%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET366+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 : n021.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 05:07:47 PM UTC 2026
% Result : Theorem 0.25s 1.60s
% Output : CNFRefutation 0.25s
% 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(thI47,conjecture,
! [X1] : member(empty_set,power_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI47) ).
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,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,negated_conjecture,
~ ! [X1] : member(empty_set,power_set(X1)),
inference(assume_negation,[status(cth)],[thI47]) ).
fof(i_0_14,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(i_0_15,plain,
! [X48,X49,X50] :
( ( ~ member(X48,union(X49,X50))
| member(X48,X49)
| member(X48,X50) )
& ( ~ member(X48,X49)
| member(X48,union(X49,X50)) )
& ( ~ member(X48,X50)
| member(X48,union(X49,X50)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
fof(i_0_16,plain,
! [X52,X53,X54] :
( ( member(X52,X54)
| ~ member(X52,difference(X54,X53)) )
& ( ~ member(X52,X53)
| ~ member(X52,difference(X54,X53)) )
& ( ~ member(X52,X54)
| member(X52,X53)
| member(X52,difference(X54,X53)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).
fof(i_0_17,plain,
! [X45,X46,X47] :
( ( member(X45,X46)
| ~ member(X45,intersection(X46,X47)) )
& ( member(X45,X47)
| ~ member(X45,intersection(X46,X47)) )
& ( ~ member(X45,X46)
| ~ member(X45,X47)
| member(X45,intersection(X46,X47)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
fof(i_0_18,plain,
! [X66,X67,X68,X69,X70] :
( ( ~ member(X66,product(X67))
| ~ member(X68,X67)
| member(X66,X68) )
& ( member(esk3_2(X69,X70),X70)
| member(X69,product(X70)) )
& ( ~ member(X69,esk3_2(X69,X70))
| member(X69,product(X70)) ) ),
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,
! [X35,X36,X37,X38,X39] :
( ( ~ subset(X35,X36)
| ~ member(X37,X35)
| member(X37,X36) )
& ( member(esk1_2(X38,X39),X38)
| subset(X38,X39) )
& ( ~ member(esk1_2(X38,X39),X39)
| subset(X38,X39) ) ),
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,
! [X60,X61,X63,X64,X65] :
( ( member(esk2_2(X60,X61),X61)
| ~ member(X60,sum(X61)) )
& ( member(X60,esk2_2(X60,X61))
| ~ member(X60,sum(X61)) )
& ( ~ member(X65,X64)
| ~ member(X63,X65)
| member(X63,sum(X64)) ) ),
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,
! [X57,X58,X59] :
( ( ~ member(X57,unordered_pair(X58,X59))
| X57 = X58
| X57 = X59 )
& ( X57 != X58
| member(X57,unordered_pair(X58,X59)) )
& ( X57 != X59
| member(X57,unordered_pair(X58,X59)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).
fof(i_0_22,plain,
! [X41,X42] :
( ( subset(X41,X42)
| ~ equal_set(X41,X42) )
& ( subset(X42,X41)
| ~ equal_set(X41,X42) )
& ( ~ subset(X41,X42)
| ~ subset(X42,X41)
| equal_set(X41,X42) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
fof(i_0_23,plain,
! [X43,X44] :
( ( ~ member(X43,power_set(X44))
| subset(X43,X44) )
& ( ~ subset(X43,X44)
| member(X43,power_set(X44)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(i_0_24,plain,
! [X55,X56] :
( ( ~ member(X55,singleton(X56))
| X55 = X56 )
& ( X55 != X56
| member(X55,singleton(X56)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
fof(i_0_25,negated_conjecture,
~ member(empty_set,power_set(esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_26,plain,
! [X51] : ~ member(X51,empty_set),
inference(variable_rename,[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,negated_conjecture,
~ member(empty_set,power_set(esk4_0)),
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_24]),
[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
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_57_001,axiom,
X1 = X1 ).
cnf(i_0_58_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_59_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_60_004,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_61_005,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_62_006,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_63_007,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_64_008,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_65_009,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_66,plain,
member(X1,unordered_pair(X1,X2)),
inference(equality_inference,[],[48]) ).
cnf(i_0_67,plain,
member(X1,unordered_pair(X2,X1)),
inference(equality_inference,[],[49]) ).
cnf(i_0_68,plain,
member(X1,singleton(X1)),
inference(equality_inference,[],[55]) ).
cnf(i_0_69,plain,
~ subset(empty_set,esk4_0),
inference(scs_inference,[],[i_0_54,i_0_50]) ).
cnf(i_0_70,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_71,plain,
$false,
inference(scs_inference,[],[i_0_54,i_0_56,i_0_50,i_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET366+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.10 % 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
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue May 5 02:22:41 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 0.25/1.60 % Version : CSE_E---1.7
% 0.25/1.60 % Problem : theBenchmark.p
% 0.25/1.60 % SZS status Theorem for theBenchmark.p
% 0.25/1.60 % SZS output start CNFRefutation
% See solution above
% 0.25/1.62 % Total time : 1.273s
%------------------------------------------------------------------------------