%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU165+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n023.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 05:10:53 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 60 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 25 ~; 25 |; 7 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 7 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t106_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[t106_zfmisc_1]) ).
fof(c_0_4,plain,
! [X37,X38,X39,X40] :
( ( in(X37,X39)
| ~ in(ordered_pair(X37,X38),cartesian_product2(X39,X40)) )
& ( in(X38,X40)
| ~ in(ordered_pair(X37,X38),cartesian_product2(X39,X40)) )
& ( ~ in(X37,X39)
| ~ in(X38,X40)
| in(ordered_pair(X37,X38),cartesian_product2(X39,X40)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_5,plain,
! [X31,X32] : ordered_pair(X31,X32) = unordered_pair(unordered_pair(X31,X32),singleton(X31)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_6,negated_conjecture,
( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) )
& ( in(esk3_0,esk5_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) )
& ( in(esk4_0,esk6_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_7,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( in(esk4_0,esk6_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( in(esk4_0,esk6_0)
| in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( in(esk3_0,esk5_0)
| in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk6_0)
| ~ in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_16,negated_conjecture,
in(esk4_0,esk6_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( in(esk3_0,esk5_0)
| in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_19,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0))
| ~ in(esk3_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_20,negated_conjecture,
in(esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_8]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU165+3 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:46:54 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------