%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET019+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 : n027.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 05:06:53 PM UTC 2026
% Result : Theorem 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 48)
% Comments :
%------------------------------------------------------------------------------
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(thI02,conjecture,
! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,X1) )
=> equal_set(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02) ).
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,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(i_0_13,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(i_0_14,negated_conjecture,
~ ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,X1) )
=> equal_set(X1,X2) ),
inference(assume_negation,[status(cth)],[thI02]) ).
fof(i_0_15,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_16,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_12])])]) ).
fof(i_0_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,plain,
! [X52] : ~ member(X52,empty_set),
inference(variable_rename,[status(thm)],[i_0_13]) ).
fof(i_0_26,negated_conjecture,
( subset(esk4_0,esk5_0)
& subset(esk5_0,esk4_0)
& ~ equal_set(esk4_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])])]) ).
cnf(i_0_27,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_28,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_29,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_30,plain,
( member(X1,product(X2))
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_31,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_32,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_33,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_34,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_35,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_36,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_37,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
( member(X1,X3)
| ~ member(X1,product(X2))
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_39,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_40,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_41,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_42,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_43,plain,
( member(esk3_2(X1,X2),X2)
| member(X1,product(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_44,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_45,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_46,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_47,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_48,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_49,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_50,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_51,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_52,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_53,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_54,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_55,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_56,negated_conjecture,
~ equal_set(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_57,negated_conjecture,
subset(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_58,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_59,axiom,
X1 = X1 ).
cnf(i_0_60,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_61,axiom,
( X1 = X2
| X1 != X3
| 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_66,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_67,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_59_001,axiom,
X1 = X1 ).
cnf(i_0_60_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_61_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_62_004,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_63_005,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_64_006,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_65_007,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_66_008,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_67_009,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_68,plain,
member(X1,unordered_pair(X1,X2)),
inference(equality_inference,[],[48]) ).
cnf(i_0_69,plain,
member(X1,unordered_pair(X2,X1)),
inference(equality_inference,[],[49]) ).
cnf(i_0_70,plain,
member(X1,singleton(X1)),
inference(equality_inference,[],[54]) ).
cnf(i_0_71,plain,
$false,
inference(scs_inference,[],[i_0_56,i_0_58,i_0_57,i_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET019+4 : TPTP v9.2.1. Released v2.2.0.
% 0.11/0.12 % 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 : n027.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 02:05:35 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Theorem for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.63 % Total time : 1.272s
%------------------------------------------------------------------------------