TSTP Solution File: SEU157+2 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU157+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.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 : 600s
% DateTime : Tue Jul 19 09:17:16 EDT 2022
% Result : Theorem 0.28s 13.47s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 16 unt; 0 def)
% Number of atoms : 231 ( 86 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 246 ( 92 ~; 121 |; 23 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 175 ( 17 sgn 68 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t69_enumset1) ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d2_zfmisc_1) ).
fof(l55_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/solver/bin/../tmp/theBenchmark.p',l55_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',commutativity_k2_tarski) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d2_tarski) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',l2_zfmisc_1) ).
fof(t33_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t33_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d3_tarski) ).
fof(c_0_9,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_11,plain,
! [X7,X8,X9,X10,X10,X13,X14,X7,X8,X9,X16,X17] :
( ( in(esk7_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk8_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk7_4(X7,X8,X9,X10),esk8_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(esk9_3(X7,X8,X9),X9)
| ~ in(X16,X7)
| ~ in(X17,X8)
| esk9_3(X7,X8,X9) != ordered_pair(X16,X17)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk10_3(X7,X8,X9),X7)
| in(esk9_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk11_3(X7,X8,X9),X8)
| in(esk9_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk9_3(X7,X8,X9) = ordered_pair(esk10_3(X7,X8,X9),esk11_3(X7,X8,X9))
| in(esk9_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])])]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,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)],[l55_zfmisc_1]) ).
cnf(c_0_15,plain,
( X4 = ordered_pair(esk7_4(X2,X3,X1,X4),esk8_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_18,negated_conjecture,
( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) )
& ( in(esk1_0,esk3_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) )
& ( in(esk2_0,esk4_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_19,plain,
! [X5,X6,X7,X8,X8,X5,X6,X7] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk12_3(X5,X6,X7) != X5
| ~ in(esk12_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk12_3(X5,X6,X7) != X6
| ~ in(esk12_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk12_3(X5,X6,X7),X7)
| esk12_3(X5,X6,X7) = X5
| esk12_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tarski])])])])])])]) ).
cnf(c_0_20,plain,
( X4 = unordered_pair(unordered_pair(esk7_4(X2,X3,X1,X4),esk8_4(X2,X3,X1,X4)),unordered_pair(esk7_4(X2,X3,X1,X4),esk7_4(X2,X3,X1,X4)))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( unordered_pair(unordered_pair(esk7_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4)),unordered_pair(esk7_4(X1,X2,X3,X4),esk8_4(X1,X2,X3,X4))) = X4
| X3 != cartesian_product2(X1,X2)
| ~ in(X4,X3) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( in(esk1_0,esk3_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_22,c_0_16]) ).
fof(c_0_26,lemma,
! [X3,X4,X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])])]) ).
cnf(c_0_27,plain,
( in(esk7_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| X2 != unordered_pair(X1,X3) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( unordered_pair(unordered_pair(esk7_4(X1,X2,cartesian_product2(X1,X2),X3),esk7_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk7_4(X1,X2,cartesian_product2(X1,X2),X3),esk8_4(X1,X2,cartesian_product2(X1,X2),X3))) = X3
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( in(unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0))
| in(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_31,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( in(esk7_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))),unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))))) = unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_36,lemma,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ordered_pair(X5,X6) != ordered_pair(X7,X8) )
& ( X6 = X8
| ordered_pair(X5,X6) != ordered_pair(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
cnf(c_0_37,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( in(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk3_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_39,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X3,X1)) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( in(unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| in(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,lemma,
( subset(unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))),esk3_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))) = unordered_pair(esk1_0,esk1_0)
| unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))) = unordered_pair(esk1_0,esk2_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,lemma,
( X2 = X4
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_16]),c_0_16]) ).
cnf(c_0_46,negated_conjecture,
( in(esk2_0,esk4_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_42,c_0_16]) ).
fof(c_0_47,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk5_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk5_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
cnf(c_0_48,lemma,
( unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))) = unordered_pair(esk1_0,esk1_0)
| subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)) != unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_21]) ).
cnf(c_0_50,negated_conjecture,
( in(unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0))
| in(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[c_0_46,c_0_21]) ).
cnf(c_0_51,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,lemma,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| subset(unordered_pair(esk1_0,esk1_0),esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_37]) ).
cnf(c_0_53,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_54,plain,
( in(esk8_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_55,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)) != unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_56,negated_conjecture,
( unordered_pair(unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))),unordered_pair(esk7_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))))) = unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))
| in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( ~ in(esk2_0,esk4_0)
| ~ in(esk1_0,esk3_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_58,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_59,lemma,
( subset(unordered_pair(esk1_0,esk1_0),esk3_0)
| in(X1,esk3_0)
| ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5))
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(rw,[status(thm)],[c_0_53,c_0_16]) ).
cnf(c_0_61,plain,
( in(esk8_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_62,lemma,
( X1 = esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)))
| in(esk2_0,esk4_0)
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X1)) != unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0)
| ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_57,c_0_16]) ).
cnf(c_0_64,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[c_0_58,c_0_13]) ).
cnf(c_0_65,lemma,
subset(unordered_pair(esk1_0,esk1_0),esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_34]),c_0_37]) ).
cnf(c_0_66,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X3 != cartesian_product2(X4,X5)
| ~ in(X2,X5)
| ~ in(X1,X4) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( in(esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))),esk4_0)
| in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
cnf(c_0_68,lemma,
( esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0))) = esk2_0
| in(esk2_0,esk4_0) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[c_0_63,c_0_21]) ).
cnf(c_0_70,lemma,
in(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_72,negated_conjecture,
in(esk2_0,esk4_0),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_74,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,esk2_0),unordered_pair(X1,X1)),cartesian_product2(X2,esk4_0))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_72])]) ).
cnf(c_0_76,lemma,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_70]),c_0_21]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU157+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 02:55:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.28/13.47 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.28/13.47 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.28/13.47 # Preprocessing time : 0.018 s
% 0.28/13.47
% 0.28/13.47 # Proof found!
% 0.28/13.47 # SZS status Theorem
% 0.28/13.47 # SZS output start CNFRefutation
% See solution above
% 0.28/13.48 # Proof object total steps : 77
% 0.28/13.48 # Proof object clause steps : 58
% 0.28/13.48 # Proof object formula steps : 19
% 0.28/13.48 # Proof object conjectures : 22
% 0.28/13.48 # Proof object clause conjectures : 19
% 0.28/13.48 # Proof object formula conjectures : 3
% 0.28/13.48 # Proof object initial clauses used : 16
% 0.28/13.48 # Proof object initial formulas used : 9
% 0.28/13.48 # Proof object generating inferences : 26
% 0.28/13.48 # Proof object simplifying inferences : 23
% 0.28/13.48 # Training examples: 0 positive, 0 negative
% 0.28/13.48 # Parsed axioms : 87
% 0.28/13.48 # Removed by relevancy pruning/SinE : 55
% 0.28/13.48 # Initial clauses : 58
% 0.28/13.48 # Removed in clause preprocessing : 2
% 0.28/13.48 # Initial clauses in saturation : 56
% 0.28/13.48 # Processed clauses : 23157
% 0.28/13.48 # ...of these trivial : 536
% 0.28/13.48 # ...subsumed : 18164
% 0.28/13.48 # ...remaining for further processing : 4457
% 0.28/13.48 # Other redundant clauses eliminated : 315
% 0.28/13.48 # Clauses deleted for lack of memory : 266172
% 0.28/13.48 # Backward-subsumed : 36
% 0.28/13.48 # Backward-rewritten : 894
% 0.28/13.48 # Generated clauses : 514302
% 0.28/13.48 # ...of the previous two non-trivial : 473878
% 0.28/13.48 # Contextual simplify-reflections : 1616
% 0.28/13.48 # Paramodulations : 513492
% 0.28/13.48 # Factorizations : 347
% 0.28/13.48 # Equation resolutions : 461
% 0.28/13.48 # Current number of processed clauses : 3520
% 0.28/13.48 # Positive orientable unit clauses : 637
% 0.28/13.48 # Positive unorientable unit clauses: 1
% 0.28/13.48 # Negative unit clauses : 263
% 0.28/13.48 # Non-unit-clauses : 2619
% 0.28/13.48 # Current number of unprocessed clauses: 109577
% 0.28/13.48 # ...number of literals in the above : 397852
% 0.28/13.48 # Current number of archived formulas : 0
% 0.28/13.48 # Current number of archived clauses : 934
% 0.28/13.48 # Clause-clause subsumption calls (NU) : 2090397
% 0.28/13.48 # Rec. Clause-clause subsumption calls : 1331529
% 0.28/13.48 # Non-unit clause-clause subsumptions : 12502
% 0.28/13.48 # Unit Clause-clause subsumption calls : 14678
% 0.28/13.48 # Rewrite failures with RHS unbound : 0
% 0.28/13.48 # BW rewrite match attempts : 4321
% 0.28/13.48 # BW rewrite match successes : 36
% 0.28/13.48 # Condensation attempts : 0
% 0.28/13.48 # Condensation successes : 0
% 0.28/13.48 # Termbank termtop insertions : 57644855
% 0.28/13.48
% 0.28/13.48 # -------------------------------------------------
% 0.28/13.48 # User time : 12.906 s
% 0.28/13.48 # System time : 0.107 s
% 0.28/13.48 # Total time : 13.013 s
% 0.28/13.48 # Maximum resident set size: 145368 pages
% 0.31/23.40 eprover: CPU time limit exceeded, terminating
% 0.31/23.41 eprover: CPU time limit exceeded, terminating
% 0.31/23.41 eprover: CPU time limit exceeded, terminating
% 0.31/23.41 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.41 eprover: No such file or directory
% 0.31/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.42 eprover: No such file or directory
% 0.31/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.42 eprover: No such file or directory
% 0.31/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.43 eprover: No such file or directory
% 0.31/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.43 eprover: No such file or directory
% 0.31/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.43 eprover: No such file or directory
% 0.31/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.43 eprover: No such file or directory
% 0.31/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.43 eprover: No such file or directory
% 0.31/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.43 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.44 eprover: No such file or directory
% 0.31/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.45 eprover: No such file or directory
% 0.31/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.45 eprover: No such file or directory
% 0.31/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.45 eprover: No such file or directory
% 0.31/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.45 eprover: No such file or directory
% 0.31/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.45 eprover: No such file or directory
% 0.31/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.45 eprover: No such file or directory
% 0.31/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.46 eprover: No such file or directory
% 0.31/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.46 eprover: No such file or directory
% 0.31/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.46 eprover: No such file or directory
% 0.31/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.46 eprover: No such file or directory
% 0.31/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.46 eprover: No such file or directory
% 0.31/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.46 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.48 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------