%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU165+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n025.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 8.42s 5.80s
% Output : CNFRefutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 81 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 32 ~; 33 |; 7 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 69 ( 10 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
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,lemma,
! [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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_5,plain,
! [X301,X302] : ordered_pair(X301,X302) = unordered_pair(unordered_pair(X301,X302),singleton(X301)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_6,lemma,
! [X422] : unordered_pair(X422,X422) = singleton(X422),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,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_8,lemma,
! [X334,X335,X336,X337] :
( ( in(X334,X336)
| ~ in(ordered_pair(X334,X335),cartesian_product2(X336,X337)) )
& ( in(X335,X337)
| ~ in(ordered_pair(X334,X335),cartesian_product2(X336,X337)) )
& ( ~ in(X334,X336)
| ~ in(X335,X337)
| in(ordered_pair(X334,X335),cartesian_product2(X336,X337)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( ( ~ in(ordered_pair(esk19_0,esk20_0),cartesian_product2(esk21_0,esk22_0))
| ~ in(esk19_0,esk21_0)
| ~ in(esk20_0,esk22_0) )
& ( in(esk19_0,esk21_0)
| in(ordered_pair(esk19_0,esk20_0),cartesian_product2(esk21_0,esk22_0)) )
& ( in(esk20_0,esk22_0)
| in(ordered_pair(esk19_0,esk20_0),cartesian_product2(esk21_0,esk22_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
! [X205,X206] : unordered_pair(X205,X206) = unordered_pair(X206,X205),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_15,negated_conjecture,
( in(esk20_0,esk22_0)
| in(ordered_pair(esk19_0,esk20_0),cartesian_product2(esk21_0,esk22_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(ordered_pair(esk19_0,esk20_0),cartesian_product2(esk21_0,esk22_0))
| ~ in(esk19_0,esk21_0)
| ~ in(esk20_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( in(esk20_0,esk22_0)
| in(unordered_pair(unordered_pair(esk19_0,esk20_0),unordered_pair(esk19_0,esk19_0)),cartesian_product2(esk21_0,esk22_0)) ),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_20,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( in(esk19_0,esk21_0)
| in(ordered_pair(esk19_0,esk20_0),cartesian_product2(esk21_0,esk22_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk19_0,esk21_0)
| ~ in(esk20_0,esk22_0)
| ~ in(unordered_pair(unordered_pair(esk19_0,esk20_0),unordered_pair(esk19_0,esk19_0)),cartesian_product2(esk21_0,esk22_0)) ),
inference(rw,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_23,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( in(unordered_pair(unordered_pair(esk19_0,esk19_0),unordered_pair(esk19_0,esk20_0)),cartesian_product2(esk21_0,esk22_0))
| in(esk20_0,esk22_0) ),
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
( in(esk19_0,esk21_0)
| in(unordered_pair(unordered_pair(esk19_0,esk20_0),unordered_pair(esk19_0,esk19_0)),cartesian_product2(esk21_0,esk22_0)) ),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk19_0,esk19_0),unordered_pair(esk19_0,esk20_0)),cartesian_product2(esk21_0,esk22_0))
| ~ in(esk19_0,esk21_0)
| ~ in(esk20_0,esk22_0) ),
inference(rw,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
in(esk20_0,esk22_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),cartesian_product2(X2,X4)) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( in(unordered_pair(unordered_pair(esk19_0,esk19_0),unordered_pair(esk19_0,esk20_0)),cartesian_product2(esk21_0,esk22_0))
| in(esk19_0,esk21_0) ),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_31,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk19_0,esk19_0),unordered_pair(esk19_0,esk20_0)),cartesian_product2(esk21_0,esk22_0))
| ~ in(esk19_0,esk21_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
in(esk19_0,esk21_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_35,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk19_0,esk19_0),unordered_pair(esk19_0,esk20_0)),cartesian_product2(esk21_0,esk22_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_36,lemma,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU165+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.33 % Computer : n025.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 02:46:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 8.42/5.80 % Version : CSE_E---1.7
% 8.42/5.80 % Problem : theBenchmark.p
% 8.42/5.80 % SZS status Theorem for theBenchmark.p
% 8.42/5.80 % SZS output start CNFRefutation
% See solution above
% 8.42/5.82 % Total time : 4.374s
%------------------------------------------------------------------------------