TSTP Solution File: SEU291+2 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SEU291+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 19:31:19 EDT 2023
% Result : Theorem 5.95s 1.26s
% Output : CNFRefutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 98 ( 36 unt; 0 def)
% Number of atoms : 258 ( 83 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 258 ( 98 ~; 99 |; 35 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 155 ( 13 sgn; 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t9_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t9_funct_2) ).
fof(t16_relset_1,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(X1,X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t16_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',redefinition_m2_relset_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',d1_zfmisc_1) ).
fof(t12_relset_1,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t12_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',redefinition_k4_relset_1) ).
fof(d1_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',d1_funct_2) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t1_subset) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',l32_xboole_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t5_subset) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',d1_xboole_0) ).
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',d1_relset_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t3_boole) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t3_subset) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t2_xboole_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',cc1_relset_1) ).
fof(t64_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t64_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',fc1_xboole_0) ).
fof(t60_relat_1,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p',t60_relat_1) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t9_funct_2]) ).
fof(c_0_20,lemma,
! [X42,X43,X44,X45] :
( ~ relation_of2_as_subset(X45,X44,X42)
| ~ subset(X42,X43)
| relation_of2_as_subset(X45,X44,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_relset_1])]) ).
fof(c_0_21,negated_conjecture,
( function(esk4_0)
& quasi_total(esk4_0,esk1_0,esk2_0)
& relation_of2_as_subset(esk4_0,esk1_0,esk2_0)
& subset(esk2_0,esk3_0)
& ( esk2_0 != empty_set
| esk1_0 = empty_set )
& ( ~ function(esk4_0)
| ~ quasi_total(esk4_0,esk1_0,esk3_0)
| ~ relation_of2_as_subset(esk4_0,esk1_0,esk3_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_22,lemma,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
relation_of2_as_subset(esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X32,X33,X34] :
( ( ~ relation_of2_as_subset(X34,X32,X33)
| relation_of2(X34,X32,X33) )
& ( ~ relation_of2(X34,X32,X33)
| relation_of2_as_subset(X34,X32,X33) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_25,negated_conjecture,
( relation_of2_as_subset(esk4_0,esk1_0,X1)
| ~ subset(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X259,X260,X261,X262,X263,X264] :
( ( ~ in(X261,X260)
| subset(X261,X259)
| X260 != powerset(X259) )
& ( ~ subset(X262,X259)
| in(X262,X260)
| X260 != powerset(X259) )
& ( ~ in(esk72_2(X263,X264),X264)
| ~ subset(esk72_2(X263,X264),X263)
| X264 = powerset(X263) )
& ( in(esk72_2(X263,X264),X264)
| subset(esk72_2(X263,X264),X263)
| X264 = powerset(X263) ) ),
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_zfmisc_1])])])])])]) ).
fof(c_0_28,lemma,
! [X35,X36,X37] :
( ( subset(relation_dom(X37),X35)
| ~ relation_of2_as_subset(X37,X35,X36) )
& ( subset(relation_rng(X37),X36)
| ~ relation_of2_as_subset(X37,X35,X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).
fof(c_0_29,plain,
! [X346,X347,X348] :
( ~ relation_of2(X348,X346,X347)
| relation_dom_as_subset(X346,X347,X348) = relation_dom(X348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
cnf(c_0_30,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
relation_of2_as_subset(esk4_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( ~ function(esk4_0)
| ~ quasi_total(esk4_0,esk1_0,esk3_0)
| ~ relation_of2_as_subset(esk4_0,esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,negated_conjecture,
function(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,lemma,
( subset(relation_rng(X1),X2)
| ~ relation_of2_as_subset(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,plain,
! [X23,X24,X25] :
( ( ~ quasi_total(X25,X23,X24)
| X23 = relation_dom_as_subset(X23,X24,X25)
| X24 = empty_set
| ~ relation_of2_as_subset(X25,X23,X24) )
& ( X23 != relation_dom_as_subset(X23,X24,X25)
| quasi_total(X25,X23,X24)
| X24 = empty_set
| ~ relation_of2_as_subset(X25,X23,X24) )
& ( ~ quasi_total(X25,X23,X24)
| X23 = relation_dom_as_subset(X23,X24,X25)
| X23 != empty_set
| ~ relation_of2_as_subset(X25,X23,X24) )
& ( X23 != relation_dom_as_subset(X23,X24,X25)
| quasi_total(X25,X23,X24)
| X23 != empty_set
| ~ relation_of2_as_subset(X25,X23,X24) )
& ( ~ quasi_total(X25,X23,X24)
| X25 = empty_set
| X23 = empty_set
| X24 != empty_set
| ~ relation_of2_as_subset(X25,X23,X24) )
& ( X25 != empty_set
| quasi_total(X25,X23,X24)
| X23 = empty_set
| X24 != empty_set
| ~ relation_of2_as_subset(X25,X23,X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_37,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
relation_of2(esk4_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( ~ quasi_total(esk4_0,esk1_0,esk3_0)
| ~ relation_of2_as_subset(esk4_0,esk1_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
relation_of2(esk4_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
fof(c_0_41,plain,
! [X372,X373] :
( ~ in(X372,X373)
| element(X372,X373) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_42,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
subset(relation_rng(esk4_0),esk2_0),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
fof(c_0_44,lemma,
! [X235,X236] :
( ( set_difference(X235,X236) != empty_set
| subset(X235,X236) )
& ( ~ subset(X235,X236)
| set_difference(X235,X236) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_45,plain,
( quasi_total(X3,X1,X2)
| X2 = empty_set
| X1 != relation_dom_as_subset(X1,X2,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
relation_dom_as_subset(esk1_0,esk3_0,esk4_0) = relation_dom(esk4_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
~ quasi_total(esk4_0,esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_31])]) ).
cnf(c_0_48,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| X3 = empty_set
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,negated_conjecture,
quasi_total(esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_50,negated_conjecture,
relation_dom_as_subset(esk1_0,esk2_0,esk4_0) = relation_dom(esk4_0),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
fof(c_0_51,plain,
! [X388,X389,X390] :
( ~ in(X388,X389)
| ~ element(X389,powerset(X390))
| ~ empty(X390) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_52,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,negated_conjecture,
in(relation_rng(esk4_0),powerset(esk2_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_54,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_55,plain,
! [X393,X394,X395] :
( ( ~ relation_of2(X395,X393,X394)
| subset(X395,cartesian_product2(X393,X394)) )
& ( ~ subset(X395,cartesian_product2(X393,X394))
| relation_of2(X395,X393,X394) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])]) ).
cnf(c_0_56,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,negated_conjecture,
( esk3_0 = empty_set
| relation_dom(esk4_0) != esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_31])]),c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( relation_dom(esk4_0) = esk1_0
| esk2_0 = empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_23])]) ).
fof(c_0_59,plain,
! [X248] : set_difference(X248,empty_set) = X248,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_60,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,negated_conjecture,
element(relation_rng(esk4_0),powerset(esk2_0)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_62,plain,
! [X228,X229,X230] :
( ( X228 != empty_set
| ~ in(X229,X228) )
& ( in(esk69_1(X230),X230)
| X230 = 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_54])])])])]) ).
fof(c_0_63,plain,
! [X320,X321] :
( ( ~ element(X320,powerset(X321))
| subset(X320,X321) )
& ( ~ subset(X320,X321)
| element(X320,powerset(X321)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_64,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_65,lemma,
! [X243] : subset(empty_set,X243),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_66,negated_conjecture,
set_difference(esk2_0,esk3_0) = empty_set,
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_67,negated_conjecture,
( esk2_0 = empty_set
| esk3_0 = empty_set ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( ~ empty(esk2_0)
| ~ in(X1,relation_rng(esk4_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
( in(esk69_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_71,plain,
! [X349,X350,X351] :
( ~ element(X351,powerset(cartesian_product2(X349,X350)))
| relation(X351) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_72,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,negated_conjecture,
subset(esk4_0,cartesian_product2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_64,c_0_40]) ).
cnf(c_0_74,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_75,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( esk1_0 = empty_set
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_77,negated_conjecture,
esk2_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
fof(c_0_78,lemma,
! [X254] :
( ( relation_dom(X254) != empty_set
| X254 = empty_set
| ~ relation(X254) )
& ( relation_rng(X254) != empty_set
| X254 = empty_set
| ~ relation(X254) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])]) ).
cnf(c_0_79,negated_conjecture,
( relation_rng(esk4_0) = empty_set
| ~ empty(esk2_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_81,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,negated_conjecture,
element(esk4_0,powerset(cartesian_product2(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( quasi_total(X3,X1,X2)
| X1 != relation_dom_as_subset(X1,X2,X3)
| X1 != empty_set
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_84,lemma,
relation_of2(empty_set,X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_85,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]) ).
cnf(c_0_86,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_87,negated_conjecture,
esk1_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_88,lemma,
( X1 = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,negated_conjecture,
relation_rng(esk4_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_77]),c_0_80])]) ).
cnf(c_0_90,negated_conjecture,
relation(esk4_0),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,plain,
( quasi_total(X1,empty_set,X2)
| relation_dom_as_subset(empty_set,X2,X1) != empty_set
| ~ relation_of2_as_subset(X1,empty_set,X2) ),
inference(er,[status(thm)],[c_0_83]) ).
cnf(c_0_92,lemma,
relation_dom_as_subset(X1,X2,empty_set) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_84]),c_0_85]) ).
cnf(c_0_93,lemma,
relation_of2_as_subset(empty_set,X1,X2),
inference(spm,[status(thm)],[c_0_86,c_0_84]) ).
cnf(c_0_94,negated_conjecture,
~ quasi_total(esk4_0,empty_set,esk3_0),
inference(rw,[status(thm)],[c_0_47,c_0_87]) ).
cnf(c_0_95,lemma,
esk4_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_96,lemma,
quasi_total(empty_set,empty_set,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU291+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Oct 2 09:14:39 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.45 Running first-order model finding
% 0.15/0.45 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.8oKoluCpdp/E---3.1_11860.p
% 5.95/1.26 # Version: 3.1pre001
% 5.95/1.26 # Preprocessing class: FSLSSMSSSSSNFFN.
% 5.95/1.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.95/1.26 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.95/1.26 # Starting new_bool_3 with 300s (1) cores
% 5.95/1.26 # Starting new_bool_1 with 300s (1) cores
% 5.95/1.26 # Starting sh5l with 300s (1) cores
% 5.95/1.26 # sh5l with pid 11940 completed with status 0
% 5.95/1.26 # Result found by sh5l
% 5.95/1.26 # Preprocessing class: FSLSSMSSSSSNFFN.
% 5.95/1.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.95/1.26 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.95/1.26 # Starting new_bool_3 with 300s (1) cores
% 5.95/1.26 # Starting new_bool_1 with 300s (1) cores
% 5.95/1.26 # Starting sh5l with 300s (1) cores
% 5.95/1.26 # SinE strategy is gf500_gu_R04_F100_L20000
% 5.95/1.26 # Search class: FGHSM-SMLM32-MFFFFFNN
% 5.95/1.26 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 5.95/1.26 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 23s (1) cores
% 5.95/1.26 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 11943 completed with status 0
% 5.95/1.26 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 5.95/1.26 # Preprocessing class: FSLSSMSSSSSNFFN.
% 5.95/1.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.95/1.26 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.95/1.26 # Starting new_bool_3 with 300s (1) cores
% 5.95/1.26 # Starting new_bool_1 with 300s (1) cores
% 5.95/1.26 # Starting sh5l with 300s (1) cores
% 5.95/1.26 # SinE strategy is gf500_gu_R04_F100_L20000
% 5.95/1.26 # Search class: FGHSM-SMLM32-MFFFFFNN
% 5.95/1.26 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 5.95/1.26 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 23s (1) cores
% 5.95/1.26 # Preprocessing time : 0.018 s
% 5.95/1.26 # Presaturation interreduction done
% 5.95/1.26
% 5.95/1.26 # Proof found!
% 5.95/1.26 # SZS status Theorem
% 5.95/1.26 # SZS output start CNFRefutation
% See solution above
% 5.95/1.26 # Parsed axioms : 384
% 5.95/1.26 # Removed by relevancy pruning/SinE : 29
% 5.95/1.26 # Initial clauses : 1402
% 5.95/1.26 # Removed in clause preprocessing : 4
% 5.95/1.26 # Initial clauses in saturation : 1398
% 5.95/1.26 # Processed clauses : 4951
% 5.95/1.26 # ...of these trivial : 115
% 5.95/1.26 # ...subsumed : 1292
% 5.95/1.26 # ...remaining for further processing : 3544
% 5.95/1.26 # Other redundant clauses eliminated : 443
% 5.95/1.26 # Clauses deleted for lack of memory : 0
% 5.95/1.26 # Backward-subsumed : 7
% 5.95/1.26 # Backward-rewritten : 773
% 5.95/1.26 # Generated clauses : 12755
% 5.95/1.26 # ...of the previous two non-redundant : 11579
% 5.95/1.26 # ...aggressively subsumed : 0
% 5.95/1.26 # Contextual simplify-reflections : 214
% 5.95/1.26 # Paramodulations : 12410
% 5.95/1.26 # Factorizations : 2
% 5.95/1.26 # NegExts : 0
% 5.95/1.26 # Equation resolutions : 446
% 5.95/1.26 # Total rewrite steps : 4398
% 5.95/1.26 # Propositional unsat checks : 0
% 5.95/1.26 # Propositional check models : 0
% 5.95/1.26 # Propositional check unsatisfiable : 0
% 5.95/1.26 # Propositional clauses : 0
% 5.95/1.26 # Propositional clauses after purity: 0
% 5.95/1.26 # Propositional unsat core size : 0
% 5.95/1.26 # Propositional preprocessing time : 0.000
% 5.95/1.26 # Propositional encoding time : 0.000
% 5.95/1.26 # Propositional solver time : 0.000
% 5.95/1.26 # Success case prop preproc time : 0.000
% 5.95/1.26 # Success case prop encoding time : 0.000
% 5.95/1.26 # Success case prop solver time : 0.000
% 5.95/1.26 # Current number of processed clauses : 1145
% 5.95/1.26 # Positive orientable unit clauses : 275
% 5.95/1.26 # Positive unorientable unit clauses: 4
% 5.95/1.26 # Negative unit clauses : 246
% 5.95/1.26 # Non-unit-clauses : 620
% 5.95/1.26 # Current number of unprocessed clauses: 9231
% 5.95/1.26 # ...number of literals in the above : 20856
% 5.95/1.26 # Current number of archived formulas : 0
% 5.95/1.26 # Current number of archived clauses : 2082
% 5.95/1.26 # Clause-clause subsumption calls (NU) : 1159970
% 5.95/1.26 # Rec. Clause-clause subsumption calls : 163954
% 5.95/1.26 # Non-unit clause-clause subsumptions : 686
% 5.95/1.26 # Unit Clause-clause subsumption calls : 24228
% 5.95/1.26 # Rewrite failures with RHS unbound : 0
% 5.95/1.26 # BW rewrite match attempts : 661
% 5.95/1.26 # BW rewrite match successes : 112
% 5.95/1.26 # Condensation attempts : 0
% 5.95/1.26 # Condensation successes : 0
% 5.95/1.26 # Termbank termtop insertions : 220872
% 5.95/1.26
% 5.95/1.26 # -------------------------------------------------
% 5.95/1.26 # User time : 0.750 s
% 5.95/1.26 # System time : 0.024 s
% 5.95/1.26 # Total time : 0.774 s
% 5.95/1.26 # Maximum resident set size: 5744 pages
% 5.95/1.26
% 5.95/1.26 # -------------------------------------------------
% 5.95/1.26 # User time : 0.759 s
% 5.95/1.26 # System time : 0.027 s
% 5.95/1.26 # Total time : 0.786 s
% 5.95/1.26 # Maximum resident set size: 2172 pages
% 5.95/1.26 % E---3.1 exiting
%------------------------------------------------------------------------------