%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET703+4 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 05:08:21 PM UTC 2026
% Result : Theorem 233.34s 118.02s
% Output : CNFRefutation 234.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_117)
% Comments :
%------------------------------------------------------------------------------
fof(thI41,conjecture,
! [X1,X2] : equal_set(union(singleton(X1),singleton(X2)),unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI41) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET006+0.ax',product) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(i_0_12,negated_conjecture,
~ ! [X1,X2] : equal_set(union(singleton(X1),singleton(X2)),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[thI41]) ).
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,
~ equal_set(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_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(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_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,axiom,
X1 = X1 ).
cnf(i_0_58,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_59,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_492,plain,
~ member(esk1_2(singleton(X1),empty_set),difference(X2,unordered_pair(X1,X3))),
inference(scs_inference,[],[i_0_117,i_0_67,i_0_125,i_0_54,i_0_30,i_0_49,i_0_50,i_0_42,i_0_43,i_0_29]) ).
cnf(i_0_499,plain,
~ member(X1,sum(empty_set)),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_568,plain,
~ member(X1,difference(empty_set,X2)),
inference(rename_variables,[],[i_0_109]) ).
cnf(i_0_571,plain,
member(X1,difference(unordered_pair(X2,X1),empty_set)),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_591,plain,
~ member(X1,intersection(empty_set,X2)),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_599,plain,
member(X1,product(empty_set)),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_605,plain,
~ member(X1,intersection(X2,empty_set)),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_614,plain,
~ member(X1,sum(empty_set)),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_619,plain,
~ member(X1,union(empty_set,empty_set)),
inference(rename_variables,[],[i_0_130]) ).
cnf(i_0_650,plain,
member(X1,product(empty_set)),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_678,plain,
~ member(X1,intersection(X2,empty_set)),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_693,plain,
~ member(X1,difference(empty_set,X2)),
inference(rename_variables,[],[i_0_109]) ).
cnf(i_0_716,plain,
~ member(X1,intersection(empty_set,X2)),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_718,plain,
member(esk3_2(X1,unordered_pair(X2,empty_set)),unordered_pair(X2,empty_set)),
inference(scs_inference,[],[i_0_127,i_0_44]) ).
cnf(i_0_733,plain,
member(X1,product(empty_set)),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_736,plain,
~ member(X1,sum(empty_set)),
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_746,plain,
~ member(X1,union(empty_set,empty_set)),
inference(rename_variables,[],[i_0_130]) ).
cnf(i_0_785,plain,
~ member(X1,intersection(X2,empty_set)),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_787,plain,
member(X1,esk2_2(X1,product(empty_set))),
inference(scs_inference,[],[i_0_141,i_0_38]) ).
cnf(i_0_789,plain,
subset(X1,sum(product(empty_set))),
inference(scs_inference,[],[i_0_141,i_0_38,i_0_32]) ).
cnf(i_0_790,plain,
member(X1,sum(product(empty_set))),
inference(rename_variables,[],[i_0_141]) ).
cnf(i_0_792,plain,
sum(product(empty_set)) != empty_set,
inference(scs_inference,[],[i_0_141,i_0_38,i_0_32,i_0_92]) ).
cnf(i_0_793,plain,
~ member(sum(product(empty_set)),singleton(empty_set)),
inference(scs_inference,[],[i_0_141,i_0_38,i_0_32,i_0_92,i_0_54]) ).
cnf(i_0_810,plain,
member(X1,product(empty_set)),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_823,plain,
~ member(X1,difference(empty_set,X2)),
inference(rename_variables,[],[i_0_109]) ).
cnf(i_0_840,plain,
member(X1,product(empty_set)),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_843,plain,
~ member(X1,intersection(empty_set,X2)),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_909,plain,
member(X1,product(empty_set)),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_173,plain,
member(X1,product(difference(empty_set,X2))),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_122,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_176,plain,
member(esk1_2(unordered_pair(X1,X2),empty_set),unordered_pair(X1,X2)),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_122,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47]) ).
cnf(i_0_178,plain,
empty_set != power_set(X1),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_122,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58]) ).
cnf(i_0_179,plain,
~ member(X1,product(product(empty_set))),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_174,i_0_122,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58,i_0_39]) ).
cnf(i_0_182,plain,
~ member(X1,union(difference(empty_set,X2),difference(empty_set,X2))),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_174,i_0_122,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58,i_0_39,i_0_28]) ).
cnf(i_0_184,plain,
member(X1,intersection(product(empty_set),product(empty_set))),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_174,i_0_122,i_0_180,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58,i_0_39,i_0_28,i_0_30]) ).
cnf(i_0_186,plain,
member(X1,difference(product(empty_set),difference(empty_set,X2))),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_174,i_0_122,i_0_180,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58,i_0_39,i_0_28,i_0_30,i_0_36]) ).
cnf(i_0_189,plain,
~ member(power_set(X1),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_174,i_0_122,i_0_180,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58,i_0_39,i_0_28,i_0_30,i_0_36,i_0_40]) ).
cnf(i_0_191,plain,
~ member(X1,esk3_2(X1,product(empty_set))),
inference(scs_inference,[],[i_0_109,i_0_171,i_0_174,i_0_122,i_0_180,i_0_146,i_0_84,i_0_52,i_0_53,i_0_48,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_47,i_0_58,i_0_39,i_0_28,i_0_30,i_0_36,i_0_40,i_0_31]) ).
cnf(i_0_243,plain,
member(X1,product(intersection(X2,empty_set))),
inference(scs_inference,[],[i_0_113,i_0_241,i_0_125,i_0_145,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_246,plain,
~ member(X1,union(intersection(X2,empty_set),intersection(X2,empty_set))),
inference(scs_inference,[],[i_0_113,i_0_241,i_0_244,i_0_125,i_0_145,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_248,plain,
member(esk1_2(singleton(X1),empty_set),intersection(singleton(X1),singleton(X1))),
inference(scs_inference,[],[i_0_113,i_0_241,i_0_244,i_0_125,i_0_145,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_250,plain,
member(esk1_2(singleton(X1),empty_set),difference(singleton(X1),intersection(X2,empty_set))),
inference(scs_inference,[],[i_0_113,i_0_241,i_0_244,i_0_125,i_0_145,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]) ).
cnf(i_0_253,plain,
~ member(esk1_2(singleton(empty_set),empty_set),unordered_pair(singleton(X1),singleton(X1))),
inference(scs_inference,[],[i_0_113,i_0_241,i_0_244,i_0_125,i_0_145,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_311,plain,
~ member(X1,sum(union(empty_set,empty_set))),
inference(scs_inference,[],[i_0_101,i_0_130,i_0_299,i_0_87,i_0_68,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_314,plain,
member(X1,intersection(intersection(unordered_pair(X2,X1),unordered_pair(X2,X1)),singleton(X1))),
inference(scs_inference,[],[i_0_132,i_0_101,i_0_130,i_0_299,i_0_87,i_0_68,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_320,plain,
~ member(singleton(X1),union(power_set(empty_set),power_set(empty_set))),
inference(scs_inference,[],[i_0_132,i_0_101,i_0_130,i_0_299,i_0_312,i_0_87,i_0_68,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]) ).
cnf(i_0_322,plain,
~ member(unordered_pair(X1,X2),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_132,i_0_101,i_0_130,i_0_299,i_0_312,i_0_87,i_0_68,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_345,plain,
member(X1,union(product(empty_set),X2)),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_351,plain,
~ member(unordered_pair(X1,X2),difference(singleton(empty_set),X3)),
inference(scs_inference,[],[i_0_301,i_0_33]) ).
cnf(i_0_353,plain,
~ member(unordered_pair(X1,X2),intersection(singleton(empty_set),X3)),
inference(scs_inference,[],[i_0_301,i_0_33,i_0_34]) ).
cnf(i_0_355,plain,
~ member(unordered_pair(X1,X2),intersection(X3,singleton(empty_set))),
inference(scs_inference,[],[i_0_301,i_0_33,i_0_34,i_0_35]) ).
cnf(i_0_357,plain,
member(X1,difference(union(X2,singleton(X1)),sum(empty_set))),
inference(scs_inference,[],[i_0_301,i_0_296,i_0_119,i_0_33,i_0_34,i_0_35,i_0_36]) ).
cnf(i_0_360,plain,
~ member(unordered_pair(X1,X2),union(singleton(empty_set),singleton(empty_set))),
inference(scs_inference,[],[i_0_301,i_0_296,i_0_119,i_0_33,i_0_34,i_0_35,i_0_36,i_0_28]) ).
cnf(i_0_403,plain,
~ member(power_set(X1),difference(singleton(empty_set),X2)),
inference(scs_inference,[],[i_0_156,i_0_33]) ).
cnf(i_0_405,plain,
~ member(power_set(X1),intersection(singleton(empty_set),X2)),
inference(scs_inference,[],[i_0_156,i_0_33,i_0_34]) ).
cnf(i_0_407,plain,
~ member(power_set(X1),intersection(X2,singleton(empty_set))),
inference(scs_inference,[],[i_0_156,i_0_33,i_0_34,i_0_35]) ).
cnf(i_0_441,plain,
~ member(X1,difference(union(empty_set,empty_set),X2)),
inference(rename_variables,[],[i_0_414]) ).
cnf(i_0_453,plain,
~ member(X1,intersection(union(empty_set,empty_set),X2)),
inference(rename_variables,[],[i_0_416]) ).
cnf(i_0_466,plain,
union(singleton(X1),X2) != intersection(X3,union(empty_set,empty_set)),
inference(scs_inference,[],[i_0_418,i_0_236,i_0_63]) ).
cnf(i_0_467,plain,
~ member(X1,intersection(X2,union(empty_set,empty_set))),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_468,plain,
intersection(X1,union(empty_set,empty_set)) != union(singleton(X2),X3),
inference(scs_inference,[],[i_0_418,i_0_236,i_0_63,i_0_58]) ).
cnf(i_0_473,plain,
member(esk1_2(singleton(X1),empty_set),union(X2,singleton(X1))),
inference(rename_variables,[],[i_0_238]) ).
cnf(i_0_509,plain,
member(esk1_2(singleton(X1),empty_set),union(unordered_pair(X2,X1),X3)),
inference(scs_inference,[],[i_0_486,i_0_42]) ).
cnf(i_0_511,plain,
member(esk1_2(singleton(X1),empty_set),union(X2,unordered_pair(X3,X1))),
inference(scs_inference,[],[i_0_486,i_0_42,i_0_43]) ).
cnf(i_0_513,plain,
~ member(esk1_2(singleton(X1),empty_set),difference(X2,unordered_pair(X3,X1))),
inference(scs_inference,[],[i_0_486,i_0_42,i_0_43,i_0_29]) ).
cnf(i_0_515,plain,
X1 = esk1_2(singleton(X1),empty_set),
inference(scs_inference,[],[i_0_486,i_0_479,i_0_42,i_0_43,i_0_29,i_0_58]) ).
cnf(i_0_516,plain,
equal_set(esk1_2(singleton(empty_set),empty_set),empty_set),
inference(scs_inference,[],[i_0_486,i_0_479,i_0_72,i_0_42,i_0_43,i_0_29,i_0_58,i_0_60]) ).
cnf(i_0_517,plain,
equal_set(empty_set,esk1_2(singleton(empty_set),empty_set)),
inference(scs_inference,[],[i_0_486,i_0_479,i_0_72,i_0_42,i_0_43,i_0_29,i_0_58,i_0_60,i_0_61]) ).
cnf(i_0_518,plain,
member(esk1_2(singleton(X1),empty_set),intersection(unordered_pair(X1,X2),unordered_pair(X1,X2))),
inference(scs_inference,[],[i_0_484,i_0_486,i_0_479,i_0_72,i_0_42,i_0_43,i_0_29,i_0_58,i_0_60,i_0_61,i_0_30]) ).
cnf(i_0_520,plain,
subset(esk1_2(singleton(empty_set),empty_set),X1),
inference(scs_inference,[],[i_0_484,i_0_486,i_0_479,i_0_72,i_0_69,i_0_42,i_0_43,i_0_29,i_0_58,i_0_60,i_0_61,i_0_30,i_0_64]) ).
cnf(c_0_530,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
i_0_45 ).
cnf(c_0_531,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
i_0_47 ).
cnf(c_0_532,plain,
( member(esk1_2(X1,X2),X1)
| equal_set(X2,X1)
| ~ subset(X2,X1) ),
inference(spm,[status(thm)],[c_0_530,c_0_531]) ).
cnf(c_0_533,negated_conjecture,
~ equal_set(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),
i_0_27 ).
cnf(c_0_534,plain,
( member(esk1_2(X1,X2),X1)
| member(esk1_2(X2,X1),X2)
| equal_set(X1,X2) ),
inference(spm,[status(thm)],[c_0_532,c_0_531]) ).
cnf(c_0_535,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
i_0_28 ).
cnf(c_0_536,negated_conjecture,
( member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_533,c_0_534]) ).
cnf(c_0_537,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
i_0_54 ).
cnf(c_0_538,plain,
( member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk5_0)) ),
inference(spm,[status(thm)],[c_0_535,c_0_536]) ).
cnf(c_0_539,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0)) ),
inference(spm,[status(thm)],[c_0_537,c_0_538]) ).
cnf(c_0_540,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
i_0_40 ).
cnf(c_0_541,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_537,c_0_539]) ).
cnf(c_0_542,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X3 ),
i_0_50 ).
cnf(c_0_543,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
i_0_32 ).
cnf(c_0_544,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0 ),
inference(spm,[status(thm)],[c_0_540,c_0_541]) ).
cnf(c_0_545,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_542]) ).
cnf(c_0_546,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| subset(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_544]),c_0_545])]) ).
cnf(c_0_547,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| equal_set(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0)))
| ~ subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_530,c_0_546]) ).
cnf(c_0_548,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
i_0_52 ).
cnf(c_0_549,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| equal_set(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_547,c_0_531]),c_0_540]) ).
cnf(c_0_550,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_548,c_0_549]) ).
cnf(c_0_551,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
i_0_49 ).
cnf(c_0_552,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_530,c_0_550]),c_0_533]),c_0_546]) ).
cnf(c_0_553,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_551]) ).
cnf(c_0_554,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| subset(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_552]),c_0_553])]) ).
cnf(c_0_555,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| equal_set(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0)))
| ~ subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_530,c_0_554]) ).
cnf(c_0_556,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| equal_set(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_555,c_0_531]),c_0_540]) ).
cnf(c_0_557,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_548,c_0_556]) ).
cnf(c_0_558,plain,
member(esk1_2(singleton(X1),empty_set),union(X2,singleton(X1))),
i_0_473 ).
cnf(c_0_559,plain,
X1 = esk1_2(singleton(X1),empty_set),
i_0_515 ).
cnf(c_0_560,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_530,c_0_557]),c_0_533]),c_0_554]) ).
cnf(c_0_561,plain,
member(X1,union(X2,singleton(X1))),
inference(rw,[status(thm)],[c_0_558,c_0_559]) ).
cnf(c_0_562,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_560]),c_0_561])]) ).
cnf(c_0_563,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| ~ subset(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_530,c_0_562]),c_0_533]) ).
cnf(c_0_564,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_563,c_0_531]) ).
cnf(c_0_565,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk5_0)) ),
inference(spm,[status(thm)],[c_0_535,c_0_564]) ).
cnf(c_0_566,plain,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0)) ),
inference(spm,[status(thm)],[c_0_537,c_0_565]) ).
cnf(c_0_567,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_537,c_0_566]) ).
cnf(c_0_568,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
i_0_55 ).
cnf(c_0_569,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_567]),c_0_545])]),c_0_563]) ).
cnf(c_0_570,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
i_0_42 ).
cnf(c_0_571,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_568]) ).
cnf(c_0_572,plain,
esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_569]),c_0_553])]),c_0_563]) ).
cnf(c_0_573,plain,
member(X1,union(singleton(X1),X2)),
inference(spm,[status(thm)],[c_0_570,c_0_571]) ).
cnf(c_0_574,plain,
subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_572]),c_0_573])]) ).
cnf(c_0_575,plain,
~ subset(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_530,c_0_574]),c_0_533]) ).
cnf(c_0_576,plain,
member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),union(singleton(esk4_0),singleton(esk5_0))),
inference(spm,[status(thm)],[c_0_575,c_0_531]) ).
cnf(c_0_577,plain,
( member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk5_0)) ),
inference(spm,[status(thm)],[c_0_535,c_0_576]) ).
cnf(c_0_578,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0)) ),
inference(spm,[status(thm)],[c_0_537,c_0_577]) ).
cnf(c_0_579,plain,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_537,c_0_578]) ).
cnf(c_0_580,plain,
esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_579]),c_0_545])]),c_0_575]) ).
cnf(c_0_581,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_543,c_0_580]),c_0_553])]),c_0_575]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET703+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n010.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:32:06 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 233.34/118.02 % Version : CSE_E---1.7
% 233.34/118.02 % Problem : theBenchmark.p
% 233.34/118.02 % SZS status Theorem for theBenchmark.p
% 233.34/118.02 % SZS output start CNFRefutation
% See solution above
% 234.46/119.05 % Total time : 114.193s
%------------------------------------------------------------------------------