TSTP Solution File: SEU544^1 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU544^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.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 15:08:51 EDT 2024
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 64
% Syntax : Number of formulae : 95 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 725 ( 123 equ; 0 cnn)
% Maximal formula atoms : 201 ( 7 avg)
% Number of connectives : 2504 ( 210 ~; 194 |; 177 &;1494 @)
% ( 94 <=>; 335 =>; 0 <=; 0 <~>)
% Maximal formula depth : 248 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 106 usr; 66 con; 0-3 aty)
% Number of variables : 600 ( 36 ^ 487 !; 77 ?; 600 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
epred1_0: $o ).
thf(decl_95,type,
esk1_2: $i > $i > $i ).
thf(decl_96,type,
esk2_2: $i > $i > $i ).
thf(decl_97,type,
esk3_2: $i > $i > $i ).
thf(decl_98,type,
esk4_1: $i > $i ).
thf(decl_99,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_100,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_101,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_102,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_103,type,
esk9_1: $i > $i ).
thf(decl_104,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_105,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_106,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_107,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_108,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_109,type,
esk15_2: $i > $i > $i ).
thf(decl_110,type,
esk16_2: $i > $i > $i ).
thf(decl_111,type,
esk17_1: $i > $i ).
thf(decl_112,type,
esk18_1: $i > $i ).
thf(decl_113,type,
esk19_1: $i > $i ).
thf(decl_114,type,
esk20_2: $i > $i > $i ).
thf(decl_115,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_116,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_117,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_118,type,
esk24_1: $i > $i ).
thf(decl_119,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_120,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_121,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_122,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_123,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_124,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_125,type,
epred2_0: $i > $o ).
thf(decl_126,type,
esk31_0: $i ).
thf(decl_127,type,
esk32_1: $i > $i ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',exuE2) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',exu) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',exuE1) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',replAx) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',nonemptyI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',descrp) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',dsetconstrI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptyE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',dsetconstrER) ).
thf(exuI1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',exuI1) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',prop2setI) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptysetE) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',notdexE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptysetimpfalse) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',notdallE) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',noeltsimpempty) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',upairsetIL) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',upairsetE) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',quantDeMorgan2) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mNAnA3Z5SV/E---3.1_18165.p',setextAx) ).
thf(c_0_63,plain,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE2]) ).
thf(c_0_64,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_65,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_66,plain,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE1]) ).
thf(c_0_67,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_68,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_69,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_70,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_71,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_72,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X194: $i] :
( ( X1 @ X194 )
& ! [X195: $i] :
( ( X1 @ X195 )
=> ( X194 = X195 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_73,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X192: $i] :
( ( X1 @ X192 )
& ! [X193: $i] :
( ( X1 @ X193 )
=> ( X192 = X193 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_65,c_0_64]) ).
thf(c_0_74,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X190: $i] :
( ( X1 @ X190 )
& ! [X191: $i] :
( ( X1 @ X191 )
=> ( X190 = X191 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_66,c_0_64]) ).
thf(c_0_75,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X186: $i] :
( ( X6 @ X2 @ X186 )
& ! [X187: $i] :
( ( X6 @ X2 @ X187 )
=> ( X186 = X187 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_67,c_0_64]) ).
thf(c_0_76,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_77,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_78,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_68]) ).
thf(c_0_79,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_69,c_0_68]) ).
thf(c_0_80,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_68]) ).
thf(c_0_81,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_82,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_68]) ).
thf(c_0_83,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_84,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_85,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X188: $i] :
( ( X1 @ X188 )
& ! [X189: $i] :
( ( X1 @ X189 )
=> ( X188 = X189 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_70,c_0_64]) ).
thf(c_0_86,plain,
( epred1_0
<=> ! [X225: $i] :
? [X226: $i] :
( ! [X227: $i] :
( ( in @ X227 @ X226 )
=> ! [X228: $i] :
( ( in @ X228 @ X227 )
=> ( in @ X228 @ X225 ) ) )
& ! [X229: $i,X230: $i] :
( ( ( in @ X229 @ X225 )
& ( in @ X230 @ X225 ) )
=> ( ! [X231: $i] :
( ( in @ X231 @ X226 )
=> ( ( in @ X229 @ X231 )
<=> ( in @ X230 @ X231 ) ) )
=> ( X229 = X230 ) ) )
& ! [X232: $i,X233: $i] :
( ( ( in @ X232 @ X226 )
& ( in @ X233 @ X226 ) )
=> ( ! [X234: $i] :
( ( in @ X234 @ X232 )
=> ( in @ X234 @ X233 ) )
| ! [X235: $i] :
( ( in @ X235 @ X233 )
=> ( in @ X235 @ X232 ) ) ) )
& ! [X236: $i] :
( ( ! [X237: $i] :
( ( in @ X237 @ X236 )
=> ( in @ X237 @ X225 ) )
& ? [X238: $i] : ( in @ X238 @ X236 ) )
=> ? [X239: $i,X240: $i] :
( ( in @ X239 @ X226 )
& ( in @ X240 @ X236 )
& ~ ? [X241: $i] :
( ( in @ X241 @ X239 )
& ( in @ X241 @ X236 ) )
& ! [X242: $i] :
( ( in @ X242 @ X226 )
=> ( ! [X243: $i] :
( ( in @ X243 @ X242 )
=> ( in @ X243 @ X239 ) )
| ( in @ X240 @ X242 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_87,negated_conjecture,
~ ( ! [X196: $i,X197: $i] :
( ! [X198: $i] :
( ( in @ X198 @ X196 )
<=> ( in @ X198 @ X197 ) )
=> ( X196 = X197 ) )
=> ( ! [X199: $i] :
~ ( in @ X199 @ emptyset )
=> ( ! [X200: $i,X201: $i,X202: $i] :
( ( in @ X202 @ ( setadjoin @ X200 @ X201 ) )
<=> ( ( X202 = X200 )
| ( in @ X202 @ X201 ) ) )
=> ( ! [X203: $i,X204: $i] :
( ( in @ X204 @ ( powerset @ X203 ) )
<=> ! [X205: $i] :
( ( in @ X205 @ X204 )
=> ( in @ X205 @ X203 ) ) )
=> ( ! [X206: $i,X207: $i] :
( ( in @ X207 @ ( setunion @ X206 ) )
<=> ? [X208: $i] :
( ( in @ X207 @ X208 )
& ( in @ X208 @ X206 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X209: $i] :
( ( in @ X209 @ omega )
=> ( in @ ( setadjoin @ X209 @ X209 ) @ omega ) )
=> ( ! [X210: $i] :
( ( ( in @ emptyset @ X210 )
& ! [X211: $i] :
( ( ( in @ X211 @ omega )
& ( in @ X211 @ X210 ) )
=> ( in @ ( setadjoin @ X211 @ X211 ) @ X210 ) ) )
=> ! [X212: $i] :
( ( in @ X212 @ omega )
=> ( in @ X212 @ X210 ) ) )
=> ( ! [X213: $i > $i > $o,X214: $i] :
( ! [X215: $i] :
( ( in @ X215 @ X214 )
=> ? [X216: $i] :
( ( X213 @ X215 @ X216 )
& ! [X217: $i] :
( ( X213 @ X215 @ X217 )
=> ( X216 = X217 ) ) ) )
=> ? [X218: $i] :
! [X219: $i] :
( ( in @ X219 @ X218 )
<=> ? [X220: $i] :
( ( in @ X220 @ X214 )
& ( X213 @ X220 @ X219 ) ) ) )
=> ( ! [X221: $i] :
( ? [X222: $i] : ( in @ X222 @ X221 )
=> ? [X223: $i] :
( ( in @ X223 @ X221 )
& ~ ? [X224: $i] :
( ( in @ X224 @ X223 )
& ( in @ X224 @ X221 ) ) ) )
=> ( epred1_0
=> ( ! [X244: $i > $o] :
( ? [X245: $i] :
( ( X244 @ X245 )
& ! [X246: $i] :
( ( X244 @ X246 )
=> ( X245 = X246 ) ) )
=> ( X244
@ ( descr
@ ^ [Z0: $i] : ( X244 @ Z0 ) ) ) )
=> ( ! [X247: $i,X248: $i > $o,X249: $i] :
( ( in @ X249 @ X247 )
=> ( ( X248 @ X249 )
=> ( in @ X249 @ ( dsetconstr @ X247 @ X248 ) ) ) )
=> ( ! [X250: $i,X251: $i > $o,X252: $i] :
( ( in @ X252 @ ( dsetconstr @ X250 @ X251 ) )
=> ( in @ X252 @ X250 ) )
=> ( ! [X253: $i,X254: $i > $o,X255: $i] :
( ( in @ X255 @ ( dsetconstr @ X253 @ X254 ) )
=> ( X254 @ X255 ) )
=> ( ! [X256: $i > $o] :
( ? [X257: $i] :
( ( X256 @ X257 )
& ! [X258: $i] :
( ( X256 @ X258 )
=> ( X257 = X258 ) ) )
=> ? [X259: $i] :
( ( X256 @ X259 )
& ! [X260: $i] :
( ( X256 @ X260 )
=> ( X259 = X260 ) ) ) )
=> ( ! [X261: $o,X262: $i] :
( ( in @ X262 @ ( prop2set @ X261 ) )
=> X261 )
=> ( ! [X263: $i] :
( ( in @ X263 @ emptyset )
=> ! [X264: $o] : X264 )
=> ( ! [X265: $i] :
( ( in @ X265 @ emptyset )
=> ~ $true )
=> ( ! [X266: $i] :
~ ( in @ X266 @ emptyset )
=> ( ! [X267: $i > $o] :
( ? [X268: $i] :
( ( X267 @ X268 )
& ! [X269: $i] :
( ( X267 @ X269 )
=> ( X268 = X269 ) ) )
=> ? [X270: $i] : ( X267 @ X270 ) )
=> ( ! [X271: $i,X272: $i] :
( ! [X273: $i] :
( ( in @ X273 @ X271 )
=> ( in @ X273 @ X272 ) )
=> ( ! [X274: $i] :
( ( in @ X274 @ X272 )
=> ( in @ X274 @ X271 ) )
=> ( X271 = X272 ) ) )
=> ( ! [X275: $i] :
( ! [X276: $i] :
~ ( in @ X276 @ X275 )
=> ( X275 = emptyset ) )
=> ( ! [X277: $i] :
( ! [X278: $i] :
~ ( in @ X278 @ X277 )
=> ( X277 = emptyset ) )
=> ( ! [X279: $i,X280: $i > $o,X281: $i] :
( ( in @ X281 @ X279 )
=> ( ( in @ X281 @ ( dsetconstr @ X279 @ X280 ) )
<=> ( X280 @ X281 ) ) )
=> ( ! [X282: $i] :
( ( X282 != emptyset )
=> ? [X283: $i] : ( in @ X283 @ X282 ) )
=> ( ! [X284: $i,X285: $i > $o,X286: $i] :
( ( in @ X286 @ X284 )
=> ( ( X285 @ X286 )
=> ( ( dsetconstr @ X284 @ X285 )
!= emptyset ) ) )
=> ( ! [X287: $i] :
( ? [X288: $i] : ( in @ X288 @ X287 )
=> ( X287 != emptyset ) )
=> ( ! [X289: $i,X290: $i] : ( in @ X289 @ ( setadjoin @ X289 @ X290 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X291: $i,X292: $i,X293: $i] :
( ( in @ X293 @ X292 )
=> ( in @ X293 @ ( setadjoin @ X291 @ X292 ) ) )
=> ( ! [X294: $i,X295: $i,X296: $i] :
( ( in @ X296 @ ( setadjoin @ X294 @ X295 ) )
=> ! [X297: $o] :
( ( ( X296 = X294 )
=> X297 )
=> ( ( ( in @ X296 @ X295 )
=> X297 )
=> X297 ) ) )
=> ( ! [X298: $i,X299: $i,X300: $i] :
( ( in @ X300 @ ( setadjoin @ X298 @ X299 ) )
=> ( ( X300 = X298 )
| ( in @ X300 @ X299 ) ) )
=> ( ! [X301: $i] :
( ( dsetconstr @ X301
@ ^ [Z0: $i] : $true )
= X301 )
=> ( ! [X302: $i,X303: $i] :
( ! [X304: $i] :
( ( in @ X304 @ X303 )
=> ( in @ X304 @ X302 ) )
=> ( in @ X303 @ ( powerset @ X302 ) ) )
=> ( ! [X305: $i] : ( in @ emptyset @ ( powerset @ X305 ) )
=> ( ! [X306: $i] : ( in @ emptyset @ ( powerset @ X306 ) )
=> ( ! [X307: $i,X308: $i,X309: $i] :
( ( in @ X308 @ ( powerset @ X307 ) )
=> ( ( in @ X309 @ X308 )
=> ( in @ X309 @ X307 ) ) )
=> ( ! [X310: $i,X311: $i,X312: $i] :
( ( in @ X311 @ X312 )
=> ( ( in @ X312 @ X310 )
=> ( in @ X311 @ ( setunion @ X310 ) ) ) )
=> ( ! [X313: $i,X314: $i] :
( ( in @ X314 @ ( setunion @ X313 ) )
=> ! [X315: $o] :
( ! [X316: $i] :
( ( in @ X314 @ X316 )
=> ( ( in @ X316 @ X313 )
=> X315 ) )
=> X315 ) )
=> ( ! [X317: $i,X318: $i] :
( ( in @ X318 @ X317 )
=> ( in @ X318 @ ( powerset @ ( setunion @ X317 ) ) ) )
=> ( ! [X319: $i > $o] :
( ? [X320: $i] :
( ( X319 @ X320 )
& ! [X321: $i] :
( ( X319 @ X321 )
=> ( X320 = X321 ) ) )
=> ? [X322: $i] :
! [X323: $i] :
( ( X319 @ X323 )
<=> ( X323 = X322 ) ) )
=> ( ! [X324: $i] :
( ( X324 != emptyset )
=> ? [X325: $i] :
( ( in @ X325 @ X324 )
& $true ) )
=> ( ! [X326: $i,X327: $i] :
( ( in @ X326 @ ( setadjoin @ X327 @ emptyset ) )
=> ( X326 = X327 ) )
=> ( ! [X328: $i,X329: $i] :
( ( X328 != X329 )
=> ~ ( in @ X329 @ ( setadjoin @ X328 @ emptyset ) ) )
=> ( ! [X330: $i,X331: $i] :
( ( X330 = X331 )
=> ( in @ X330 @ ( setadjoin @ X331 @ emptyset ) ) )
=> ( ! [X332: $i,X333: $i] :
( ( in @ X332 @ ( setadjoin @ X333 @ emptyset ) )
=> ( in @ X333 @ ( setadjoin @ X332 @ emptyset ) ) )
=> ( ! [X334: $i,X335: $i,X336: $i] :
( ( in @ X336 @ ( setadjoin @ X334 @ ( setadjoin @ X335 @ emptyset ) ) )
=> ( ( X336 = X334 )
| ( X336 = X335 ) ) )
=> ( ! [X337: $i,X338: $i] : ( in @ X337 @ ( setadjoin @ X337 @ ( setadjoin @ X338 @ emptyset ) ) )
=> ( ! [X339: $i,X340: $i] : ( in @ X340 @ ( setadjoin @ X339 @ ( setadjoin @ X340 @ emptyset ) ) )
=> ( ! [X341: $i,X342: $i > $o] :
( ? [X343: $i] :
( ( in @ X343 @ X341 )
& ( X342 @ X343 ) )
=> ( ( ( dsetconstr @ X341 @ X342 )
= emptyset )
=> ~ $true ) )
=> ( ! [X344: $i > $o,X345: $i] :
( ( in @ X345 @ emptyset )
=> ( X344 @ X345 ) )
=> ( ! [X346: $i,X347: $i > $o] :
( ~ ! [X348: $i] :
( ( in @ X348 @ X346 )
=> ( X347 @ X348 ) )
=> ? [X349: $i] :
( ( in @ X349 @ X346 )
& ~ ( X347 @ X349 ) ) )
=> ( ! [X350: $i,X351: $i > $o] :
( ! [X352: $i] :
( ( in @ X352 @ X350 )
=> ~ ( X351 @ X352 ) )
=> ~ ? [X353: $i] :
( ( in @ X353 @ X350 )
& ( X351 @ X353 ) ) )
=> ( ! [X354: $i,X355: $i > $o] :
( ~ ? [X356: $i] :
( ( in @ X356 @ X354 )
& ( X355 @ X356 ) )
=> ! [X357: $i] :
( ( in @ X357 @ X354 )
=> ~ ( X355 @ X357 ) ) )
=> ( ! [X358: $i,X359: $i > $o] :
( ? [X360: $i] :
( ( in @ X360 @ X358 )
& ~ ( X359 @ X360 ) )
=> ~ ! [X361: $i] :
( ( in @ X361 @ X358 )
=> ( X359 @ X361 ) ) )
=> ( ! [X362: $o] :
( X362
=> ( in @ emptyset @ ( prop2set @ X362 ) ) )
=> ( ! [X363: $o] :
( X363
=> ( set2prop @ ( prop2set @ X363 ) ) )
=> ( ! [X364: $i,X365: $i > $o] :
( ~ ? [X366: $i] :
( ( in @ X366 @ X364 )
& ( X365 @ X366 ) )
=> ! [X367: $i] :
( ( in @ X367 @ X364 )
=> ~ ( X365 @ X367 ) ) )
=> ( ! [X368: $i,X369: $i > $o] :
( ~ ! [X370: $i] :
( ( in @ X370 @ X368 )
=> ( X369 @ X370 ) )
=> ? [X371: $i] :
( ( in @ X371 @ X368 )
& ~ ( X369 @ X371 ) ) )
=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X372: $i] :
( ( X1 @ X372 )
& ! [X373: $i] :
( ( X1 @ X373 )
=> ( X372 = X373 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[exuI1])]),c_0_71]),c_0_64]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),emptysetE]),prop2set2propI]),notdexE]),emptysetimpfalse]),notdallE]),c_0_72]),c_0_73]),notinemptyset]),c_0_74]),c_0_75]),setext]),emptyI]),c_0_76]),noeltsimpempty]),c_0_77]),upairsetIL]),c_0_78]),c_0_79]),c_0_80]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_81]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_82]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIR]),c_0_83]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),c_0_84]),prop2setE]),c_0_85]),wellorderingAx]),foundationAx]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_86]) ).
thf(c_0_88,negated_conjecture,
! [X374: $i,X375: $i,X377: $i,X378: $i,X379: $i,X380: $i,X381: $i,X382: $i,X383: $i,X384: $i,X385: $i,X387: $i,X388: $i,X390: $i,X391: $i,X392: $i,X393: $i,X394: $i,X396: $i,X397: $i > $i > $o,X398: $i,X400: $i,X403: $i,X405: $i,X406: $i,X407: $i,X408: $i,X410: $i,X411: $i > $o,X412: $i,X414: $i,X415: $i > $o,X416: $i,X417: $i,X418: $i > $o,X419: $i,X420: $i,X421: $i > $o,X422: $i,X423: $i > $o,X424: $i,X427: $i,X428: $o,X429: $i,X430: $i,X431: $o,X432: $i,X433: $i,X434: $i > $o,X435: $i,X438: $i,X439: $i,X442: $i,X444: $i,X446: $i,X447: $i > $o,X448: $i,X449: $i,X451: $i,X452: $i > $o,X453: $i,X454: $i,X455: $i,X456: $i,X457: $i,X458: $i,X459: $i,X460: $i,X461: $i,X462: $i,X463: $i,X464: $o,X465: $i,X466: $i,X467: $i,X468: $i,X469: $i,X470: $i,X472: $i,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i,X478: $i,X479: $i,X480: $i,X481: $i,X482: $o,X484: $i,X485: $i,X486: $i > $o,X487: $i,X490: $i,X491: $i,X492: $i,X494: $i,X495: $i,X496: $i,X497: $i,X498: $i,X499: $i,X500: $i,X501: $i,X502: $i,X503: $i,X504: $i,X505: $i,X506: $i,X507: $i,X508: $i,X509: $i,X510: $i > $o,X511: $i,X512: $i > $o,X513: $i,X514: $i,X515: $i > $o,X516: $i,X518: $i,X519: $i > $o,X521: $i,X522: $i,X523: $i > $o,X525: $i,X526: $i,X527: $i > $o,X528: $i,X530: $o,X531: $o,X532: $i,X533: $i > $o,X535: $i,X536: $i,X537: $i > $o,X538: $i,X542: $i,X543: $i] :
( ( ~ ( in @ ( esk1_2 @ X374 @ X375 ) @ X374 )
| ~ ( in @ ( esk1_2 @ X374 @ X375 ) @ X375 )
| ( X374 = X375 ) )
& ( ( in @ ( esk1_2 @ X374 @ X375 ) @ X374 )
| ( in @ ( esk1_2 @ X374 @ X375 ) @ X375 )
| ( X374 = X375 ) )
& ~ ( in @ X377 @ emptyset )
& ( ~ ( in @ X380 @ ( setadjoin @ X378 @ X379 ) )
| ( X380 = X378 )
| ( in @ X380 @ X379 ) )
& ( ( X380 != X378 )
| ( in @ X380 @ ( setadjoin @ X378 @ X379 ) ) )
& ( ~ ( in @ X380 @ X379 )
| ( in @ X380 @ ( setadjoin @ X378 @ X379 ) ) )
& ( ~ ( in @ X382 @ ( powerset @ X381 ) )
| ~ ( in @ X383 @ X382 )
| ( in @ X383 @ X381 ) )
& ( ( in @ ( esk2_2 @ X384 @ X385 ) @ X385 )
| ( in @ X385 @ ( powerset @ X384 ) ) )
& ( ~ ( in @ ( esk2_2 @ X384 @ X385 ) @ X384 )
| ( in @ X385 @ ( powerset @ X384 ) ) )
& ( ( in @ X388 @ ( esk3_2 @ X387 @ X388 ) )
| ~ ( in @ X388 @ ( setunion @ X387 ) ) )
& ( ( in @ ( esk3_2 @ X387 @ X388 ) @ X387 )
| ~ ( in @ X388 @ ( setunion @ X387 ) ) )
& ( ~ ( in @ X391 @ X392 )
| ~ ( in @ X392 @ X390 )
| ( in @ X391 @ ( setunion @ X390 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X393 @ omega )
| ( in @ ( setadjoin @ X393 @ X393 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X394 ) @ omega )
| ~ ( in @ emptyset @ X394 )
| ~ ( in @ X396 @ omega )
| ( in @ X396 @ X394 ) )
& ( ( in @ ( esk4_1 @ X394 ) @ X394 )
| ~ ( in @ emptyset @ X394 )
| ~ ( in @ X396 @ omega )
| ( in @ X396 @ X394 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X394 ) @ ( esk4_1 @ X394 ) ) @ X394 )
| ~ ( in @ emptyset @ X394 )
| ~ ( in @ X396 @ omega )
| ( in @ X396 @ X394 ) )
& ( ( in @ ( esk8_3 @ X397 @ X398 @ X403 ) @ X398 )
| ~ ( in @ X403 @ ( esk7_2 @ X397 @ X398 ) )
| ( in @ ( esk5_2 @ X397 @ X398 ) @ X398 ) )
& ( ( X397 @ ( esk8_3 @ X397 @ X398 @ X403 ) @ X403 )
| ~ ( in @ X403 @ ( esk7_2 @ X397 @ X398 ) )
| ( in @ ( esk5_2 @ X397 @ X398 ) @ X398 ) )
& ( ~ ( in @ X406 @ X398 )
| ~ ( X397 @ X406 @ X405 )
| ( in @ X405 @ ( esk7_2 @ X397 @ X398 ) )
| ( in @ ( esk5_2 @ X397 @ X398 ) @ X398 ) )
& ( ( in @ ( esk8_3 @ X397 @ X398 @ X403 ) @ X398 )
| ~ ( in @ X403 @ ( esk7_2 @ X397 @ X398 ) )
| ( X397 @ ( esk5_2 @ X397 @ X398 ) @ ( esk6_3 @ X397 @ X398 @ X400 ) )
| ~ ( X397 @ ( esk5_2 @ X397 @ X398 ) @ X400 ) )
& ( ( X397 @ ( esk8_3 @ X397 @ X398 @ X403 ) @ X403 )
| ~ ( in @ X403 @ ( esk7_2 @ X397 @ X398 ) )
| ( X397 @ ( esk5_2 @ X397 @ X398 ) @ ( esk6_3 @ X397 @ X398 @ X400 ) )
| ~ ( X397 @ ( esk5_2 @ X397 @ X398 ) @ X400 ) )
& ( ~ ( in @ X406 @ X398 )
| ~ ( X397 @ X406 @ X405 )
| ( in @ X405 @ ( esk7_2 @ X397 @ X398 ) )
| ( X397 @ ( esk5_2 @ X397 @ X398 ) @ ( esk6_3 @ X397 @ X398 @ X400 ) )
| ~ ( X397 @ ( esk5_2 @ X397 @ X398 ) @ X400 ) )
& ( ( in @ ( esk8_3 @ X397 @ X398 @ X403 ) @ X398 )
| ~ ( in @ X403 @ ( esk7_2 @ X397 @ X398 ) )
| ( X400
!= ( esk6_3 @ X397 @ X398 @ X400 ) )
| ~ ( X397 @ ( esk5_2 @ X397 @ X398 ) @ X400 ) )
& ( ( X397 @ ( esk8_3 @ X397 @ X398 @ X403 ) @ X403 )
| ~ ( in @ X403 @ ( esk7_2 @ X397 @ X398 ) )
| ( X400
!= ( esk6_3 @ X397 @ X398 @ X400 ) )
| ~ ( X397 @ ( esk5_2 @ X397 @ X398 ) @ X400 ) )
& ( ~ ( in @ X406 @ X398 )
| ~ ( X397 @ X406 @ X405 )
| ( in @ X405 @ ( esk7_2 @ X397 @ X398 ) )
| ( X400
!= ( esk6_3 @ X397 @ X398 @ X400 ) )
| ~ ( X397 @ ( esk5_2 @ X397 @ X398 ) @ X400 ) )
& ( ( in @ ( esk9_1 @ X407 ) @ X407 )
| ~ ( in @ X408 @ X407 ) )
& ( ~ ( in @ X410 @ ( esk9_1 @ X407 ) )
| ~ ( in @ X410 @ X407 )
| ~ ( in @ X408 @ X407 ) )
& epred1_0
& ( ( X411 @ ( esk10_2 @ X411 @ X412 ) )
| ~ ( X411 @ X412 )
| ( X411 @ ( descr @ X411 ) ) )
& ( ( X412
!= ( esk10_2 @ X411 @ X412 ) )
| ~ ( X411 @ X412 )
| ( X411 @ ( descr @ X411 ) ) )
& ( ~ ( in @ X416 @ X414 )
| ~ ( X415 @ X416 )
| ( in @ X416 @ ( dsetconstr @ X414 @ X415 ) ) )
& ( ~ ( in @ X419 @ ( dsetconstr @ X417 @ X418 ) )
| ( in @ X419 @ X417 ) )
& ( ~ ( in @ X422 @ ( dsetconstr @ X420 @ X421 ) )
| ( X421 @ X422 ) )
& ( ( X423 @ ( esk12_1 @ X423 ) )
| ( X423 @ ( esk11_2 @ X423 @ X424 ) )
| ~ ( X423 @ X424 ) )
& ( ~ ( X423 @ X427 )
| ( ( esk12_1 @ X423 )
= X427 )
| ( X423 @ ( esk11_2 @ X423 @ X424 ) )
| ~ ( X423 @ X424 ) )
& ( ( X423 @ ( esk12_1 @ X423 ) )
| ( X424
!= ( esk11_2 @ X423 @ X424 ) )
| ~ ( X423 @ X424 ) )
& ( ~ ( X423 @ X427 )
| ( ( esk12_1 @ X423 )
= X427 )
| ( X424
!= ( esk11_2 @ X423 @ X424 ) )
| ~ ( X423 @ X424 ) )
& ( ~ ( in @ X429 @ ( prop2set @ X428 ) )
| X428 )
& ( ~ ( in @ X430 @ emptyset )
| X431 )
& ( ~ ( in @ X432 @ emptyset )
| ~ $true )
& ~ ( in @ X433 @ emptyset )
& ( ( X434 @ ( esk13_2 @ X434 @ X435 ) )
| ~ ( X434 @ X435 )
| ( X434 @ ( esk14_1 @ X434 ) ) )
& ( ( X435
!= ( esk13_2 @ X434 @ X435 ) )
| ~ ( X434 @ X435 )
| ( X434 @ ( esk14_1 @ X434 ) ) )
& ( ( in @ ( esk16_2 @ X438 @ X439 ) @ X439 )
| ( X438 = X439 )
| ( in @ ( esk15_2 @ X438 @ X439 ) @ X438 ) )
& ( ~ ( in @ ( esk16_2 @ X438 @ X439 ) @ X438 )
| ( X438 = X439 )
| ( in @ ( esk15_2 @ X438 @ X439 ) @ X438 ) )
& ( ( in @ ( esk16_2 @ X438 @ X439 ) @ X439 )
| ( X438 = X439 )
| ~ ( in @ ( esk15_2 @ X438 @ X439 ) @ X439 ) )
& ( ~ ( in @ ( esk16_2 @ X438 @ X439 ) @ X438 )
| ( X438 = X439 )
| ~ ( in @ ( esk15_2 @ X438 @ X439 ) @ X439 ) )
& ( ( in @ ( esk17_1 @ X442 ) @ X442 )
| ( X442 = emptyset ) )
& ( ( in @ ( esk18_1 @ X444 ) @ X444 )
| ( X444 = emptyset ) )
& ( ~ ( in @ X448 @ ( dsetconstr @ X446 @ X447 ) )
| ( X447 @ X448 )
| ~ ( in @ X448 @ X446 ) )
& ( ~ ( X447 @ X448 )
| ( in @ X448 @ ( dsetconstr @ X446 @ X447 ) )
| ~ ( in @ X448 @ X446 ) )
& ( ( X449 = emptyset )
| ( in @ ( esk19_1 @ X449 ) @ X449 ) )
& ( ~ ( in @ X453 @ X451 )
| ~ ( X452 @ X453 )
| ( ( dsetconstr @ X451 @ X452 )
!= emptyset ) )
& ( ~ ( in @ X455 @ X454 )
| ( X454 != emptyset ) )
& ( in @ X456 @ ( setadjoin @ X456 @ X457 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X460 @ X459 )
| ( in @ X460 @ ( setadjoin @ X458 @ X459 ) ) )
& ( ( in @ X463 @ X462 )
| X464
| ( X463 = X461 )
| ~ ( in @ X463 @ ( setadjoin @ X461 @ X462 ) ) )
& ( ~ X464
| X464
| ( X463 = X461 )
| ~ ( in @ X463 @ ( setadjoin @ X461 @ X462 ) ) )
& ( ( in @ X463 @ X462 )
| X464
| ~ X464
| ~ ( in @ X463 @ ( setadjoin @ X461 @ X462 ) ) )
& ( ~ X464
| X464
| ~ X464
| ~ ( in @ X463 @ ( setadjoin @ X461 @ X462 ) ) )
& ( ~ ( in @ X467 @ ( setadjoin @ X465 @ X466 ) )
| ( X467 = X465 )
| ( in @ X467 @ X466 ) )
& ( ( dsetconstr @ X468
@ ^ [Z0: $i] : $true )
= X468 )
& ( ( in @ ( esk20_2 @ X469 @ X470 ) @ X470 )
| ( in @ X470 @ ( powerset @ X469 ) ) )
& ( ~ ( in @ ( esk20_2 @ X469 @ X470 ) @ X469 )
| ( in @ X470 @ ( powerset @ X469 ) ) )
& ( in @ emptyset @ ( powerset @ X472 ) )
& ( in @ emptyset @ ( powerset @ X473 ) )
& ( ~ ( in @ X475 @ ( powerset @ X474 ) )
| ~ ( in @ X476 @ X475 )
| ( in @ X476 @ X474 ) )
& ( ~ ( in @ X478 @ X479 )
| ~ ( in @ X479 @ X477 )
| ( in @ X478 @ ( setunion @ X477 ) ) )
& ( ( in @ X481 @ ( esk21_3 @ X480 @ X481 @ X482 ) )
| X482
| ~ ( in @ X481 @ ( setunion @ X480 ) ) )
& ( ( in @ ( esk21_3 @ X480 @ X481 @ X482 ) @ X480 )
| X482
| ~ ( in @ X481 @ ( setunion @ X480 ) ) )
& ( ~ X482
| X482
| ~ ( in @ X481 @ ( setunion @ X480 ) ) )
& ( ~ ( in @ X485 @ X484 )
| ( in @ X485 @ ( powerset @ ( setunion @ X484 ) ) ) )
& ( ~ ( X486 @ X490 )
| ( X490
= ( esk23_1 @ X486 ) )
| ( X486 @ ( esk22_2 @ X486 @ X487 ) )
| ~ ( X486 @ X487 ) )
& ( ( X491
!= ( esk23_1 @ X486 ) )
| ( X486 @ X491 )
| ( X486 @ ( esk22_2 @ X486 @ X487 ) )
| ~ ( X486 @ X487 ) )
& ( ~ ( X486 @ X490 )
| ( X490
= ( esk23_1 @ X486 ) )
| ( X487
!= ( esk22_2 @ X486 @ X487 ) )
| ~ ( X486 @ X487 ) )
& ( ( X491
!= ( esk23_1 @ X486 ) )
| ( X486 @ X491 )
| ( X487
!= ( esk22_2 @ X486 @ X487 ) )
| ~ ( X486 @ X487 ) )
& ( ( in @ ( esk24_1 @ X492 ) @ X492 )
| ( X492 = emptyset ) )
& ( $true
| ( X492 = emptyset ) )
& ( ~ ( in @ X494 @ ( setadjoin @ X495 @ emptyset ) )
| ( X494 = X495 ) )
& ( ( X496 = X497 )
| ~ ( in @ X497 @ ( setadjoin @ X496 @ emptyset ) ) )
& ( ( X498 != X499 )
| ( in @ X498 @ ( setadjoin @ X499 @ emptyset ) ) )
& ( ~ ( in @ X500 @ ( setadjoin @ X501 @ emptyset ) )
| ( in @ X501 @ ( setadjoin @ X500 @ emptyset ) ) )
& ( ~ ( in @ X504 @ ( setadjoin @ X502 @ ( setadjoin @ X503 @ emptyset ) ) )
| ( X504 = X502 )
| ( X504 = X503 ) )
& ( in @ X505 @ ( setadjoin @ X505 @ ( setadjoin @ X506 @ emptyset ) ) )
& ( in @ X508 @ ( setadjoin @ X507 @ ( setadjoin @ X508 @ emptyset ) ) )
& ( ~ ( in @ X511 @ X509 )
| ~ ( X510 @ X511 )
| ( ( dsetconstr @ X509 @ X510 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X513 @ emptyset )
| ( X512 @ X513 ) )
& ( ( in @ ( esk25_2 @ X514 @ X515 ) @ X514 )
| ~ ( in @ X516 @ X514 )
| ( X515 @ X516 ) )
& ( ~ ( X515 @ ( esk25_2 @ X514 @ X515 ) )
| ~ ( in @ X516 @ X514 )
| ( X515 @ X516 ) )
& ( ( in @ ( esk26_2 @ X518 @ X519 ) @ X518 )
| ~ ( in @ X521 @ X518 )
| ~ ( X519 @ X521 ) )
& ( ( X519 @ ( esk26_2 @ X518 @ X519 ) )
| ~ ( in @ X521 @ X518 )
| ~ ( X519 @ X521 ) )
& ( ( in @ ( esk27_2 @ X522 @ X523 ) @ X522 )
| ~ ( in @ X525 @ X522 )
| ~ ( X523 @ X525 ) )
& ( ( X523 @ ( esk27_2 @ X522 @ X523 ) )
| ~ ( in @ X525 @ X522 )
| ~ ( X523 @ X525 ) )
& ( ( in @ ( esk28_2 @ X526 @ X527 ) @ X526 )
| ~ ( in @ X528 @ X526 )
| ( X527 @ X528 ) )
& ( ~ ( X527 @ ( esk28_2 @ X526 @ X527 ) )
| ~ ( in @ X528 @ X526 )
| ( X527 @ X528 ) )
& ( ~ X530
| ( in @ emptyset @ ( prop2set @ X530 ) ) )
& ( ~ X531
| ( set2prop @ ( prop2set @ X531 ) ) )
& ( ( in @ ( esk29_2 @ X532 @ X533 ) @ X532 )
| ~ ( in @ X535 @ X532 )
| ~ ( X533 @ X535 ) )
& ( ( X533 @ ( esk29_2 @ X532 @ X533 ) )
| ~ ( in @ X535 @ X532 )
| ~ ( X533 @ X535 ) )
& ( ( in @ ( esk30_2 @ X536 @ X537 ) @ X536 )
| ~ ( in @ X538 @ X536 )
| ( X537 @ X538 ) )
& ( ~ ( X537 @ ( esk30_2 @ X536 @ X537 ) )
| ~ ( in @ X538 @ X536 )
| ( X537 @ X538 ) )
& ( epred2_0 @ esk31_0 )
& ( ~ ( epred2_0 @ X542 )
| ( esk31_0 = X542 ) )
& ( ( epred2_0 @ ( esk32_1 @ X543 ) )
| ~ ( epred2_0 @ X543 ) )
& ( ( X543
!= ( esk32_1 @ X543 ) )
| ~ ( epred2_0 @ X543 ) ) ),
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_87])])])])])])]) ).
thf(c_0_89,negated_conjecture,
! [X2: $i] :
( ( esk31_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_90,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ ( esk32_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_91,negated_conjecture,
! [X2: $i] :
( ( X2
!= ( esk32_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_92,negated_conjecture,
! [X2: $i] :
( ( ( esk32_1 @ X2 )
= esk31_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_93,negated_conjecture,
epred2_0 @ esk31_0,
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92])]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU544^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 21 16:02:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/eprover-ho --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.mNAnA3Z5SV/E---3.1_18165.p
% 0.19/0.51 # Version: 3.2.0-ho
% 0.19/0.51 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.19/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.51 # Starting sh5l with 300s (1) cores
% 0.19/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.19/0.51 # sh5l with pid 18244 completed with status 0
% 0.19/0.51 # Result found by sh5l
% 0.19/0.51 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.19/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.51 # Starting sh5l with 300s (1) cores
% 0.19/0.51 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.51 # Search class: HGHSM-FFMM31-SHSSMSBN
% 0.19/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 # Starting new_ho_10 with 181s (1) cores
% 0.19/0.51 # new_ho_10 with pid 18247 completed with status 0
% 0.19/0.51 # Result found by new_ho_10
% 0.19/0.51 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.19/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.51 # Starting sh5l with 300s (1) cores
% 0.19/0.51 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.51 # Search class: HGHSM-FFMM31-SHSSMSBN
% 0.19/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 # Starting new_ho_10 with 181s (1) cores
% 0.19/0.51 # Preprocessing time : 0.003 s
% 0.19/0.51 # Presaturation interreduction done
% 0.19/0.51
% 0.19/0.51 # Proof found!
% 0.19/0.51 # SZS status Theorem
% 0.19/0.51 # SZS output start CNFRefutation
% See solution above
% 0.19/0.51 # Parsed axioms : 135
% 0.19/0.51 # Removed by relevancy pruning/SinE : 72
% 0.19/0.51 # Initial clauses : 120
% 0.19/0.51 # Removed in clause preprocessing : 5
% 0.19/0.51 # Initial clauses in saturation : 115
% 0.19/0.51 # Processed clauses : 133
% 0.19/0.51 # ...of these trivial : 3
% 0.19/0.51 # ...subsumed : 14
% 0.19/0.51 # ...remaining for further processing : 116
% 0.19/0.51 # Other redundant clauses eliminated : 6
% 0.19/0.51 # Clauses deleted for lack of memory : 0
% 0.19/0.51 # Backward-subsumed : 0
% 0.19/0.51 # Backward-rewritten : 1
% 0.19/0.51 # Generated clauses : 9
% 0.19/0.51 # ...of the previous two non-redundant : 5
% 0.19/0.51 # ...aggressively subsumed : 0
% 0.19/0.51 # Contextual simplify-reflections : 0
% 0.19/0.51 # Paramodulations : 3
% 0.19/0.51 # Factorizations : 0
% 0.19/0.51 # NegExts : 0
% 0.19/0.51 # Equation resolutions : 6
% 0.19/0.51 # Disequality decompositions : 0
% 0.19/0.51 # Total rewrite steps : 20
% 0.19/0.51 # ...of those cached : 13
% 0.19/0.51 # Propositional unsat checks : 0
% 0.19/0.51 # Propositional check models : 0
% 0.19/0.51 # Propositional check unsatisfiable : 0
% 0.19/0.51 # Propositional clauses : 0
% 0.19/0.51 # Propositional clauses after purity: 0
% 0.19/0.51 # Propositional unsat core size : 0
% 0.19/0.51 # Propositional preprocessing time : 0.000
% 0.19/0.51 # Propositional encoding time : 0.000
% 0.19/0.51 # Propositional solver time : 0.000
% 0.19/0.51 # Success case prop preproc time : 0.000
% 0.19/0.51 # Success case prop encoding time : 0.000
% 0.19/0.51 # Success case prop solver time : 0.000
% 0.19/0.51 # Current number of processed clauses : 14
% 0.19/0.51 # Positive orientable unit clauses : 7
% 0.19/0.51 # Positive unorientable unit clauses: 0
% 0.19/0.51 # Negative unit clauses : 2
% 0.19/0.51 # Non-unit-clauses : 5
% 0.19/0.51 # Current number of unprocessed clauses: 83
% 0.19/0.51 # ...number of literals in the above : 255
% 0.19/0.51 # Current number of archived formulas : 0
% 0.19/0.51 # Current number of archived clauses : 97
% 0.19/0.51 # Clause-clause subsumption calls (NU) : 2529
% 0.19/0.51 # Rec. Clause-clause subsumption calls : 1147
% 0.19/0.51 # Non-unit clause-clause subsumptions : 12
% 0.19/0.51 # Unit Clause-clause subsumption calls : 3
% 0.19/0.51 # Rewrite failures with RHS unbound : 0
% 0.19/0.51 # BW rewrite match attempts : 2
% 0.19/0.51 # BW rewrite match successes : 1
% 0.19/0.51 # Condensation attempts : 133
% 0.19/0.51 # Condensation successes : 3
% 0.19/0.51 # Termbank termtop insertions : 18553
% 0.19/0.51 # Search garbage collected termcells : 6414
% 0.19/0.51
% 0.19/0.51 # -------------------------------------------------
% 0.19/0.51 # User time : 0.024 s
% 0.19/0.51 # System time : 0.002 s
% 0.19/0.51 # Total time : 0.026 s
% 0.19/0.51 # Maximum resident set size: 3628 pages
% 0.19/0.51
% 0.19/0.51 # -------------------------------------------------
% 0.19/0.51 # User time : 0.026 s
% 0.19/0.51 # System time : 0.006 s
% 0.19/0.51 # Total time : 0.032 s
% 0.19/0.51 # Maximum resident set size: 1860 pages
% 0.19/0.51 % E---3.1 exiting
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------