TSTP Solution File: SEU157+2 by E---3.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU157+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n020.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 : Mon Jun 24 15:05:54 EDT 2024
% Result : Theorem 225.18s 28.96s
% Output : CNFRefutation 225.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 111 ( 47 unt; 0 def)
% Number of atoms : 285 ( 121 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 280 ( 106 ~; 124 |; 31 &)
% ( 14 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 5 con; 0-4 aty)
% Number of variables : 236 ( 19 sgn 124 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',l55_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',l23_zfmisc_1) ).
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/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',d2_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',commutativity_k2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',d2_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',d1_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',d1_tarski) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',l1_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/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t33_zfmisc_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t28_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t7_xboole_1) ).
fof(l3_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',l3_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',reflexivity_r1_tarski) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t12_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t36_xboole_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',d4_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t48_xboole_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',t40_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p',commutativity_k3_xboole_0) ).
fof(c_0_19,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]) ).
fof(c_0_20,lemma,
! [X99,X100] :
( ~ in(X99,X100)
| set_union2(singleton(X99),X100) = X100 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])])]) ).
fof(c_0_21,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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).
fof(c_0_22,plain,
! [X26,X27,X28,X29,X32,X33,X34,X35,X36,X37,X39,X40] :
( ( in(esk8_4(X26,X27,X28,X29),X26)
| ~ in(X29,X28)
| X28 != cartesian_product2(X26,X27) )
& ( in(esk9_4(X26,X27,X28,X29),X27)
| ~ in(X29,X28)
| X28 != cartesian_product2(X26,X27) )
& ( X29 = ordered_pair(esk8_4(X26,X27,X28,X29),esk9_4(X26,X27,X28,X29))
| ~ in(X29,X28)
| X28 != cartesian_product2(X26,X27) )
& ( ~ in(X33,X26)
| ~ in(X34,X27)
| X32 != ordered_pair(X33,X34)
| in(X32,X28)
| X28 != cartesian_product2(X26,X27) )
& ( ~ in(esk10_3(X35,X36,X37),X37)
| ~ in(X39,X35)
| ~ in(X40,X36)
| esk10_3(X35,X36,X37) != ordered_pair(X39,X40)
| X37 = cartesian_product2(X35,X36) )
& ( in(esk11_3(X35,X36,X37),X35)
| in(esk10_3(X35,X36,X37),X37)
| X37 = cartesian_product2(X35,X36) )
& ( in(esk12_3(X35,X36,X37),X36)
| in(esk10_3(X35,X36,X37),X37)
| X37 = cartesian_product2(X35,X36) )
& ( esk10_3(X35,X36,X37) = ordered_pair(esk11_3(X35,X36,X37),esk12_3(X35,X36,X37))
| in(esk10_3(X35,X36,X37),X37)
| X37 = cartesian_product2(X35,X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[d2_zfmisc_1])])])])])])]) ).
cnf(c_0_23,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( in(esk2_0,esk4_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X141,X142] : set_union2(X141,X142) = set_union2(X142,X141),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_26,negated_conjecture,
( 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_21]) ).
fof(c_0_27,plain,
! [X143,X144,X145,X146,X147,X148,X149,X150] :
( ( ~ in(X146,X145)
| in(X146,X143)
| in(X146,X144)
| X145 != set_union2(X143,X144) )
& ( ~ in(X147,X143)
| in(X147,X145)
| X145 != set_union2(X143,X144) )
& ( ~ in(X147,X144)
| in(X147,X145)
| X145 != set_union2(X143,X144) )
& ( ~ in(esk18_3(X148,X149,X150),X148)
| ~ in(esk18_3(X148,X149,X150),X150)
| X150 = set_union2(X148,X149) )
& ( ~ in(esk18_3(X148,X149,X150),X149)
| ~ in(esk18_3(X148,X149,X150),X150)
| X150 = set_union2(X148,X149) )
& ( in(esk18_3(X148,X149,X150),X150)
| in(esk18_3(X148,X149,X150),X148)
| in(esk18_3(X148,X149,X150),X149)
| X150 = set_union2(X148,X149) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[d2_xboole_0])])])])])])]) ).
fof(c_0_28,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_29,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( set_union2(singleton(ordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0)) = cartesian_product2(esk3_0,esk4_0)
| in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( set_union2(singleton(ordered_pair(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0)) = cartesian_product2(esk3_0,esk4_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
fof(c_0_33,plain,
! [X92,X93,X94,X95,X96,X97] :
( ( ~ in(X94,X93)
| X94 = X92
| X93 != singleton(X92) )
& ( X95 != X92
| in(X95,X93)
| X93 != singleton(X92) )
& ( ~ in(esk14_2(X96,X97),X97)
| esk14_2(X96,X97) != X96
| X97 = singleton(X96) )
& ( in(esk14_2(X96,X97),X97)
| esk14_2(X96,X97) = X96
| X97 = singleton(X96) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[d1_tarski])])])])])])]) ).
fof(c_0_34,lemma,
! [X1] : singleton(X1) != empty_set,
inference(fof_simplification,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_35,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_36,plain,
! [X13,X14,X15] :
( ( X13 != empty_set
| ~ in(X14,X13) )
& ( in(esk5_1(X15),X15)
| X15 = empty_set ) ),
inference(fof_nnf,[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_28])])])])])]) ).
cnf(c_0_37,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_29])]) ).
cnf(c_0_38,negated_conjecture,
( set_union2(cartesian_product2(esk3_0,esk4_0),singleton(ordered_pair(esk1_0,esk2_0))) = cartesian_product2(esk3_0,esk4_0)
| in(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,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) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_40,negated_conjecture,
( set_union2(cartesian_product2(esk3_0,esk4_0),singleton(ordered_pair(esk1_0,esk2_0))) = cartesian_product2(esk3_0,esk4_0)
| in(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_41,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_42,lemma,
! [X51] : singleton(X51) != empty_set,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_43,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( in(esk5_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,negated_conjecture,
( set_union2(cartesian_product2(esk3_0,esk4_0),singleton(ordered_pair(esk1_0,esk2_0))) = cartesian_product2(esk3_0,esk4_0)
| in(ordered_pair(X1,esk2_0),cartesian_product2(X2,esk4_0))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( set_union2(cartesian_product2(esk3_0,esk4_0),singleton(ordered_pair(esk1_0,esk2_0))) = cartesian_product2(esk3_0,esk4_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_38]) ).
cnf(c_0_47,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_48,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( X1 = empty_set
| in(esk5_1(X1),set_union2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
set_union2(cartesian_product2(esk3_0,esk4_0),singleton(ordered_pair(esk1_0,esk2_0))) = cartesian_product2(esk3_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_40]),c_0_46]) ).
cnf(c_0_51,plain,
esk5_1(singleton(X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_44]),c_0_48]) ).
cnf(c_0_52,plain,
( X1 = ordered_pair(esk8_4(X2,X3,X4,X1),esk9_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_53,negated_conjecture,
in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_48]) ).
cnf(c_0_54,plain,
( ordered_pair(esk8_4(X1,X2,cartesian_product2(X1,X2),X3),esk9_4(X1,X2,cartesian_product2(X1,X2),X3)) = X3
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_52]) ).
fof(c_0_55,lemma,
! [X47,X48,X49,X50] :
( ( X47 = X49
| ordered_pair(X47,X48) != ordered_pair(X49,X50) )
& ( X48 = X50
| ordered_pair(X47,X48) != ordered_pair(X49,X50) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])])]) ).
cnf(c_0_56,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_53])]) ).
cnf(c_0_57,negated_conjecture,
( ordered_pair(esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0))) = ordered_pair(esk1_0,esk2_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_26]) ).
cnf(c_0_58,negated_conjecture,
( ordered_pair(esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0))) = ordered_pair(esk1_0,esk2_0)
| in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_24]) ).
cnf(c_0_59,plain,
( in(esk8_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_60,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
ordered_pair(esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0))) = ordered_pair(esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
fof(c_0_62,lemma,
! [X182,X183] :
( ~ subset(X182,X183)
| set_intersection2(X182,X183) = X182 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
fof(c_0_63,lemma,
! [X155,X156] : subset(X155,set_union2(X155,X156)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_64,plain,
( in(esk8_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_65,lemma,
( X1 = esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0))
| ordered_pair(X1,X2) != ordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_66,lemma,
! [X103,X104,X105] :
( ~ subset(X103,X104)
| in(X105,X103)
| subset(X103,set_difference(X104,singleton(X105))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])])]) ).
fof(c_0_67,plain,
! [X66] : subset(X66,X66),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_68,lemma,
! [X153,X154] :
( ~ subset(X153,X154)
| set_union2(X153,X154) = X154 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])]) ).
fof(c_0_69,lemma,
! [X131,X132] : subset(set_difference(X131,X132),X131),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_70,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
cnf(c_0_71,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,negated_conjecture,
in(esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_74,lemma,
esk8_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)) = esk1_0,
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_75,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_76,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_78,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_79,plain,
! [X119,X120,X121,X122,X123,X124,X125,X126] :
( ( in(X122,X119)
| ~ in(X122,X121)
| X121 != set_difference(X119,X120) )
& ( ~ in(X122,X120)
| ~ in(X122,X121)
| X121 != set_difference(X119,X120) )
& ( ~ in(X123,X119)
| in(X123,X120)
| in(X123,X121)
| X121 != set_difference(X119,X120) )
& ( ~ in(esk17_3(X124,X125,X126),X126)
| ~ in(esk17_3(X124,X125,X126),X124)
| in(esk17_3(X124,X125,X126),X125)
| X126 = set_difference(X124,X125) )
& ( in(esk17_3(X124,X125,X126),X124)
| in(esk17_3(X124,X125,X126),X126)
| X126 = set_difference(X124,X125) )
& ( ~ in(esk17_3(X124,X125,X126),X125)
| in(esk17_3(X124,X125,X126),X126)
| X126 = set_difference(X124,X125) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_70])])])])])])]) ).
cnf(c_0_80,plain,
( in(esk9_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_81,lemma,
! [X139,X140] : set_difference(X139,set_difference(X139,X140)) = set_intersection2(X139,X140),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_82,lemma,
! [X135,X136] : set_difference(set_union2(X135,X136),X136) = set_difference(X135,X136),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(c_0_83,plain,
! [X160,X161] : set_intersection2(X160,X161) = set_intersection2(X161,X160),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_84,lemma,
set_intersection2(X1,set_union2(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_85,negated_conjecture,
in(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_86,lemma,
( subset(X1,set_difference(X1,singleton(X2)))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_31]) ).
cnf(c_0_88,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( in(esk9_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_80]) ).
cnf(c_0_90,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_91,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_92,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_93,lemma,
set_intersection2(X1,set_union2(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_31]) ).
cnf(c_0_94,negated_conjecture,
~ in(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_85])]) ).
cnf(c_0_95,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_86]),c_0_87]) ).
cnf(c_0_96,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_88]) ).
cnf(c_0_97,negated_conjecture,
in(esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),esk4_0),
inference(spm,[status(thm)],[c_0_89,c_0_53]) ).
cnf(c_0_98,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93]) ).
cnf(c_0_99,lemma,
set_difference(esk4_0,singleton(esk2_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_91,c_0_31]) ).
cnf(c_0_101,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_102,negated_conjecture,
ordered_pair(esk1_0,esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0))) = ordered_pair(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_61,c_0_74]) ).
cnf(c_0_103,negated_conjecture,
~ in(esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),set_difference(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,lemma,
set_difference(singleton(esk2_0),esk4_0) = singleton(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_105,lemma,
( X1 = esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0))
| ordered_pair(X2,X1) != ordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_106,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_107,negated_conjecture,
~ in(esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)),singleton(esk2_0)),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,lemma,
esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)) = esk2_0,
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_109,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_106])]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_109])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU157+2 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n020.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 : 300
% 0.12/0.33 % DateTime : Fri Jun 21 12:06:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.iZ8TXEBtiY/E---3.1_27548.p
% 225.18/28.96 # Version: 3.2.0
% 225.18/28.96 # Preprocessing class: FSLSSMSSSSSNFFN.
% 225.18/28.96 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 225.18/28.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 225.18/28.96 # Starting new_bool_3 with 300s (1) cores
% 225.18/28.96 # Starting new_bool_1 with 300s (1) cores
% 225.18/28.96 # Starting sh5l with 300s (1) cores
% 225.18/28.96 # new_bool_3 with pid 27627 completed with status 0
% 225.18/28.96 # Result found by new_bool_3
% 225.18/28.96 # Preprocessing class: FSLSSMSSSSSNFFN.
% 225.18/28.96 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 225.18/28.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 225.18/28.96 # Starting new_bool_3 with 300s (1) cores
% 225.18/28.96 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 225.18/28.96 # Search class: FGHSM-FFMS32-SFFFFFNN
% 225.18/28.96 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 225.18/28.96 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 181s (1) cores
% 225.18/28.96 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 27630 completed with status 0
% 225.18/28.96 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 225.18/28.96 # Preprocessing class: FSLSSMSSSSSNFFN.
% 225.18/28.96 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 225.18/28.96 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 225.18/28.96 # Starting new_bool_3 with 300s (1) cores
% 225.18/28.96 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 225.18/28.96 # Search class: FGHSM-FFMS32-SFFFFFNN
% 225.18/28.96 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 225.18/28.96 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 181s (1) cores
% 225.18/28.96 # Preprocessing time : 0.003 s
% 225.18/28.96 # Presaturation interreduction done
% 225.18/28.96
% 225.18/28.96 # Proof found!
% 225.18/28.96 # SZS status Theorem
% 225.18/28.96 # SZS output start CNFRefutation
% See solution above
% 225.18/28.96 # Parsed axioms : 87
% 225.18/28.96 # Removed by relevancy pruning/SinE : 24
% 225.18/28.96 # Initial clauses : 109
% 225.18/28.96 # Removed in clause preprocessing : 0
% 225.18/28.96 # Initial clauses in saturation : 109
% 225.18/28.96 # Processed clauses : 75782
% 225.18/28.96 # ...of these trivial : 1918
% 225.18/28.96 # ...subsumed : 62229
% 225.18/28.96 # ...remaining for further processing : 11635
% 225.18/28.96 # Other redundant clauses eliminated : 457
% 225.18/28.96 # Clauses deleted for lack of memory : 0
% 225.18/28.96 # Backward-subsumed : 280
% 225.18/28.96 # Backward-rewritten : 344
% 225.18/28.96 # Generated clauses : 2025274
% 225.18/28.96 # ...of the previous two non-redundant : 1800392
% 225.18/28.96 # ...aggressively subsumed : 0
% 225.18/28.96 # Contextual simplify-reflections : 24
% 225.18/28.96 # Paramodulations : 2023072
% 225.18/28.96 # Factorizations : 1714
% 225.18/28.96 # NegExts : 0
% 225.18/28.96 # Equation resolutions : 476
% 225.18/28.96 # Disequality decompositions : 0
% 225.18/28.96 # Total rewrite steps : 686270
% 225.18/28.96 # ...of those cached : 627668
% 225.18/28.96 # Propositional unsat checks : 2
% 225.18/28.96 # Propositional check models : 0
% 225.18/28.96 # Propositional check unsatisfiable : 0
% 225.18/28.96 # Propositional clauses : 0
% 225.18/28.96 # Propositional clauses after purity: 0
% 225.18/28.96 # Propositional unsat core size : 0
% 225.18/28.96 # Propositional preprocessing time : 0.000
% 225.18/28.96 # Propositional encoding time : 2.731
% 225.18/28.96 # Propositional solver time : 1.613
% 225.18/28.96 # Success case prop preproc time : 0.000
% 225.18/28.96 # Success case prop encoding time : 0.000
% 225.18/28.96 # Success case prop solver time : 0.000
% 225.18/28.96 # Current number of processed clauses : 10870
% 225.18/28.96 # Positive orientable unit clauses : 2038
% 225.18/28.96 # Positive unorientable unit clauses: 4
% 225.18/28.96 # Negative unit clauses : 4308
% 225.18/28.96 # Non-unit-clauses : 4520
% 225.18/28.96 # Current number of unprocessed clauses: 1719860
% 225.18/28.96 # ...number of literals in the above : 5765464
% 225.18/28.96 # Current number of archived formulas : 0
% 225.18/28.96 # Current number of archived clauses : 742
% 225.18/28.96 # Clause-clause subsumption calls (NU) : 2002099
% 225.18/28.96 # Rec. Clause-clause subsumption calls : 530118
% 225.18/28.96 # Non-unit clause-clause subsumptions : 14680
% 225.18/28.96 # Unit Clause-clause subsumption calls : 1371768
% 225.18/28.96 # Rewrite failures with RHS unbound : 0
% 225.18/28.96 # BW rewrite match attempts : 58449
% 225.18/28.96 # BW rewrite match successes : 199
% 225.18/28.96 # Condensation attempts : 0
% 225.18/28.96 # Condensation successes : 0
% 225.18/28.96 # Termbank termtop insertions : 47205264
% 225.18/28.96 # Search garbage collected termcells : 1788
% 225.18/28.96
% 225.18/28.96 # -------------------------------------------------
% 225.18/28.96 # User time : 26.978 s
% 225.18/28.96 # System time : 1.069 s
% 225.18/28.96 # Total time : 28.047 s
% 225.18/28.96 # Maximum resident set size: 2104 pages
% 225.18/28.96
% 225.18/28.96 # -------------------------------------------------
% 225.18/28.96 # User time : 26.982 s
% 225.18/28.96 # System time : 1.070 s
% 225.18/28.96 # Total time : 28.052 s
% 225.18/28.96 # Maximum resident set size: 1756 pages
% 225.18/28.96 % E---3.1 exiting
% 225.31/28.96 % E exiting
%------------------------------------------------------------------------------