma, ![X87, X88]:set_union2(X87,set_difference(X88,X87))=set_union2(X87,X88), inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_41, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_42, plain, ![X66]:set_union2(X66,empty_set)=X66, inference(variable_rename,[status(thm)],[t1_boole])).
cnf(c_0_43, lemma, (~in(X1,X2)|~in(X1,X3)|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_44, negated_conjecture, (disjoint(esk13_0,esk12_0)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
cnf(c_0_45, lemma, (disjoint(X1,set_difference(X2,X3))|in(esk9_2(X1,set_difference(X2,X3)),X2)), inference(spm,[status(thm)],[c_0_34, c_0_35])).
cnf(c_0_46, lemma, (set_difference(set_union2(X1,X2),set_difference(X2,X1))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_38]), c_0_39])).
cnf(c_0_47, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_40])).
cnf(c_0_48, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_29, c_0_41])).
cnf(c_0_49, plain, (set_union2(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_50, negated_conjecture, (~in(X1,esk12_0)|~in(X1,esk13_0)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
cnf(c_0_51, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_52, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),set_union2(X2,X3))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
cnf(c_0_53, negated_conjecture, (set_union2(esk11_0,esk12_0)=esk12_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49]), c_0_28])).
cnf(c_0_54, lemma, (disjoint(esk13_0,X1)|~in(esk9_2(esk13_0,X1),esk12_0)), inference(spm,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_55, negated_conjecture, (disjoint(X1,esk11_0)|in(esk9_2(X1,esk11_0),esk12_0)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_56, negated_conjecture, (disjoint(esk13_0,esk11_0)), inference(spm,[status(thm)],[c_0_54, c_0_55])).
cnf(c_0_57, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_58, negated_conjecture, (\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_56]), c_0_57]), ['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_6.4.0_FLAT/NLP042+1.p', ax26)).
fof(ax27, axiom, (![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax27)).
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_6.4.0_FLAT/NLP042+1.p', co1)).
fof(ax41, axiom, (![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax41)).
fof(ax11, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax11)).
fof(ax15, axiom, (![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax15)).
fof(ax16, axiom, (![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax16)).
fof(ax42, axiom, (![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax42)).
fof(ax1, axiom, (![X1]:![X2]:(woman(X1,X2)=>female(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax1)).
fof(ax25, axiom, (![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax25)).
fof(ax6, axiom, (![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax6)).
fof(ax7, axiom, (![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax7)).
fof(ax8, axiom, (![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax8)).
fof(ax38, axiom, (![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax38)).
fof(ax30, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax30)).
fof(ax31, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax31)).
fof(ax34, axiom, (![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax34)).
fof(ax21, axiom, (![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax21)).
fof(ax14, axiom, (![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax14)).
fof(ax24, axiom, (![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax24)).
fof(ax40, axiom, (![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax40)).
fof(ax4, axiom, (![X1]:![X2]:(organism(X1,X2)=>living(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax4)).
fof(ax37, axiom, (![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax37)).
fof(ax2, axiom, (![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax2)).
fof(ax39, axiom, (![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax39)).
fof(ax12, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax12)).
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_6.4.0_FLAT/NLP042+1.p', ax44)).
fof(ax20, axiom, (![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax20)).
fof(ax10, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax10)).
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_6.4.0_FLAT/NLP042+1.p', ax43)).
fof(ax19, axiom, (![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax19)).
fof(ax3, axiom, (![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax3)).
fof(ax29, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax29)).
fof(ax17, axiom, (![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax17)).
fof(ax23, axiom, (![X1]:![X2]:(object(X1,X2)=>entity(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax23)).
fof(ax32, axiom, (![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax32)).
fof(ax33, axiom, (![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax33)).
fof(ax13, axiom, (![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax13)).
fof(ax22, axiom, (![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax22)).
fof(ax18, axiom, (![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax18)).
fof(ax5, axiom, (![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax5)).
fof(ax36, axiom, (![X1]:![X2]:(order(X1,X2)=>act(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax36)).
fof(ax35, axiom, (![X1]:![X2]:(act(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax35)).
fof(ax28, axiom, (![X1]:![X2]:(order(X1,X2)=>event(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax28)).
fof(ax9, axiom, (![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/NLP042+1.p', ax9)).
fof(c_0_45, plain, (![X3]:![X4]:(~beverage(X3,X4)|food(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])).
fof(c_0_46, plain, (![X3]:![X4]:(~shake_beverage(X3,X4)|beverage(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])).
fof(c_0_47, 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_48, plain, (![X3]:![X4]:(~specific(X3,X4)|~general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax41])])])).
fof(c_0_49, plain, (![X3]:![X4]:(~abstraction(X3,X4)|general(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])).
fof(c_0_50, plain, (![X3]:![X4]:(~relname(X3,X4)|relation(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])).
fof(c_0_51, plain, (![X3]:![X4]:(~forename(X3,X4)|relname(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])).
fof(c_0_52, plain, (![X3]:![X4]:(~unisex(X3,X4)|~female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax42])])])).
fof(c_0_53, plain, (![X3]:![X4]:(~woman(X3,X4)|female(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])).
fof(c_0_54, plain, (![X3]:![X4]:(~food(X3,X4)|substance_matter(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])).
cnf(c_0_55,plain,(food(X1,X2)|~beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_45]), ['final']).
cnf(c_0_56,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46]), ['final']).
fof(c_0_57, plain, (![X3]:![X4]:(~organism(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])).
fof(c_0_58, plain, (![X3]:![X4]:(~human_person(X3,X4)|organism(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])).
fof(c_0_59, plain, (![X3]:![X4]:(~woman(X3,X4)|human_person(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])).
fof(c_0_60, 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])])])).
fof(c_0_61, plain, (![X3]:![X4]:(~existent(X3,X4)|~nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax38])])])).
fof(c_0_62, plain, (![X3]:![X4]:(~eventuality(X3,X4)|nonexistent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])])).
cnf(c_0_63,plain,(~general(X1,X2)|~specific(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_64,plain,(general(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_49]), ['final']).
fof(c_0_65, plain, (![X3]:![X4]:(~eventuality(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])).
fof(c_0_66, plain, (![X3]:![X4]:(~event(X3,X4)|eventuality(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])])).
fof(c_0_67, plain, (![X3]:![X4]:(~entity(X3,X4)|specific(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])).
fof(c_0_68, plain, (![X3]:![X4]:(~relation(X3,X4)|abstraction(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])])).
cnf(c_0_69,plain,(relation(X1,X2)|~relname(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_50]), ['final']).
cnf(c_0_70,plain,(relname(X1,X2)|~forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_51]), ['final']).
cnf(c_0_71,plain,(~female(X1,X2)|~unisex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_52]), ['final']).
cnf(c_0_72,plain,(female(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_53]), ['final']).
fof(c_0_73, plain, (![X3]:![X4]:(~substance_matter(X3,X4)|object(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])])).
cnf(c_0_74,plain,(substance_matter(X1,X2)|~food(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54]), ['final']).
cnf(c_0_75,plain,(food(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_55, c_0_56]), ['final']).
cnf(c_0_76,plain,(entity(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_57]), ['final']).
cnf(c_0_77,plain,(organism(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_58]), ['final']).
cnf(c_0_78,plain,(human_person(X1,X2)|~woman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59]), ['final']).
cnf(c_0_79,negated_conjecture,(woman(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
fof(c_0_80, plain, (![X3]:![X4]:(~nonliving(X3,X4)|~living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax40])])])).
fof(c_0_81, plain, (![X3]:![X4]:(~organism(X3,X4)|living(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])).
fof(c_0_82, plain, (![X3]:![X4]:(~animate(X3,X4)|~nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax37])])])).
fof(c_0_83, plain, (![X3]:![X4]:(~human_person(X3,X4)|animate(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])).
fof(c_0_84, plain, (![X3]:![X4]:(~nonhuman(X3,X4)|~human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax39])])])).
fof(c_0_85, plain, (![X3]:![X4]:(~abstraction(X3,X4)|nonhuman(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])).
fof(c_0_86, plain, (![X5]:![X6]:![X7]:![X8]:(((~nonreflexive(X5,X6)|~agent(X5,X6,X7))|~patient(X5,X6,X8))|X7!=X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])).
cnf(c_0_87,plain,(~nonexistent(X1,X2)|~existent(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61]), ['final']).
cnf(c_0_88,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_62]), ['final']).
fof(c_0_89, plain, (![X3]:![X4]:(~entity(X3,X4)|existent(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])).
cnf(c_0_90,plain,(~specific(X1,X2)|~abstraction(X1,X2)), inference(spm,[status(thm)],[c_0_63, c_0_64]), ['final']).
cnf(c_0_91,plain,(specific(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_65]), ['final']).
cnf(c_0_92,plain,(eventuality(X1,X2)|~event(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_66]), ['final']).
cnf(c_0_93,negated_conjecture,(event(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_94,plain,(specific(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_67]), ['final']).
cnf(c_0_95,plain,(abstraction(X1,X2)|~relation(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_68]), ['final']).
cnf(c_0_96,plain,(relation(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_69, c_0_70]), ['final']).
cnf(c_0_97,plain,(~unisex(X1,X2)|~woman(X1,X2)), inference(spm,[status(thm)],[c_0_71, c_0_72]), ['final']).
fof(c_0_98, plain, (![X3]:![X4]:(~abstraction(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax10])])).
cnf(c_0_99,plain,(object(X1,X2)|~substance_matter(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_73]), ['final']).
cnf(c_0_100,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_74, c_0_75]), ['final']).
fof(c_0_101, plain, (![X5]:![X6]:![X7]:![X8]:(((~entity(X5,X6)|~forename(X5,X7))|~of(X5,X7,X6))|((~forename(X5,X8)|X8=X7)|~of(X5,X8,X6)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])])])).
cnf(c_0_102,plain,(entity(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_76, c_0_77]), ['final']).
cnf(c_0_103,negated_conjecture,(human_person(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_78, c_0_79]), ['final']).
cnf(c_0_104,plain,(~living(X1,X2)|~nonliving(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_80]), ['final']).
cnf(c_0_105,plain,(living(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_81]), ['final']).
fof(c_0_106, plain, (![X3]:![X4]:(~object(X3,X4)|nonliving(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])).
cnf(c_0_107,plain,(~nonliving(X1,X2)|~animate(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_82]), ['final']).
cnf(c_0_108,plain,(animate(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_83]), ['final']).
cnf(c_0_109,plain,(~human(X1,X2)|~nonhuman(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_84]), ['final']).
cnf(c_0_110,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85]), ['final']).
fof(c_0_111, plain, (![X3]:![X4]:(~human_person(X3,X4)|human(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])).
cnf(c_0_112,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_113,plain,(~eventuality(X1,X2)|~existent(X1,X2)), inference(spm,[status(thm)],[c_0_87, c_0_88]), ['final']).
cnf(c_0_114,plain,(existent(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_89]), ['final']).
cnf(c_0_115,plain,(~eventuality(X1,X2)|~abstraction(X1,X2)), inference(spm,[status(thm)],[c_0_90, c_0_91]), ['final']).
cnf(c_0_116,negated_conjecture,(eventuality(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_92, c_0_93]), ['final']).
cnf(c_0_117,plain,(~abstraction(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_90, c_0_94]), ['final']).
cnf(c_0_118,plain,(abstraction(X1,X2)|~forename(X1,X2)), inference(spm,[status(thm)],[c_0_95, c_0_96]), ['final']).
fof(c_0_119, plain, (![X3]:![X4]:(~eventuality(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])).
fof(c_0_120, plain, (![X3]:![X4]:(~object(X3,X4)|unisex(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax17])])).
cnf(c_0_121,negated_conjecture,(~unisex(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_97, c_0_79]), ['final']).
cnf(c_0_122,plain,(unisex(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_98]), ['final']).
fof(c_0_123, plain, (![X3]:![X4]:(~object(X3,X4)|entity(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])).
cnf(c_0_124,plain,(object(X1,X2)|~shake_beverage(X1,X2)), inference(spm,[status(thm)],[c_0_99, c_0_100]), ['final']).
cnf(c_0_125,negated_conjecture,(shake_beverage(esk1_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_126,plain,(X2=X4|~of(X1,X2,X3)|~forename(X1,X2)|~of(X1,X4,X3)|~forename(X1,X4)|~entity(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_101]), ['final']).
cnf(c_0_127,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_128,negated_conjecture,(forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_129,negated_conjecture,(entity(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_102, c_0_103]), ['final']).
fof(c_0_130, plain, (![X3]:![X4]:(~thing(X3,X4)|singleton(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])])).
cnf(c_0_131,plain,(~nonliving(X1,X2)|~organism(X1,X2)), inference(spm,[status(thm)],[c_0_104, c_0_105]), ['final']).
cnf(c_0_132,plain,(nonliving(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_106]), ['final']).
cnf(c_0_133,plain,(~nonliving(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_107, c_0_108]), ['final']).
fof(c_0_134, plain, (![X3]:![X4]:(~eventuality(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])])).
fof(c_0_135, plain, (![X3]:![X4]:(~abstraction(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])).
fof(c_0_136, plain, (![X3]:![X4]:(~entity(X3,X4)|thing(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])])).
cnf(c_0_137,plain,(~abstraction(X1,X2)|~human(X1,X2)), inference(spm,[status(thm)],[c_0_109, c_0_110]), ['final']).
cnf(c_0_138,plain,(human(X1,X2)|~human_person(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_111]), ['final']).
fof(c_0_139, plain, (![X3]:![X4]:(~object(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])).
fof(c_0_140, plain, (![X3]:![X4]:(~organism(X3,X4)|impartial(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])).
fof(c_0_141, plain, (![X3]:![X4]:(~order(X3,X4)|act(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])).
fof(c_0_142, plain, (![X3]:![X4]:(~act(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])])).
fof(c_0_143, plain, (![X3]:![X4]:(~order(X3,X4)|event(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])).
fof(c_0_144, plain, (![X3]:![X4]:(~mia_forename(X3,X4)|forename(X3,X4))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])).
cnf(c_0_145,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)), inference(er,[status(thm)],[c_0_112]), ['final']).
cnf(c_0_146,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_147,negated_conjecture,(nonreflexive(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_148,plain,(~eventuality(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_113, c_0_114]), ['final']).
cnf(c_0_149,negated_conjecture,(~abstraction(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_115, c_0_116]), ['final']).
cnf(c_0_150,plain,(~forename(X1,X2)|~entity(X1,X2)), inference(spm,[status(thm)],[c_0_117, c_0_118]), ['final']).
cnf(c_0_151,plain,(unisex(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_119]), ['final']).
cnf(c_0_152,plain,(unisex(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_120]), ['final']).
cnf(c_0_153,negated_conjecture,(~abstraction(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_122]), ['final']).
cnf(c_0_154,plain,(entity(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_123]), ['final']).
cnf(c_0_155,negated_conjecture,(object(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_124, c_0_125]), ['final']).
cnf(c_0_156,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_128]), c_0_129])]), ['final']).
cnf(c_0_157,plain,(singleton(X1,X2)|~thing(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_130]), ['final']).
cnf(c_0_158,plain,(~object(X1,X2)|~organism(X1,X2)), inference(spm,[status(thm)],[c_0_131, c_0_132]), ['final']).
cnf(c_0_159,plain,(~object(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_133, c_0_132]), ['final']).
cnf(c_0_160,plain,(thing(X1,X2)|~eventuality(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_134]), ['final']).
cnf(c_0_161,plain,(thing(X1,X2)|~abstraction(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_135]), ['final']).
cnf(c_0_162,plain,(thing(X1,X2)|~entity(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_136]), ['final']).
cnf(c_0_163,plain,(~abstraction(X1,X2)|~human_person(X1,X2)), inference(spm,[status(thm)],[c_0_137, c_0_138]), ['final']).
cnf(c_0_164,plain,(impartial(X1,X2)|~object(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_139]), ['final']).
cnf(c_0_165,plain,(impartial(X1,X2)|~organism(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_140]), ['final']).
cnf(c_0_166,plain,(act(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_141]), ['final']).
cnf(c_0_167,plain,(event(X1,X2)|~act(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_142]), ['final']).
cnf(c_0_168,plain,(event(X1,X2)|~order(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_143]), ['final']).
cnf(c_0_169,plain,(forename(X1,X2)|~mia_forename(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_144]), ['final']).
cnf(c_0_170,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146]), c_0_147])]), ['final']).
cnf(c_0_171,negated_conjecture,(~entity(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_148, c_0_116]), ['final']).
cnf(c_0_172,negated_conjecture,(~forename(esk1_0,esk5_0)), inference(spm,[status(thm)],[c_0_149, c_0_118]), ['final']).
cnf(c_0_173,negated_conjecture,(~entity(esk1_0,esk3_0)), inference(spm,[status(thm)],[c_0_150, c_0_128]), ['final']).
cnf(c_0_174,negated_conjecture,(~eventuality(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_151]), ['final']).
cnf(c_0_175,negated_conjecture,(~object(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_121, c_0_152]), ['final']).
cnf(c_0_176,negated_conjecture,(~forename(esk1_0,esk2_0)), inference(spm,[status(thm)],[c_0_153, c_0_118]), ['final']).
cnf(c_0_177,negated_conjecture,(entity(esk1_0,esk4_0)), inference(spm,[status(thm)],[c_0_154, c_0_155]), ['final']).
cnf(c_0_178,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_179,negated_conjecture,(past(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_180,negated_conjecture,(order(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_181,negated_conjecture,(mia_forename(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
cnf(c_0_182,negated_conjecture,(actual_world(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_60]), ['final']).
# SZS output end Saturation
```

### Sample solution for SWV017+1

```# SZS output start Saturation
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_6.4.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
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_6.4.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(t_holds_key_bt_for_b, axiom, (t_holds(key(bt,b))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(intruder_can_record, axiom, (![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3))), file('/Users/schulz/EPROVER/TPTP_6.4.0_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_6.4.0_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_6.4.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(b_is_party_of_protocol, axiom, (party_of_protocol(b)), file('/Users/schulz/EPROVER/TPTP_6.4.0_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_6.4.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(t_holds_key_at_for_a, axiom, (t_holds(key(at,a))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
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_6.4.0_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_6.4.0_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_6.4.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(t_is_party_of_protocol, axiom, (party_of_protocol(t)), file('/Users/schulz/EPROVER/TPTP_6.4.0_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_6.4.0_FLAT/SWV017+1.p', intruder_composes_triples)).
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_6.4.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(a_is_party_of_protocol, axiom, (party_of_protocol(a)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
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_6.4.0_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_6.4.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(intruder_decomposes_pairs, axiom, (![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2)))), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(generated_keys_are_keys, axiom, (![X1]:a_key(generate_key(X1))), file('/Users/schulz/EPROVER/TPTP_6.4.0_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_6.4.0_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_6.4.0_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_6.4.0_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_6.4.0_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_6.4.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
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_6.4.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(an_intruder_nonce_is_a_fresh_intruder_nonce, axiom, (fresh_intruder_nonce(an_intruder_nonce)), file('/Users/schulz/EPROVER/TPTP_6.4.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(b_hold_key_bt_for_t, axiom, (b_holds(key(bt,t))), file('/Users/schulz/EPROVER/TPTP_6.4.0_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_6.4.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
fof(c_0_34, plain, (![X3]:![X4]:((message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))|(~message(sent(X3,b,pair(X3,X4)))|~fresh_to_b(X4)))&(b_stored(pair(X3,X4))|(~message(sent(X3,b,pair(X3,X4)))|~fresh_to_b(X4))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_creates_freash_nonces_in_time])])])).
fof(c_0_35, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~party_of_protocol(X5))|~party_of_protocol(X6))|message(sent(X5,X6,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_message_sent])])).
cnf(c_0_37,plain,(t_holds(key(bt,b))), inference(split_conjunct,[status(thm)],[t_holds_key_bt_for_b]), ['final']).
fof(c_0_38, plain, (![X4]:![X5]:![X6]:(~message(sent(X4,X5,X6))|intruder_message(X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_can_record])])).
cnf(c_0_39,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']).
cnf(c_0_40,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_41,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(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)), inference(split_conjunct,[status(thm)],[c_0_35]), ['final']).
cnf(c_0_43,plain,(party_of_protocol(b)), inference(split_conjunct,[status(thm)],[b_is_party_of_protocol]), ['final']).
fof(c_0_44, plain, (![X3]:![X4]:((~intruder_message(X3)|~intruder_message(X4))|intruder_message(pair(X3,X4)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_pairs])])).
cnf(c_0_47,plain,(t_holds(key(at,a))), inference(split_conjunct,[status(thm)],[t_holds_key_at_for_a]), ['final']).
fof(c_0_48, plain, (![X4]:![X5]:![X6]:(((intruder_message(X4)|~intruder_message(triple(X4,X5,X6)))&(intruder_message(X5)|~intruder_message(triple(X4,X5,X6))))&(intruder_message(X6)|~intruder_message(triple(X4,X5,X6))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_triples])])])).
cnf(c_0_49,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_38]), ['final']).
cnf(c_0_50,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_39, c_0_40]), c_0_41])]), ['final']).
cnf(c_0_51,plain,(b_stored(pair(X2,X1))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']).
cnf(c_0_52,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_39, c_0_42]), c_0_43])]), ['final']).
cnf(c_0_53,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_44]), ['final']).
cnf(c_0_55,plain,(a_stored(pair(b,an_a_nonce))), inference(split_conjunct,[status(thm)],[a_stored_message_i]), ['final']).
cnf(c_0_57,plain,(a_nonce(an_a_nonce)), inference(split_conjunct,[status(thm)],[an_a_nonce_is_a_nonce]), ['final']).
cnf(c_0_58,plain,(party_of_protocol(t)), inference(split_conjunct,[status(thm)],[t_is_party_of_protocol]), ['final']).
fof(c_0_59, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~intruder_message(X5))|~intruder_message(X6))|intruder_message(triple(X4,X5,X6)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_triples])])).
cnf(c_0_60,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_61,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_49, c_0_50]), ['final']).
fof(c_0_62, plain, (![X6]:![X7]:![X8]:(((~message(sent(X7,b,pair(encrypt(triple(X7,X6,generate_expiration_time(X8)),bt),encrypt(generate_b_nonce(X8),X6))))|~a_key(X6))|~b_stored(pair(X7,X8)))|b_holds(key(X6,X7)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_accepts_secure_session_key])])])])).
cnf(c_0_63,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_51, c_0_42]), c_0_43])]), ['final']).
cnf(c_0_65,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_52, c_0_53]), ['final']).
cnf(c_0_67,plain,(party_of_protocol(a)), inference(split_conjunct,[status(thm)],[a_is_party_of_protocol]), ['final']).
cnf(c_0_69,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_56, c_0_42]), c_0_58]), c_0_43])]), ['final']).
cnf(c_0_70,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_59]), ['final']).
cnf(c_0_71,plain,(intruder_message(b)), inference(spm,[status(thm)],[c_0_60, c_0_61]), ['final']).
cnf(c_0_72,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_73,plain,(b_holds(key(X1,X2))|~b_stored(pair(X2,X3))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))), inference(split_conjunct,[status(thm)],[c_0_62]), ['final']).
cnf(c_0_74,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_63, c_0_53]), ['final']).
fof(c_0_75, plain, (![X4]:![X5]:![X6]:(((~intruder_message(X4)|~intruder_holds(key(X5,X6)))|~party_of_protocol(X6))|intruder_message(encrypt(X4,X5)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_key_encrypts])])])])).
fof(c_0_76, plain, (![X4]:![X5]:((~intruder_message(X4)|~party_of_protocol(X5))|intruder_holds(key(X4,X5)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_holds_key])])).
fof(c_0_77, plain, (![X3]:![X4]:((intruder_message(X3)|~intruder_message(pair(X3,X4)))&(intruder_message(X4)|~intruder_message(pair(X3,X4))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_pairs])])])).
cnf(c_0_78,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_64, c_0_42]), c_0_58]), c_0_43])]), ['final']).
cnf(c_0_79,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_49, c_0_65]), ['final']).
cnf(c_0_80,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_66, c_0_42]), c_0_67]), c_0_58])]), ['final']).
cnf(c_0_82,plain,(b_stored(pair(a,an_a_nonce))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_40]), c_0_41])]), ['final']).
cnf(c_0_84,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_72, c_0_61]), ['final']).
cnf(c_0_85,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_73, c_0_74]), ['final']).
cnf(c_0_86,plain,(intruder_message(encrypt(X1,X2))|~party_of_protocol(X3)|~intruder_holds(key(X2,X3))|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_75]), ['final']).
cnf(c_0_87,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)), inference(split_conjunct,[status(thm)],[c_0_76]), ['final']).
cnf(c_0_88,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_89,plain,(intruder_message(pair(a,an_a_nonce))), inference(spm,[status(thm)],[c_0_49, c_0_40]), ['final']).
cnf(c_0_91,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_72, c_0_79]), ['final']).
cnf(c_0_94,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_73, c_0_82]), ['final']).
cnf(c_0_95,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_66, c_0_68]), ['final']).
cnf(c_0_97,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_85, c_0_42]), c_0_43])]), ['final']).
cnf(c_0_98,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_86, c_0_87])).
cnf(c_0_99,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_64, c_0_65]), c_0_71]), c_0_43])]), ['final']).
cnf(c_0_100,plain,(intruder_message(a)), inference(spm,[status(thm)],[c_0_88, c_0_89]), ['final']).
cnf(c_0_101,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_90, c_0_91]), c_0_71]), c_0_43])]), ['final']).
cnf(c_0_103,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_92, c_0_93]), ['final']).
fof(c_0_104, plain, (![X2]:a_key(generate_key(X2))), inference(variable_rename,[status(thm)],[generated_keys_are_keys])).
cnf(c_0_105,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_48]), ['final']).
cnf(c_0_106,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_94, c_0_42]), c_0_43]), c_0_67])]), ['final']).
cnf(c_0_108,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_77]), ['final']).
cnf(c_0_109,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_49, c_0_95]), ['final']).
cnf(c_0_110,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_66, c_0_96]), ['final']).
cnf(c_0_111,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_97, c_0_53]), ['final']).
cnf(c_0_112,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_98, c_0_43]), ['final']).
cnf(c_0_114,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_56, c_0_65]), c_0_100]), c_0_67])]), ['final']).
cnf(c_0_118,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_49, c_0_103]), ['final']).
cnf(c_0_119,plain,(a_key(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_104]), ['final']).
cnf(c_0_120,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_105, c_0_79]), ['final']).
cnf(c_0_121,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_106, c_0_53]), ['final']).
cnf(c_0_123,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))), inference(spm,[status(thm)],[c_0_108, c_0_109]), ['final']).
cnf(c_0_124,plain,(intruder_message(an_a_nonce)), inference(spm,[status(thm)],[c_0_108, c_0_89]), ['final']).
fof(c_0_125, plain, (![X2]:((fresh_to_b(X2)|~fresh_intruder_nonce(X2))&(intruder_message(X2)|~fresh_intruder_nonce(X2)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fresh_intruder_nonces_are_fresh_to_b])])])).
cnf(c_0_126,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_49, c_0_110]), ['final']).
cnf(c_0_127,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(generate_b_nonce(X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_111, c_0_112]), ['final']).
cnf(c_0_128,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_72, c_0_113]), ['final']).
cnf(c_0_130,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)), inference(spm,[status(thm)],[c_0_105, c_0_115])).
cnf(c_0_131,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_116, c_0_42]), c_0_58]), c_0_67])]), ['final']).
cnf(c_0_132,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_117, c_0_42]), c_0_58]), c_0_67])]), ['final']).
cnf(c_0_133,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_97, c_0_118]), c_0_119])]), c_0_120]), ['final']).
cnf(c_0_134,plain,(intruder_message(generate_b_nonce(an_a_nonce))), inference(spm,[status(thm)],[c_0_105, c_0_61]), ['final']).
cnf(c_0_135,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(generate_b_nonce(an_a_nonce))|~intruder_message(X1)|~a_key(X1)), inference(spm,[status(thm)],[c_0_121, c_0_112])).
cnf(c_0_136,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_122, c_0_42]), c_0_67]), c_0_58])]), ['final']).
fof(c_0_137, plain, (![X2]:(~fresh_intruder_nonce(X2)|fresh_intruder_nonce(generate_intruder_nonce(X2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[can_generate_more_fresh_intruder_nonces])])).
cnf(c_0_138,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_111, c_0_123]), c_0_124]), c_0_119]), c_0_41])]), ['final']).
cnf(c_0_139,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_52, c_0_109]), ['final']).
cnf(c_0_140,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_125]), ['final']).
cnf(c_0_141,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_52, c_0_126]), ['final']).
cnf(c_0_142,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_83, c_0_91]), c_0_100]), c_0_67])]), ['final']).
cnf(c_0_143,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_nonce(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)), inference(spm,[status(thm)],[c_0_127, c_0_128]), ['final']).
cnf(c_0_144,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_105, c_0_129]), ['final']).
cnf(c_0_145,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_130, c_0_81]), ['final']).
cnf(c_0_147,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_52, c_0_118]), ['final']).
cnf(c_0_148,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_63, c_0_126]), ['final']).
cnf(c_0_151,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_39, c_0_103]), c_0_100])]), ['final']).
cnf(c_0_152,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_63, c_0_109]), ['final']).
cnf(c_0_153,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_133, c_0_91]), ['final']).
cnf(c_0_154,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_125]), ['final']).
cnf(c_0_155,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_63, c_0_118]), ['final']).
cnf(c_0_156,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_51, c_0_103]), c_0_100])]), ['final']).
cnf(c_0_157,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)), inference(spm,[status(thm)],[c_0_108, c_0_118])).
cnf(c_0_158,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)|~intruder_message(X4)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~party_of_protocol(X4)), inference(spm,[status(thm)],[c_0_127, c_0_120]), ['final']).
cnf(c_0_159,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~party_of_protocol(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_134]), c_0_124]), c_0_41])]), ['final']).
cnf(c_0_160,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)],[c_0_135, c_0_134])]), ['final']).
fof(c_0_163, plain, (![X4]:![X5]:![X6]:(((~intruder_message(encrypt(X4,X5))|~intruder_holds(key(X5,X6)))|~party_of_protocol(X6))|intruder_message(X5))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_interception])])])])).
cnf(c_0_165,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(split_conjunct,[status(thm)],[c_0_137]), ['final']).
fof(c_0_166, plain, (![X2]:(~a_key(X2)|~a_nonce(X2))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[nothing_is_a_nonce_and_a_key])])).
fof(c_0_167, plain, (![X2]:~a_nonce(generate_key(X2))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[generated_keys_are_not_nonces])])).
cnf(c_0_168,plain,(b_holds(key(generate_key(an_a_nonce),b))|~intruder_message(X1)), 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_138, c_0_130]), c_0_71]), c_0_43]), c_0_124]), c_0_57]), c_0_41])])).
fof(c_0_169, plain, (![X2]:![X2]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X2)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[generated_times_and_nonces_are_nonces])])])).
cnf(c_0_170,plain,(fresh_intruder_nonce(an_intruder_nonce)), inference(split_conjunct,[status(thm)],[an_intruder_nonce_is_a_fresh_intruder_nonce]), ['final']).
cnf(c_0_171,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_139, c_0_140]), ['final']).
cnf(c_0_172,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))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_141, c_0_140]), ['final']).
cnf(c_0_175,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_143, c_0_144]), c_0_100]), c_0_119]), c_0_67])]), ['final']).
cnf(c_0_176,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(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_143, c_0_112]), c_0_105]), c_0_60]), ['final']).
cnf(c_0_177,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_143, c_0_145]), c_0_71]), c_0_119]), c_0_43])]), ['final']).
cnf(c_0_179,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_147, c_0_140]), ['final']).
cnf(c_0_180,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))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_148, c_0_140]), ['final']).
cnf(c_0_184,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_151, c_0_140]), ['final']).
cnf(c_0_186,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_152, c_0_140]), ['final']).
cnf(c_0_187,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_133, c_0_112]), c_0_60]), ['final']).
cnf(c_0_188,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~fresh_intruder_nonce(generate_key(an_a_nonce))|~intruder_message(X1)|~party_of_protocol(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153, c_0_140]), c_0_154]), ['final']).
cnf(c_0_189,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_155, c_0_140]), ['final']).
cnf(c_0_190,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_156, c_0_140]), ['final']).
cnf(c_0_191,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)), inference(spm,[status(thm)],[c_0_157, c_0_81]), ['final']).
cnf(c_0_192,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_138, c_0_112]), c_0_60]), ['final']).
cnf(c_0_194,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~intruder_message(X4)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~party_of_protocol(X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_112]), c_0_105]), c_0_60]), ['final']).
cnf(c_0_195,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)|~party_of_protocol(X3)), inference(spm,[status(thm)],[c_0_158, c_0_91]), ['final']).
cnf(c_0_196,plain,(b_holds(key(an_a_nonce,X1))|~intruder_message(X1)|~a_key(an_a_nonce)|~party_of_protocol(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_91]), c_0_124]), c_0_41])]), ['final']).
cnf(c_0_197,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)|~party_of_protocol(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_112]), c_0_105]), c_0_60]), ['final']).
cnf(c_0_198,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_160, c_0_112]), c_0_105]), ['final']).
cnf(c_0_199,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_160, c_0_84]), c_0_124])]), ['final']).
cnf(c_0_203,plain,(intruder_message(X1)|~party_of_protocol(X2)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_163]), ['final']).
cnf(c_0_208,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)), inference(spm,[status(thm)],[c_0_154, c_0_165]), ['final']).
cnf(c_0_209,plain,(~a_nonce(X1)|~a_key(X1)), inference(split_conjunct,[status(thm)],[c_0_166]), ['final']).
cnf(c_0_210,plain,(~a_nonce(generate_key(X1))), inference(split_conjunct,[status(thm)],[c_0_167]), ['final']).
cnf(c_0_211,plain,(b_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_168, c_0_81]), ['final']).
cnf(c_0_212,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))), inference(spm,[status(thm)],[c_0_88, c_0_109]), ['final']).
cnf(c_0_213,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_85, c_0_95]), c_0_124]), c_0_100]), c_0_119]), c_0_41]), c_0_67])]), ['final']).
cnf(c_0_214,plain,(a_holds(key(generate_key(an_a_nonce),b))), inference(spm,[status(thm)],[c_0_122, c_0_68]), ['final']).
cnf(c_0_215,plain,(b_holds(key(bt,t))), inference(split_conjunct,[status(thm)],[b_hold_key_bt_for_t]), ['final']).
cnf(c_0_216,plain,(a_holds(key(at,t))), inference(split_conjunct,[status(thm)],[a_holds_key_at_for_t]), ['final']).
cnf(c_0_217,plain,(a_nonce(generate_expiration_time(X1))), inference(split_conjunct,[status(thm)],[c_0_169]), ['final']).
cnf(c_0_218,plain,(intruder_message(an_intruder_nonce)), inference(spm,[status(thm)],[c_0_154, c_0_170]), ['final']).
cnf(c_0_219,plain,(a_nonce(generate_b_nonce(X1))), inference(split_conjunct,[status(thm)],[c_0_169]), ['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_7.2.0_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
```

### Sample solution for HL400001+1

```# SZS output start CNFRefutation
fof(thm_2Ebool_2ETRUTH, conjecture, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('/Users/schulz/Desktop/HL400001+1.p', thm_2Ebool_2ETRUTH)).
fof(thm_2Eextra_2Dho_2Etruth, axiom, p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)), file('/Users/schulz/Desktop/HL400001+1.p', thm_2Eextra_2Dho_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)],[thm_2Eextra_2Dho_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+2

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('/Users/schulz/Desktop/HL400001+2.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_1

```# SZS output start CNFRefutation
tff(thm_2Ebool_2ETRUTH, conjecture, p(mono_2Ec_2Ebool_2ET_2E0), file('/Users/schulz/Desktop/HL400001_1.p', thm_2Ebool_2ETRUTH)).
tff(reserved_2Eho_2Etruth, axiom, p(mono_2Ec_2Ebool_2ET_2E0), file('/Users/schulz/Desktop/HL400001_1.p', 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_2

```# SZS output start CNFRefutation
fof(conj_thm_2Ebool_2ETRUTH, conjecture, \$true, file('/Users/schulz/Desktop/HL400001_2.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
```

## Enigma,0.4

Jan Jakubuv
Czech Technical University in Prague, Czech Republic

### Sample proof for SEU140+2

```# SZS output start CNFRefutation
fof(t63_xboole_1, conjecture, ![X1, X2, X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t63_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('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', d4_xboole_0)).
fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', commutativity_k3_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_6.0.0_FLAT/SEU140+2.p', t48_xboole_1)).
fof(t40_xboole_1, lemma, ![X1, X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t40_xboole_1)).
fof(commutativity_k2_xboole_0, axiom, ![X1, X2]:set_union2(X1,X2)=set_union2(X2,X1), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', commutativity_k2_xboole_0)).
fof(l32_xboole_1, lemma, ![X1, X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', l32_xboole_1)).
fof(t7_xboole_1, lemma, ![X1, X2]:subset(X1,set_union2(X1,X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t7_xboole_1)).
fof(symmetry_r1_xboole_0, axiom, ![X1, X2]:(disjoint(X1,X2)=>disjoint(X2,X1)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', symmetry_r1_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_6.0.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(t3_boole, axiom, ![X1]:set_difference(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t3_boole)).
fof(t39_xboole_1, lemma, ![X1, X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t39_xboole_1)).
fof(t1_boole, axiom, ![X1]:set_union2(X1,empty_set)=X1, file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SEU140+2.p', t1_boole)).
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])).
fof(c_0_14, plain, ![X32, X33, X34, X35, X35, X32, X33, X34]:((((in(X35,X32)|~in(X35,X34)|X34!=set_difference(X32,X33))&(~in(X35,X33)|~in(X35,X34)|X34!=set_difference(X32,X33)))&(~in(X35,X32)|in(X35,X33)|in(X35,X34)|X34!=set_difference(X32,X33)))&((~in(esk5_3(X32,X33,X34),X34)|(~in(esk5_3(X32,X33,X34),X32)|in(esk5_3(X32,X33,X34),X33))|X34=set_difference(X32,X33))&((in(esk5_3(X32,X33,X34),X32)|in(esk5_3(X32,X33,X34),X34)|X34=set_difference(X32,X33))&(~in(esk5_3(X32,X33,X34),X33)|in(esk5_3(X32,X33,X34),X34)|X34=set_difference(X32,X33))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])])).
fof(c_0_15, plain, ![X11, X12]:set_intersection2(X11,X12)=set_intersection2(X12,X11), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).
fof(c_0_16, lemma, ![X99, X100]:set_difference(X99,set_difference(X99,X100))=set_intersection2(X99,X100), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_17, lemma, ![X95, X96]:set_difference(set_union2(X95,X96),X96)=set_difference(X95,X96), inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_18, plain, ![X9, X10]:set_union2(X9,X10)=set_union2(X10,X9), inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_19, lemma, ![X51, X52, X51, X52]:((set_difference(X51,X52)!=empty_set|subset(X51,X52))&(~subset(X51,X52)|set_difference(X51,X52)=empty_set)), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])])])).
fof(c_0_20, lemma, ![X114, X115]:subset(X114,set_union2(X114,X115)), inference(variable_rename,[status(thm)],[t7_xboole_1])).
fof(c_0_21, plain, ![X57, X58]:(~disjoint(X57,X58)|disjoint(X58,X57)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])).
fof(c_0_22, 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_23, plain, (in(X1,X2)|~in(X1,X3)|X3!=set_difference(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_24, lemma, ![X90, X91, X90, X91, X93]:(((in(esk9_2(X90,X91),X90)|disjoint(X90,X91))&(in(esk9_2(X90,X91),X91)|disjoint(X90,X91)))&(~in(X93,X90)|~in(X93,X91)|~disjoint(X90,X91))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])])).
cnf(c_0_25, plain, (set_intersection2(X1,X2)=set_intersection2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
cnf(c_0_26, lemma, (set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_16])).
cnf(c_0_27, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_28, plain, (set_union2(X1,X2)=set_union2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_29, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_30, lemma, (subset(X1,set_union2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_20])).
fof(c_0_31, plain, ![X89]:set_difference(X89,empty_set)=X89, inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_32, plain, (disjoint(X2,X1)|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_33, negated_conjecture, (disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_34, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3))), inference(er,[status(thm)],[c_0_23])).
cnf(c_0_35, lemma, (in(esk9_2(X1,X2),X2)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_36, 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_25, c_0_26]), c_0_26])).
cnf(c_0_37, lemma, (set_difference(set_union2(X1,X2),X1)=set_difference(X2,X1)), inference(spm,[status(thm)],[c_0_27, c_0_28])).
cnf(c_0_38, lemma, (set_difference(X1,set_union2(X1,X2))=empty_set), inference(spm,[status(thm)],[c_0_29, c_0_30])).
cnf(c_0_39, plain, (set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_31])).
fof(c_0_40, lemma, ![X87, X88]:set_union2(X87,set_difference(X88,X87))=set_union2(X87,X88), inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_41, negated_conjecture, (subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_42, plain, ![X66]:set_union2(X66,empty_set)=X66, inference(variable_rename,[status(thm)],[t1_boole])).
cnf(c_0_43, lemma, (~in(X1,X2)|~in(X1,X3)|~disjoint(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_44, negated_conjecture, (disjoint(esk13_0,esk12_0)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
cnf(c_0_45, lemma, (disjoint(X1,set_difference(X2,X3))|in(esk9_2(X1,set_difference(X2,X3)),X2)), inference(spm,[status(thm)],[c_0_34, c_0_35])).
cnf(c_0_46, lemma, (set_difference(set_union2(X1,X2),set_difference(X2,X1))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_38]), c_0_39])).
cnf(c_0_47, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_40])).
cnf(c_0_48, negated_conjecture, (set_difference(esk11_0,esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_29, c_0_41])).
cnf(c_0_49, plain, (set_union2(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_50, negated_conjecture, (~in(X1,esk12_0)|~in(X1,esk13_0)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
cnf(c_0_51, lemma, (in(esk9_2(X1,X2),X1)|disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_52, lemma, (disjoint(X1,X2)|in(esk9_2(X1,X2),set_union2(X2,X3))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
cnf(c_0_53, negated_conjecture, (set_union2(esk11_0,esk12_0)=esk12_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49]), c_0_28])).
cnf(c_0_54, lemma, (disjoint(esk13_0,X1)|~in(esk9_2(esk13_0,X1),esk12_0)), inference(spm,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_55, negated_conjecture, (disjoint(X1,esk11_0)|in(esk9_2(X1,esk11_0),esk12_0)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_56, negated_conjecture, (disjoint(esk13_0,esk11_0)), inference(spm,[status(thm)],[c_0_54, c_0_55])).
cnf(c_0_57, negated_conjecture, (~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_58, negated_conjecture, (\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_56]), c_0_57]), ['proof']).
# SZS output end CNFRefutation
```

## GKC 0.4

Tanel Tammet
Tallin University of Technology, Estonia

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

```    clause_number [derivation method, parent clause numbers, clause class] derived_clause_in_cnf.
```
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. Any Skolem functions and definition predicates introduced start with \$. Clausification is not reflected in the proof: the proof contains only steps on the already clausified problem. The original formulas can be traced back to using their names, which are also present in the proof, attached to input clauses.

The derivation method can be:

• 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).

### Sample solution for SEU140+2

```% SZS output start CNFRefutation for /opt/TPTP/Problems/SEU/SEU140+2.p
1: [in,d7_xboole_0, axiom] =(set_intersection2(?0,?1),empty_set) | -disjoint(?0,?1).
2: [in,t6_boole, axiom] =(X,empty_set) | -empty(X).
3: [in,rc1_xboole_0, 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: [in,t63_xboole_1, goal] disjoint(\$sk1,\$sk2).
7: [mp, 5.1, 6, fromgoal] =(set_intersection2(\$sk1,\$sk2),\$sk9).
8: [in,t12_xboole_1, axiom] =(set_union2(X,Y),Y) | -subset(X,Y).
9: [in,t63_xboole_1, goal] subset(\$sk3,\$sk1).
10: [mp, 8.1, 9, fromgoal] =(set_union2(\$sk3,\$sk1),\$sk1).
11: [in,t26_xboole_1, axiom] subset(set_intersection2(X,Y),set_intersection2(Z,Y)) | -subset(X,Z).
12: [in,t7_xboole_1, axiom] subset(X,set_union2(X,Y)).
13: [mp, 11.1, 12, fromaxiom] subset(set_intersection2(X,Y),set_intersection2(set_union2(X,Z),Y)).
14: [in,l32_xboole_1, axiom] =(set_difference(?0,?1),empty_set) | -subset(?0,?1).
15: [simp, 14, 4, fromaxiom] =(set_difference(X,Y),\$sk9) | -subset(X,Y).
16: [mp, 13, 15.1, fromaxiom] =(set_difference(set_intersection2(X,Y),set_intersection2(set_union2(X,Z),Y)),\$sk9).
17: [=, 10, 16.0.6, fromgoal] =(set_difference(set_intersection2(\$sk3,X),set_intersection2(\$sk1,X)),\$sk9).
18: [=, 7, 17.0.5, fromgoal] =(set_difference(set_intersection2(\$sk3,\$sk2),\$sk9),\$sk9).
19: [in,t3_boole, axiom] =(set_difference(X,empty_set),X).
20: [=, 4.0.R, 19.0.3, fromaxiom] =(set_difference(X,\$sk9),X).
21: [simp, 18, 20, fromgoal] =(set_intersection2(\$sk3,\$sk2),\$sk9).
22: [in,d7_xboole_0, axiom] -=(set_intersection2(?0,?1),empty_set) | disjoint(?0,?1).
23: [simp, 22, 4, fromaxiom] -=(set_intersection2(X,Y),\$sk9) | disjoint(X,Y).
24: [in,t63_xboole_1, goal] -disjoint(\$sk3,\$sk2).
25: [mp, 21, 23, 24, 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: [in,ternary_multiply_1, axiom] =(multiply(X,Y,Y),Y).
2: [in,associativity, axiom] =(multiply(multiply(X,Y,Z),U,multiply(X,Y,V)),multiply(X,Y,multiply(Z,U,V))).
3: [=, 1, 2.0.2, fromaxiom] =(multiply(X,Y,multiply(Z,X,U)),multiply(Z,X,multiply(X,Y,U))).
4: [in,right_inverse, axiom] =(multiply(X,Y,inverse(Y)),X).
5: [in,ternary_multiply_2, axiom] =(multiply(X,X,Y),X).
6: [=, 2, 5.0.1, fromaxiom] =(multiply(X,Y,multiply(Z,multiply(X,Y,Z),U)),multiply(X,Y,Z)).
7: [=, 4, 6.0.6, fromaxiom] =(multiply(X3,Y3,multiply(inverse(Y3),X3,Z3)),multiply(X3,Y3,inverse(Y3))).
8: [simp, 7, 4, fromaxiom] =(multiply(X,Y,multiply(inverse(Y),X,Z)),X).
9: [=, 3, 8.0.1, fromaxiom] =(multiply(inverse(X),Y,multiply(Y,X,Z)),Y).
10: [=, 1, 9.0.5, fromaxiom] =(multiply(inverse(X),Y,X),Y).
11: [=, 10, 4.0.1, fromaxiom] =(X,inverse(inverse(X))).
12: [in,prove_inverse_is_self_cancelling, goal] -=(inverse(inverse(a)),a).
13: [=, 11.0.R, 12.0.1, fromgoal] false
% SZS output end CNFRefutation for /opt/TPTP/Problems/BOO/BOO001-1.p
```

## iProver 3.0

Konstantin Korovin
University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS output start CNFRefutation

fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('/Users/korovin/TPTP-v7.2.0/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('/Users/korovin/TPTP-v7.2.0/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('/Users/korovin/TPTP-v7.2.0/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_3201,plain,
( ~ subset(sK10,X0)
| in(sK8(sK10,sK12),X0)
| ~ in(sK8(sK10,sK12),sK10) ),
inference(instantiation,[status(thm)],[c_17]) ).

cnf(c_5363,plain,
( ~ subset(sK10,sK11)
| in(sK8(sK10,sK12),sK11)
| ~ in(sK8(sK10,sK12),sK10) ),
inference(instantiation,[status(thm)],[c_3201]) ).

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

cnf(c_3160,plain,
( ~ disjoint(X0,sK12)
| ~ in(sK8(sK10,sK12),X0)
| ~ in(sK8(sK10,sK12),sK12) ),
inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_5258,plain,
( ~ disjoint(sK11,sK12)
| ~ in(sK8(sK10,sK12),sK11)
| ~ in(sK8(sK10,sK12),sK12) ),
inference(instantiation,[status(thm)],[c_3160]) ).

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_5363,c_5258,c_3001,c_2998,c_72,c_73,c_74]) ).

% SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```% SZS output start Model

%------ Negative definition of equality_sorted
fof(lit_def,axiom,
(! [X0,X0,X1] :
( ~(equality_sorted(X0,X0,X1)) <=>
(
(
( X0=iProver_forename_2_\$i & X0=sK4 & X1=sK3 )
)

|
(
( X0=iProver_forename_2_\$i & X0=sK4 & X1=sK1 )
)

|
(
( X0=iProver_forename_2_\$i & X0=sK3 )
&
( X1!=sK3 )
)

|
(
( X0=iProver_forename_2_\$i & X0=sK3 & X1=sK1 )
)

|
(
( X0=iProver_forename_2_\$i & X0=sK1 )
&
( X1!=sK1 )
)

|
(
( X0=iProver_forename_2_\$i & X0=sK1 & X1=sK3 )
)

|
(
( X0=iProver_forename_2_\$i & X0=sK2 )
&
( X1!=sK2 )
)

|
(
( X0=iProver_forename_2_\$i & X1=sK3 )
&
( X0!=sK3 )
)

|
(
( X0=iProver_forename_2_\$i & X1=sK1 )
&
( X0!=sK1 )
)

|
(
( X0=iProver_forename_2_\$i & X1=sK2 )
&
( X0!=sK2 )
)

)
)
)
).

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

%------ Positive definition of forename
fof(lit_def,axiom,
(! [X0,X0] :
( forename(X0,X0) <=>
(
(
( X0=sK0 & X0=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,X0,X1] :
( of(X0,X0,X1) <=>
(
(
( X0=sK0 & X0=sK2 & X1=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
```

### Sample solution for SWV017+1

```% SZS output start Model

%------ 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
```

### Sample solution for BOO001-1

```% SZS output start CNFRefutation

cnf(c_4,plain,
( X0 = multiply(inverse(X1),X1,X0) ),
file('/Users/korovin/TPTP-v7.2.0/Axioms/BOO001-0.ax', left_inverse) ).

cnf(c_2,plain,
( X0 = multiply(X1,X0,X0) ),
file('/Users/korovin/TPTP-v7.2.0/Axioms/BOO001-0.ax', ternary_multiply_1) ).

cnf(c_5,plain,
( X0 = multiply(X0,X1,inverse(X1)) ),
file('/Users/korovin/TPTP-v7.2.0/Axioms/BOO001-0.ax', right_inverse) ).

cnf(c_3,plain,
( X0 = multiply(X0,X0,X1) ),
file('/Users/korovin/TPTP-v7.2.0/Axioms/BOO001-0.ax', ternary_multiply_2) ).

cnf(c_1,plain,
( multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)) ),
file('/Users/korovin/TPTP-v7.2.0/Axioms/BOO001-0.ax', associativity) ).

cnf(c_59,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_198,plain,
( multiply(X0,X1,inverse(X1)) = multiply(X0,inverse(X1),multiply(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_3,c_59]) ).

cnf(c_200,plain,
( X0 = multiply(X0,inverse(X1),multiply(X0,X1,X2)) ),
inference(demodulation,[status(thm)],[c_5,c_198]) ).

cnf(c_1081,plain,
( X0 = multiply(X0,inverse(X1),X1) ),
inference(superposition,[status(thm)],[c_2,c_200]) ).

cnf(c_1174,plain,
( X0 = inverse(inverse(X0)) ),
inference(superposition,[status(thm)],[c_4,c_1081]) ).

cnf(c_0,negated_conjecture,
( inverse(inverse(a)) != a ),
file('/Users/korovin/TPTP-v7.2.0/Problems/BOO/BOO001-1.p', prove_inverse_is_self_cancelling) ).

cnf(c_1244,plain,
( a != a ),
inference(demodulation,[status(thm)],[c_1174,c_0]) ).

cnf(c_1245,plain,
( \$false ),
inference(equality_resolution_simp,[status(thm)],[c_1244]) ).

% SZS output end CNFRefutation
```

### Sample solution for HL400001+1

```% SZS output start CNFRefutation

fof(f17,conjecture,(
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
file('CASC_2019/sample_solutions/HAL_400001/HL400001+1.p',unknown)).

fof(f18,negated_conjecture,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(negated_conjecture,[],[f17])).

fof(f32,plain,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(flattening,[],[f18])).

fof(f87,plain,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(cnf_transformation,[],[f32])).

cnf(c_26,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[],[f88]) ).

cnf(c_27,negated_conjecture,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[],[f87]) ).

( \$false ),
inference(minisat,[status(thm)],[c_26,c_27]) ).

% SZS output end CNFRefutation
```

### Sample solution for HL400001+2

```% SZS output start CNFRefutation

fof(f14,conjecture,(
\$true),
file('CASC_2019/sample_solutions/HAL_400001/HL400001+2.p',unknown)).

fof(f15,negated_conjecture,(
~\$true),
inference(negated_conjecture,[],[f14])).

fof(f23,plain,(
\$false),
inference(true_and_false_elimination,[],[f15])).

fof(f54,plain,(
\$false),
inference(cnf_transformation,[],[f23])).

cnf(c_0,negated_conjecture,
( \$false ),
inference(cnf_transformation,[],[f54]) ).

% SZS output 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 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 HL400001^1

```% 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
```

## MaedMax 1.3

Sarah Winkler
Universität Innsbruck, Austria

### Sample proof for BOO001-1

```% SZS output start CNFRefutation
cnf(eq_0, axiom, (V = multiply(W,V,V)),
file('/tmp/SystemOnTPTP51097/BOO001-1.tptp')).
cnf(eq_1, axiom, (V = multiply(V,W,inverse(W))),
file('/tmp/SystemOnTPTP51097/BOO001-1.tptp')).
cnf(eq_2, axiom,
(multiply(V,W,multiply(X,Y,Z)) = multiply(multiply(V,W,X),Y,multiply(V,W,Z))),
file('/tmp/SystemOnTPTP51097/BOO001-1.tptp')).
cnf(eq_3, plain,
(multiply(V,W,multiply(X,Y,inverse(W))) = multiply(multiply(V,W,X),Y,V)),
inference(cp, [status(thm)], [eq_1, eq_2])).
cnf(eq_4, plain,
(multiply(V,W,inverse(W)) = multiply(multiply(V,W,X),inverse(W),V)),
inference(cp, [status(thm)], [eq_0, eq_3])).
cnf(eq_5, plain, (V = multiply(multiply(V,W,X),inverse(W),V)),
inference(rw, [status(thm)], [eq_4, eq_1])).
cnf(eq_6, plain, (V = multiply(W,inverse(W),V)),
inference(cp, [status(thm)], [eq_0, eq_5])).
cnf(eq_7, plain, (V = inverse(inverse(V))),
inference(cp, [status(thm)], [eq_6, eq_1])).
cnf(eq_8, negated_conjecture, (a != inverse(inverse(a))),
file('/tmp/SystemOnTPTP51097/BOO001-1.tptp')).
cnf(eq_9, negated_conjecture, (a != a),
inference(rw, [status(thm)], [eq_8, eq_7])).
cnf(bot, negated_conjecture, (\$false), inference(cn, [status(thm)], [eq_9])).
% SZS output end CNFRefutation
```

## MaLARea 0.6

Josef Urban
Czech Technical University in Prague, Czech Republic

### Sample solution for SEU140+2

```# SZS output start CNFRefutation
fof(t63_xboole_1, conjecture, (![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t63_xboole_1)).
fof(symmetry_r1_xboole_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', symmetry_r1_xboole_0)).
fof(t1_xboole_1, lemma, (![X1]:![X2]:![X3]:((subset(X1,X2)&subset(X2,X3))=>subset(X1,X3))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t1_xboole_1)).
fof(t40_xboole_1, lemma, (![X1]:![X2]:set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t40_xboole_1)).
fof(commutativity_k2_xboole_0, axiom, (![X1]:![X2]:set_union2(X1,X2)=set_union2(X2,X1)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', commutativity_k2_xboole_0)).
fof(t2_boole, axiom, (![X1]:set_intersection2(X1,empty_set)=empty_set), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t2_boole)).
fof(t48_xboole_1, lemma, (![X1]:![X2]:set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t48_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/SystemOnTPTP4890/SEU140+2.tptp', 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('/tmp/SystemOnTPTP4890/SEU140+2.tptp', d4_xboole_0)).
fof(l32_xboole_1, lemma, (![X1]:![X2]:(set_difference(X1,X2)=empty_set<=>subset(X1,X2))), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', l32_xboole_1)).
fof(d7_xboole_0, axiom, (![X1]:![X2]:(disjoint(X1,X2)<=>set_intersection2(X1,X2)=empty_set)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', d7_xboole_0)).
fof(t39_xboole_1, lemma, (![X1]:![X2]:set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t39_xboole_1)).
fof(t3_boole, axiom, (![X1]:set_difference(X1,empty_set)=X1), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t3_boole)).
fof(commutativity_k3_xboole_0, axiom, (![X1]:![X2]:set_intersection2(X1,X2)=set_intersection2(X2,X1)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', commutativity_k3_xboole_0)).
fof(t36_xboole_1, lemma, (![X1]:![X2]:subset(set_difference(X1,X2),X1)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t36_xboole_1)).
fof(t12_xboole_1, lemma, (![X1]:![X2]:(subset(X1,X2)=>set_union2(X1,X2)=X2)), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t12_xboole_1)).
fof(t1_boole, axiom, (![X1]:set_union2(X1,empty_set)=X1), file('/tmp/SystemOnTPTP4890/SEU140+2.tptp', t1_boole)).
fof(c_0_17, 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_18, plain, (![X3]:![X4]:(~disjoint(X3,X4)|disjoint(X4,X3))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])).
fof(c_0_19, 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_17])])])).
fof(c_0_20, lemma, (![X4]:![X5]:![X6]:((~subset(X4,X5)|~subset(X5,X6))|subset(X4,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])).
fof(c_0_21, lemma, (![X3]:![X4]:set_difference(set_union2(X3,X4),X4)=set_difference(X3,X4)), inference(variable_rename,[status(thm)],[t40_xboole_1])).
fof(c_0_22, plain, (![X3]:![X4]:set_union2(X3,X4)=set_union2(X4,X3)), inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0])).
fof(c_0_23, plain, (![X2]:set_intersection2(X2,empty_set)=empty_set), inference(variable_rename,[status(thm)],[t2_boole])).
fof(c_0_24, lemma, (![X3]:![X4]:set_difference(X3,set_difference(X3,X4))=set_intersection2(X3,X4)), inference(variable_rename,[status(thm)],[t48_xboole_1])).
fof(c_0_25, lemma, (![X4]:![X5]:![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~in(X7,X4)|~in(X7,X5))|~disjoint(X4,X5)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])])).
cnf(c_0_26,plain,(disjoint(X1,X2)|~disjoint(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_27,negated_conjecture,(disjoint(esk12_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_28, plain, (![X5]:![X6]:![X7]:![X8]:![X8]:![X5]:![X6]:![X7]:(((((in(X8,X5)|~in(X8,X7))|X7!=set_difference(X5,X6))&((~in(X8,X6)|~in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(X8,X5)|in(X8,X6))|in(X8,X7))|X7!=set_difference(X5,X6)))&(((~in(esk5_3(X5,X6,X7),X7)|(~in(esk5_3(X5,X6,X7),X5)|in(esk5_3(X5,X6,X7),X6)))|X7=set_difference(X5,X6))&(((in(esk5_3(X5,X6,X7),X5)|in(esk5_3(X5,X6,X7),X7))|X7=set_difference(X5,X6))&((~in(esk5_3(X5,X6,X7),X6)|in(esk5_3(X5,X6,X7),X7))|X7=set_difference(X5,X6)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_xboole_0])])])])])])])])).
fof(c_0_29, lemma, (![X3]:![X4]:![X3]:![X4]:((set_difference(X3,X4)!=empty_set|subset(X3,X4))&(~subset(X3,X4)|set_difference(X3,X4)=empty_set))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])])])).
cnf(c_0_30,lemma,(subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_31,negated_conjecture,(subset(esk11_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_32, plain, (![X3]:![X4]:![X3]:![X4]:((~disjoint(X3,X4)|set_intersection2(X3,X4)=empty_set)&(set_intersection2(X3,X4)!=empty_set|disjoint(X3,X4)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])])])).
cnf(c_0_33,lemma,(set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_34,plain,(set_union2(X1,X2)=set_union2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_22])).
fof(c_0_35, lemma, (![X3]:![X4]:set_union2(X3,set_difference(X4,X3))=set_union2(X3,X4)), inference(variable_rename,[status(thm)],[t39_xboole_1])).
cnf(c_0_36,plain,(set_intersection2(X1,empty_set)=empty_set), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_37,lemma,(set_difference(X1,set_difference(X1,X2))=set_intersection2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
fof(c_0_38, plain, (![X2]:set_difference(X2,empty_set)=X2), inference(variable_rename,[status(thm)],[t3_boole])).
cnf(c_0_39,lemma,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_40,negated_conjecture,(disjoint(esk13_0,esk12_0)), inference(spm,[status(thm)],[c_0_26, c_0_27])).
cnf(c_0_41,plain,(in(X4,X2)|X1!=set_difference(X2,X3)|~in(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
fof(c_0_42, plain, (![X3]:![X4]:set_intersection2(X3,X4)=set_intersection2(X4,X3)), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])).
cnf(c_0_43,lemma,(set_difference(X1,X2)=empty_set|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_44,negated_conjecture,(subset(X1,esk12_0)|~subset(X1,esk11_0)), inference(spm,[status(thm)],[c_0_30, c_0_31])).
fof(c_0_45, lemma, (![X3]:![X4]:subset(set_difference(X3,X4),X3)), inference(variable_rename,[status(thm)],[t36_xboole_1])).
fof(c_0_46, lemma, (![X3]:![X4]:(~subset(X3,X4)|set_union2(X3,X4)=X4)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])).
cnf(c_0_47,plain,(disjoint(X1,X2)|set_intersection2(X1,X2)!=empty_set), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_48,lemma,(set_difference(set_union2(X1,X2),X1)=set_difference(X2,X1)), inference(spm,[status(thm)],[c_0_33, c_0_34])).
cnf(c_0_49,lemma,(set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_35])).
cnf(c_0_50,plain,(set_difference(X1,set_difference(X1,empty_set))=empty_set), inference(rw,[status(thm)],[c_0_36, c_0_37])).
cnf(c_0_51,plain,(set_difference(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_38])).
cnf(c_0_52,negated_conjecture,(~in(X1,esk12_0)|~in(X1,esk13_0)), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_53,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_54,plain,(in(X1,X2)|~in(X1,set_difference(X2,X3))), inference(er,[status(thm)],[c_0_41])).
cnf(c_0_55,lemma,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_56,plain,(set_intersection2(X1,X2)=set_intersection2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_57,lemma,(set_difference(X1,esk12_0)=empty_set|~subset(X1,esk11_0)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
cnf(c_0_58,lemma,(subset(set_difference(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_59,plain,(set_intersection2(X1,X2)=empty_set|~disjoint(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_32])).
fof(c_0_60, plain, (![X2]:set_union2(X2,empty_set)=X2), inference(variable_rename,[status(thm)],[t1_boole])).
cnf(c_0_61,lemma,(set_union2(X1,X2)=X2|~subset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_62,plain,(disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set), inference(rw,[status(thm)],[c_0_47, c_0_37])).
cnf(c_0_63,lemma,(set_difference(set_difference(X1,X2),X2)=set_difference(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_48])).
cnf(c_0_64,plain,(set_difference(X1,X1)=empty_set), inference(rw,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_65,lemma,(disjoint(X1,esk13_0)|~in(esk9_2(X1,esk13_0),esk12_0)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_66,lemma,(disjoint(set_difference(X1,X2),X3)|in(esk9_2(set_difference(X1,X2),X3),X1)), inference(spm,[status(thm)],[c_0_54, c_0_55])).
cnf(c_0_67,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_56, c_0_37]), c_0_37])).
cnf(c_0_68,lemma,(set_difference(set_difference(esk11_0,X1),esk12_0)=empty_set), inference(spm,[status(thm)],[c_0_57, c_0_58])).
cnf(c_0_69,plain,(set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2)), inference(rw,[status(thm)],[c_0_59, c_0_37])).
cnf(c_0_70,plain,(set_union2(X1,empty_set)=X1), inference(split_conjunct,[status(thm)],[c_0_60])).
cnf(c_0_71,lemma,(set_union2(X1,set_difference(X1,X2))=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_58]), c_0_34])).
cnf(c_0_72,lemma,(disjoint(set_difference(X1,X2),X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64])])).
cnf(c_0_73,lemma,(disjoint(set_difference(esk12_0,X1),esk13_0)), inference(spm,[status(thm)],[c_0_65, c_0_66])).
cnf(c_0_74,lemma,(set_difference(esk12_0,set_difference(esk12_0,set_difference(esk11_0,X1)))=set_difference(esk11_0,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_51])).
cnf(c_0_75,lemma,(set_difference(X1,X2)=X1|~disjoint(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_69]), c_0_70]), c_0_34]), c_0_71])).
cnf(c_0_76,lemma,(disjoint(X1,set_difference(X2,X1))), inference(spm,[status(thm)],[c_0_26, c_0_72])).
cnf(c_0_77,lemma,(disjoint(set_difference(esk11_0,X1),esk13_0)), inference(spm,[status(thm)],[c_0_73, c_0_74])).
cnf(c_0_78,lemma,(set_difference(X1,set_difference(X2,X1))=X1), inference(spm,[status(thm)],[c_0_75, c_0_76])).
cnf(c_0_79,negated_conjecture,(~disjoint(esk11_0,esk13_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_80,lemma,(\$false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79]), ['proof']).
# SZS output end CNFRefutation
```

## nanoCoP---1.1

Jens Otten
University of Oslo, Norway

• the following list represents a non-clausal connection proof (a tree in which each node is labelled with a nested clause)
• I^V is a skolem term f_I(V) for variable list V
• (I^K)^V:C is the (nested) clause C with index (I^K)^V, in which I is the unique index of C, K distinguishes different copies of C, and V is the list of (instantiated) variables in C

### Sample solution for SEU140+2

```% SZS output start Proof for SEU140+2.p
[(505 ^ 0) ^ [587 ^ [], 586 ^ []] : [disjoint(586 ^ [], 587 ^ []), 506 ^ 0 : [(507 ^ 0) ^ [499 ^ [587 ^ [], 585 ^ []]] : [in(499 ^ [587 ^ [], 585 ^ []], 586 ^ []), in(499 ^ [587 ^ [], 585 ^ []], 587 ^ [])]]], [(591 ^ 1) ^ [] : [-(disjoint(586 ^ [], 587 ^ []))]], [(163 ^ 3) ^ [586 ^ [], set_difference(586 ^ [], 585 ^ []), 585 ^ []] : [-(in(499 ^ [587 ^ [], 585 ^ []], 586 ^ [])), 166 ^ 3 : [(177 ^ 3) ^ [499 ^ [587 ^ [], 585 ^ []]] : [178 ^ 3 : [(179 ^ 3) ^ [] : [in(499 ^ [587 ^ [], 585 ^ []], 585 ^ [])], (181 ^ 3) ^ [] : [in(499 ^ [587 ^ [], 585 ^ []], set_difference(586 ^ [], 585 ^ []))]]]], 586 ^ [] = set_union2(585 ^ [], set_difference(586 ^ [], 585 ^ []))], [(496 ^ 8) ^ [587 ^ [], 585 ^ []] : [-(in(499 ^ [587 ^ [], 585 ^ []], 585 ^ [])), 500 ^ 8 : [(501 ^ 8) ^ [] : []], -(disjoint(585 ^ [], 587 ^ []))], [(593 ^ 9) ^ [] : [disjoint(585 ^ [], 587 ^ [])]]], [(523 ^ 4) ^ [586 ^ [], 585 ^ []] : [-(586 ^ [] = set_union2(585 ^ [], set_difference(586 ^ [], 585 ^ []))), subset(585 ^ [], 586 ^ [])], [(589 ^ 5) ^ [] : [-(subset(585 ^ [], 586 ^ []))]]]], [(496 ^ 3) ^ [587 ^ [], 585 ^ []] : [-(in(499 ^ [587 ^ [], 585 ^ []], 587 ^ [])), 500 ^ 3 : [(503 ^ 3) ^ [] : []], -(disjoint(585 ^ [], 587 ^ []))], [(593 ^ 4) ^ [] : [disjoint(585 ^ [], 587 ^ [])]]]]

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

## 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 1.0

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(X291,X290)|in(skolem0005(X291,X290),X290),inference(split_conjunct,status(thm),[c58])).
cnf(c462,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])).
cnf(c61,plain,~in(X298,X299)|~in(X298,X300)|~disjoint(X299,X300),inference(split_conjunct,status(thm),[c58])).
cnf(c473,plain,~in(X1133,skolem0002)|~in(X1133,skolem0003),inference(resolution,status(thm),[c61, c27])).
cnf(c4215,plain,~in(skolem0005(skolem0001,skolem0003),skolem0002),inference(resolution,status(thm),[c473, c462])).
cnf(c59,plain,disjoint(X283,X282)|in(skolem0005(X283,X282),X283),inference(split_conjunct,status(thm),[c58])).
cnf(c443,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,X595)|~in(X596,X594)|in(X596,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(X264,X263)|X263=set_union2(X264,set_difference(X263,X264)),inference(split_conjunct,status(thm),[c45])).
cnf(c401,plain,skolem0002=set_union2(skolem0001,set_difference(skolem0002,skolem0001)),inference(resolution,status(thm),[c46, c26])).
cnf(c6542,plain,~in(X3177,skolem0001)|in(X3177,skolem0002),inference(resolution,status(thm),[c401, c210])).
cnf(c22208,plain,in(skolem0005(skolem0001,skolem0003),skolem0002),inference(resolution,status(thm),[c6542, c443])).
cnf(c42965,plain,\$false,inference(resolution,status(thm),[c22208, c4215])).
# SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```# SZS output start Saturation
cnf(reflexivity,axiom,X99=X99,eq_axiom).
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])).
cnf(c28,plain,X362!=X359|X358!=X357|X360!=X361|~of(X362,X358,X360)|of(X359,X357,X361),eq_axiom).
cnf(c313,plain,skolem0001!=X484|skolem0003!=X485|skolem0002!=X483|of(X484,X485,X483),inference(resolution,status(thm),[c28, c43])).
cnf(c378,plain,skolem0001!=X515|skolem0003!=X516|of(X515,X516,skolem0002),inference(resolution,status(thm),[c313, reflexivity])).
cnf(c399,plain,skolem0001!=X517|of(X517,skolem0003,skolem0002),inference(resolution,status(thm),[c378, reflexivity])).
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(X458,X459)|~forename(X458,X460)|~of(X458,X460,X459)|~forename(X458,X461)|X461=X460|~of(X458,X461,X459),inference(split_conjunct,status(thm),[c59])).
cnf(c365,plain,~entity(skolem0001,skolem0002)|~forename(skolem0001,X514)|~of(skolem0001,X514,skolem0002)|~forename(skolem0001,skolem0003)|skolem0003=X514,inference(resolution,status(thm),[c60, c43])).
cnf(c50,negated_conjecture,patient(skolem0001,skolem0005,skolem0004),inference(split_conjunct,status(thm),[c41])).
cnf(c18,plain,X268!=X265|X264!=X263|X266!=X267|~patient(X268,X264,X266)|patient(X265,X263,X267),eq_axiom).
cnf(c267,plain,skolem0001!=X474|skolem0005!=X476|skolem0004!=X475|patient(X474,X476,X475),inference(resolution,status(thm),[c18, c50])).
cnf(c373,plain,skolem0001!=X511|skolem0005!=X512|patient(X511,X512,skolem0004),inference(resolution,status(thm),[c267, reflexivity])).
cnf(c396,plain,skolem0001!=X513|patient(X513,skolem0005,skolem0004),inference(resolution,status(thm),[c373, reflexivity])).
cnf(c49,negated_conjecture,agent(skolem0001,skolem0005,skolem0002),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(X451,X449)|~agent(X451,X449,X450)|~patient(X451,X449,X448)|X450!=X448,inference(split_conjunct,status(thm),[c55])).
cnf(c360,plain,~nonreflexive(skolem0001,skolem0005)|~agent(skolem0001,skolem0005,X509)|X509!=skolem0004,inference(resolution,status(thm),[c56, c50])).
cnf(c394,plain,~nonreflexive(skolem0001,skolem0005)|skolem0002!=skolem0004,inference(resolution,status(thm),[c360, c49])).
cnf(c3,plain,X144!=X141|X140!=X139|X142!=X143|~agent(X144,X140,X142)|agent(X141,X139,X143),eq_axiom).
cnf(c201,plain,skolem0001!=X467|skolem0005!=X469|skolem0002!=X468|agent(X467,X469,X468),inference(resolution,status(thm),[c3, c49])).
cnf(c369,plain,skolem0001!=X508|skolem0005!=X507|agent(X508,X507,skolem0002),inference(resolution,status(thm),[c201, reflexivity])).
cnf(c393,plain,skolem0001!=X510|agent(X510,skolem0005,skolem0002),inference(resolution,status(thm),[c369, 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(X162,X161)|beverage(X162,X161),inference(split_conjunct,status(thm),[c113])).
cnf(c209,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(X163,X164)|food(X163,X164),inference(split_conjunct,status(thm),[c116])).
cnf(c210,plain,food(skolem0001,skolem0004),inference(resolution,status(thm),[c117, c209])).
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(X166,X165)|substance_matter(X166,X165),inference(split_conjunct,status(thm),[c119])).
cnf(c211,plain,substance_matter(skolem0001,skolem0004),inference(resolution,status(thm),[c120, c210])).
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(X171,X172)|object(X171,X172),inference(split_conjunct,status(thm),[c122])).
cnf(c212,plain,object(skolem0001,skolem0004),inference(resolution,status(thm),[c123, c211])).
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,X190)|nonliving(X189,X190),inference(split_conjunct,status(thm),[c137])).
cnf(c220,plain,nonliving(skolem0001,skolem0004),inference(resolution,status(thm),[c138, c212])).
cnf(c37,plain,X442!=X440|X441!=X443|~nonliving(X442,X441)|nonliving(X440,X443),eq_axiom).
cnf(c356,plain,skolem0001!=X503|skolem0004!=X504|nonliving(X503,X504),inference(resolution,status(thm),[c37, c220])).
cnf(c390,plain,skolem0001!=X506|nonliving(X506,skolem0004),inference(resolution,status(thm),[c356, reflexivity])).
cnf(c53,negated_conjecture,order(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
cnf(c36,plain,X433!=X431|X432!=X434|~order(X433,X432)|order(X431,X434),eq_axiom).
cnf(c352,plain,skolem0001!=X501|skolem0005!=X502|order(X501,X502),inference(resolution,status(thm),[c36, c53])).
cnf(c389,plain,skolem0001!=X505|order(X505,skolem0005),inference(resolution,status(thm),[c352, reflexivity])).
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,X232)|human_person(X231,X232),inference(split_conjunct,status(thm),[c170])).
cnf(c240,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(X234,X233)|organism(X234,X233),inference(split_conjunct,status(thm),[c173])).
cnf(c241,plain,organism(skolem0001,skolem0002),inference(resolution,status(thm),[c174, c240])).
cnf(c35,plain,X423!=X421|X422!=X424|~organism(X423,X422)|organism(X421,X424),eq_axiom).
cnf(c347,plain,skolem0001!=X498|skolem0002!=X497|organism(X498,X497),inference(resolution,status(thm),[c35, c241])).
cnf(c386,plain,skolem0001!=X500|organism(X500,skolem0002),inference(resolution,status(thm),[c347, reflexivity])).
cnf(c34,plain,X415!=X413|X414!=X416|~human_person(X415,X414)|human_person(X413,X416),eq_axiom).
cnf(c343,plain,skolem0001!=X495|skolem0002!=X496|human_person(X495,X496),inference(resolution,status(thm),[c34, c240])).
cnf(c385,plain,skolem0001!=X499|human_person(X499,skolem0002),inference(resolution,status(thm),[c343, 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(X188,X187)|existent(X188,X187),inference(split_conjunct,status(thm),[c134])).
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(X240,X239)|entity(X240,X239),inference(split_conjunct,status(thm),[c176])).
cnf(c245,plain,entity(skolem0001,skolem0002),inference(resolution,status(thm),[c177, c241])).
cnf(c249,plain,existent(skolem0001,skolem0002),inference(resolution,status(thm),[c245, c135])).
cnf(c33,plain,X406!=X404|X405!=X407|~existent(X406,X405)|existent(X404,X407),eq_axiom).
cnf(c339,plain,skolem0001!=X491|skolem0002!=X492|existent(X491,X492),inference(resolution,status(thm),[c33, c249])).
cnf(c382,plain,skolem0001!=X494|existent(X494,skolem0002),inference(resolution,status(thm),[c339, reflexivity])).
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(X174,X173)|entity(X174,X173),inference(split_conjunct,status(thm),[c125])).
cnf(c213,plain,entity(skolem0001,skolem0004),inference(resolution,status(thm),[c126, c212])).
cnf(c219,plain,existent(skolem0001,skolem0004),inference(resolution,status(thm),[c135, c213])).
cnf(c338,plain,skolem0001!=X489|skolem0004!=X490|existent(X489,X490),inference(resolution,status(thm),[c33, c219])).
cnf(c381,plain,skolem0001!=X493|existent(X493,skolem0004),inference(resolution,status(thm),[c338, reflexivity])).
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(c195,plain,act(skolem0001,skolem0005),inference(resolution,status(thm),[c87, c53])).
cnf(c32,plain,X396!=X394|X395!=X397|~act(X396,X395)|act(X394,X397),eq_axiom).
cnf(c333,plain,skolem0001!=X486|skolem0005!=X487|act(X486,X487),inference(resolution,status(thm),[c32, c195])).
cnf(c379,plain,skolem0001!=X488|act(X488,skolem0005),inference(resolution,status(thm),[c333, reflexivity])).
cnf(c31,plain,X388!=X386|X387!=X389|~beverage(X388,X387)|beverage(X386,X389),eq_axiom).
cnf(c329,plain,skolem0001!=X480|skolem0004!=X481|beverage(X480,X481),inference(resolution,status(thm),[c31, c209])).
cnf(c376,plain,skolem0001!=X482|beverage(X482,skolem0004),inference(resolution,status(thm),[c329, 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(X179,X180)|thing(X179,X180),inference(split_conjunct,status(thm),[c128])).
cnf(c247,plain,thing(skolem0001,skolem0002),inference(resolution,status(thm),[c245, c129])).
cnf(c30,plain,X379!=X377|X378!=X380|~thing(X379,X378)|thing(X377,X380),eq_axiom).
cnf(c325,plain,skolem0001!=X477|skolem0002!=X478|thing(X477,X478),inference(resolution,status(thm),[c30, c247])).
cnf(c374,plain,skolem0001!=X479|thing(X479,skolem0002),inference(resolution,status(thm),[c325, reflexivity])).
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(X200,X199)|relname(X200,X199),inference(split_conjunct,status(thm),[c146])).
cnf(c225,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(X205,X206)|relation(X205,X206),inference(split_conjunct,status(thm),[c149])).
cnf(c227,plain,relation(skolem0001,skolem0003),inference(resolution,status(thm),[c150, c225])).
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(X208,X207)|abstraction(X208,X207),inference(split_conjunct,status(thm),[c152])).
cnf(c229,plain,abstraction(skolem0001,skolem0003),inference(resolution,status(thm),[c153, c227])).
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(X214,X213)|thing(X214,X213),inference(split_conjunct,status(thm),[c155])).
cnf(c231,plain,thing(skolem0001,skolem0003),inference(resolution,status(thm),[c156, c229])).
cnf(c324,plain,skolem0001!=X471|skolem0003!=X472|thing(X471,X472),inference(resolution,status(thm),[c30, c231])).
cnf(c371,plain,skolem0001!=X473|thing(X473,skolem0003),inference(resolution,status(thm),[c324, reflexivity])).
cnf(c215,plain,thing(skolem0001,skolem0004),inference(resolution,status(thm),[c129, c213])).
cnf(c323,plain,skolem0001!=X465|skolem0004!=X466|thing(X465,X466),inference(resolution,status(thm),[c30, c215])).
cnf(c368,plain,skolem0001!=X470|thing(X470,skolem0004),inference(resolution,status(thm),[c323, 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(c197,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(X135,X136)|thing(X135,X136),inference(split_conjunct,status(thm),[c95])).
cnf(c199,plain,thing(skolem0001,skolem0005),inference(resolution,status(thm),[c96, c197])).
cnf(c322,plain,skolem0001!=X462|skolem0005!=X463|thing(X462,X463),inference(resolution,status(thm),[c30, c199])).
cnf(c366,plain,skolem0001!=X464|thing(X464,skolem0005),inference(resolution,status(thm),[c322, 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(X216,X215)|nonhuman(X216,X215),inference(split_conjunct,status(thm),[c158])).
cnf(c234,plain,nonhuman(skolem0001,skolem0003),inference(resolution,status(thm),[c159, c229])).
cnf(c29,plain,X369!=X367|X368!=X370|~nonhuman(X369,X368)|nonhuman(X367,X370),eq_axiom).
cnf(c317,plain,skolem0001!=X456|skolem0003!=X455|nonhuman(X456,X455),inference(resolution,status(thm),[c29, c234])).
cnf(c363,plain,skolem0001!=X457|nonhuman(X457,skolem0003),inference(resolution,status(thm),[c317, reflexivity])).
cnf(c27,plain,X350!=X348|X349!=X351|~shake_beverage(X350,X349)|shake_beverage(X348,X351),eq_axiom).
cnf(c309,plain,skolem0001!=X453|skolem0004!=X452|shake_beverage(X453,X452),inference(resolution,status(thm),[c27, c47])).
cnf(c361,plain,skolem0001!=X454|shake_beverage(X454,skolem0004),inference(resolution,status(thm),[c309, reflexivity])).
cnf(c26,plain,X340!=X338|X339!=X341|~eventuality(X340,X339)|eventuality(X338,X341),eq_axiom).
cnf(c304,plain,skolem0001!=X445|skolem0005!=X446|eventuality(X445,X446),inference(resolution,status(thm),[c26, c197])).
cnf(c358,plain,skolem0001!=X447|eventuality(X447,skolem0005),inference(resolution,status(thm),[c304, reflexivity])).
cnf(c52,negated_conjecture,nonreflexive(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
cnf(c25,plain,X332!=X330|X331!=X333|~nonreflexive(X332,X331)|nonreflexive(X330,X333),eq_axiom).
cnf(c300,plain,skolem0001!=X439|skolem0005!=X438|nonreflexive(X439,X438),inference(resolution,status(thm),[c25, c52])).
cnf(c355,plain,skolem0001!=X444|nonreflexive(X444,skolem0005),inference(resolution,status(thm),[c300, 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(X221,X222)|general(X221,X222),inference(split_conjunct,status(thm),[c161])).
cnf(c236,plain,general(skolem0001,skolem0003),inference(resolution,status(thm),[c162, c229])).
cnf(c24,plain,X323!=X321|X322!=X324|~general(X323,X322)|general(X321,X324),eq_axiom).
cnf(c296,plain,skolem0001!=X436|skolem0003!=X435|general(X436,X435),inference(resolution,status(thm),[c24, c236])).
cnf(c353,plain,skolem0001!=X437|general(X437,skolem0003),inference(resolution,status(thm),[c296, 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(X181,X182)|specific(X181,X182),inference(split_conjunct,status(thm),[c131])).
cnf(c248,plain,specific(skolem0001,skolem0002),inference(resolution,status(thm),[c245, c132])).
cnf(c23,plain,X313!=X311|X312!=X314|~specific(X313,X312)|specific(X311,X314),eq_axiom).
cnf(c291,plain,skolem0001!=X429|skolem0002!=X428|specific(X429,X428),inference(resolution,status(thm),[c23, c248])).
cnf(c350,plain,skolem0001!=X430|specific(X430,skolem0002),inference(resolution,status(thm),[c291, reflexivity])).
cnf(c218,plain,specific(skolem0001,skolem0004),inference(resolution,status(thm),[c132, c213])).
cnf(c290,plain,skolem0001!=X426|skolem0004!=X425|specific(X426,X425),inference(resolution,status(thm),[c23, c218])).
cnf(c348,plain,skolem0001!=X427|specific(X427,skolem0004),inference(resolution,status(thm),[c290, 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(X146,X145)|specific(X146,X145),inference(split_conjunct,status(thm),[c101])).
cnf(c203,plain,specific(skolem0001,skolem0005),inference(resolution,status(thm),[c102, c197])).
cnf(c289,plain,skolem0001!=X419|skolem0005!=X418|specific(X419,X418),inference(resolution,status(thm),[c23, c203])).
cnf(c345,plain,skolem0001!=X420|specific(X420,skolem0005),inference(resolution,status(thm),[c289, reflexivity])).
cnf(c22,plain,X305!=X303|X304!=X306|~relname(X305,X304)|relname(X303,X306),eq_axiom).
cnf(c285,plain,skolem0001!=X412|skolem0003!=X411|relname(X412,X411),inference(resolution,status(thm),[c22, c225])).
cnf(c342,plain,skolem0001!=X417|relname(X417,skolem0003),inference(resolution,status(thm),[c285, 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(X147,X148)|nonexistent(X147,X148),inference(split_conjunct,status(thm),[c104])).
cnf(c204,plain,nonexistent(skolem0001,skolem0005),inference(resolution,status(thm),[c105, c197])).
cnf(c21,plain,X296!=X294|X295!=X297|~nonexistent(X296,X295)|nonexistent(X294,X297),eq_axiom).
cnf(c281,plain,skolem0001!=X408|skolem0005!=X409|nonexistent(X408,X409),inference(resolution,status(thm),[c21, c204])).
cnf(c340,plain,skolem0001!=X410|nonexistent(X410,skolem0005),inference(resolution,status(thm),[c281, reflexivity])).
cnf(c20,plain,X286!=X284|X285!=X287|~object(X286,X285)|object(X284,X287),eq_axiom).
cnf(c276,plain,skolem0001!=X402|skolem0004!=X401|object(X402,X401),inference(resolution,status(thm),[c20, c212])).
cnf(c336,plain,skolem0001!=X403|object(X403,skolem0004),inference(resolution,status(thm),[c276, reflexivity])).
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(X246,X245)|impartial(X246,X245),inference(split_conjunct,status(thm),[c179])).
cnf(c253,plain,impartial(skolem0001,skolem0002),inference(resolution,status(thm),[c180, c241])).
cnf(c19,plain,X278!=X276|X277!=X279|~impartial(X278,X277)|impartial(X276,X279),eq_axiom).
cnf(c272,plain,skolem0001!=X398|skolem0002!=X399|impartial(X398,X399),inference(resolution,status(thm),[c19, c253])).
cnf(c334,plain,skolem0001!=X400|impartial(X400,skolem0002),inference(resolution,status(thm),[c272, 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(X195,X196)|impartial(X195,X196),inference(split_conjunct,status(thm),[c140])).
cnf(c223,plain,impartial(skolem0001,skolem0004),inference(resolution,status(thm),[c141, c212])).
cnf(c271,plain,skolem0001!=X391|skolem0004!=X392|impartial(X391,X392),inference(resolution,status(thm),[c19, c223])).
cnf(c331,plain,skolem0001!=X393|impartial(X393,skolem0004),inference(resolution,status(thm),[c271, reflexivity])).
cnf(c8,plain,X185!=X183|X184!=X186|~female(X185,X184)|female(X183,X186),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(X262,X261)|female(X262,X261),inference(split_conjunct,status(thm),[c191])).
cnf(c264,plain,female(skolem0001,skolem0002),inference(resolution,status(thm),[c192, c44])).
cnf(c266,plain,skolem0001!=X385|skolem0002!=X384|female(X385,X384),inference(resolution,status(thm),[c264, c8])).
cnf(c328,plain,skolem0001!=X390|female(X390,skolem0002),inference(resolution,status(thm),[c266, reflexivity])).
cnf(c11,plain,X211!=X209|X210!=X212|~animate(X211,X210)|animate(X209,X212),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(X259,X260)|animate(X259,X260),inference(split_conjunct,status(thm),[c188])).
cnf(c262,plain,animate(skolem0001,skolem0002),inference(resolution,status(thm),[c189, c240])).
cnf(c263,plain,skolem0001!=X382|skolem0002!=X381|animate(X382,X381),inference(resolution,status(thm),[c262, c11])).
cnf(c326,plain,skolem0001!=X383|animate(X383,skolem0002),inference(resolution,status(thm),[c263, reflexivity])).
cnf(c17,plain,X257!=X255|X256!=X258|~woman(X257,X256)|woman(X255,X258),eq_axiom).
cnf(c261,plain,skolem0001!=X374|skolem0002!=X375|woman(X374,X375),inference(resolution,status(thm),[c17, c44])).
cnf(c320,plain,skolem0001!=X376|woman(X376,skolem0002),inference(resolution,status(thm),[c261, reflexivity])).
cnf(c1,plain,X124!=X122|X123!=X125|~human(X124,X123)|human(X122,X125),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(X253,X254)|human(X253,X254),inference(split_conjunct,status(thm),[c185])).
cnf(c258,plain,human(skolem0001,skolem0002),inference(resolution,status(thm),[c186, c240])).
cnf(c260,plain,skolem0001!=X372|skolem0002!=X371|human(X372,X371),inference(resolution,status(thm),[c258, c1])).
cnf(c318,plain,skolem0001!=X373|human(X373,skolem0002),inference(resolution,status(thm),[c260, reflexivity])).
cnf(c13,plain,X227!=X225|X226!=X228|~living(X227,X226)|living(X225,X228),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(X247,X248)|living(X247,X248),inference(split_conjunct,status(thm),[c182])).
cnf(c254,plain,living(skolem0001,skolem0002),inference(resolution,status(thm),[c183, c241])).
cnf(c257,plain,skolem0001!=X365|skolem0002!=X364|living(X365,X364),inference(resolution,status(thm),[c254, c13])).
cnf(c315,plain,skolem0001!=X366|living(X366,skolem0002),inference(resolution,status(thm),[c257, reflexivity])).
cnf(c16,plain,X251!=X249|X250!=X252|~food(X251,X250)|food(X249,X252),eq_axiom).
cnf(c255,plain,skolem0001!=X355|skolem0004!=X356|food(X355,X356),inference(resolution,status(thm),[c16, c210])).
cnf(c312,plain,skolem0001!=X363|food(X363,skolem0004),inference(resolution,status(thm),[c255, reflexivity])).
cnf(c0,plain,X110!=X108|X109!=X111|~singleton(X110,X109)|singleton(X108,X111),eq_axiom).
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,X137)|singleton(X138,X137),inference(split_conjunct,status(thm),[c98])).
cnf(c250,plain,singleton(skolem0001,skolem0002),inference(resolution,status(thm),[c247, c99])).
cnf(c252,plain,skolem0001!=X353|skolem0002!=X352|singleton(X353,X352),inference(resolution,status(thm),[c250, c0])).
cnf(c310,plain,skolem0001!=X354|singleton(X354,skolem0002),inference(resolution,status(thm),[c252, reflexivity])).
cnf(c15,plain,X243!=X241|X242!=X244|~substance_matter(X243,X242)|substance_matter(X241,X244),eq_axiom).
cnf(c251,plain,skolem0001!=X345|skolem0004!=X346|substance_matter(X345,X346),inference(resolution,status(thm),[c15, c211])).
cnf(c307,plain,skolem0001!=X347|substance_matter(X347,skolem0004),inference(resolution,status(thm),[c251, reflexivity])).
cnf(c4,plain,X151!=X149|X150!=X152|~entity(X151,X150)|entity(X149,X152),eq_axiom).
cnf(c246,plain,skolem0001!=X342|skolem0002!=X343|entity(X342,X343),inference(resolution,status(thm),[c245, c4])).
cnf(c305,plain,skolem0001!=X344|entity(X344,skolem0002),inference(resolution,status(thm),[c246, reflexivity])).
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(X224,X223)|unisex(X224,X223),inference(split_conjunct,status(thm),[c164])).
cnf(c238,plain,unisex(skolem0001,skolem0003),inference(resolution,status(thm),[c165, c229])).
cnf(c14,plain,X237!=X235|X236!=X238|~unisex(X237,X236)|unisex(X235,X238),eq_axiom).
cnf(c244,plain,skolem0001!=X336|skolem0003!=X335|unisex(X336,X335),inference(resolution,status(thm),[c14, c238])).
cnf(c302,plain,skolem0001!=X337|unisex(X337,skolem0003),inference(resolution,status(thm),[c244, 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(X197,X198)|unisex(X197,X198),inference(split_conjunct,status(thm),[c143])).
cnf(c224,plain,unisex(skolem0001,skolem0004),inference(resolution,status(thm),[c144, c212])).
cnf(c243,plain,skolem0001!=X329|skolem0004!=X328|unisex(X329,X328),inference(resolution,status(thm),[c14, c224])).
cnf(c299,plain,skolem0001!=X334|unisex(X334,skolem0004),inference(resolution,status(thm),[c243, 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(X154,X153)|unisex(X154,X153),inference(split_conjunct,status(thm),[c107])).
cnf(c206,plain,unisex(skolem0001,skolem0005),inference(resolution,status(thm),[c108, c197])).
cnf(c242,plain,skolem0001!=X326|skolem0005!=X325|unisex(X326,X325),inference(resolution,status(thm),[c14, c206])).
cnf(c297,plain,skolem0001!=X327|unisex(X327,skolem0005),inference(resolution,status(thm),[c242, reflexivity])).
cnf(c12,plain,X219!=X217|X218!=X220|~event(X219,X218)|event(X217,X220),eq_axiom).
cnf(c235,plain,skolem0001!=X319|skolem0005!=X318|event(X319,X318),inference(resolution,status(thm),[c12, c48])).
cnf(c294,plain,skolem0001!=X320|event(X320,skolem0005),inference(resolution,status(thm),[c235, reflexivity])).
cnf(c232,plain,singleton(skolem0001,skolem0003),inference(resolution,status(thm),[c231, c99])).
cnf(c233,plain,skolem0001!=X316|skolem0003!=X315|singleton(X316,X315),inference(resolution,status(thm),[c232, c0])).
cnf(c292,plain,skolem0001!=X317|singleton(X317,skolem0003),inference(resolution,status(thm),[c233, reflexivity])).
cnf(c6,plain,X169!=X167|X168!=X170|~abstraction(X169,X168)|abstraction(X167,X170),eq_axiom).
cnf(c230,plain,skolem0001!=X309|skolem0003!=X308|abstraction(X309,X308),inference(resolution,status(thm),[c229, c6])).
cnf(c287,plain,skolem0001!=X310|abstraction(X310,skolem0003),inference(resolution,status(thm),[c230, reflexivity])).
cnf(c7,plain,X177!=X175|X176!=X178|~relation(X177,X176)|relation(X175,X178),eq_axiom).
cnf(c228,plain,skolem0001!=X302|skolem0003!=X301|relation(X302,X301),inference(resolution,status(thm),[c227, c7])).
cnf(c284,plain,skolem0001!=X307|relation(X307,skolem0003),inference(resolution,status(thm),[c228, reflexivity])).
cnf(c45,negated_conjecture,mia_forename(skolem0001,skolem0003),inference(split_conjunct,status(thm),[c41])).
cnf(c10,plain,X203!=X201|X202!=X204|~mia_forename(X203,X202)|mia_forename(X201,X204),eq_axiom).
cnf(c226,plain,skolem0001!=X299|skolem0003!=X298|mia_forename(X299,X298),inference(resolution,status(thm),[c10, c45])).
cnf(c282,plain,skolem0001!=X300|mia_forename(X300,skolem0003),inference(resolution,status(thm),[c226, reflexivity])).
cnf(c9,plain,X193!=X191|X192!=X194|~forename(X193,X192)|forename(X191,X194),eq_axiom).
cnf(c222,plain,skolem0001!=X291|skolem0003!=X292|forename(X291,X292),inference(resolution,status(thm),[c9, c46])).
cnf(c279,plain,skolem0001!=X293|forename(X293,skolem0003),inference(resolution,status(thm),[c222, reflexivity])).
cnf(c216,plain,singleton(skolem0001,skolem0004),inference(resolution,status(thm),[c215, c99])).
cnf(c217,plain,skolem0001!=X289|skolem0004!=X288|singleton(X289,X288),inference(resolution,status(thm),[c216, c0])).
cnf(c277,plain,skolem0001!=X290|singleton(X290,skolem0004),inference(resolution,status(thm),[c217, reflexivity])).
cnf(c214,plain,skolem0001!=X281|skolem0004!=X282|entity(X281,X282),inference(resolution,status(thm),[c213, c4])).
cnf(c274,plain,skolem0001!=X283|entity(X283,skolem0004),inference(resolution,status(thm),[c214, reflexivity])).
cnf(c51,negated_conjecture,past(skolem0001,skolem0005),inference(split_conjunct,status(thm),[c41])).
cnf(c5,plain,X159!=X157|X158!=X160|~past(X159,X158)|past(X157,X160),eq_axiom).
cnf(c208,plain,skolem0001!=X274|skolem0005!=X275|past(X274,X275),inference(resolution,status(thm),[c5, c51])).
cnf(c270,plain,skolem0001!=X280|past(X280,skolem0005),inference(resolution,status(thm),[c208, reflexivity])).
cnf(c200,plain,singleton(skolem0001,skolem0005),inference(resolution,status(thm),[c99, c199])).
cnf(c202,plain,skolem0001!=X272|skolem0005!=X271|singleton(X272,X271),inference(resolution,status(thm),[c200, c0])).
cnf(c268,plain,skolem0001!=X273|singleton(X273,skolem0005),inference(resolution,status(thm),[c202, reflexivity])).
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(X106,X107)|~female(X106,X107),inference(split_conjunct,status(thm),[c63])).
cnf(c265,plain,~unisex(skolem0001,skolem0002),inference(resolution,status(thm),[c264, 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(X116,X117)|~human(X116,X117),inference(split_conjunct,status(thm),[c75])).
cnf(c259,plain,~nonhuman(skolem0001,skolem0002),inference(resolution,status(thm),[c258, 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(X114,X115)|~living(X114,X115),inference(split_conjunct,status(thm),[c71])).
cnf(c256,plain,~nonliving(skolem0001,skolem0002),inference(resolution,status(thm),[c254, 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(X230,X229)|forename(X230,X229),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(c237,plain,~specific(skolem0001,skolem0003),inference(resolution,status(thm),[c236, 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(c221,plain,~animate(skolem0001,skolem0004),inference(resolution,status(thm),[c220, 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(X156,X155)|event(X156,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(c205,plain,~existent(skolem0001,skolem0005),inference(resolution,status(thm),[c204, c80])).
cnf(c2,plain,X133!=X132|~actual_world(X133)|actual_world(X132),eq_axiom).
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(X129,X128)|event(X129,X128),inference(split_conjunct,status(thm),[c89])).
cnf(transitivity,axiom,X104!=X103|X103!=X105|X104=X105,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 NLP042+1

```# SZS status Timeout
```

## Satallax 3.3

Michael Färber
Universität Innsbruck, Austria

### Sample solution for SET014^4

```% SZS output start Proof
thf(ty_\$i, type, \$i : \$tType).
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,((~(sP2) | ~(sP1)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(2,plain,(~(sP7) | sP2),inference(all_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])],[h10,h11,h6,1,2])).
thf(4,plain,((~(sP4) | ~(sP3)) | sP6),inference(prop_rule,[status(thm)],[])).
thf(5,plain,(~(sP5) | sP4),inference(all_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])],[h10,h12,h7,4,5])).
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])).
% SZS output end Proof
```

## 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
```

## Twee 2.2

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 Proof
Axiom 1 (associativity): multiply(multiply(X, Y, Z), W, multiply(X, Y, V)) = multiply(X, Y, multiply(Z, W, V)).
Axiom 2 (ternary_multiply_1): multiply(X, Y, Y) = Y.
Axiom 3 (right_inverse): multiply(X, Y, inverse(Y)) = X.

Goal 1 (prove_inverse_is_self_cancelling): inverse(inverse(a)) = a.
Proof:
inverse(inverse(a))
= { by axiom 3 (right_inverse) }
multiply(inverse(inverse(a)), a, inverse(a))
= { by axiom 2 (ternary_multiply_1) }
multiply(inverse(inverse(a)), a, multiply(a, inverse(a), inverse(a)))
= { by axiom 1 (associativity) }
multiply(multiply(inverse(inverse(a)), a, a), inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))
= { by axiom 2 (ternary_multiply_1) }
multiply(a, inverse(a), multiply(inverse(inverse(a)), a, inverse(a)))
= { by axiom 3 (right_inverse) }
multiply(a, inverse(a), inverse(inverse(a)))
= { by axiom 3 (right_inverse) }
a
% SZS output end Proof
```

## Vampire 4.3

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 4.4

Giles Reger
University of Manchester, United Kingdom

### Sample proof for SET014^4

```% SZS output start Proof for SET014^4
thf(func_def_0, type, in: (\$i > ((\$i > \$o) > \$o))).
thf(func_def_1, type, is_a: (\$i > ((\$i > \$o) > \$o))).
thf(func_def_2, type, emptyset: (\$i > \$o)).
thf(func_def_3, type, unord_pair: (\$i > (\$i > (\$i > \$o)))).
thf(func_def_4, type, singleton: (\$i > (\$i > \$o))).
thf(func_def_5, type, union: ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_6, type, excl_union: ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_7, type, intersection: ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_8, type, setminus: ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_9, type, complement: ((\$i > \$o) > (\$i > \$o))).
thf(func_def_10, type, disjoint: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_11, type, subset: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_12, type, meets: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_13, type, misses: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_16, type, vAPP_12_5: (((\$i > \$o) > ((\$i > \$o) > \$o)) * (\$i > \$o)) > ((\$i > \$o) > \$o)).
thf(func_def_17, type, vAPP_6_5: (((\$i > \$o) > \$o) * (\$i > \$o)) > \$o).
thf(func_def_18, type, vAPP_11_5: (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) * (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))).
thf(func_def_19, type, vAPP_10_5: (((\$i > \$o) > (\$i > \$o)) * (\$i > \$o)) > (\$i > \$o)).
thf(func_def_20, type, iCOMB_10: ((\$i > \$o) > (\$i > \$o))).
thf(func_def_21, type, cCOMB_13: (((\$i > \$o) > (\$i > \$o)) > (\$i > ((\$i > \$o) > \$o)))).
thf(func_def_22, type, vAPP_13_10: ((((\$i > \$o) > (\$i > \$o)) > (\$i > ((\$i > \$o) > \$o))) * ((\$i > \$o) > (\$i > \$o))) > (\$i > ((\$i > \$o) > \$o))).
thf(func_def_23, type, vAPP_7_0: ((\$i > ((\$i > \$o) > \$o)) * \$i) > ((\$i > \$o) > \$o)).
thf(func_def_24, type, vEQUALS_8: (\$i > (\$i > \$o))).
thf(func_def_25, type, vAPP_8_0: ((\$i > (\$i > \$o)) * \$i) > (\$i > \$o)).
thf(func_def_26, type, vAPP_5_0: ((\$i > \$o) * \$i) > \$o).
thf(func_def_27, type, vEQUALS_12: ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_28, type, bCOMB_15: (((\$i > \$o) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))))).
thf(func_def_29, type, vAPP_15_12: ((((\$i > \$o) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) * ((\$i > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_30, type, vAPP_14_10: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))) * ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_31, type, cCOMB_16: (((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_32, type, vAPP_16_12: ((((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))) * ((\$i > \$o) > ((\$i > \$o) > \$o))) > ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_33, type, bCOMB_19: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))))).
thf(func_def_34, type, vAPP_19_14: (((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))))) * (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))))).
thf(func_def_35, type, vAPP_18_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_36, type, bCOMB_21: ((((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))))).
thf(func_def_37, type, vAPP_21_16: (((((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))))) * (((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))))).
thf(func_def_38, type, vAPP_20_17: ((((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) * ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_39, type, cCOMB_20: (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))))).
thf(func_def_40, type, vAPP_17_5: (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > \$o))) * (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_41, type, vNOT_22: (\$o > \$o)).
thf(func_def_42, type, vAPP_22_1: ((\$o > \$o) * \$o) > \$o).
thf(func_def_43, type, vAND_23: (\$o > (\$o > \$o))).
thf(func_def_44, type, vAPP_23_1: ((\$o > (\$o > \$o)) * \$o) > (\$o > \$o)).
thf(func_def_45, type, bCOMB_26: ((\$o > (\$o > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o))))).
thf(func_def_46, type, vAPP_26_23: (((\$o > (\$o > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o)))) * (\$o > (\$o > \$o))) > ((\$i > \$o) > (\$i > (\$o > \$o)))).
thf(func_def_47, type, vAPP_25_5: (((\$i > \$o) > (\$i > (\$o > \$o))) * (\$i > \$o)) > (\$i > (\$o > \$o))).
thf(func_def_48, type, sCOMB_27: ((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_49, type, vAPP_27_24: (((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o))) * (\$i > (\$o > \$o))) > ((\$i > \$o) > (\$i > \$o))).
thf(func_def_50, type, vSIGMA_6: ((\$i > \$o) > \$o)).
thf(func_def_51, type, bCOMB_29: (((\$i > \$o) > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o)))).
thf(func_def_52, type, vAPP_29_6: ((((\$i > \$o) > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o))) * ((\$i > \$o) > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o))).
thf(func_def_53, type, vAPP_28_10: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o)) * ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > \$o)).
thf(func_def_54, type, bCOMB_31: ((\$o > \$o) > (((\$i > \$o) > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_55, type, vAPP_31_22: (((\$o > \$o) > (((\$i > \$o) > \$o) > ((\$i > \$o) > \$o))) * (\$o > \$o)) > (((\$i > \$o) > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_56, type, vAPP_30_6: ((((\$i > \$o) > \$o) > ((\$i > \$o) > \$o)) * ((\$i > \$o) > \$o)) > ((\$i > \$o) > \$o)).
thf(func_def_57, type, bCOMB_33: (((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_58, type, vAPP_33_27: ((((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_59, type, vAPP_32_25: ((((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) * ((\$i > \$o) > (\$i > (\$o > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_60, type, bCOMB_35: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > \$o))))).
thf(func_def_61, type, vAPP_35_28: (((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) * (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_62, type, vAPP_34_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > \$o))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > \$o))).
thf(func_def_63, type, bCOMB_36: ((((\$i > \$o) > \$o) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o))))).
thf(func_def_64, type, vAPP_36_30: (((((\$i > \$o) > \$o) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))) * (((\$i > \$o) > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > \$o)) > ((\$i > \$o) > ((\$i > \$o) > \$o)))).
thf(func_def_65, type, bCOMB_37: ((\$o > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_66, type, vAPP_37_22: (((\$o > \$o) > ((\$i > \$o) > (\$i > \$o))) * (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o))).
thf(func_def_67, type, bCOMB_39: (((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_68, type, vAPP_39_10: ((((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) * ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_69, type, vAPP_38_10: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))) * ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > (\$i > \$o))).
thf(func_def_70, type, bCOMB_42: ((((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))))).
thf(func_def_71, type, vAPP_42_39: (((((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))))) * (((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_72, type, vAPP_41_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_73, type, cCOMB_44: (((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_74, type, vAPP_44_40: ((((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_75, type, vAPP_43_10: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) * ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_76, type, vOR_23: (\$o > (\$o > \$o))).
thf(func_def_77, type, bCOMB_46: (((\$i > \$o) > (\$i > \$o)) > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))))).
thf(func_def_78, type, vAPP_46_10: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))) * ((\$i > \$o) > (\$i > \$o))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))).
thf(func_def_79, type, vAPP_45_8: (((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))) * (\$i > (\$i > \$o))) > (\$i > (\$i > \$o))).
thf(func_def_80, type, bCOMB_51: (((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > (\$o > \$o)))))).
thf(func_def_81, type, vAPP_51_25: ((((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > (\$o > \$o))))) * ((\$i > \$o) > (\$i > (\$o > \$o)))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > (\$o > \$o))))).
thf(func_def_82, type, vAPP_50_8: (((\$i > (\$i > \$o)) > (\$i > (\$i > (\$o > \$o)))) * (\$i > (\$i > \$o))) > (\$i > (\$i > (\$o > \$o)))).
thf(func_def_83, type, bCOMB_53: (((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > (\$i > (\$o > \$o))) > (\$i > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_84, type, vAPP_53_27: ((((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > (\$i > (\$o > \$o))) > (\$i > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > (\$o > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > (\$i > (\$o > \$o))) > (\$i > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_85, type, vAPP_52_49: (((\$i > (\$i > (\$o > \$o))) > (\$i > ((\$i > \$o) > (\$i > \$o)))) * (\$i > (\$i > (\$o > \$o)))) > (\$i > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_86, type, bCOMB_55: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))) > ((\$i > ((\$i > \$o) > (\$i > \$o))) > (\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))))))).
thf(func_def_87, type, vAPP_55_46: (((((\$i > \$o) > (\$i > \$o)) > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))) > ((\$i > ((\$i > \$o) > (\$i > \$o))) > (\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))))) * (((\$i > \$o) > (\$i > \$o)) > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))))) > ((\$i > ((\$i > \$o) > (\$i > \$o))) > (\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))))).
thf(func_def_88, type, vAPP_54_48: (((\$i > ((\$i > \$o) > (\$i > \$o))) > (\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))))) * (\$i > ((\$i > \$o) > (\$i > \$o)))) > (\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))))).
thf(func_def_89, type, cCOMB_57: ((\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > (\$i > \$o)))))).
thf(func_def_90, type, vAPP_57_47: (((\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o)))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > (\$i > \$o))))) * (\$i > ((\$i > (\$i > \$o)) > (\$i > (\$i > \$o))))) > ((\$i > (\$i > \$o)) > (\$i > (\$i > (\$i > \$o))))).
thf(func_def_91, type, vAPP_56_8: (((\$i > (\$i > \$o)) > (\$i > (\$i > (\$i > \$o)))) * (\$i > (\$i > \$o))) > (\$i > (\$i > (\$i > \$o)))).
thf(func_def_92, type, bCOMB_59: (((\$i > \$o) > (\$i > (\$o > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o)))))).
thf(func_def_93, type, vAPP_59_25: ((((\$i > \$o) > (\$i > (\$o > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o))))) * ((\$i > \$o) > (\$i > (\$o > \$o)))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o))))).
thf(func_def_94, type, vAPP_58_10: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o)))) * ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > (\$i > (\$o > \$o)))).
thf(func_def_95, type, sCOMB_60: (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_96, type, vAPP_60_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_97, type, bCOMB_64: ((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o))))))).
thf(func_def_98, type, vAPP_64_58: (((((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o)))))) * (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > (\$o > \$o))))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o)))))).
thf(func_def_99, type, vAPP_63_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o))))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o))))).
thf(func_def_100, type, bCOMB_66: ((((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))))).
thf(func_def_101, type, vAPP_66_32: (((((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))))) * (((\$i > \$o) > (\$i > (\$o > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_102, type, vAPP_65_62: ((((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > (\$o > \$o))))) > ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_103, type, bCOMB_68: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))))).
thf(func_def_104, type, vAPP_68_60: (((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))))) * (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))) > (((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_105, type, vAPP_67_61: ((((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > \$o) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))) > ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_106, type, sCOMB_70: (((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))))).
thf(func_def_107, type, vAPP_70_40: ((((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))) * ((\$i > \$o) > (((\$i > \$o) > (\$i > \$o)) > ((\$i > \$o) > (\$i > \$o))))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))))).
thf(func_def_108, type, vAPP_69_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))).
thf(func_def_109, type, kCOMB_71: (\$o > (\$i > \$o))).
thf(func_def_110, type, vAPP_71_1: ((\$o > (\$i > \$o)) * \$o) > (\$i > \$o)).
thf(func_def_111, type, vIMP_23: (\$o > (\$o > \$o))).
thf(func_def_112, type, vPI_6: ((\$i > \$o) > \$o)).
thf(func_def_113, type, vAPP_9_0: ((\$i > (\$i > (\$i > \$o))) * \$i) > (\$i > (\$i > \$o))).
thf(func_def_114, type, sK0: (((\$i > \$o) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > ((\$i > \$o) > \$o)) > (\$i > \$o)))).
thf(func_def_115, type, vAPP_73_12: ((((\$i > \$o) > ((\$i > \$o) > \$o)) > (((\$i > \$o) > ((\$i > \$o) > \$o)) > (\$i > \$o))) * ((\$i > \$o) > ((\$i > \$o) > \$o))) > (((\$i > \$o) > ((\$i > \$o) > \$o)) > (\$i > \$o))).
thf(func_def_116, type, vAPP_72_12: ((((\$i > \$o) > ((\$i > \$o) > \$o)) > (\$i > \$o)) * ((\$i > \$o) > ((\$i > \$o) > \$o))) > (\$i > \$o)).
thf(func_def_117, type, sK1: (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (\$i > \$o)))).
thf(func_def_118, type, vAPP_75_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (\$i > \$o))) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > (((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (\$i > \$o))).
thf(func_def_119, type, vAPP_74_11: ((((\$i > \$o) > ((\$i > \$o) > (\$i > \$o))) > (\$i > \$o)) * ((\$i > \$o) > ((\$i > \$o) > (\$i > \$o)))) > (\$i > \$o)).
thf(func_def_120, type, sK2: (((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > (\$i > \$o)))).
thf(func_def_121, type, vAPP_77_10: ((((\$i > \$o) > (\$i > \$o)) > (((\$i > \$o) > (\$i > \$o)) > (\$i > \$o))) * ((\$i > \$o) > (\$i > \$o))) > (((\$i > \$o) > (\$i > \$o)) > (\$i > \$o))).
thf(func_def_122, type, vAPP_76_10: ((((\$i > \$o) > (\$i > \$o)) > (\$i > \$o)) * ((\$i > \$o) > (\$i > \$o))) > (\$i > \$o)).
thf(func_def_123, type, sK3: ((\$i > (\$i > (\$i > \$o))) > ((\$i > (\$i > (\$i > \$o))) > \$i))).
thf(func_def_124, type, vAPP_79_9: (((\$i > (\$i > (\$i > \$o))) > ((\$i > (\$i > (\$i > \$o))) > \$i)) * (\$i > (\$i > (\$i > \$o)))) > ((\$i > (\$i > (\$i > \$o))) > \$i)).
thf(func_def_125, type, vAPP_78_9: (((\$i > (\$i > (\$i > \$o))) > \$i) * (\$i > (\$i > (\$i > \$o)))) > \$i).
thf(func_def_126, type, sK4: ((\$i > (\$i > \$o)) > ((\$i > (\$i > \$o)) > \$i))).
thf(func_def_127, type, vAPP_81_8: (((\$i > (\$i > \$o)) > ((\$i > (\$i > \$o)) > \$i)) * (\$i > (\$i > \$o))) > ((\$i > (\$i > \$o)) > \$i)).
thf(func_def_128, type, vAPP_80_8: (((\$i > (\$i > \$o)) > \$i) * (\$i > (\$i > \$o))) > \$i).
thf(func_def_129, type, sK5: ((\$i > ((\$i > \$o) > \$o)) > ((\$i > ((\$i > \$o) > \$o)) > \$i))).
thf(func_def_130, type, vAPP_83_7: (((\$i > ((\$i > \$o) > \$o)) > ((\$i > ((\$i > \$o) > \$o)) > \$i)) * (\$i > ((\$i > \$o) > \$o))) > ((\$i > ((\$i > \$o) > \$o)) > \$i)).
thf(func_def_131, type, vAPP_82_7: (((\$i > ((\$i > \$o) > \$o)) > \$i) * (\$i > ((\$i > \$o) > \$o))) > \$i).
thf(func_def_132, type, sK6: ((\$i > \$o) > ((\$i > \$o) > \$i))).
thf(func_def_133, type, vAPP_85_5: (((\$i > \$o) > ((\$i > \$o) > \$i)) * (\$i > \$o)) > ((\$i > \$o) > \$i)).
thf(func_def_134, type, vAPP_84_5: (((\$i > \$o) > \$i) * (\$i > \$o)) > \$i).
thf(func_def_135, type, sK7: (\$i > \$o)).
thf(func_def_136, type, sK8: (\$i > \$o)).
thf(func_def_137, type, sK9: (\$i > \$o)).
thf(func_def_138, type, vAPP_24_0: ((\$i > (\$o > \$o)) * \$i) > (\$o > \$o)).
thf(f6,axiom,(
union = ^[X0 : (\$i > \$o), X2 : (\$i > \$o), X3 : \$i] : (X2 @ X3) | (X0 @ X3)),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SET/SET014^4.p',unknown)).
thf(f12,axiom,(
subset = ^[X0 : (\$i > \$o), X2 : (\$i > \$o)] : ! [X3] : ((X0 @ X3) => (X2 @ X3))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SET/SET014^4.p',unknown)).
thf(f15,conjecture,(
! [X0 : (\$i > \$o),X2 : (\$i > \$o),X4 : (\$i > \$o)] : ((((subset @ X2) @ X4) & ((subset @ X0) @ X4)) => ((subset @ ((union @ X0) @ X2)) @ X4))),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/SET/SET014^4.p',unknown)).
thf(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])).
thf(f17,plain,(
(\$false != \$true)),
introduced(fool_axiom,[])).
thf(f18,plain,(
~! [X0 : (\$i > \$o),X1 : (\$i > \$o),X2 : (\$i > \$o)] : ((((subset @ X1) @ X2) & ((subset @ X0) @ X2)) => ((subset @ ((union @ X0) @ X1)) @ X2))),
inference(rectify,[],[f16])).
thf(f19,plain,(
~! [X0 : (\$i > \$o),X1 : (\$i > \$o),X2 : (\$i > \$o)] : (((\$true = subset @ X1 @ X2) & (\$true = subset @ X0 @ X2)) => (\$true = subset @ (union @ X0 @ X1) @ X2))),
inference(fool_elimination,[],[f18])).
thf(f41,plain,(
union = ^[X0 : (\$i > \$o), X1 : (\$i > \$o), X2 : \$i] : (X1 @ X2) | (X0 @ X2)),
inference(rectify,[],[f6])).
thf(f42,plain,(
union = bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vOR_23)),
inference(fool_elimination,[],[f41])).
thf(f43,plain,(
subset = ^[X0 : (\$i > \$o), X1 : (\$i > \$o)] : ! [X2] : ((X0 @ X2) => (X1 @ X2))),
inference(rectify,[],[f12])).
thf(f44,plain,(
subset = bCOMB_35 @ (bCOMB_29 @ vPI_6) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23))),
inference(fool_elimination,[],[f43])).
thf(f59,plain,(
? [X0 : (\$i > \$o),X1 : (\$i > \$o),X2 : (\$i > \$o)] : ((\$true != subset @ (union @ X0 @ X1) @ X2) & ((\$true = subset @ X1 @ X2) & (\$true = subset @ X0 @ X2)))),
inference(ennf_transformation,[],[f19])).
thf(f60,plain,(
? [X0 : (\$i > \$o),X1 : (\$i > \$o),X2 : (\$i > \$o)] : ((\$true != subset @ (union @ X0 @ X1) @ X2) & (\$true = subset @ X1 @ X2) & (\$true = subset @ X0 @ X2))),
inference(flattening,[],[f59])).
thf(f75,plain,(
? [X0 : (\$i > \$o),X1 : (\$i > \$o),X2 : (\$i > \$o)] : ((\$true != subset @ (union @ X0 @ X1) @ X2) & (\$true = subset @ X1 @ X2) & (\$true = subset @ X0 @ X2)) => ((\$true != subset @ (union @ sK7 @ sK8) @ sK9) & (\$true = subset @ sK8 @ sK9) & (\$true = subset @ sK7 @ sK9))),
introduced(choice_axiom,[])).
thf(f76,plain,(
(\$true != subset @ (union @ sK7 @ sK8) @ sK9) & (\$true = subset @ sK8 @ sK9) & (\$true = subset @ sK7 @ sK9)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f60,f75])).
thf(f84,plain,(
(\$true = subset @ sK7 @ sK9)),
inference(cnf_transformation,[],[f76])).
thf(f85,plain,(
(\$true = subset @ sK8 @ sK9)),
inference(cnf_transformation,[],[f76])).
thf(f86,plain,(
(\$true != subset @ (union @ sK7 @ sK8) @ sK9)),
inference(cnf_transformation,[],[f76])).
thf(f99,plain,(
union = bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vOR_23)),
inference(cnf_transformation,[],[f42])).
thf(f100,plain,(
subset = bCOMB_35 @ (bCOMB_29 @ vPI_6) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23))),
inference(cnf_transformation,[],[f44])).
thf(f102,plain,(
(\$true != bCOMB_35 @ (bCOMB_29 @ vPI_6) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23)) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vOR_23) @ sK7 @ sK8) @ sK9)),
inference(definition_unfolding,[],[f86,f100,f99])).
thf(f103,plain,(
(\$true = bCOMB_35 @ (bCOMB_29 @ vPI_6) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23)) @ sK8 @ sK9)),
inference(definition_unfolding,[],[f85,f100])).
thf(f104,plain,(
(\$true = bCOMB_35 @ (bCOMB_29 @ vPI_6) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23)) @ sK7 @ sK9)),
inference(definition_unfolding,[],[f84,f100])).
thf(f105,plain,(
(\$true = bCOMB_29 @ vPI_6 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23) @ sK7) @ sK9)),
inference(B_combinator_elimination,[],[f104])).
thf(f106,plain,(
(\$true = vPI_6 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23) @ sK7 @ sK9))),
inference(B_combinator_elimination,[],[f105])).
thf(f107,plain,(
(\$true = vPI_6 @ (sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ sK7) @ sK9))),
inference(B_combinator_elimination,[],[f106])).
thf(f108,plain,(
( ! [X1] : ((\$true = sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ sK7) @ sK9 @ X1)) )),
inference(HOL_PI_constant_elimination,[],[f107])).
thf(f109,plain,(
( ! [X1] : ((\$true = bCOMB_26 @ vIMP_23 @ sK7 @ X1 @ (sK9 @ X1))) )),
inference(S_combinator_elimination,[],[f108])).
thf(f110,plain,(
( ! [X1] : ((\$true = vIMP_23 @ (sK7 @ X1) @ (sK9 @ X1))) )),
inference(B_combinator_elimination,[],[f109])).
thf(f111,plain,(
( ! [X1] : ((\$true = sK9 @ X1) | (\$false = sK7 @ X1)) )),
inference(HOL_binary_constant_elimination,[],[f110])).
thf(f112,plain,(
(\$true = bCOMB_29 @ vPI_6 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23) @ sK8) @ sK9)),
inference(B_combinator_elimination,[],[f103])).
thf(f113,plain,(
(\$true = vPI_6 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23) @ sK8 @ sK9))),
inference(B_combinator_elimination,[],[f112])).
thf(f114,plain,(
(\$true = vPI_6 @ (sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ sK8) @ sK9))),
inference(B_combinator_elimination,[],[f113])).
thf(f115,plain,(
( ! [X1] : ((\$true = sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ sK8) @ sK9 @ X1)) )),
inference(HOL_PI_constant_elimination,[],[f114])).
thf(f116,plain,(
( ! [X1] : ((\$true = bCOMB_26 @ vIMP_23 @ sK8 @ X1 @ (sK9 @ X1))) )),
inference(S_combinator_elimination,[],[f115])).
thf(f117,plain,(
( ! [X1] : ((\$true = vIMP_23 @ (sK8 @ X1) @ (sK9 @ X1))) )),
inference(B_combinator_elimination,[],[f116])).
thf(f118,plain,(
( ! [X1] : ((\$true = sK9 @ X1) | (\$false = sK8 @ X1)) )),
inference(HOL_binary_constant_elimination,[],[f117])).
thf(f119,plain,(
(\$true != bCOMB_29 @ vPI_6 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vOR_23) @ sK7 @ sK8)) @ sK9)),
inference(B_combinator_elimination,[],[f102])).
thf(f120,plain,(
(\$true != vPI_6 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vIMP_23) @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vOR_23) @ sK7 @ sK8) @ sK9))),
inference(B_combinator_elimination,[],[f119])).
thf(f121,plain,(
(\$true != vPI_6 @ (sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ (bCOMB_33 @ sCOMB_27 @ (bCOMB_26 @ vOR_23) @ sK7 @ sK8)) @ sK9))),
inference(B_combinator_elimination,[],[f120])).
thf(f122,plain,(
(\$true != vPI_6 @ (sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ (sCOMB_27 @ (bCOMB_26 @ vOR_23 @ sK7) @ sK8)) @ sK9))),
inference(B_combinator_elimination,[],[f121])).
thf(f123,plain,(
(\$false = sCOMB_27 @ (bCOMB_26 @ vIMP_23 @ (sCOMB_27 @ (bCOMB_26 @ vOR_23 @ sK7) @ sK8)) @ sK9 @ sK10)),
inference(HOL_SIGMA_constant_elimination,[],[f122])).
thf(f124,plain,(
(\$false = bCOMB_26 @ vIMP_23 @ (sCOMB_27 @ (bCOMB_26 @ vOR_23 @ sK7) @ sK8) @ sK10 @ (sK9 @ sK10))),
inference(S_combinator_elimination,[],[f123])).
thf(f125,plain,(
(\$false = vIMP_23 @ (sCOMB_27 @ (bCOMB_26 @ vOR_23 @ sK7) @ sK8 @ sK10) @ (sK9 @ sK10))),
inference(B_combinator_elimination,[],[f124])).
thf(f126,plain,(
(\$false = vIMP_23 @ (bCOMB_26 @ vOR_23 @ sK7 @ sK10 @ (sK8 @ sK10)) @ (sK9 @ sK10))),
inference(S_combinator_elimination,[],[f125])).
thf(f127,plain,(
(\$false = vIMP_23 @ (vOR_23 @ (sK7 @ sK10) @ (sK8 @ sK10)) @ (sK9 @ sK10))),
inference(B_combinator_elimination,[],[f126])).
thf(f130,plain,(
(\$true = vOR_23 @ (sK7 @ sK10) @ (sK8 @ sK10))),
inference(HOL_binary_constant_elimination,[],[f127])).
thf(f131,plain,(
(\$false = sK9 @ sK10)),
inference(HOL_binary_constant_elimination,[],[f127])).
thf(f134,plain,(
(\$true = sK7 @ sK10) | (\$true = sK8 @ sK10)),
inference(HOL_binary_constant_elimination,[],[f130])).
thf(f136,plain,(
(\$false = \$true) | (\$false = sK8 @ sK10)),
inference(superposition,[],[f131,f118])).
thf(f137,plain,(
(\$false = \$true) | (\$false = sK7 @ sK10)),
inference(superposition,[],[f131,f111])).
thf(f140,plain,(
(\$false = sK8 @ sK10)),
inference(subsumption_resolution,[],[f136,f17])).
thf(f143,plain,(
(\$false = \$true) | (\$true = sK7 @ sK10)),
inference(backward_demodulation,[],[f140,f134])).
thf(f144,plain,(
(\$true = sK7 @ sK10)),
inference(subsumption_resolution,[],[f143,f17])).
thf(f151,plain,(
(\$false = sK7 @ sK10)),
inference(subsumption_resolution,[],[f137,f17])).
thf(f152,plain,(
(\$false = \$true)),
inference(backward_demodulation,[],[f151,f144])).
thf(f153,plain,(
\$false),
inference(subsumption_resolution,[],[f152,f17])).
% 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_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
```

### Sample proof for BOO001-1

```% SZS output start Proof for BOO001-1
fof(f1,axiom,(
( ! [X4,X2,X0,X3,X1] : (multiply(X0,X1,multiply(X2,X3,X4)) = multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4))) )),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/BOO/BOO001-1.p',associativity)).
fof(f2,axiom,(
( ! [X2,X3] : (multiply(X3,X2,X2) = X2) )),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/BOO/BOO001-1.p',ternary_multiply_1)).
fof(f5,axiom,(
( ! [X2,X3] : (multiply(X2,X3,inverse(X3)) = X2) )),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/BOO/BOO001-1.p',right_inverse)).
fof(f6,axiom,(
inverse(inverse(a)) != a),
file('/Users/giles/TPTP/TPTP-v7.0.0/Problems/BOO/BOO001-1.p',prove_inverse_is_self_cancelling)).
fof(f7,plain,(
~sP0(inverse(inverse(a)))),
introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP0])])).
fof(f8,plain,(
sP0(a)),
inference(inequality_splitting,[],[f6,f7])).
fof(f9,plain,(
( ! [X2,X0,X3,X1] : (multiply(X0,X1,multiply(X1,X2,X3)) = multiply(X1,X2,multiply(X0,X1,X3))) )),
inference(superposition,[],[f1,f2])).
fof(f34,plain,(
( ! [X4,X5,X3] : (multiply(X5,X3,X4) = multiply(X3,X4,multiply(X5,X3,X4))) )),
inference(superposition,[],[f9,f2])).
fof(f134,plain,(
( ! [X31,X32] : (multiply(X32,inverse(X32),X31) = X31) )),
inference(superposition,[],[f34,f5])).
fof(f150,plain,(
( ! [X21] : (inverse(inverse(X21)) = X21) )),
inference(superposition,[],[f134,f5])).
fof(f163,plain,(
~sP0(a)),
inference(backward_demodulation,[],[f150,f7])).
fof(f165,plain,(
\$false),
inference(subsumption_resolution,[],[f163,f8])).
% SZS output end Proof for BOO001-1
```

### Sample proof for HL400001^1

```% SZS output start Proof for HL400001^1
tff(type_def_5, type, u: \$tType).
tff(type_def_6, type, d: \$tType).
tff(type_def_7, type, du: \$tType).
thf(func_def_0, type, tyop_2Emin_2Ebool: d).
thf(func_def_1, type, tyop_2Emin_2Efun: (d > (d > d))).
thf(func_def_2, type, s: (d > (u > du))).
thf(func_def_3, type, app_2E2: (du > (du > u))).
thf(func_def_4, type, combin_i_2E0: u).
thf(func_def_5, type, combin_k_2E0: u).
thf(func_def_6, type, combin_s_2E0: u).
thf(func_def_7, type, c_2Ebool_2E_21_2E0: u).
thf(func_def_8, type, c_2Ebool_2E_21_2E1: (du > u)).
thf(func_def_9, type, c_2Ebool_2E_2F_5C_2E0: u).
thf(func_def_10, type, c_2Ebool_2E_2F_5C_2E2: (du > (du > u))).
thf(func_def_11, type, c_2Emin_2E_3D_2E0: u).
thf(func_def_12, type, c_2Emin_2E_3D_2E2: (du > (du > u))).
thf(func_def_13, type, c_2Emin_2E_3D_3D_3E_2E0: u).
thf(func_def_14, type, c_2Emin_2E_3D_3D_3E_2E2: (du > (du > u))).
thf(func_def_15, type, c_2Ebool_2E_3F_2E0: u).
thf(func_def_16, type, c_2Ebool_2E_3F_2E1: (du > u)).
thf(func_def_17, type, c_2Ebool_2EF_2E0: u).
thf(func_def_18, type, c_2Ebool_2ET_2E0: u).
thf(func_def_19, type, c_2Ebool_2E_5C_2F_2E0: u).
thf(func_def_20, type, c_2Ebool_2E_5C_2F_2E2: (du > (du > u))).
thf(func_def_21, type, c_2Ebool_2E_7E_2E0: u).
thf(func_def_22, type, c_2Ebool_2E_7E_2E1: (du > u)).
thf(func_def_23, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ((\$o > \$o) > (\$o > \$o))).
thf(func_def_24, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ((\$o > (\$o > \$o)) > (\$o > (\$o > \$o)))).
thf(func_def_25, type, mono_2Ec_2Ebool_2E_2F_5C: (\$o > (\$o > \$o))).
thf(func_def_26, type, mono_2Ec_2Emin_2E_3D_3D_3E: (\$o > (\$o > \$o))).
thf(func_def_27, type, mono_2Ec_2Ebool_2EF: \$o).
thf(func_def_28, type, mono_2Ec_2Ebool_2ET: \$o).
thf(func_def_29, type, mono_2Ec_2Ebool_2E_5C_2F: (\$o > (\$o > \$o))).
thf(func_def_30, type, mono_2Ec_2Ebool_2E_7E: (\$o > \$o)).
thf(func_def_31, type, i_mono_2Etyop_2Emin_2Ebool: (\$o > u)).
thf(func_def_32, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ((\$o > \$o) > u)).
thf(func_def_33, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ((\$o > (\$o > \$o)) > u)).
thf(func_def_34, type, j_mono_2Etyop_2Emin_2Ebool: (du > \$o)).
thf(func_def_35, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (du > (\$o > \$o))).
thf(func_def_36, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (du > (\$o > (\$o > \$o)))).
thf(func_def_37, type, vNOT_14: (\$o > \$o)).
thf(func_def_38, type, vAPP_14_1: ((\$o > \$o) * \$o) > \$o).
thf(func_def_41, type, vAPP_9_6: ((d > (d > d)) * d) > (d > d)).
thf(func_def_42, type, vAPP_8_6: ((d > d) * d) > d).
thf(func_def_43, type, vAPP_11_6: ((d > (u > du)) * d) > (u > du)).
thf(func_def_44, type, vAPP_19_14: (((\$o > \$o) > u) * (\$o > \$o)) > u).
thf(func_def_45, type, vAPP_10_5: ((u > du) * u) > du).
thf(func_def_46, type, vAPP_22_7: ((du > (\$o > \$o)) * du) > (\$o > \$o)).
thf(func_def_47, type, vAPP_20_16: (((\$o > (\$o > \$o)) > u) * (\$o > (\$o > \$o))) > u).
thf(func_def_48, type, vAPP_23_7: ((du > (\$o > (\$o > \$o))) * du) > (\$o > (\$o > \$o))).
thf(func_def_49, type, vAPP_18_1: ((\$o > u) * \$o) > u).
thf(func_def_50, type, vAPP_21_7: ((du > \$o) * du) > \$o).
thf(func_def_51, type, vAPP_16_1: ((\$o > (\$o > \$o)) * \$o) > (\$o > \$o)).
thf(func_def_52, type, vAPP_12_7: ((du > u) * du) > u).
thf(func_def_53, type, vAPP_13_7: ((du > (du > u)) * du) > (du > u)).
thf(func_def_54, type, vAPP_15_14: (((\$o > \$o) > (\$o > \$o)) * (\$o > \$o)) > (\$o > \$o)).
thf(func_def_55, type, vAPP_17_16: (((\$o > (\$o > \$o)) > (\$o > (\$o > \$o))) * (\$o > (\$o > \$o))) > (\$o > (\$o > \$o))).
thf(func_def_56, type, sK0: \$o).
thf(func_def_58, type, vAND_16: (\$o > (\$o > \$o))).
thf(func_def_59, type, vOR_16: (\$o > (\$o > \$o))).
thf(func_def_60, type, vIMP_16: (\$o > (\$o > \$o))).
thf(f26,axiom,(
mono_2Ec_2Ebool_2ET <=> ! [X15 : \$o] : (X15 = X15)),
file('HL400001^1.p',unknown)).
thf(f27,conjecture,(
mono_2Ec_2Ebool_2ET),
file('HL400001^1.p',unknown)).
thf(f28,negated_conjecture,(
~mono_2Ec_2Ebool_2ET),
inference(negated_conjecture,[],[f27])).
thf(f30,plain,(
~mono_2Ec_2Ebool_2ET),
inference(rectify,[],[f28])).
thf(f31,plain,(
~(mono_2Ec_2Ebool_2ET = \$true)),
inference(fool_elimination,[],[f30])).
thf(f32,plain,(
mono_2Ec_2Ebool_2ET <=> ! [X0 : \$o] : (X0 = X0)),
inference(rectify,[],[f26])).
thf(f33,plain,(
(mono_2Ec_2Ebool_2ET = \$true) <=> ! [X0 : \$o] : (X0 = X0)),
inference(fool_elimination,[],[f32])).
thf(f95,plain,(
(mono_2Ec_2Ebool_2ET != \$true)),
inference(flattening,[],[f31])).
thf(f96,plain,(
((mono_2Ec_2Ebool_2ET = \$true) | ? [X0 : \$o] : (X0 != X0)) & (! [X0 : \$o] : (X0 = X0) | (mono_2Ec_2Ebool_2ET != \$true))),
inference(nnf_transformation,[],[f33])).
thf(f97,plain,(
((mono_2Ec_2Ebool_2ET = \$true) | ? [X0 : \$o] : (X0 != X0)) & (! [X1 : \$o] : (X1 = X1) | (mono_2Ec_2Ebool_2ET != \$true))),
inference(rectify,[],[f96])).
thf(f98,plain,(
? [X0 : \$o] : (X0 != X0) => (sK0 != sK0)),
introduced(choice_axiom,[])).
thf(f99,plain,(
((mono_2Ec_2Ebool_2ET = \$true) | (sK0 != sK0)) & (! [X1 : \$o] : (X1 = X1) | (mono_2Ec_2Ebool_2ET != \$true))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f97,f98])).
thf(f100,plain,(
(mono_2Ec_2Ebool_2ET != \$true)),
inference(cnf_transformation,[],[f95])).
thf(f102,plain,(
(mono_2Ec_2Ebool_2ET = \$true) | (sK0 != sK0)),
inference(cnf_transformation,[],[f99])).
thf(f103,plain,(
(mono_2Ec_2Ebool_2ET = \$true)),
inference(trivial_inequality_removal,[],[f102])).
thf(f104,plain,(
\$false),
inference(subsumption_resolution,[],[f103,f100])).
% SZS output end Proof for HL400001^1
```

### Sample proof for HL400001^2

```% SZS output start Proof for HL400001^2
tff(type_def_5, type, del: \$tType).
thf(func_def_0, type, bool: del).
thf(func_def_1, type, ind: del).
thf(func_def_2, type, arr: (del > (del > del))).
thf(func_def_3, type, mem: (\$i > (del > \$o))).
thf(func_def_4, type, ap: (\$i > (\$i > \$i))).
thf(func_def_5, type, lam: (del > ((\$i > \$i) > \$i))).
thf(func_def_6, type, p: (\$i > \$o)).
thf(func_def_7, type, inj__o: (\$o > \$i)).
thf(func_def_9, type, fo__c_2Ebool_2ET: \$o).
thf(func_def_10, type, c_2Emin_2E_3D: (del > \$i)).
thf(func_def_13, type, vAPP_15_1: ((\$o > \$i) * \$o) > \$i).
thf(func_def_14, type, vAPP_13_5: ((del > ((\$i > \$i) > \$i)) * del) > ((\$i > \$i) > \$i)).
thf(func_def_15, type, iCOMB_10: (\$i > \$i)).
thf(func_def_16, type, vAPP_12_10: (((\$i > \$i) > \$i) * (\$i > \$i)) > \$i).
thf(func_def_17, type, vAPP_14_0: ((\$i > \$o) * \$i) > \$o).
thf(func_def_18, type, vAPP_9_0: ((\$i > (del > \$o)) * \$i) > (del > \$o)).
thf(func_def_19, type, vAPP_8_5: ((del > \$o) * del) > \$o).
thf(func_def_20, type, vAPP_16_5: ((del > \$i) * del) > \$i).
thf(func_def_21, type, vAPP_7_5: ((del > (del > del)) * del) > (del > del)).
thf(func_def_22, type, vAPP_6_5: ((del > del) * del) > del).
thf(func_def_23, type, vAPP_11_0: ((\$i > (\$i > \$i)) * \$i) > (\$i > \$i)).
thf(func_def_24, type, vAPP_10_0: ((\$i > \$i) * \$i) > \$i).
thf(func_def_26, type, vAND_18: (\$o > (\$o > \$o))).
thf(func_def_27, type, vOR_18: (\$o > (\$o > \$o))).
thf(func_def_28, type, vIMP_18: (\$o > (\$o > \$o))).
thf(func_def_29, type, vNOT_17: (\$o > \$o)).
thf(func_def_30, type, vAPP_18_1: ((\$o > (\$o > \$o)) * \$o) > (\$o > \$o)).
thf(func_def_31, type, vAPP_17_1: ((\$o > \$o) * \$o) > \$o).
thf(f14,conjecture,(
\$true),
file('HL400001^2.p',unknown)).
thf(f15,negated_conjecture,(
~\$true),
inference(negated_conjecture,[],[f14])).
thf(f49,plain,(
\$false),
inference(true_and_false_elimination,[],[f15])).
thf(f50,plain,(
\$false),
inference(cnf_transformation,[],[f49])).
% SZS output end Proof for HL400001^2
```

### Sample proof for HL400001_1

```% SZS output start Proof for HL400001_1
tff(type_def_5, type, u: \$tType).
tff(type_def_6, type, d: \$tType).
tff(type_def_7, type, du: \$tType).
tff(type_def_8, type, mono_2Etyop_2Emin_2Ebool: \$tType).
tff(type_def_9, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: \$tType).
tff(type_def_10, type, mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: \$tType).
tff(func_def_0, type, tyop_2Emin_2Ebool: d).
tff(func_def_1, type, tyop_2Emin_2Efun: (d * d) > d).
tff(func_def_2, type, s: (d * u) > du).
tff(func_def_3, type, app_2E2: (du * du) > u).
tff(func_def_4, type, combin_i_2E0: u).
tff(func_def_5, type, combin_k_2E0: u).
tff(func_def_6, type, combin_s_2E0: u).
tff(func_def_7, type, c_2Ebool_2E_21_2E0: u).
tff(func_def_8, type, c_2Ebool_2E_21_2E1: du > u).
tff(func_def_9, type, c_2Ebool_2E_2F_5C_2E0: u).
tff(func_def_10, type, c_2Ebool_2E_2F_5C_2E2: (du * du) > u).
tff(func_def_11, type, c_2Emin_2E_3D_2E0: u).
tff(func_def_12, type, c_2Emin_2E_3D_2E2: (du * du) > u).
tff(func_def_13, type, c_2Emin_2E_3D_3D_3E_2E0: u).
tff(func_def_14, type, c_2Emin_2E_3D_3D_3E_2E2: (du * du) > u).
tff(func_def_15, type, c_2Ebool_2E_3F_2E0: u).
tff(func_def_16, type, c_2Ebool_2E_3F_2E1: du > u).
tff(func_def_17, type, c_2Ebool_2EF_2E0: u).
tff(func_def_18, type, c_2Ebool_2ET_2E0: u).
tff(func_def_19, type, c_2Ebool_2E_5C_2F_2E0: u).
tff(func_def_20, type, c_2Ebool_2E_5C_2F_2E2: (du * du) > u).
tff(func_def_21, type, c_2Ebool_2E_7E_2E0: u).
tff(func_def_22, type, c_2Ebool_2E_7E_2E1: du > u).
tff(func_def_23, type, mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: (mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool) > mono_2Etyop_2Emin_2Ebool).
tff(func_def_24, type, mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29).
tff(func_def_25, type, mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29).
tff(func_def_26, type, mono_2Ec_2Ebool_2E_2F_5C_2E2: (mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool) > mono_2Etyop_2Emin_2Ebool).
tff(func_def_27, type, mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29).
tff(func_def_28, type, mono_2Ec_2Emin_2E_3D_3D_3E_2E2: (mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool) > mono_2Etyop_2Emin_2Ebool).
tff(func_def_29, type, mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool).
tff(func_def_30, type, mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool).
tff(func_def_31, type, mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29).
tff(func_def_32, type, mono_2Ec_2Ebool_2E_5C_2F_2E2: (mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool) > mono_2Etyop_2Emin_2Ebool).
tff(func_def_33, type, mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29).
tff(func_def_34, type, mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool).
tff(func_def_35, type, i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u).
tff(func_def_36, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u).
tff(func_def_37, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u).
tff(func_def_38, type, j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool).
tff(func_def_39, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29).
tff(func_def_40, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29).
tff(func_def_41, type, sK0: mono_2Etyop_2Emin_2Ebool).
tff(func_def_42, type, sK1: (d * u) > u).
tff(func_def_43, type, sK2: (d * u) > u).
tff(func_def_44, type, sK3: (d * d * u * u) > u).
tff(pred_def_1, type, p: mono_2Etyop_2Emin_2Ebool > \$o).
tff(f3,axiom,(
p(mono_2Ec_2Ebool_2ET_2E0)),
file('HL400001_1.p',reserved_2Eho_2Etruth)).
tff(f32,conjecture,(
p(mono_2Ec_2Ebool_2ET_2E0)),
file('HL400001_1.p',thm_2Ebool_2ETRUTH)).
tff(f33,negated_conjecture,(
~p(mono_2Ec_2Ebool_2ET_2E0)),
inference(negated_conjecture,[],[f32])).
tff(f34,plain,(
~p(mono_2Ec_2Ebool_2ET_2E0)),
inference(flattening,[],[f33])).
tff(f98,plain,(
~p(mono_2Ec_2Ebool_2ET_2E0)),
inference(cnf_transformation,[],[f34])).
tff(f100,plain,(
p(mono_2Ec_2Ebool_2ET_2E0)),
inference(cnf_transformation,[],[f3])).
tff(f151,plain,(
\$false),
inference(subsumption_resolution,[],[f100,f98])).
% SZS output end Proof for HL400001_1
```

### Sample proof for HL400001_2

```% SZS output start Proof for HL400001_2
tff(type_def_5, type, del: \$tType).
tff(type_def_6, type, tp__o: \$tType).
tff(func_def_0, type, bool: del).
tff(func_def_1, type, ind: del).
tff(func_def_2, type, arr: (del * del) > del).
tff(func_def_4, type, k: (del * \$i) > \$i).
tff(func_def_5, type, i: del > \$i).
tff(func_def_6, type, inj__o: tp__o > \$i).
tff(func_def_7, type, surj__o: \$i > tp__o).
tff(func_def_8, type, c_2Emin_2E_3D: del > \$i).
tff(func_def_10, type, fo__c_2Ebool_2ET: tp__o).
tff(pred_def_1, type, mem: (\$i * del) > \$o).
tff(f15,conjecture,(
\$true),
file('HL400001_2.p',conj_thm_2Ebool_2ETRUTH)).
tff(f16,negated_conjecture,(
~\$true),
inference(negated_conjecture,[],[f15])).
tff(f17,plain,(
\$false),
inference(true_and_false_elimination,[],[f16])).
tff(f18,plain,(
\$false),
inference(cnf_transformation,[],[f17])).
% SZS output end Proof for HL400001_2
```

### Sample proof for HL400001+1

```% SZS output start Proof for HL400001+1
fof(f3,axiom,(
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
file('HL400001+1.p',thm_2Eextra_2Dho_2Etruth)).
fof(f17,conjecture,(
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
file('HL400001+1.p',thm_2Ebool_2ETRUTH)).
fof(f18,negated_conjecture,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(negated_conjecture,[],[f17])).
fof(f19,plain,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(flattening,[],[f18])).
fof(f36,plain,(
~p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(cnf_transformation,[],[f19])).
fof(f38,plain,(
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),
inference(cnf_transformation,[],[f3])).
fof(f80,plain,(
\$false),
inference(global_subsumption,[],[f36,f38])).
% SZS output end Proof for HL400001+1
```

### Sample proof for HL400001+2

```% SZS output start Proof for HL400001+2
fof(f14,conjecture,(
\$true),
file('HL400001+2.p',conj_thm_2Ebool_2ETRUTH)).
fof(f15,negated_conjecture,(
~\$true),
inference(negated_conjecture,[],[f14])).
fof(f16,plain,(
\$false),
inference(true_and_false_elimination,[],[f15])).
fof(f38,plain,(
\$false),
inference(cnf_transformation,[],[f16])).
% SZS output end Proof for HL400001+2
```

## Waldmeister 710

Thomas Hillenbrand
Max-Planck-Institut für Informatik, Germany

### Sample proof for BOO001-1

```% SZS output start CNFRefutation
cnf('0.1.0.0',axiom,
( X1 = multiply(X2,X1,X1) ),
file('/tmp/WALDMEISTER_48444_quokka')).
cnf('0.1.1.0',plain,
( X1 = multiply(X2,X1,X1) ),
inference(weigh,[status(thm)],['0.1.0.0']),
[weight('<0,0,0,[0,0,0,1]>')]).
cnf('0.1.2.0',plain,
( multiply(X1,X2,X2) = X2 ),
inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
[x,rule_1]).
cnf('0.2.0.0',axiom,
( X1 = multiply(X1,X2,inverse(X2)) ),
file('/tmp/WALDMEISTER_48444_quokka')).
cnf('0.2.1.0',plain,
( X1 = multiply(X1,X2,inverse(X2)) ),
inference(weigh,[status(thm)],['0.2.0.0']),
[weight('<1,0,0,[0,0,0,2]>')]).
cnf('0.2.2.0',plain,
( multiply(X1,X2,inverse(X2)) = X1 ),
inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
[x,rule_2]).
cnf('0.3.0.0',axiom,
( X1 = multiply(X1,X1,X2) ),
file('/tmp/WALDMEISTER_48444_quokka')).
cnf('0.3.1.0',plain,
( X1 = multiply(X1,X1,X2) ),
inference(weigh,[status(thm)],['0.3.0.0']),
[weight('<2,0,0,[0,0,0,3]>')]).
cnf('0.3.2.0',plain,
( multiply(X1,X1,X2) = X1 ),
inference(orient,[status(thm)],['0.3.1.0',theory(equality)]),
[x,rule_3]).
cnf('0.4.0.0',axiom,
( X1 = multiply(inverse(X2),X2,X1) ),
file('/tmp/WALDMEISTER_48444_quokka')).
cnf('0.4.1.0',plain,
( X1 = multiply(inverse(X2),X2,X1) ),
inference(weigh,[status(thm)],['0.4.0.0']),
[weight('<3,0,0,[0,0,0,4]>')]).
cnf('0.4.2.0',plain,
( multiply(inverse(X1),X1,X2) = X2 ),
inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
[x,rule_4]).
cnf('0.5.0.0',axiom,
( multiply(X1,X2,multiply(X3,X4,X5)) = multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) ),
file('/tmp/WALDMEISTER_48444_quokka')).
cnf('0.5.1.0',plain,
( multiply(X1,X2,multiply(X3,X4,X5)) = multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) ),
inference(weigh,[status(thm)],['0.5.0.0']),
[weight('<4,0,0,[0,0,0,5]>')]).
cnf('0.5.2.0',plain,
( multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X1,X2,multiply(X3,X4,X5)) ),
inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
[x,rule_5]).
cnf('0.7.0.0',plain,
( multiply(X1,X2,multiply(X3,X4,X2)) = multiply(multiply(X1,X2,X3),X4,X2) ),
inference(cp,[status(thm)],['0.5.2.0','0.1.2.0',theory(equality)]),
[pos('L.3','L')]).
cnf('0.7.1.0',plain,
( multiply(X1,X2,multiply(X3,X4,X2)) = multiply(multiply(X1,X2,X3),X4,X2) ),
inference(weigh,[status(thm)],['0.7.0.0']),
[weight('<7,5,1,[1,0,0,6]>')]).
cnf('0.7.2.0',plain,
( multiply(multiply(X1,X2,X3),X4,X2) = multiply(X1,X2,multiply(X3,X4,X2)) ),
inference(orient,[status(thm)],['0.7.1.0',theory(equality)]),
[x,rule_7]).
cnf('0.11.0.0',plain,
( multiply(X1,X2,multiply(inverse(X2),X3,X2)) = multiply(X1,X3,X2) ),
inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
[pos('L.1','L')]).
cnf('0.11.1.0',plain,
( multiply(X1,X2,multiply(inverse(X2),X3,X2)) = multiply(X1,X3,X2) ),
inference(weigh,[status(thm)],['0.11.0.0']),
[weight('<8,7,2,[1,0,0,1]>')]).
cnf('0.11.2.0',plain,
( multiply(X1,X2,multiply(inverse(X2),X3,X2)) = multiply(X1,X3,X2) ),
inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
[u,rule_11]).
cnf('0.12.0.0',plain,
( multiply(X1,inverse(X2),X2) = multiply(X1,X2,inverse(X2)) ),
inference(cp,[status(thm)],['0.11.2.0','0.3.2.0',theory(equality)]),
[pos('L.3','L')]).
cnf('0.12.0.1',plain,
( multiply(X1,inverse(X2),X2) = X1 ),
inference(reduction,[status(thm)],['0.12.0.0','0.2.2.0',theory(equality)]),
[pos('R','L')]).
cnf('0.12.1.0',plain,
( multiply(X1,inverse(X2),X2) = X1 ),
inference(weigh,[status(thm)],['0.12.0.1']),
[weight('<5,11,3,[1,0,0,3]>')]).
cnf('0.12.2.0',plain,
( multiply(X1,inverse(X2),X2) = X1 ),
inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
[u,rule_12]).
cnf('0.13.0.0',plain,
( inverse(inverse(X1)) = X1 ),
inference(cp,[status(thm)],['0.12.2.0','0.4.2.0',theory(equality)]),
[pos('L','L')]).
cnf('0.13.1.0',plain,
( inverse(inverse(X1)) = X1 ),
inference(weigh,[status(thm)],['0.13.0.0']),
[weight('<3,12,4,[1,0,0,0]>')]).
cnf('0.13.2.0',plain,
( inverse(inverse(X1)) = X1 ),
inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
[u,rule_13]).
cnf('1.0.0.0',conjecture,
( inverse(inverse(a)) = a ),
file('/tmp/WALDMEISTER_48444_quokka',conjecture_1)).
cnf('1.0.0.1',plain,
( a = a ),
inference(reduction,[status(thm)],['1.0.0.0','0.13.2.0',theory(equality)]),
[pos('L','L')]).
cnf('1.0.0.2',plain,
( \$true ),
inference(trivial,[status(thm)],['1.0.0.1',theory(equality)]),
[conjecture_1]).
% SZS output end CNFRefutation
```

## Zipperposition 1.5

Petar Vukmirović
Vrije Universiteit Amsterdam, The Netherlands

### Sample proof 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 = (^[V_1:(\$i > \$o),V_2:(\$i > \$o)]: (![X2]: (V_1(X2) => V_2(X2)))),
define([status(thm)])).
tff(union, axiom, union() = ^[X:(\$i > \$o),Y:(\$i > \$o),U]: (Y(U) | X(U))).
tff('1', plain,
union = (^[V_1:(\$i > \$o),V_2:(\$i > \$o),V_3]: (V_2(V_3) | V_1(V_3))),
define([status(thm)])).
tff(zf_stmt_0, conjecture,
(![X2:(\$i > \$o),X3:(\$i > \$o),X4:(\$i > \$o)]:
(((![X5]: (X3(X5) => X4(X5))) & (![X6]: (X2(X6) => X4(X6)))) =>
(![X7]: ((X3(X7) | X2(X7)) => X4(X7)))))).
tff(zf_stmt_1, negated_conjecture,
(~
(![X2:(\$i > \$o),X3:(\$i > \$o),X4:(\$i > \$o)]:
(((![X5]: (X3(X5) => X4(X5))) & (![X6]: (X2(X6) => X4(X6)))) =>
(![X7]: ((X3(X7) | X2(X7)) => X4(X7))))))).
tff('2', plain, (sk_X3_(sk_X7_) | sk_X2_(sk_X7_)),
inference('cnf', [status(esa)], [zf_stmt_1])).
tff('3', plain, (sk_X3_(sk_X7_)) <= ((sk_X3_(sk_X7_))),
inference('split', [status(esa)], ['2'])).
tff('4', plain, ![X35]: (sk_X4_(X35) | ~ sk_X3_(X35)),
inference('cnf', [status(esa)], [zf_stmt_1])).
tff('5', plain, (sk_X4_(sk_X7_)) <= ((sk_X3_(sk_X7_))),
inference('sup-', [status(thm)], ['3', '4'])).
tff('6', plain, ~ sk_X4_(sk_X7_),
inference('cnf', [status(esa)], [zf_stmt_1])).
tff('7', plain, (\$false) <= ((sk_X3_(sk_X7_))),
inference('sup-', [status(thm)], ['5', '6'])).
tff('8', plain, (sk_X3_(sk_X7_)) | (sk_X2_(sk_X7_)),
inference('split', [status(esa)], ['2'])).
tff('9', plain, (sk_X2_(sk_X7_)) <= ((sk_X2_(sk_X7_))),
inference('split', [status(esa)], ['2'])).
tff('10', plain, ![X36]: (sk_X4_(X36) | ~ sk_X2_(X36)),
inference('cnf', [status(esa)], [zf_stmt_1])).
tff('11', plain, (sk_X4_(sk_X7_)) <= ((sk_X2_(sk_X7_))),
inference('sup-', [status(thm)], ['9', '10'])).
tff('12', plain, ~ (sk_X2_(sk_X7_)),
inference('sup-', [status(thm)], ['11', '6'])).
tff('13', plain, (sk_X3_(sk_X7_)),
inference('sat_resolution', [status(thm)], ['8', '12'])).
tff('14', plain, \$false, inference('simpl_trail', [status(thm)], ['7', '13'])).

% SZS output end Refutation
```

### Sample proof for SEU140+2

```% SZS output start Refutation
tff(t63_xboole_1, conjecture,
(![A,B,C]: ((disjoint(B,C) & subset(A,B)) => disjoint(A,C)))).
tff(zf_stmt_0, negated_conjecture,
(~(![A,B,C]: ((disjoint(B,C) & subset(A,B)) => disjoint(A,C))))).
tff('0', plain, ~ disjoint(sk_A_2, sk_C_4),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(t3_xboole_0, axiom,
(![A,B]:
((~(disjoint(A,B) & (?[C]: (in(C,B) & in(C,A))))) &
(~((![C]: (~(in(C,B) & in(C,A)))) & (~disjoint(A,B))))))).
tff('1', plain,
![X86, X87]: (in(sk_C_2(X86, X87), X86) | disjoint(X87, X86)),
inference('cnf', [status(esa)], [t3_xboole_0])).
tff('2', plain, subset(sk_A_2, sk_B_1),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff(d3_tarski, axiom,
(![A,B]: (subset(A,B) <=> (![C]: (in(C,A) => in(C,B)))))).
tff('3', plain,
![X20, X21, X22]: (~ in(X20, X21) | in(X20, X22) | ~ subset(X21, X22)),
inference('cnf', [status(esa)], [d3_tarski])).
tff('4', plain, ![X0]: (~ in(X0, sk_A_2) | in(X0, sk_B_1)),
inference('s_sup-', [status(thm)], ['2', '3'])).
tff('5', plain,
![X0]: (disjoint(X0, sk_A_2) | in(sk_C_2(sk_A_2, X0), sk_B_1)),
inference('s_sup-', [status(thm)], ['1', '4'])).
tff('6', plain,
![X86, X87]: (in(sk_C_2(X86, X87), X87) | disjoint(X87, X86)),
inference('cnf', [status(esa)], [t3_xboole_0])).
tff('7', plain, disjoint(sk_B_1, sk_C_4),
inference('cnf', [status(esa)], [zf_stmt_0])).
tff('8', plain,
![X87, X88, X89]:
(~ disjoint(X87, X88) | ~ in(X89, X87) | ~ in(X89, X88)),
inference('cnf', [status(esa)], [t3_xboole_0])).
tff('9', plain, ![X0]: (~ in(X0, sk_B_1) | ~ in(X0, sk_C_4)),
inference('s_sup-', [status(thm)], ['7', '8'])).
tff('10', plain,
![X0]: (disjoint(sk_C_4, X0) | ~ in(sk_C_2(X0, sk_C_4), sk_B_1)),
inference('s_sup-', [status(thm)], ['6', '9'])).
tff('11', plain, (disjoint(sk_C_4, sk_A_2) | disjoint(sk_C_4, sk_A_2)),
inference('s_sup-', [status(thm)], ['5', '10'])).
tff('12', plain, disjoint(sk_C_4, sk_A_2),
inference('simplify', [status(thm)], ['11'])).
tff(symmetry_r1_xboole_0, axiom, (![A,B]: (disjoint(A,B) => disjoint(B,A)))).
tff('13', plain, ![X53, X54]: (disjoint(X53, X54) | ~ disjoint(X54, X53)),
inference('cnf', [status(esa)], [symmetry_r1_xboole_0])).
tff('14', plain, disjoint(sk_A_2, sk_C_4),
inference('s_sup-', [status(thm)], ['12', '13'])).
tff('15', plain, \$false, inference('demod', [status(thm)], ['0', '14'])).

% SZS output end Refutation
```