%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET002+3 : 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 : n011.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 05:06:45 PM UTC 2026
% Result : Theorem 0.24s 1.61s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 28)
% Comments :
%------------------------------------------------------------------------------
fof(prove_idempotency_of_union,conjecture,
! [X1] : union(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(subset_union,axiom,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(i_0_8,negated_conjecture,
~ ! [X1] : union(X1,X1) = X1,
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
fof(i_0_9,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ member(X39,X37)
| member(X39,X38)
| X37 != X38 )
& ( ~ member(X40,X38)
| member(X40,X37)
| X37 != X38 )
& ( ~ member(esk2_2(X41,X42),X41)
| ~ member(esk2_2(X41,X42),X42)
| X41 = X42 )
& ( member(esk2_2(X41,X42),X41)
| member(esk2_2(X41,X42),X42)
| X41 = X42 ) ),
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_10,plain,
! [X23,X24,X25] :
( ( ~ member(X25,union(X23,X24))
| member(X25,X23)
| member(X25,X24) )
& ( ~ member(X25,X23)
| member(X25,union(X23,X24)) )
& ( ~ member(X25,X24)
| member(X25,union(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(i_0_11,plain,
! [X30,X31,X32,X33,X34] :
( ( ~ subset(X30,X31)
| ~ member(X32,X30)
| member(X32,X31) )
& ( member(esk1_2(X33,X34),X33)
| subset(X33,X34) )
& ( ~ member(esk1_2(X33,X34),X34)
| subset(X33,X34) ) ),
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_12,plain,
! [X26,X27] :
( ( subset(X26,X27)
| X26 != X27 )
& ( subset(X27,X26)
| X26 != X27 )
& ( ~ subset(X26,X27)
| ~ subset(X27,X26)
| X26 = X27 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
fof(i_0_13,plain,
! [X21,X22] :
( ~ subset(X21,X22)
| union(X21,X22) = X22 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_union])]) ).
fof(i_0_14,plain,
! [X28,X29] : union(X28,X29) = union(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(i_0_15,negated_conjecture,
union(esk3_0,esk3_0) != esk3_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])]) ).
fof(i_0_16,plain,
! [X36] : subset(X36,X36),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(i_0_17,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_18,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_19,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_20,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_21,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_22,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_23,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_24,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_25,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_26,plain,
( union(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_27,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_28,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_29,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_30,negated_conjecture,
union(esk3_0,esk3_0) != esk3_0,
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_31,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_32,axiom,
X1 = X1 ).
cnf(i_0_33,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_32_001,axiom,
X1 = X1 ).
cnf(i_0_33_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35_004,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_36_005,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_37_006,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_38_007,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_39_008,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_40_009,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_41,plain,
subset(X1,X1),
inference(equality_inference,[],[28]) ).
cnf(i_0_42,plain,
subset(X1,X1),
inference(equality_inference,[],[29]) ).
cnf(i_0_43,plain,
$false,
inference(scs_inference,[],[i_0_30,i_0_31,i_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET002+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:03:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.24/1.61 % Version : CSE_E---1.7
% 0.24/1.61 % Problem : theBenchmark.p
% 0.24/1.61 % SZS status Theorem for theBenchmark.p
% 0.24/1.61 % SZS output start CNFRefutation
% See solution above
% 0.24/1.62 % Total time : 1.271s
%------------------------------------------------------------------------------