%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET605+3 : 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 : n001.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 05:08:06 PM UTC 2026
% Result : Theorem 0.28s 1.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 48)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(prove_th76,conjecture,
! [X1,X2] : difference(X1,union(X1,X2)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th76) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(difference_empty_set,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(i_0_12,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(i_0_13,negated_conjecture,
~ ! [X1,X2] : difference(X1,union(X1,X2)) = empty_set,
inference(assume_negation,[status(cth)],[prove_th76]) ).
fof(i_0_14,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(i_0_15,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(i_0_16,plain,
! [X56,X57,X58,X59,X60,X61] :
( ( ~ member(X58,X56)
| member(X58,X57)
| X56 != X57 )
& ( ~ member(X59,X57)
| member(X59,X56)
| X56 != X57 )
& ( ~ member(esk3_2(X60,X61),X60)
| ~ member(esk3_2(X60,X61),X61)
| X60 = X61 )
& ( member(esk3_2(X60,X61),X60)
| member(esk3_2(X60,X61),X61)
| X60 = X61 ) ),
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)],[equal_member_defn])])])])])]) ).
fof(i_0_17,plain,
! [X34,X35,X36] :
( ( ~ member(X36,union(X34,X35))
| member(X36,X34)
| member(X36,X35) )
& ( ~ member(X36,X34)
| member(X36,union(X34,X35)) )
& ( ~ member(X36,X35)
| member(X36,union(X34,X35)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(i_0_18,plain,
! [X38,X39,X40] :
( ( member(X40,X38)
| ~ member(X40,difference(X38,X39)) )
& ( ~ member(X40,X39)
| ~ member(X40,difference(X38,X39)) )
& ( ~ member(X40,X38)
| member(X40,X39)
| member(X40,difference(X38,X39)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).
fof(i_0_19,plain,
! [X45,X46,X47,X48,X49] :
( ( ~ subset(X45,X46)
| ~ member(X47,X45)
| member(X47,X46) )
& ( member(esk1_2(X48,X49),X48)
| subset(X48,X49) )
& ( ~ member(esk1_2(X48,X49),X49)
| subset(X48,X49) ) ),
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_defn])])])])])]) ).
fof(i_0_20,negated_conjecture,
difference(esk4_0,union(esk4_0,esk5_0)) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_21,plain,
! [X41,X42] :
( ( subset(X41,X42)
| X41 != X42 )
& ( subset(X42,X41)
| X41 != X42 )
& ( ~ subset(X41,X42)
| ~ subset(X42,X41)
| X41 = X42 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
fof(i_0_22,plain,
! [X30,X31] : subset(X30,union(X30,X31)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
fof(i_0_23,plain,
! [X32,X33] :
( ( difference(X32,X33) != empty_set
| subset(X32,X33) )
& ( ~ subset(X32,X33)
| difference(X32,X33) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])]) ).
fof(i_0_24,plain,
! [X52,X53,X54] :
( ( ~ empty(X52)
| ~ member(X53,X52) )
& ( member(esk2_1(X54),X54)
| empty(X54) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])])])])]) ).
fof(i_0_25,plain,
! [X43,X44] : union(X43,X44) = union(X44,X43),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(i_0_26,plain,
! [X37] : ~ member(X37,empty_set),
inference(variable_rename,[status(thm)],[i_0_15]) ).
fof(i_0_27,plain,
! [X51] : subset(X51,X51),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(i_0_28,plain,
( X1 = X2
| ~ member(esk3_2(X1,X2),X1)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_29,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_30,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_31,plain,
( member(esk3_2(X1,X2),X1)
| member(esk3_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_32,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_34,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_35,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_36,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_37,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_38,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_39,negated_conjecture,
difference(esk4_0,union(esk4_0,esk5_0)) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_40,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_41,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_42,plain,
( subset(X1,X2)
| difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_43,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_44,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_45,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_46,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_47,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_48,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_49,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_50,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_51,axiom,
X1 = X1 ).
cnf(i_0_52,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_53,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_54,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_56,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_57,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_51_001,axiom,
X1 = X1 ).
cnf(i_0_52_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_53_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_54_004,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_55_005,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_56_006,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_57_007,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_58_008,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_59_009,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_60_010,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_61_011,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_62_012,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_63,plain,
subset(X1,X1),
inference(equality_inference,[],[48]) ).
cnf(i_0_64,plain,
subset(X1,X1),
inference(equality_inference,[],[49]) ).
cnf(i_0_65,plain,
$false,
inference(scs_inference,[],[i_0_39,i_0_41,i_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET605+3 : 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 : n001.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:30:18 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.28/1.62 % Version : CSE_E---1.7
% 0.28/1.62 % Problem : theBenchmark.p
% 0.28/1.62 % SZS status Theorem for theBenchmark.p
% 0.28/1.62 % SZS output start CNFRefutation
% See solution above
% 0.28/1.64 % Total time : 1.274s
%------------------------------------------------------------------------------