%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN966+1 : TPTP v9.2.1. Released v3.1.0.
% 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 : n022.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 05:51:09 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 53 ( 18 ~; 22 |; 5 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X1,X2] :
( eq(X1,X2)
<=> ! [X3] :
( a_member_of(X3,X1)
<=> a_member_of(X3,X2) ) )
=> ! [X4,X5] :
( eq(X4,X5)
=> eq(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(c_0_1,negated_conjecture,
~ ( ! [X1,X2] :
( eq(X1,X2)
<=> ! [X3] :
( a_member_of(X3,X1)
<=> a_member_of(X3,X2) ) )
=> ! [X4,X5] :
( eq(X4,X5)
=> eq(X5,X4) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(c_0_2,negated_conjecture,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ a_member_of(X13,X11)
| a_member_of(X13,X12)
| ~ eq(X11,X12) )
& ( ~ a_member_of(X14,X12)
| a_member_of(X14,X11)
| ~ eq(X11,X12) )
& ( ~ a_member_of(esk1_2(X15,X16),X15)
| ~ a_member_of(esk1_2(X15,X16),X16)
| eq(X15,X16) )
& ( a_member_of(esk1_2(X15,X16),X15)
| a_member_of(esk1_2(X15,X16),X16)
| eq(X15,X16) )
& eq(esk2_0,esk3_0)
& ~ eq(esk3_0,esk2_0) ),
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)],[c_0_1])])])])])]) ).
cnf(c_0_3,negated_conjecture,
( a_member_of(X1,X3)
| ~ a_member_of(X1,X2)
| ~ eq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( a_member_of(esk1_2(X1,X2),X1)
| a_member_of(esk1_2(X1,X2),X2)
| eq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( a_member_of(esk1_2(X1,X2),X2)
| a_member_of(esk1_2(X1,X2),X3)
| eq(X1,X2)
| ~ eq(X3,X1) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
eq(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( a_member_of(esk1_2(esk3_0,X1),esk2_0)
| a_member_of(esk1_2(esk3_0,X1),X1)
| eq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,negated_conjecture,
~ eq(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( eq(X1,X2)
| ~ a_member_of(esk1_2(X1,X2),X1)
| ~ a_member_of(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
a_member_of(esk1_2(esk3_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_7]),c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( a_member_of(X1,X3)
| ~ a_member_of(X1,X2)
| ~ eq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
~ a_member_of(esk1_2(esk3_0,esk2_0),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( a_member_of(esk1_2(esk3_0,esk2_0),X1)
| ~ eq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_6])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN966+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 08:52:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------