%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET580+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 : 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 05:08:01 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 92 ( 3 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 102 ( 43 ~; 43 |; 9 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 4 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th23,conjecture,
! [X1,X2,X3] :
( member(X1,symmetric_difference(X2,X3))
<=> ~ ( member(X1,X2)
<=> member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th23) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
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(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(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( member(X1,symmetric_difference(X2,X3))
<=> ~ ( member(X1,X2)
<=> member(X1,X3) ) ),
inference(assume_negation,[status(cth)],[prove_th23]) ).
fof(c_0_5,negated_conjecture,
( ( ~ member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
& ( ~ member(esk2_0,esk4_0)
| member(esk2_0,esk3_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
& ( ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0)
| member(esk2_0,symmetric_difference(esk3_0,esk4_0)) )
& ( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X28,X29] : symmetric_difference(X28,X29) = union(difference(X28,X29),difference(X29,X28)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
cnf(c_0_8,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X22,X23,X24] :
( ( ~ member(X24,union(X22,X23))
| member(X24,X22)
| member(X24,X23) )
& ( ~ member(X24,X22)
| member(X24,union(X22,X23)) )
& ( ~ member(X24,X23)
| member(X24,union(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_11,plain,
! [X25,X26,X27] :
( ( member(X27,X25)
| ~ member(X27,difference(X25,X26)) )
& ( ~ member(X27,X26)
| ~ member(X27,difference(X25,X26)) )
& ( ~ member(X27,X25)
| member(X27,X26)
| member(X27,difference(X25,X26)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0)
| ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( member(esk2_0,symmetric_difference(esk3_0,esk4_0))
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
~ member(esk2_0,difference(esk4_0,esk3_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_21,negated_conjecture,
( member(esk2_0,esk3_0)
| ~ member(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( member(esk2_0,esk4_0)
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,symmetric_difference(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( member(esk2_0,esk3_0)
| member(esk2_0,esk4_0)
| member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
inference(rw,[status(thm)],[c_0_19,c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)))
| ~ member(esk2_0,esk4_0) ),
inference(csr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( member(esk2_0,esk4_0)
| ~ member(esk2_0,esk3_0)
| ~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) ),
inference(rw,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_27,negated_conjecture,
member(esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_21]),c_0_14]) ).
cnf(c_0_28,negated_conjecture,
~ member(esk2_0,esk4_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_17]),c_0_15]) ).
cnf(c_0_29,negated_conjecture,
~ member(esk2_0,union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),c_0_28]) ).
cnf(c_0_30,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
~ member(esk2_0,difference(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_18]),c_0_27])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET580+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 : n021.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 02:28:55 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------