%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET012+4 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:48 PM UTC 2026
% Result : Theorem 207.69s 89.68s
% Output : CNFRefutation 208.59s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_182)
% Comments :
%------------------------------------------------------------------------------
fof(thI23,conjecture,
! [X1,X4] :
( subset(X1,X4)
=> equal_set(difference(X4,difference(X4,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI23) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(product,axiom,
! [X3,X1] :
( member(X3,product(X1))
<=> ! [X5] :
( member(X5,X1)
=> member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',product) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(i_0_12,negated_conjecture,
~ ! [X1,X4] :
( subset(X1,X4)
=> equal_set(difference(X4,difference(X4,X1)),X1) ),
inference(assume_negation,[status(cth)],[thI23]) ).
fof(i_0_13,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(i_0_14,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(i_0_15,negated_conjecture,
( subset(esk4_0,esk5_0)
& ~ equal_set(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).
fof(i_0_16,plain,
! [X49,X50,X51] :
( ( ~ member(X49,union(X50,X51))
| member(X49,X50)
| member(X49,X51) )
& ( ~ member(X49,X50)
| member(X49,union(X50,X51)) )
& ( ~ member(X49,X51)
| member(X49,union(X50,X51)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
fof(i_0_17,plain,
! [X53,X54,X55] :
( ( member(X53,X55)
| ~ member(X53,difference(X55,X54)) )
& ( ~ member(X53,X54)
| ~ member(X53,difference(X55,X54)) )
& ( ~ member(X53,X55)
| member(X53,X54)
| member(X53,difference(X55,X54)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_18,plain,
! [X46,X47,X48] :
( ( member(X46,X47)
| ~ member(X46,intersection(X47,X48)) )
& ( member(X46,X48)
| ~ member(X46,intersection(X47,X48)) )
& ( ~ member(X46,X47)
| ~ member(X46,X48)
| member(X46,intersection(X47,X48)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
fof(i_0_19,plain,
! [X67,X68,X69,X70,X71] :
( ( ~ member(X67,product(X68))
| ~ member(X69,X68)
| member(X67,X69) )
& ( member(esk3_2(X70,X71),X71)
| member(X70,product(X71)) )
& ( ~ member(X70,esk3_2(X70,X71))
| member(X70,product(X71)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[product])])])])])]) ).
fof(i_0_20,plain,
! [X36,X37,X38,X39,X40] :
( ( ~ subset(X36,X37)
| ~ member(X38,X36)
| member(X38,X37) )
& ( member(esk1_2(X39,X40),X39)
| subset(X39,X40) )
& ( ~ member(esk1_2(X39,X40),X40)
| subset(X39,X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).
fof(i_0_21,plain,
! [X61,X62,X64,X65,X66] :
( ( member(esk2_2(X61,X62),X62)
| ~ member(X61,sum(X62)) )
& ( member(X61,esk2_2(X61,X62))
| ~ member(X61,sum(X62)) )
& ( ~ member(X66,X65)
| ~ member(X64,X66)
| member(X64,sum(X65)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sum])])])])])]) ).
fof(i_0_22,plain,
! [X58,X59,X60] :
( ( ~ member(X58,unordered_pair(X59,X60))
| X58 = X59
| X58 = X60 )
& ( X58 != X59
| member(X58,unordered_pair(X59,X60)) )
& ( X58 != X60
| member(X58,unordered_pair(X59,X60)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).
fof(i_0_23,plain,
! [X42,X43] :
( ( subset(X42,X43)
| ~ equal_set(X42,X43) )
& ( subset(X43,X42)
| ~ equal_set(X42,X43) )
& ( ~ subset(X42,X43)
| ~ subset(X43,X42)
| equal_set(X42,X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
fof(i_0_24,plain,
! [X44,X45] :
( ( ~ member(X44,power_set(X45))
| subset(X44,X45) )
& ( ~ subset(X44,X45)
| member(X44,power_set(X45)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(i_0_25,plain,
! [X56,X57] :
( ( ~ member(X56,singleton(X57))
| X56 = X57 )
& ( X56 != X57
| member(X56,singleton(X57)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
fof(i_0_26,plain,
! [X52] : ~ member(X52,empty_set),
inference(variable_rename,[status(thm)],[i_0_14]) ).
cnf(i_0_27,negated_conjecture,
~ equal_set(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_28,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_29,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_30,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_31,plain,
( member(X1,product(X2))
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_32,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_33,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_34,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_35,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_36,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_37,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_38,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,plain,
( member(X1,X3)
| ~ member(X1,product(X2))
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_40,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_41,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_42,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_43,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_44,plain,
( member(esk3_2(X1,X2),X2)
| member(X1,product(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_45,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_46,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_47,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_48,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_49,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_50,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_51,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_52,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_53,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_54,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_55,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_56,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_57,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_58,axiom,
X1 = X1 ).
cnf(i_0_59,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_60,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_66,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_253,plain,
member(esk1_2(unordered_pair(X1,X2),empty_set),union(unordered_pair(X1,X2),X3)),
inference(scs_inference,[],[i_0_182,i_0_116,i_0_80,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42]) ).
cnf(i_0_255,plain,
member(esk1_2(unordered_pair(X1,X2),empty_set),union(X3,unordered_pair(X1,X2))),
inference(scs_inference,[],[i_0_182,i_0_116,i_0_80,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43]) ).
cnf(i_0_257,plain,
~ member(X1,sum(intersection(X2,empty_set))),
inference(scs_inference,[],[i_0_182,i_0_116,i_0_80,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37]) ).
cnf(i_0_260,plain,
member(X1,product(intersection(X2,empty_set))),
inference(scs_inference,[],[i_0_182,i_0_116,i_0_258,i_0_80,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44]) ).
cnf(i_0_277,plain,
~ member(power_set(X1),difference(unordered_pair(empty_set,empty_set),X2)),
inference(scs_inference,[],[i_0_195,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33]) ).
cnf(i_0_279,plain,
~ member(power_set(X1),intersection(unordered_pair(empty_set,empty_set),X2)),
inference(scs_inference,[],[i_0_195,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34]) ).
cnf(i_0_281,plain,
~ member(power_set(X1),intersection(X2,unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_195,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35]) ).
cnf(i_0_283,plain,
member(esk1_2(singleton(X1),empty_set),union(singleton(X1),X2)),
inference(scs_inference,[],[i_0_195,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42]) ).
cnf(i_0_285,plain,
member(esk1_2(singleton(X1),empty_set),union(X2,singleton(X1))),
inference(scs_inference,[],[i_0_195,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43]) ).
cnf(i_0_287,plain,
~ member(X1,sum(sum(empty_set))),
inference(scs_inference,[],[i_0_195,i_0_122,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37]) ).
cnf(i_0_290,plain,
member(X1,product(sum(empty_set))),
inference(scs_inference,[],[i_0_195,i_0_122,i_0_288,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44]) ).
cnf(i_0_295,plain,
member(esk1_2(singleton(X1),empty_set),intersection(singleton(X1),singleton(X1))),
inference(scs_inference,[],[i_0_195,i_0_122,i_0_288,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44,i_0_28,i_0_30]) ).
cnf(i_0_297,plain,
~ member(unordered_pair(X1,X2),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_195,i_0_122,i_0_288,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44,i_0_28,i_0_30,i_0_40]) ).
cnf(i_0_301,plain,
member(power_set(X1),difference(union(product(empty_set),X2),unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_170,i_0_195,i_0_122,i_0_288,i_0_88,i_0_128,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44,i_0_28,i_0_30,i_0_40,i_0_41,i_0_36]) ).
cnf(i_0_361,plain,
member(X1,product(difference(empty_set,X2))),
inference(rename_variables,[],[i_0_177]) ).
cnf(i_0_517,plain,
~ member(power_set(X1),intersection(singleton(empty_set),X2)),
inference(rename_variables,[],[i_0_443]) ).
cnf(i_0_573,plain,
member(X1,difference(product(empty_set),difference(empty_set,X2))),
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_812,plain,
member(esk1_2(unordered_pair(X1,X2),empty_set),difference(unordered_pair(X1,X2),empty_set)),
inference(scs_inference,[],[i_0_56,i_0_182,i_0_36]) ).
cnf(i_0_815,plain,
~ member(X1,union(union(empty_set,empty_set),empty_set)),
inference(scs_inference,[],[i_0_56,i_0_813,i_0_133,i_0_182,i_0_36,i_0_28]) ).
cnf(i_0_242,plain,
subset(esk4_0,esk5_0),
inference(equality_inference,[],[237]) ).
cnf(i_0_263,plain,
~ member(X1,union(esk3_2(X1,power_set(X2)),intersection(X3,empty_set))),
inference(scs_inference,[],[i_0_182,i_0_235,i_0_116,i_0_258,i_0_261,i_0_80,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44,i_0_28]) ).
cnf(i_0_271,plain,
~ member(empty_set,unordered_pair(singleton(X1),singleton(X1))),
inference(scs_inference,[],[i_0_182,i_0_235,i_0_116,i_0_258,i_0_261,i_0_264,i_0_80,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_42,i_0_43,i_0_37,i_0_44,i_0_28,i_0_30,i_0_36,i_0_40]) ).
cnf(i_0_315,plain,
~ member(unordered_pair(X1,X2),difference(unordered_pair(empty_set,empty_set),X3)),
inference(scs_inference,[],[i_0_297,i_0_90,i_0_133,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33]) ).
cnf(i_0_317,plain,
~ member(unordered_pair(X1,X2),intersection(unordered_pair(empty_set,empty_set),X3)),
inference(scs_inference,[],[i_0_297,i_0_90,i_0_133,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34]) ).
cnf(i_0_319,plain,
~ member(unordered_pair(X1,X2),intersection(X3,unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_297,i_0_90,i_0_133,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35]) ).
cnf(i_0_321,plain,
~ member(X1,sum(union(empty_set,empty_set))),
inference(scs_inference,[],[i_0_297,i_0_90,i_0_133,i_0_309,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_37]) ).
cnf(i_0_324,plain,
member(empty_set,intersection(power_set(X1),power_set(X1))),
inference(scs_inference,[],[i_0_297,i_0_90,i_0_133,i_0_309,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_37,i_0_30]) ).
cnf(i_0_331,plain,
~ member(empty_set,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))),
inference(scs_inference,[],[i_0_297,i_0_172,i_0_90,i_0_133,i_0_309,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_37,i_0_30,i_0_36,i_0_28,i_0_40]) ).
cnf(i_0_335,plain,
~ member(power_set(X1),intersection(unordered_pair(empty_set,empty_set),X2)),
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_427,plain,
esk1_2(unordered_pair(empty_set,empty_set),empty_set) != singleton(X1),
inference(scs_inference,[],[i_0_419,i_0_253,i_0_158,i_0_33,i_0_34,i_0_35,i_0_63]) ).
cnf(i_0_428,plain,
member(esk1_2(unordered_pair(X1,X2),empty_set),union(unordered_pair(X1,X2),X3)),
inference(rename_variables,[],[i_0_253]) ).
cnf(i_0_431,plain,
~ member(unordered_pair(X1,X2),union(power_set(empty_set),power_set(empty_set))),
inference(scs_inference,[],[i_0_419,i_0_253,i_0_158,i_0_33,i_0_34,i_0_35,i_0_63,i_0_40,i_0_28]) ).
cnf(i_0_479,plain,
member(X1,product(intersection(empty_set,X2))),
inference(rename_variables,[],[i_0_220]) ).
cnf(i_0_496,plain,
member(X1,product(intersection(X2,empty_set))),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_503,plain,
unordered_pair(X1,X2) != union(intersection(X3,union(empty_set,empty_set)),difference(empty_set,X4)),
inference(scs_inference,[],[i_0_498,i_0_218,i_0_68,i_0_63,i_0_64]) ).
cnf(i_0_505,plain,
union(intersection(X1,union(empty_set,empty_set)),difference(empty_set,X2)) != unordered_pair(X3,X4),
inference(scs_inference,[],[i_0_498,i_0_218,i_0_68,i_0_63,i_0_64,i_0_59]) ).
cnf(i_0_515,plain,
esk1_2(singleton(empty_set),empty_set) != power_set(X1),
inference(scs_inference,[],[i_0_443,i_0_295,i_0_63]) ).
cnf(i_0_516,plain,
member(esk1_2(singleton(X1),empty_set),intersection(singleton(X1),singleton(X1))),
inference(rename_variables,[],[i_0_295]) ).
cnf(i_0_518,plain,
product(empty_set) != union(difference(sum(empty_set),X1),intersection(X2,empty_set)),
inference(scs_inference,[],[i_0_507,i_0_443,i_0_295,i_0_125,i_0_63,i_0_64]) ).
cnf(i_0_531,plain,
member(esk1_2(unordered_pair(X1,X2),empty_set),union(X3,unordered_pair(X1,X2))),
inference(rename_variables,[],[i_0_255]) ).
cnf(i_0_545,plain,
union(X1,power_set(X2)) != intersection(X3,sum(empty_set)),
inference(scs_inference,[],[i_0_471,i_0_306,i_0_230,i_0_63,i_0_64]) ).
cnf(i_0_555,plain,
member(esk1_2(singleton(X1),empty_set),union(singleton(X1),X2)),
inference(rename_variables,[],[i_0_283]) ).
cnf(i_0_574,plain,
member(esk4_0,power_set(esk5_0)),
inference(equality_inference,[],[571]) ).
cnf(i_0_604,plain,
member(empty_set,intersection(singleton(empty_set),singleton(empty_set))),
inference(scs_inference,[],[i_0_100,i_0_295,i_0_128,i_0_54,i_0_49,i_0_50,i_0_42,i_0_43,i_0_29,i_0_62,i_0_30,i_0_41,i_0_63]) ).
cnf(i_0_605,plain,
member(esk1_2(singleton(X1),empty_set),intersection(singleton(X1),singleton(X1))),
inference(rename_variables,[],[i_0_295]) ).
cnf(i_0_606,plain,
~ member(X1,esk1_2(singleton(empty_set),empty_set)),
inference(scs_inference,[],[i_0_100,i_0_295,i_0_128,i_0_56,i_0_54,i_0_49,i_0_50,i_0_42,i_0_43,i_0_29,i_0_62,i_0_30,i_0_41,i_0_63,i_0_64]) ).
cnf(i_0_333,plain,
esk1_2(unordered_pair(empty_set,empty_set),empty_set) != power_set(X1),
inference(scs_inference,[],[i_0_297,i_0_279,i_0_172,i_0_266,i_0_90,i_0_133,i_0_309,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_37,i_0_30,i_0_36,i_0_28,i_0_40,i_0_63]) ).
cnf(i_0_336,plain,
union(X1,product(empty_set)) != unordered_pair(empty_set,empty_set),
inference(scs_inference,[],[i_0_297,i_0_279,i_0_172,i_0_327,i_0_266,i_0_90,i_0_133,i_0_309,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_37,i_0_30,i_0_36,i_0_28,i_0_40,i_0_63,i_0_64]) ).
cnf(i_0_338,plain,
power_set(X1) != esk1_2(unordered_pair(empty_set,empty_set),empty_set),
inference(scs_inference,[],[i_0_297,i_0_279,i_0_172,i_0_327,i_0_266,i_0_90,i_0_133,i_0_309,i_0_106,i_0_42,i_0_43,i_0_44,i_0_54,i_0_29,i_0_33,i_0_34,i_0_35,i_0_37,i_0_30,i_0_36,i_0_28,i_0_40,i_0_63,i_0_64,i_0_59]) ).
cnf(i_0_506,plain,
member(esk4_0,union(X1,power_set(esk5_0))),
inference(equality_inference,[],[502]) ).
cnf(i_0_520,plain,
~ member(esk1_2(singleton(empty_set),empty_set),singleton(power_set(X1))),
inference(scs_inference,[],[i_0_515,i_0_54]) ).
cnf(i_0_522,plain,
power_set(X1) != esk1_2(singleton(empty_set),empty_set),
inference(scs_inference,[],[i_0_515,i_0_54,i_0_59]) ).
cnf(i_0_523,plain,
~ member(esk1_2(singleton(empty_set),empty_set),unordered_pair(power_set(X1),power_set(X1))),
inference(scs_inference,[],[i_0_515,i_0_54,i_0_59,i_0_40]) ).
cnf(i_0_525,plain,
union(difference(sum(empty_set),X1),intersection(X2,empty_set)) != product(empty_set),
inference(scs_inference,[],[i_0_518,i_0_59]) ).
cnf(i_0_530,plain,
esk1_2(unordered_pair(empty_set,empty_set),empty_set) != unordered_pair(X1,X2),
inference(scs_inference,[],[i_0_255,i_0_329,i_0_63]) ).
cnf(i_0_532,plain,
intersection(power_set(X1),power_set(X1)) != intersection(sum(empty_set),X2),
inference(scs_inference,[],[i_0_469,i_0_324,i_0_255,i_0_329,i_0_63,i_0_64]) ).
cnf(i_0_547,plain,
member(esk4_0,intersection(power_set(esk5_0),power_set(esk5_0))),
inference(equality_inference,[],[544]) ).
cnf(i_0_548,plain,
intersection(X1,sum(empty_set)) != union(X2,power_set(X3)),
inference(scs_inference,[],[i_0_545,i_0_59]) ).
cnf(c_0_69,negated_conjecture,
~ equal_set(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),
i_0_27 ).
cnf(c_0_70,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
i_0_45 ).
cnf(c_0_71,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
i_0_33 ).
cnf(c_0_72,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
i_0_47 ).
cnf(c_0_73,negated_conjecture,
( ~ subset(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0)))
| ~ subset(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),esk5_0)
| ~ subset(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_76,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
i_0_29 ).
cnf(c_0_77,plain,
( member(X1,X2)
| member(X1,difference(X3,X2))
| ~ member(X1,X3) ),
i_0_36 ).
cnf(c_0_78,plain,
( member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),esk4_0)
| member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_72]) ).
cnf(c_0_79,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_72]) ).
cnf(c_0_80,plain,
( member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),difference(esk5_0,X1))
| member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),esk4_0)
| member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
i_0_32 ).
cnf(c_0_82,plain,
( member(X1,X2)
| ~ subset(X3,X2)
| ~ member(X1,X3) ),
i_0_46 ).
cnf(c_0_83,negated_conjecture,
subset(esk4_0,esk5_0),
i_0_57 ).
cnf(c_0_84,plain,
( subset(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0)
| member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_84]),c_0_72]) ).
cnf(c_0_87,negated_conjecture,
member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),esk5_0),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_88,plain,
( member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),difference(esk5_0,X1))
| member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_87]) ).
cnf(c_0_89,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
i_0_48 ).
cnf(c_0_90,plain,
( subset(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0)))
| member(esk1_2(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),difference(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_81,c_0_88]) ).
cnf(c_0_91,plain,
( member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),esk5_0)
| ~ member(esk4_0,power_set(difference(esk5_0,difference(esk5_0,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_75,c_0_89]) ).
cnf(c_0_92,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
i_0_51 ).
cnf(c_0_93,plain,
subset(esk4_0,difference(esk5_0,difference(esk5_0,esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_90]),c_0_86])]) ).
cnf(c_0_94,plain,
( member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),difference(esk5_0,X1))
| member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),X1)
| ~ member(esk4_0,power_set(difference(esk5_0,difference(esk5_0,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_77,c_0_91]) ).
cnf(c_0_95,plain,
member(esk4_0,power_set(difference(esk5_0,difference(esk5_0,esk4_0)))),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,plain,
( member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),difference(esk5_0,X1))
| member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_97,negated_conjecture,
~ subset(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_93])]) ).
cnf(c_0_98,plain,
member(esk1_2(difference(esk5_0,difference(esk5_0,esk4_0)),esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_96]),c_0_97]) ).
cnf(c_0_99,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_98]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET012+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:03:52 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 207.69/89.68 % Version : CSE_E---1.7
% 207.69/89.68 % Problem : theBenchmark.p
% 207.69/89.68 % SZS status Theorem for theBenchmark.p
% 207.69/89.68 % SZS output start CNFRefutation
% See solution above
% 208.59/90.58 % Total time : 87.785s
%------------------------------------------------------------------------------