TSTP Solution File: SEU157+2 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SEU157+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:24:59 EDT 2023
% Result : Theorem 348.15s 44.50s
% Output : CNFRefutation 348.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 110 ( 46 unt; 0 def)
% Number of atoms : 284 ( 120 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 279 ( 105 ~; 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 : 235 ( 19 sgn; 123 !; 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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',l55_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',d2_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',d2_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',d1_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',d1_tarski) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',t33_zfmisc_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',t28_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',l3_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',reflexivity_r1_tarski) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',t12_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p',t40_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.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(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(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(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(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(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])])])])])]) ).
cnf(c_0_34,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X13,X14,X15] :
( ( X13 != empty_set
| ~ in(X14,X13) )
& ( in(esk5_1(X15),X15)
| X15 = empty_set ) ),
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_36,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_37,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_38,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_39,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_40,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_41,lemma,
! [X51] : singleton(X51) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_42,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( in(esk5_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,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_36,c_0_37]) ).
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(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_37]) ).
cnf(c_0_46,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_47,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( X1 = empty_set
| in(esk5_1(X1),set_union2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,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_44,c_0_39]),c_0_45]) ).
cnf(c_0_50,plain,
esk5_1(singleton(X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_47]) ).
cnf(c_0_51,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_52,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_48,c_0_49]),c_0_50]),c_0_47]) ).
cnf(c_0_53,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_51]) ).
fof(c_0_54,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
cnf(c_0_55,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_52])]) ).
cnf(c_0_56,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_53,c_0_26]) ).
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(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_24]) ).
cnf(c_0_58,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_59,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,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_55,c_0_56]),c_0_57]) ).
fof(c_0_61,lemma,
! [X182,X183] :
( ~ subset(X182,X183)
| set_intersection2(X182,X183) = X182 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_62,lemma,
! [X155,X156] : subset(X155,set_union2(X155,X156)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_63,plain,
( in(esk8_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_64,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_59,c_0_60]) ).
fof(c_0_65,lemma,
! [X103,X104,X105] :
( ~ subset(X103,X104)
| in(X105,X103)
| subset(X103,set_difference(X104,singleton(X105))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(c_0_66,plain,
! [X66] : subset(X66,X66),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_67,lemma,
! [X153,X154] :
( ~ subset(X153,X154)
| set_union2(X153,X154) = X154 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_68,lemma,
! [X131,X132] : subset(set_difference(X131,X132),X131),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_69,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_70,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,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_63,c_0_52]) ).
cnf(c_0_73,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_64]) ).
cnf(c_0_74,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_76,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_78,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(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_69])])])])])]) ).
cnf(c_0_79,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_80,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_81,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_82,plain,
! [X160,X161] : set_intersection2(X160,X161) = set_intersection2(X161,X160),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_83,lemma,
set_intersection2(X1,set_union2(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_84,negated_conjecture,
in(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_85,lemma,
( subset(X1,set_difference(X1,singleton(X2)))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_31]) ).
cnf(c_0_87,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_88,plain,
( in(esk9_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_89,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_90,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_91,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_92,lemma,
set_intersection2(X1,set_union2(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_83,c_0_31]) ).
cnf(c_0_93,negated_conjecture,
~ in(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_84])]) ).
cnf(c_0_94,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_85]),c_0_86]) ).
cnf(c_0_95,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_96,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_88,c_0_52]) ).
cnf(c_0_97,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_89,c_0_90]),c_0_91]),c_0_92]) ).
cnf(c_0_98,lemma,
set_difference(esk4_0,singleton(esk2_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_90,c_0_31]) ).
cnf(c_0_100,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_101,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_60,c_0_73]) ).
cnf(c_0_102,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_95,c_0_96]) ).
cnf(c_0_103,lemma,
set_difference(singleton(esk2_0),esk4_0) = singleton(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_104,lemma,
( esk9_4(esk3_0,esk4_0,cartesian_product2(esk3_0,esk4_0),ordered_pair(esk1_0,esk2_0)) = X1
| ordered_pair(esk1_0,esk2_0) != ordered_pair(X2,X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_106,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_102,c_0_103]) ).
cnf(c_0_107,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_104]) ).
cnf(c_0_108,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_105])]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107]),c_0_108])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU157+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 2400
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Oct 2 08:20:53 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.whiWCA7rNQ/E---3.1_22912.p
% 348.15/44.50 # Version: 3.1pre001
% 348.15/44.50 # Preprocessing class: FSLSSMSSSSSNFFN.
% 348.15/44.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 348.15/44.50 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 348.15/44.50 # Starting new_bool_3 with 300s (1) cores
% 348.15/44.50 # Starting new_bool_1 with 300s (1) cores
% 348.15/44.50 # Starting sh5l with 300s (1) cores
% 348.15/44.50 # new_bool_1 with pid 22992 completed with status 0
% 348.15/44.50 # Result found by new_bool_1
% 348.15/44.50 # Preprocessing class: FSLSSMSSSSSNFFN.
% 348.15/44.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 348.15/44.50 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 348.15/44.50 # Starting new_bool_3 with 300s (1) cores
% 348.15/44.50 # Starting new_bool_1 with 300s (1) cores
% 348.15/44.50 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 348.15/44.50 # Search class: FGHSM-FFMS32-SFFFFFNN
% 348.15/44.50 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 348.15/44.50 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 181s (1) cores
% 348.15/44.50 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 22995 completed with status 0
% 348.15/44.50 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 348.15/44.50 # Preprocessing class: FSLSSMSSSSSNFFN.
% 348.15/44.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 348.15/44.50 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 348.15/44.50 # Starting new_bool_3 with 300s (1) cores
% 348.15/44.50 # Starting new_bool_1 with 300s (1) cores
% 348.15/44.50 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 348.15/44.50 # Search class: FGHSM-FFMS32-SFFFFFNN
% 348.15/44.50 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 348.15/44.50 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 181s (1) cores
% 348.15/44.50 # Preprocessing time : 0.002 s
% 348.15/44.50 # Presaturation interreduction done
% 348.15/44.50
% 348.15/44.50 # Proof found!
% 348.15/44.50 # SZS status Theorem
% 348.15/44.50 # SZS output start CNFRefutation
% See solution above
% 348.15/44.50 # Parsed axioms : 87
% 348.15/44.50 # Removed by relevancy pruning/SinE : 24
% 348.15/44.50 # Initial clauses : 109
% 348.15/44.50 # Removed in clause preprocessing : 0
% 348.15/44.50 # Initial clauses in saturation : 109
% 348.15/44.50 # Processed clauses : 75606
% 348.15/44.50 # ...of these trivial : 1926
% 348.15/44.50 # ...subsumed : 62056
% 348.15/44.50 # ...remaining for further processing : 11624
% 348.15/44.50 # Other redundant clauses eliminated : 457
% 348.15/44.50 # Clauses deleted for lack of memory : 0
% 348.15/44.50 # Backward-subsumed : 278
% 348.15/44.50 # Backward-rewritten : 342
% 348.15/44.50 # Generated clauses : 2023455
% 348.15/44.50 # ...of the previous two non-redundant : 1798269
% 348.15/44.50 # ...aggressively subsumed : 0
% 348.15/44.50 # Contextual simplify-reflections : 24
% 348.15/44.50 # Paramodulations : 2021259
% 348.15/44.50 # Factorizations : 1708
% 348.15/44.50 # NegExts : 0
% 348.15/44.50 # Equation resolutions : 476
% 348.15/44.50 # Total rewrite steps : 687111
% 348.15/44.50 # Propositional unsat checks : 2
% 348.15/44.50 # Propositional check models : 0
% 348.15/44.50 # Propositional check unsatisfiable : 0
% 348.15/44.50 # Propositional clauses : 0
% 348.15/44.50 # Propositional clauses after purity: 0
% 348.15/44.50 # Propositional unsat core size : 0
% 348.15/44.50 # Propositional preprocessing time : 0.000
% 348.15/44.50 # Propositional encoding time : 3.980
% 348.15/44.50 # Propositional solver time : 2.171
% 348.15/44.50 # Success case prop preproc time : 0.000
% 348.15/44.50 # Success case prop encoding time : 0.000
% 348.15/44.50 # Success case prop solver time : 0.000
% 348.15/44.50 # Current number of processed clauses : 10863
% 348.15/44.50 # Positive orientable unit clauses : 2042
% 348.15/44.50 # Positive unorientable unit clauses: 4
% 348.15/44.50 # Negative unit clauses : 4300
% 348.15/44.50 # Non-unit-clauses : 4517
% 348.15/44.50 # Current number of unprocessed clauses: 1717917
% 348.15/44.50 # ...number of literals in the above : 5759517
% 348.15/44.50 # Current number of archived formulas : 0
% 348.15/44.50 # Current number of archived clauses : 738
% 348.15/44.50 # Clause-clause subsumption calls (NU) : 1991331
% 348.15/44.50 # Rec. Clause-clause subsumption calls : 528410
% 348.15/44.50 # Non-unit clause-clause subsumptions : 14622
% 348.15/44.50 # Unit Clause-clause subsumption calls : 1346423
% 348.15/44.50 # Rewrite failures with RHS unbound : 0
% 348.15/44.50 # BW rewrite match attempts : 58712
% 348.15/44.50 # BW rewrite match successes : 197
% 348.15/44.50 # Condensation attempts : 0
% 348.15/44.50 # Condensation successes : 0
% 348.15/44.50 # Termbank termtop insertions : 47188092
% 348.15/44.50
% 348.15/44.50 # -------------------------------------------------
% 348.15/44.50 # User time : 42.197 s
% 348.15/44.50 # System time : 1.415 s
% 348.15/44.50 # Total time : 43.612 s
% 348.15/44.50 # Maximum resident set size: 2104 pages
% 348.15/44.50
% 348.15/44.50 # -------------------------------------------------
% 348.15/44.50 # User time : 42.202 s
% 348.15/44.50 # System time : 1.415 s
% 348.15/44.50 # Total time : 43.618 s
% 348.15/44.50 # Maximum resident set size: 1748 pages
% 348.15/44.50 % E---3.1 exiting
% 348.15/44.50 % E---3.1 exiting
%------------------------------------------------------------------------------