%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU281+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n029.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 05:11:20 PM UTC 2026
% Result : Theorem 2.01s 1.94s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of formulae : 67 ( 5 unt; 0 def)
% Number of atoms : 429 ( 199 equ)
% Maximal formula atoms : 198 ( 6 avg)
% Number of connectives : 558 ( 196 ~; 283 |; 74 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 68 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-3 aty)
% Number of variables : 158 ( 1 sgn 22 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_tarski__e16_22__wellord2__2,axiom,
! [X1,X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& X7 = singleton(X6) )
& X3 = X5
& ? [X8,X9] :
( ordered_pair(X8,X9) = X5
& in(X8,X1)
& X9 = singleton(X8) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,cartesian_product2(X1,X2))
& X5 = X4
& ? [X10,X11] :
( ordered_pair(X10,X11) = X4
& in(X10,X1)
& X11 = singleton(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(s1_xboole_0__e16_22__wellord2__1,conjecture,
! [X1,X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& X6 = singleton(X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(c_0_2,plain,
! [X64,X72,X74,X78,X79,X80,X81] :
( ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk11_1(X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk11_1(X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk11_1(X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk11_1(X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk11_1(X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| esk10_1(X64) = esk11_1(X64) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk13_1(X64),esk14_1(X64)) = esk11_1(X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk13_1(X64),esk14_1(X64)) = esk11_1(X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk13_1(X64),esk14_1(X64)) = esk11_1(X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk13_1(X64),esk14_1(X64)) = esk11_1(X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk13_1(X64),esk14_1(X64)) = esk11_1(X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| ordered_pair(esk13_1(X64),esk14_1(X64)) = esk11_1(X64) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| in(esk13_1(X64),X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| in(esk13_1(X64),X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| in(esk13_1(X64),X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| in(esk13_1(X64),X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| in(esk13_1(X64),X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| in(esk13_1(X64),X64) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| esk14_1(X64) = singleton(esk13_1(X64)) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk14_1(X64) = singleton(esk13_1(X64)) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk14_1(X64) = singleton(esk13_1(X64)) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| esk14_1(X64) = singleton(esk13_1(X64)) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| esk14_1(X64) = singleton(esk13_1(X64)) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| esk14_1(X64) = singleton(esk13_1(X64)) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk12_1(X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk12_1(X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk12_1(X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk12_1(X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| esk10_1(X64) = esk12_1(X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| esk10_1(X64) = esk12_1(X64) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk15_1(X64),esk16_1(X64)) = esk12_1(X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk15_1(X64),esk16_1(X64)) = esk12_1(X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk15_1(X64),esk16_1(X64)) = esk12_1(X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk15_1(X64),esk16_1(X64)) = esk12_1(X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| ordered_pair(esk15_1(X64),esk16_1(X64)) = esk12_1(X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| ordered_pair(esk15_1(X64),esk16_1(X64)) = esk12_1(X64) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| in(esk15_1(X64),X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| in(esk15_1(X64),X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| in(esk15_1(X64),X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| in(esk15_1(X64),X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| in(esk15_1(X64),X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| in(esk15_1(X64),X64) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| esk16_1(X64) = singleton(esk15_1(X64)) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk16_1(X64) = singleton(esk15_1(X64)) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk16_1(X64) = singleton(esk15_1(X64)) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| esk16_1(X64) = singleton(esk15_1(X64)) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| esk16_1(X64) = singleton(esk15_1(X64)) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| esk16_1(X64) = singleton(esk15_1(X64)) )
& ( in(esk18_3(X64,X72,X74),cartesian_product2(X64,X72))
| ~ in(X74,esk17_2(X64,X72))
| esk11_1(X64) != esk12_1(X64) )
& ( esk18_3(X64,X72,X74) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk11_1(X64) != esk12_1(X64) )
& ( ordered_pair(esk19_3(X64,X72,X74),esk20_3(X64,X72,X74)) = X74
| ~ in(X74,esk17_2(X64,X72))
| esk11_1(X64) != esk12_1(X64) )
& ( in(esk19_3(X64,X72,X74),X64)
| ~ in(X74,esk17_2(X64,X72))
| esk11_1(X64) != esk12_1(X64) )
& ( esk20_3(X64,X72,X74) = singleton(esk19_3(X64,X72,X74))
| ~ in(X74,esk17_2(X64,X72))
| esk11_1(X64) != esk12_1(X64) )
& ( ~ in(X79,cartesian_product2(X64,X72))
| X79 != X78
| ordered_pair(X80,X81) != X78
| ~ in(X80,X64)
| X81 != singleton(X80)
| in(X78,esk17_2(X64,X72))
| esk11_1(X64) != esk12_1(X64) ) ),
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)],[s1_tarski__e16_22__wellord2__2])])])])])]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& X6 = singleton(X5) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e16_22__wellord2__1]) ).
cnf(c_0_4,plain,
( in(X4,esk17_2(X2,X3))
| esk10_1(X2) = esk11_1(X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_5,negated_conjecture,
! [X46,X48,X49] :
( ( ~ in(esk3_1(X46),X46)
| ~ in(esk3_1(X46),cartesian_product2(esk1_0,esk2_0))
| ordered_pair(X48,X49) != esk3_1(X46)
| ~ in(X48,esk1_0)
| X49 != singleton(X48) )
& ( in(esk3_1(X46),cartesian_product2(esk1_0,esk2_0))
| in(esk3_1(X46),X46) )
& ( ordered_pair(esk4_1(X46),esk5_1(X46)) = esk3_1(X46)
| in(esk3_1(X46),X46) )
& ( in(esk4_1(X46),esk1_0)
| in(esk3_1(X46),X46) )
& ( esk5_1(X46) = singleton(esk4_1(X46))
| in(esk3_1(X46),X46) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
cnf(c_0_6,plain,
( esk10_1(X1) = esk11_1(X1)
| in(ordered_pair(X2,singleton(X2)),esk17_2(X1,X3))
| ~ in(ordered_pair(X2,singleton(X2)),cartesian_product2(X1,X3))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,negated_conjecture,
( esk5_1(X1) = singleton(esk4_1(X1))
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( esk10_1(X1) = esk11_1(X1)
| in(ordered_pair(esk4_1(X2),esk5_1(X2)),esk17_2(X1,X3))
| in(esk3_1(X2),X2)
| ~ in(ordered_pair(esk4_1(X2),esk5_1(X2)),cartesian_product2(X1,X3))
| ~ in(esk4_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( ordered_pair(esk4_1(X1),esk5_1(X1)) = esk3_1(X1)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( esk10_1(X1) = esk11_1(X1)
| in(esk3_1(X2),esk17_2(X1,X3))
| in(esk3_1(X2),X2)
| ~ in(esk3_1(X2),cartesian_product2(X1,X3))
| ~ in(esk4_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( in(esk3_1(X1),cartesian_product2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( in(esk4_1(X1),esk1_0)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| in(esk3_1(X1),esk17_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_14,plain,
( in(esk18_3(X1,X2,X3),cartesian_product2(X1,X2))
| esk10_1(X1) = esk11_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( esk18_3(X1,X2,X3) = X3
| esk10_1(X1) = esk11_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(esk3_1(X1),X1)
| ~ in(esk3_1(X1),cartesian_product2(esk1_0,esk2_0))
| ordered_pair(X2,X3) != esk3_1(X1)
| ~ in(X2,esk1_0)
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| in(esk18_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( esk18_3(X1,X2,esk3_1(esk17_2(X1,X2))) = esk3_1(esk17_2(X1,X2))
| esk10_1(X1) = esk11_1(X1)
| in(esk3_1(esk17_2(X1,X2)),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_20,plain,
( in(X4,esk17_2(X2,X3))
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5)
| esk11_1(X2) != esk12_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_21,plain,
( in(X4,esk17_2(X2,X3))
| esk10_1(X2) = esk12_1(X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_22,negated_conjecture,
( ordered_pair(X1,singleton(X1)) != esk3_1(X2)
| ~ in(esk3_1(X2),cartesian_product2(esk1_0,esk2_0))
| ~ in(esk3_1(X2),X2)
| ~ in(X1,esk1_0) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| in(esk3_1(esk17_2(esk1_0,esk2_0)),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( esk20_3(X1,X2,X3) = singleton(esk19_3(X1,X2,X3))
| esk10_1(X1) = esk11_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_25,plain,
( in(esk19_3(X1,X2,X3),X1)
| esk10_1(X1) = esk11_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_26,plain,
( in(ordered_pair(X1,singleton(X1)),esk17_2(X2,X3))
| esk12_1(X2) != esk11_1(X2)
| ~ in(ordered_pair(X1,singleton(X1)),cartesian_product2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])])]) ).
cnf(c_0_27,plain,
( esk10_1(X1) = esk12_1(X1)
| in(ordered_pair(X2,singleton(X2)),esk17_2(X1,X3))
| ~ in(ordered_pair(X2,singleton(X2)),cartesian_product2(X1,X3))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])])]) ).
cnf(c_0_28,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| ordered_pair(X1,singleton(X1)) != esk3_1(esk17_2(esk1_0,esk2_0))
| ~ in(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15]) ).
cnf(c_0_29,negated_conjecture,
( singleton(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) = esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))
| esk10_1(esk1_0) = esk11_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| in(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk1_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
( in(ordered_pair(esk4_1(X1),esk5_1(X1)),esk17_2(X2,X3))
| in(esk3_1(X1),X1)
| esk12_1(X2) != esk11_1(X2)
| ~ in(ordered_pair(esk4_1(X1),esk5_1(X1)),cartesian_product2(X2,X3))
| ~ in(esk4_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_7]) ).
cnf(c_0_32,negated_conjecture,
( esk10_1(X1) = esk12_1(X1)
| in(ordered_pair(esk4_1(X2),esk5_1(X2)),esk17_2(X1,X3))
| in(esk3_1(X2),X2)
| ~ in(ordered_pair(esk4_1(X2),esk5_1(X2)),cartesian_product2(X1,X3))
| ~ in(esk4_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_7]) ).
cnf(c_0_33,plain,
( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) = X3
| esk10_1(X1) = esk11_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_34,negated_conjecture,
( esk10_1(esk1_0) = esk11_1(esk1_0)
| ordered_pair(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) != esk3_1(esk17_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( in(esk3_1(X1),esk17_2(X2,X3))
| in(esk3_1(X1),X1)
| esk12_1(X2) != esk11_1(X2)
| ~ in(esk3_1(X1),cartesian_product2(X2,X3))
| ~ in(esk4_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_9]) ).
cnf(c_0_36,negated_conjecture,
( esk10_1(X1) = esk12_1(X1)
| in(esk3_1(X2),esk17_2(X1,X3))
| in(esk3_1(X2),X2)
| ~ in(esk3_1(X2),cartesian_product2(X1,X3))
| ~ in(esk4_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_9]) ).
cnf(c_0_37,negated_conjecture,
esk10_1(esk1_0) = esk11_1(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_15]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( in(esk3_1(X1),esk17_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1)
| esk12_1(esk1_0) != esk11_1(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_11]),c_0_12]) ).
cnf(c_0_39,negated_conjecture,
( in(esk3_1(X1),esk17_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_11]),c_0_37]),c_0_12]),c_0_38]) ).
cnf(c_0_40,plain,
( in(esk18_3(X1,X2,X3),cartesian_product2(X1,X2))
| esk10_1(X1) = esk12_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_41,negated_conjecture,
in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(esk1_0,esk2_0)),
inference(ef,[status(thm)],[c_0_39]) ).
cnf(c_0_42,plain,
( esk18_3(X1,X2,X3) = X3
| esk10_1(X1) = esk12_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_43,negated_conjecture,
( esk12_1(esk1_0) = esk11_1(esk1_0)
| in(esk18_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),cartesian_product2(esk1_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( esk18_3(X1,X2,esk3_1(esk17_2(X1,X2))) = esk3_1(esk17_2(X1,X2))
| esk10_1(X1) = esk12_1(X1)
| in(esk3_1(esk17_2(X1,X2)),cartesian_product2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_11]) ).
cnf(c_0_45,negated_conjecture,
( esk12_1(esk1_0) = esk11_1(esk1_0)
| in(esk3_1(esk17_2(esk1_0,esk2_0)),cartesian_product2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_37])]) ).
cnf(c_0_46,plain,
( esk20_3(X1,X2,X3) = singleton(esk19_3(X1,X2,X3))
| esk10_1(X1) = esk12_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_47,plain,
( in(esk19_3(X1,X2,X3),X1)
| esk10_1(X1) = esk12_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_48,plain,
( in(esk18_3(X1,X2,X3),cartesian_product2(X1,X2))
| ~ in(X3,esk17_2(X1,X2))
| esk11_1(X1) != esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_49,plain,
( esk18_3(X1,X2,X3) = X3
| ~ in(X3,esk17_2(X1,X2))
| esk11_1(X1) != esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_50,negated_conjecture,
( esk12_1(esk1_0) = esk11_1(esk1_0)
| ordered_pair(X1,singleton(X1)) != esk3_1(esk17_2(esk1_0,esk2_0))
| ~ in(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_45]),c_0_41])]) ).
cnf(c_0_51,negated_conjecture,
( singleton(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) = esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))
| esk12_1(esk1_0) = esk11_1(esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_41]),c_0_37]) ).
cnf(c_0_52,negated_conjecture,
( esk12_1(esk1_0) = esk11_1(esk1_0)
| in(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_37]) ).
cnf(c_0_53,plain,
( in(X1,cartesian_product2(X2,X3))
| esk12_1(X2) != esk11_1(X2)
| ~ in(X1,esk17_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) = X3
| esk10_1(X1) = esk12_1(X1)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_55,negated_conjecture,
( esk12_1(esk1_0) = esk11_1(esk1_0)
| ordered_pair(esk19_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0))),esk20_3(esk1_0,esk2_0,esk3_1(esk17_2(esk1_0,esk2_0)))) != esk3_1(esk17_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( ordered_pair(X1,singleton(X1)) != esk3_1(X2)
| esk12_1(esk1_0) != esk11_1(esk1_0)
| ~ in(esk3_1(X2),esk17_2(esk1_0,esk2_0))
| ~ in(esk3_1(X2),X2)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
esk12_1(esk1_0) = esk11_1(esk1_0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_37]),c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( ordered_pair(X1,singleton(X1)) != esk3_1(X2)
| ~ in(esk3_1(X2),esk17_2(esk1_0,esk2_0))
| ~ in(esk3_1(X2),X2)
| ~ in(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_59,negated_conjecture,
( ordered_pair(X1,singleton(X1)) != esk3_1(esk17_2(esk1_0,esk2_0))
| ~ in(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_41])]) ).
cnf(c_0_60,plain,
( esk20_3(X1,X2,X3) = singleton(esk19_3(X1,X2,X3))
| ~ in(X3,esk17_2(X1,X2))
| esk11_1(X1) != esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_61,negated_conjecture,
( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) != esk3_1(esk17_2(esk1_0,esk2_0))
| esk12_1(X1) != esk11_1(X1)
| ~ in(esk19_3(X1,X2,X3),esk1_0)
| ~ in(X3,esk17_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,plain,
( ordered_pair(esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) = X3
| ~ in(X3,esk17_2(X1,X2))
| esk11_1(X1) != esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_63,negated_conjecture,
( esk12_1(X1) != esk11_1(X1)
| ~ in(esk19_3(X1,X2,esk3_1(esk17_2(esk1_0,esk2_0))),esk1_0)
| ~ in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(X1,X2)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_64,plain,
( in(esk19_3(X1,X2,X3),X1)
| ~ in(X3,esk17_2(X1,X2))
| esk11_1(X1) != esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_65,negated_conjecture,
~ in(esk3_1(esk17_2(esk1_0,esk2_0)),esk17_2(esk1_0,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_57])]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_41,c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU281+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.16/0.33 % Computer : n029.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:54:14 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 2.01/1.94 % Version : CSE_E---1.7
% 2.01/1.94 % Problem : theBenchmark.p
% 2.01/1.94 % SZS status Theorem for theBenchmark.p
% 2.01/1.94 % SZS output start CNFRefutation
% See solution above
% 2.01/1.94 % Total time : 1.370s
%------------------------------------------------------------------------------