TPTP Problem File: PRO010+3.p

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```%------------------------------------------------------------------------------
% File     : PRO010+3 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Processes
% Problem  : PSL cliff problem coe-7.1.3
% Version  : Especial : Augmented > Especial.
% English  :
% Refs     : [Hal09] Halcomb (2009), Email to G. Sutcliffe
% Source   : [Hal09]
% Names    : psl-1016-subset-618-lemmas__coe-7.1.3-pd [Hal09]

% Status   : Theorem
% Rating   : 0.19 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.10 v6.4.0, 0.12 v6.3.0, 0.17 v6.2.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.10 v5.1.0, 0.19 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0
% Syntax   : Number of formulae    :   63 (  12 unt;   0 def)
%            Number of atoms       :  216 (  18 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  181 (  28   ~;   6   |;  93   &)
%                                         (   7 <=>;  47  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   18 (  17 usr;   0 prp; 1-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :  170 ( 145   !;  25   ?)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
fof(sos,axiom,
! [X0,X1] :
( occurrence_of(X1,X0)
=> ( activity(X0)
& activity_occurrence(X1) ) ) ).

fof(sos_01,axiom,
! [X2] :
( activity_occurrence(X2)
=> ? [X3] :
( activity(X3)
& occurrence_of(X2,X3) ) ) ).

fof(sos_02,axiom,
! [X4,X5,X6] :
( ( occurrence_of(X4,X5)
& occurrence_of(X4,X6) )
=> X5 = X6 ) ).

fof(sos_03,axiom,
! [X7] :
( activity(X7)
=> subactivity(X7,X7) ) ).

fof(sos_04,axiom,
! [X8,X9] :
( earlier(X8,X9)
=> ~ earlier(X9,X8) ) ).

fof(sos_05,axiom,
! [X10,X11,X12] :
( ( earlier(X10,X11)
& earlier(X11,X12) )
=> earlier(X10,X12) ) ).

fof(sos_06,axiom,
! [X13,X14,X15] :
( ( earlier(X13,X14)
& earlier(X15,X14) )
=> ( earlier(X15,X13)
| earlier(X13,X15)
| X13 = X15 ) ) ).

fof(sos_07,axiom,
! [X16,X17] :
( occurrence_of(X16,X17)
=> ( arboreal(X16)
<=> atomic(X17) ) ) ).

fof(sos_08,axiom,
! [X18] :
( legal(X18)
=> arboreal(X18) ) ).

fof(sos_09,axiom,
! [X19,X20] :
( ( legal(X19)
& earlier(X20,X19) )
=> legal(X20) ) ).

fof(sos_10,axiom,
! [X21,X22] :
( precedes(X21,X22)
<=> ( earlier(X21,X22)
& legal(X22) ) ) ).

fof(sos_11,axiom,
! [X23,X24,X25] :
( min_precedes(X24,X25,X23)
=> ? [X26,X27] :
( subactivity(X26,X23)
& subactivity(X27,X23)
& atocc(X24,X26)
& atocc(X25,X27) ) ) ).

fof(sos_12,axiom,
! [X28,X29] :
( root(X29,X28)
=> ? [X30] :
( subactivity(X30,X28)
& atocc(X29,X30) ) ) ).

fof(sos_13,axiom,
! [X31,X32,X33] :
( min_precedes(X31,X32,X33)
=> ? [X34] :
( root(X34,X33)
& min_precedes(X34,X32,X33) ) ) ).

fof(sos_14,axiom,
! [X35,X36,X37] :
( min_precedes(X35,X36,X37)
=> ~ root(X36,X37) ) ).

fof(sos_15,axiom,
! [X38,X39,X40] :
( min_precedes(X38,X39,X40)
=> precedes(X38,X39) ) ).

fof(sos_16,axiom,
! [X41,X42] :
( root(X41,X42)
=> legal(X41) ) ).

fof(sos_17,axiom,
! [X43,X44] :
( ( atocc(X43,X44)
& legal(X43) )
=> root(X43,X44) ) ).

fof(sos_18,axiom,
! [X45,X46,X47,X48] :
( ( min_precedes(X45,X46,X48)
& min_precedes(X45,X47,X48)
& precedes(X46,X47) )
=> min_precedes(X46,X47,X48) ) ).

fof(sos_19,axiom,
! [X49,X50,X51] :
( min_precedes(X49,X50,X51)
=> ~ atomic(X51) ) ).

fof(sos_20,axiom,
! [X52,X53,X54,X55] :
( ( min_precedes(X53,X52,X55)
& min_precedes(X54,X52,X55)
& precedes(X53,X54) )
=> min_precedes(X53,X54,X55) ) ).

fof(sos_21,axiom,
! [X56,X57] :
( leaf(X56,X57)
<=> ( ( root(X56,X57)
| ? [X58] : min_precedes(X58,X56,X57) )
& ~ ? [X59] : min_precedes(X56,X59,X57) ) ) ).

fof(sos_22,axiom,
! [X60,X61,X62] :
( next_subocc(X60,X61,X62)
<=> ( min_precedes(X60,X61,X62)
& ~ ? [X63] :
( min_precedes(X60,X63,X62)
& min_precedes(X63,X61,X62) ) ) ) ).

fof(sos_23,axiom,
! [X64,X65] :
( atocc(X64,X65)
<=> ? [X66] :
( subactivity(X65,X66)
& atomic(X66)
& occurrence_of(X64,X66) ) ) ).

fof(sos_24,axiom,
! [X67,X68] :
( subactivity_occurrence(X67,X68)
=> ( activity_occurrence(X67)
& activity_occurrence(X68) ) ) ).

fof(sos_25,axiom,
! [X69,X70,X71] :
( min_precedes(X70,X71,X69)
=> ? [X72] :
( occurrence_of(X72,X69)
& subactivity_occurrence(X70,X72)
& subactivity_occurrence(X71,X72) ) ) ).

fof(sos_26,axiom,
! [X73,X74] :
( ( root(X74,X73)
& ~ atomic(X73) )
=> ? [X75] :
( occurrence_of(X75,X73)
& subactivity_occurrence(X74,X75) ) ) ).

fof(sos_27,axiom,
! [X76,X77] :
( ( occurrence_of(X77,X76)
& ~ atomic(X76) )
=> ? [X78] :
( root(X78,X76)
& subactivity_occurrence(X78,X77) ) ) ).

fof(sos_28,axiom,
! [X79,X80,X81,X82] :
( ( occurrence_of(X80,X79)
& arboreal(X81)
& arboreal(X82)
& subactivity_occurrence(X81,X80)
& subactivity_occurrence(X82,X80) )
=> ( min_precedes(X81,X82,X79)
| min_precedes(X82,X81,X79)
| X81 = X82 ) ) ).

fof(sos_29,axiom,
! [X83,X84,X85,X86] :
( ( min_precedes(X83,X84,X85)
& occurrence_of(X86,X85)
& subactivity_occurrence(X84,X86) )
=> subactivity_occurrence(X83,X86) ) ).

fof(sos_30,axiom,
! [X87,X88,X89,X90] :
( ( occurrence_of(X89,X87)
& occurrence_of(X90,X88)
& ~ atomic(X87)
& subactivity_occurrence(X89,X90) )
=> subactivity(X87,X88) ) ).

fof(sos_31,axiom,
! [X91,X92,X93] :
( ( subactivity_occurrence(X91,X92)
& subactivity_occurrence(X92,X93) )
=> subactivity_occurrence(X91,X93) ) ).

fof(sos_32,axiom,
! [X94,X95,X96,X97] :
( ( occurrence_of(X96,X94)
& occurrence_of(X97,X95)
& subactivity(X94,X95)
& ~ subactivity_occurrence(X96,X97) )
=> ? [X98] :
( subactivity_occurrence(X98,X97)
& ~ subactivity_occurrence(X98,X96) ) ) ).

fof(sos_33,axiom,
! [X99,X100] :
( root_occ(X99,X100)
<=> ? [X101] :
( occurrence_of(X100,X101)
& subactivity_occurrence(X99,X100)
& root(X99,X101) ) ) ).

fof(sos_34,axiom,
! [X102,X103] :
( leaf_occ(X102,X103)
<=> ? [X104] :
( occurrence_of(X103,X104)
& subactivity_occurrence(X102,X103)
& leaf(X102,X104) ) ) ).

fof(sos_35,axiom,
! [X105,X106,X107,X108] :
( ( occurrence_of(X107,X108)
& root_occ(X105,X107)
& root_occ(X106,X107) )
=> X105 = X106 ) ).

fof(sos_36,axiom,
! [X109,X110,X111,X112] :
( ( occurrence_of(X111,X112)
& ~ atomic(X112)
& leaf_occ(X109,X111)
& leaf_occ(X110,X111) )
=> X109 = X110 ) ).

fof(sos_37,axiom,
! [X113,X114,X115] :
( ( occurrence_of(X113,X115)
& leaf_occ(X114,X113) )
=> ~ ? [X116] : min_precedes(X114,X116,X115) ) ).

fof(sos_38,axiom,
! [X117,X118,X119] :
( ( occurrence_of(X117,X119)
& root_occ(X118,X117) )
=> ~ ? [X120] : min_precedes(X120,X118,X119) ) ).

fof(sos_39,axiom,
! [X121,X122,X123,X124,X125] :
( ( next_subocc(X121,X122,X124)
& next_subocc(X121,X123,X124)
& occurrence_of(X125,X124)
& subactivity_occurrence(X123,X125)
& subactivity_occurrence(X122,X125) )
=> X122 = X123 ) ).

fof(sos_40,axiom,
! [X126,X127,X128,X129] :
( ( next_subocc(X127,X126,X129)
& next_subocc(X128,X126,X129) )
=> X127 = X128 ) ).

fof(sos_41,axiom,
! [X130,X131,X132,X133] :
( ( occurrence_of(X130,X133)
& leaf_occ(X131,X130)
& root_occ(X132,X130)
& X131 != X132 )
=> min_precedes(X132,X131,X133) ) ).

fof(sos_42,axiom,
! [X134,X135,X136,X137] :
( ( occurrence_of(X135,X134)
& subactivity_occurrence(X136,X135)
& root_occ(X137,X135)
& arboreal(X136)
& ~ min_precedes(X137,X136,X134) )
=> X137 = X136 ) ).

fof(sos_43,axiom,
! [X138,X139,X140,X141] :
( ( occurrence_of(X139,X138)
& subactivity_occurrence(X140,X139)
& leaf_occ(X141,X139)
& arboreal(X140)
& ~ min_precedes(X140,X141,X138) )
=> X141 = X140 ) ).

fof(sos_44,axiom,
! [X142,X143,X144] :
( next_subocc(X142,X143,X144)
=> ( arboreal(X142)
& arboreal(X143) ) ) ).

fof(sos_45,axiom,
! [X145,X146] :
( ( leaf(X145,X146)
& ~ atomic(X146) )
=> ? [X147] :
( occurrence_of(X147,X146)
& leaf_occ(X145,X147) ) ) ).

fof(sos_46,axiom,
! [X148,X149,X150] :
( min_precedes(X148,X149,X150)
=> arboreal(X148) ) ).

fof(sos_47,axiom,
! [X151,X152,X153,X154,X155] :
( ( occurrence_of(X152,X151)
& root_occ(X154,X152)
& leaf_occ(X155,X152)
& subactivity_occurrence(X153,X152)
& min_precedes(X153,X155,X151)
& X153 != X154 )
=> min_precedes(X154,X153,X151) ) ).

fof(sos_48,axiom,
! [X156,X157,X158,X159,X160] :
( ( occurrence_of(X157,X156)
& root_occ(X159,X157)
& leaf_occ(X160,X157)
& subactivity_occurrence(X158,X157)
& min_precedes(X159,X158,X156)
& X158 != X160 )
=> min_precedes(X158,X160,X156) ) ).

fof(sos_49,axiom,
! [X161] :
( occurrence_of(X161,tptp0)
=> ? [X162,X163,X164] :
( occurrence_of(X162,tptp3)
& root_occ(X162,X161)
& occurrence_of(X163,tptp4)
& next_subocc(X162,X163,tptp0)
& ( occurrence_of(X164,tptp1)
| occurrence_of(X164,tptp2) )
& next_subocc(X163,X164,tptp0)
& leaf_occ(X164,X161) ) ) ).

fof(sos_50,axiom,
activity(tptp0) ).

fof(sos_51,axiom,
~ atomic(tptp0) ).

fof(sos_52,axiom,
atomic(tptp4) ).

fof(sos_53,axiom,
atomic(tptp1) ).

fof(sos_54,axiom,
atomic(tptp2) ).

fof(sos_55,axiom,
atomic(tptp3) ).

fof(sos_56,axiom,
tptp4 != tptp3 ).

fof(sos_57,axiom,
tptp4 != tptp1 ).

fof(sos_58,axiom,
tptp4 != tptp2 ).

fof(sos_59,axiom,
tptp3 != tptp1 ).

fof(sos_60,axiom,
tptp3 != tptp2 ).

fof(sos_61,axiom,
tptp1 != tptp2 ).

fof(goals,conjecture,
! [X165] :
( occurrence_of(X165,tptp0)
=> ? [X166,X167] :
( leaf_occ(X167,X165)
& ( occurrence_of(X167,tptp1)
=> ~ ? [X168] :
( occurrence_of(X168,tptp2)
& min_precedes(X166,X168,tptp0) ) )
& ( occurrence_of(X167,tptp2)
=> ~ ? [X169] :
( occurrence_of(X169,tptp1)
& min_precedes(X166,X169,tptp0) ) ) ) ) ).

%------------------------------------------------------------------------------
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