TSTP Solution File: SEU551^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU551^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 : Tue May 21 03:28:07 EDT 2024
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 190
% Syntax : Number of formulae : 225 ( 19 unt; 121 typ; 0 def)
% Number of atoms : 844 ( 215 equ; 0 cnn)
% Maximal formula atoms : 253 ( 8 avg)
% Number of connectives : 3340 ( 302 ~; 331 |; 225 &;1961 @)
% ( 117 <=>; 404 =>; 0 <=; 0 <~>)
% Maximal formula depth : 313 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 233 ( 233 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 121 usr; 72 con; 0-3 aty)
% Number of variables : 726 ( 54 ^ 576 !; 96 ?; 726 :)
% 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_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_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
epred1_0: $o ).
thf(decl_102,type,
esk1_2: $i > $i > $i ).
thf(decl_103,type,
esk2_2: $i > $i > $i ).
thf(decl_104,type,
esk3_2: $i > $i > $i ).
thf(decl_105,type,
esk4_1: $i > $i ).
thf(decl_106,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_107,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_108,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_109,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_110,type,
esk9_1: $i > $i ).
thf(decl_111,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_112,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_113,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_114,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_115,type,
esk14_2: $i > $i > $i ).
thf(decl_116,type,
esk15_2: $i > $i > $i ).
thf(decl_117,type,
esk16_1: $i > $i ).
thf(decl_118,type,
esk17_1: $i > $i ).
thf(decl_119,type,
esk18_1: $i > $i ).
thf(decl_120,type,
esk19_2: $i > $i > $i ).
thf(decl_121,type,
esk20_3: $i > $i > $o > $i ).
thf(decl_122,type,
esk21_2: ( $i > $o ) > $i > $i ).
thf(decl_123,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_124,type,
esk23_1: $i > $i ).
thf(decl_125,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_126,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_127,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_128,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_129,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_130,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_131,type,
esk30_2: ( $i > $o ) > $i > $i ).
thf(decl_132,type,
esk31_1: ( $i > $o ) > $i ).
thf(decl_133,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_134,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_135,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_136,type,
esk35_2: ( $i > $o ) > $i > $i ).
thf(decl_137,type,
esk36_1: ( $i > $o ) > $i ).
thf(decl_138,type,
esk37_2: ( $i > $o ) > $i > $i ).
thf(decl_139,type,
esk38_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_140,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_141,type,
esk40_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_142,type,
esk41_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_143,type,
esk42_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_144,type,
esk43_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
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/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',replAx) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
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/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',dsetconstrER) ).
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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptyset__Cong,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
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
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/benchmark/theBenchmark.p',notdexE) ).
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/benchmark/theBenchmark.p',notdallE) ).
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/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_68,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_69,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_70,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_71,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_72,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_73,plain,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI3]) ).
thf(c_0_74,plain,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI2]) ).
thf(c_0_75,plain,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE3u]) ).
thf(c_0_76,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_77,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_78,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_79,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_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,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X223: $i] :
( ( X1 @ X223 )
& ! [X224: $i] :
( ( X1 @ X224 )
=> ( X223 = X224 ) ) )
<=> ? [X225: $i] :
( ( X17 @ X225 )
& ! [X226: $i] :
( ( X17 @ X226 )
=> ( X225 = X226 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_82,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X211: $i] :
( ( X1 @ X211 )
& ! [X212: $i] :
( ( X1 @ X212 )
=> ( X211 = X212 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_71,c_0_70]) ).
thf(c_0_83,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X215: $i] :
( ( X1 @ X215 )
& ! [X216: $i] :
( ( X1 @ X216 )
=> ( X215 = X216 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_72,c_0_70]) ).
thf(c_0_84,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X217: $i] :
( ( X1 @ X217 )
& ! [X218: $i] :
( ( X1 @ X218 )
=> ( X217 = X218 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_73,c_0_70]) ).
thf(c_0_85,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X219: $i] :
( ( X1 @ X219 )
& ! [X220: $i] :
( ( X1 @ X220 )
=> ( X219 = X220 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_74,c_0_70]) ).
thf(c_0_86,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X221: $i] :
( ( X1 @ X221 )
& ! [X222: $i] :
( ( X1 @ X222 )
=> ( X221 = X222 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_75,c_0_70]) ).
thf(c_0_87,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_88,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_68]) ).
thf(c_0_89,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_76,c_0_68]) ).
thf(c_0_90,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_91,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X213: $i] :
( ( X1 @ X213 )
& ! [X214: $i] :
( ( X1 @ X214 )
=> ( X213 = X214 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_77,c_0_70]) ).
thf(c_0_92,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_68]) ).
thf(c_0_93,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_94,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X209: $i] :
( ( X1 @ X209 )
& ! [X210: $i] :
( ( X1 @ X210 )
=> ( X209 = X210 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_78,c_0_70]) ).
thf(c_0_95,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_96,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_97,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_98,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X207: $i] :
( ( X6 @ X2 @ X207 )
& ! [X208: $i] :
( ( X6 @ X2 @ X208 )
=> ( X207 = X208 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_79,c_0_70]) ).
thf(c_0_99,plain,
( epred1_0
<=> ! [X256: $i] :
? [X257: $i] :
( ! [X258: $i] :
( ( in @ X258 @ X257 )
=> ! [X259: $i] :
( ( in @ X259 @ X258 )
=> ( in @ X259 @ X256 ) ) )
& ! [X260: $i,X261: $i] :
( ( ( in @ X260 @ X256 )
& ( in @ X261 @ X256 ) )
=> ( ! [X262: $i] :
( ( in @ X262 @ X257 )
=> ( ( in @ X260 @ X262 )
<=> ( in @ X261 @ X262 ) ) )
=> ( X260 = X261 ) ) )
& ! [X263: $i,X264: $i] :
( ( ( in @ X263 @ X257 )
& ( in @ X264 @ X257 ) )
=> ( ! [X265: $i] :
( ( in @ X265 @ X263 )
=> ( in @ X265 @ X264 ) )
| ! [X266: $i] :
( ( in @ X266 @ X264 )
=> ( in @ X266 @ X263 ) ) ) )
& ! [X267: $i] :
( ( ! [X268: $i] :
( ( in @ X268 @ X267 )
=> ( in @ X268 @ X256 ) )
& ? [X269: $i] : ( in @ X269 @ X267 ) )
=> ? [X270: $i,X271: $i] :
( ( in @ X270 @ X257 )
& ( in @ X271 @ X267 )
& ~ ? [X272: $i] :
( ( in @ X272 @ X270 )
& ( in @ X272 @ X267 ) )
& ! [X273: $i] :
( ( in @ X273 @ X257 )
=> ( ! [X274: $i] :
( ( in @ X274 @ X273 )
=> ( in @ X274 @ X270 ) )
| ( in @ X271 @ X273 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_100,negated_conjecture,
~ ( ! [X227: $i,X228: $i] :
( ! [X229: $i] :
( ( in @ X229 @ X227 )
<=> ( in @ X229 @ X228 ) )
=> ( X227 = X228 ) )
=> ( ! [X230: $i] :
~ ( in @ X230 @ emptyset )
=> ( ! [X231: $i,X232: $i,X233: $i] :
( ( in @ X233 @ ( setadjoin @ X231 @ X232 ) )
<=> ( ( X233 = X231 )
| ( in @ X233 @ X232 ) ) )
=> ( ! [X234: $i,X235: $i] :
( ( in @ X235 @ ( powerset @ X234 ) )
<=> ! [X236: $i] :
( ( in @ X236 @ X235 )
=> ( in @ X236 @ X234 ) ) )
=> ( ! [X237: $i,X238: $i] :
( ( in @ X238 @ ( setunion @ X237 ) )
<=> ? [X239: $i] :
( ( in @ X238 @ X239 )
& ( in @ X239 @ X237 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X240: $i] :
( ( in @ X240 @ omega )
=> ( in @ ( setadjoin @ X240 @ X240 ) @ omega ) )
=> ( ! [X241: $i] :
( ( ( in @ emptyset @ X241 )
& ! [X242: $i] :
( ( ( in @ X242 @ omega )
& ( in @ X242 @ X241 ) )
=> ( in @ ( setadjoin @ X242 @ X242 ) @ X241 ) ) )
=> ! [X243: $i] :
( ( in @ X243 @ omega )
=> ( in @ X243 @ X241 ) ) )
=> ( ! [X244: $i > $i > $o,X245: $i] :
( ! [X246: $i] :
( ( in @ X246 @ X245 )
=> ? [X247: $i] :
( ( X244 @ X246 @ X247 )
& ! [X248: $i] :
( ( X244 @ X246 @ X248 )
=> ( X247 = X248 ) ) ) )
=> ? [X249: $i] :
! [X250: $i] :
( ( in @ X250 @ X249 )
<=> ? [X251: $i] :
( ( in @ X251 @ X245 )
& ( X244 @ X251 @ X250 ) ) ) )
=> ( ! [X252: $i] :
( ? [X253: $i] : ( in @ X253 @ X252 )
=> ? [X254: $i] :
( ( in @ X254 @ X252 )
& ~ ? [X255: $i] :
( ( in @ X255 @ X254 )
& ( in @ X255 @ X252 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X275: $i,X276: $i > $o,X277: $i] :
( ( in @ X277 @ X275 )
=> ( ( X276 @ X277 )
=> ( in @ X277
@ ( dsetconstr @ X275
@ ^ [Z0: $i] : ( X276 @ Z0 ) ) ) ) )
=> ( ! [X278: $i,X279: $i > $o,X280: $i] :
( ( in @ X280
@ ( dsetconstr @ X278
@ ^ [Z0: $i] : ( X279 @ Z0 ) ) )
=> ( in @ X280 @ X278 ) )
=> ( ! [X281: $i,X282: $i > $o,X283: $i] :
( ( in @ X283
@ ( dsetconstr @ X281
@ ^ [Z0: $i] : ( X282 @ Z0 ) ) )
=> ( X282 @ X283 ) )
=> ( ! [X284: $i > $o] :
( ? [X285: $i] :
( ( X284 @ X285 )
& ! [X286: $i] :
( ( X284 @ X286 )
=> ( X285 = X286 ) ) )
=> ? [X287: $i] :
( ( X284 @ X287 )
& ! [X288: $i] :
( ( X284 @ X288 )
=> ( X287 = X288 ) ) ) )
=> ( ! [X289: $o,X290: $i] :
( ( in @ X290 @ ( prop2set @ X289 ) )
=> X289 )
=> ( ! [X291: $i] :
( ( in @ X291 @ emptyset )
=> ! [X292: $o] : X292 )
=> ( ! [X293: $i] :
~ ( in @ X293 @ emptyset )
=> ( ! [X294: $i] :
~ ( in @ X294 @ emptyset )
=> ( ! [X295: $i > $o] :
( ? [X296: $i] :
( ( X295 @ X296 )
& ! [X297: $i] :
( ( X295 @ X297 )
=> ( X296 = X297 ) ) )
=> ? [X298: $i] : ( X295 @ X298 ) )
=> ( ! [X299: $i,X300: $i] :
( ! [X301: $i] :
( ( in @ X301 @ X299 )
=> ( in @ X301 @ X300 ) )
=> ( ! [X302: $i] :
( ( in @ X302 @ X300 )
=> ( in @ X302 @ X299 ) )
=> ( X299 = X300 ) ) )
=> ( ! [X303: $i] :
( ! [X304: $i] :
~ ( in @ X304 @ X303 )
=> ( X303 = emptyset ) )
=> ( ! [X305: $i] :
( ! [X306: $i] :
~ ( in @ X306 @ X305 )
=> ( X305 = emptyset ) )
=> ( ! [X307: $i,X308: $i > $o,X309: $i] :
( ( in @ X309 @ X307 )
=> ( ( in @ X309
@ ( dsetconstr @ X307
@ ^ [Z0: $i] : ( X308 @ Z0 ) ) )
<=> ( X308 @ X309 ) ) )
=> ( ! [X310: $i] :
( ( X310 != emptyset )
=> ? [X311: $i] : ( in @ X311 @ X310 ) )
=> ( ! [X312: $i,X313: $i > $o,X314: $i] :
( ( in @ X314 @ X312 )
=> ( ( X313 @ X314 )
=> ( ( dsetconstr @ X312
@ ^ [Z0: $i] : ( X313 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X315: $i] :
( ? [X316: $i] : ( in @ X316 @ X315 )
=> ( X315 != emptyset ) )
=> ( ! [X317: $i,X318: $i] : ( in @ X317 @ ( setadjoin @ X317 @ X318 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X319: $i,X320: $i,X321: $i] :
( ( in @ X321 @ X320 )
=> ( in @ X321 @ ( setadjoin @ X319 @ X320 ) ) )
=> ( ! [X322: $i,X323: $i,X324: $i] :
( ( in @ X324 @ ( setadjoin @ X322 @ X323 ) )
=> ! [X325: $o] :
( ( ( X324 = X322 )
=> X325 )
=> ( ( ( in @ X324 @ X323 )
=> X325 )
=> X325 ) ) )
=> ( ! [X326: $i,X327: $i,X328: $i] :
( ( in @ X328 @ ( setadjoin @ X326 @ X327 ) )
=> ( ( X328 = X326 )
| ( in @ X328 @ X327 ) ) )
=> ( ! [X329: $i] :
( ( dsetconstr @ X329
@ ^ [Z0: $i] : $true )
= X329 )
=> ( ! [X330: $i,X331: $i] :
( ! [X332: $i] :
( ( in @ X332 @ X331 )
=> ( in @ X332 @ X330 ) )
=> ( in @ X331 @ ( powerset @ X330 ) ) )
=> ( ! [X333: $i] : ( in @ emptyset @ ( powerset @ X333 ) )
=> ( ! [X334: $i] : ( in @ emptyset @ ( powerset @ X334 ) )
=> ( ! [X335: $i,X336: $i,X337: $i] :
( ( in @ X336 @ ( powerset @ X335 ) )
=> ( ( in @ X337 @ X336 )
=> ( in @ X337 @ X335 ) ) )
=> ( ! [X338: $i,X339: $i,X340: $i] :
( ( in @ X339 @ X340 )
=> ( ( in @ X340 @ X338 )
=> ( in @ X339 @ ( setunion @ X338 ) ) ) )
=> ( ! [X341: $i,X342: $i] :
( ( in @ X342 @ ( setunion @ X341 ) )
=> ! [X343: $o] :
( ! [X344: $i] :
( ( in @ X342 @ X344 )
=> ( ( in @ X344 @ X341 )
=> X343 ) )
=> X343 ) )
=> ( ! [X345: $i,X346: $i] :
( ( in @ X346 @ X345 )
=> ( in @ X346 @ ( powerset @ ( setunion @ X345 ) ) ) )
=> ( ! [X347: $i > $o] :
( ? [X348: $i] :
( ( X347 @ X348 )
& ! [X349: $i] :
( ( X347 @ X349 )
=> ( X348 = X349 ) ) )
=> ? [X350: $i] :
! [X351: $i] :
( ( X347 @ X351 )
<=> ( X351 = X350 ) ) )
=> ( ! [X352: $i] :
( ( X352 != emptyset )
=> ? [X353: $i] : ( in @ X353 @ X352 ) )
=> ( ! [X354: $i,X355: $i] :
( ( in @ X354 @ ( setadjoin @ X355 @ emptyset ) )
=> ( X354 = X355 ) )
=> ( ! [X356: $i,X357: $i] :
( ( X356 != X357 )
=> ~ ( in @ X357 @ ( setadjoin @ X356 @ emptyset ) ) )
=> ( ! [X358: $i,X359: $i] :
( ( X358 = X359 )
=> ( in @ X358 @ ( setadjoin @ X359 @ emptyset ) ) )
=> ( ! [X360: $i,X361: $i] :
( ( in @ X360 @ ( setadjoin @ X361 @ emptyset ) )
=> ( in @ X361 @ ( setadjoin @ X360 @ emptyset ) ) )
=> ( ! [X362: $i,X363: $i,X364: $i] :
( ( in @ X364 @ ( setadjoin @ X362 @ ( setadjoin @ X363 @ emptyset ) ) )
=> ( ( X364 = X362 )
| ( X364 = X363 ) ) )
=> ( ! [X365: $i,X366: $i] : ( in @ X365 @ ( setadjoin @ X365 @ ( setadjoin @ X366 @ emptyset ) ) )
=> ( ! [X367: $i,X368: $i] : ( in @ X368 @ ( setadjoin @ X367 @ ( setadjoin @ X368 @ emptyset ) ) )
=> ( ! [X369: $i,X370: $i > $o] :
( ? [X371: $i] :
( ( in @ X371 @ X369 )
& ( X370 @ X371 ) )
=> ( ( dsetconstr @ X369
@ ^ [Z0: $i] : ( X370 @ Z0 ) )
!= emptyset ) )
=> ( ! [X372: $i > $o,X373: $i] :
( ( in @ X373 @ emptyset )
=> ( X372 @ X373 ) )
=> ( ! [X374: $i,X375: $i > $o] :
( ~ ! [X376: $i] :
( ( in @ X376 @ X374 )
=> ( X375 @ X376 ) )
=> ? [X377: $i] :
( ( in @ X377 @ X374 )
& ~ ( X375 @ X377 ) ) )
=> ( ! [X378: $i,X379: $i > $o] :
( ! [X380: $i] :
( ( in @ X380 @ X378 )
=> ~ ( X379 @ X380 ) )
=> ~ ? [X381: $i] :
( ( in @ X381 @ X378 )
& ( X379 @ X381 ) ) )
=> ( ! [X382: $i,X383: $i > $o] :
( ~ ? [X384: $i] :
( ( in @ X384 @ X382 )
& ( X383 @ X384 ) )
=> ! [X385: $i] :
( ( in @ X385 @ X382 )
=> ~ ( X383 @ X385 ) ) )
=> ( ! [X386: $i,X387: $i > $o] :
( ? [X388: $i] :
( ( in @ X388 @ X386 )
& ~ ( X387 @ X388 ) )
=> ~ ! [X389: $i] :
( ( in @ X389 @ X386 )
=> ( X387 @ X389 ) ) )
=> ( ! [X390: $o] :
( X390
=> ( in @ emptyset @ ( prop2set @ X390 ) ) )
=> ( prop2set2propI
=> ( ! [X391: $i,X392: $i > $o] :
( ~ ? [X393: $i] :
( ( in @ X393 @ X391 )
& ( X392 @ X393 ) )
=> ! [X394: $i] :
( ( in @ X394 @ X391 )
=> ~ ( X392 @ X394 ) ) )
=> ( ! [X395: $i,X396: $i > $o] :
( ~ ! [X397: $i] :
( ( in @ X397 @ X395 )
=> ( X396 @ X397 ) )
=> ? [X398: $i] :
( ( in @ X398 @ X395 )
& ~ ( X396 @ X398 ) ) )
=> ( ! [X399: $i > $o] :
( ? [X400: $i] :
( ( X399 @ X400 )
& ! [X401: $i] :
( ( X399 @ X401 )
=> ( X400 = X401 ) ) )
=> ? [X402: $i] :
( ( X399 @ X402 )
& ! [X403: $i] :
( ( X399 @ X403 )
=> ( X402 = X403 ) ) ) )
=> ( ! [X404: $i > $o] :
( ? [X405: $i] : ( X404 @ X405 )
=> ( ! [X406: $i,X407: $i] :
( ( X404 @ X406 )
=> ( ( X404 @ X407 )
=> ( X406 = X407 ) ) )
=> ? [X408: $i] :
( ( X404 @ X408 )
& ! [X409: $i] :
( ( X404 @ X409 )
=> ( X408 = X409 ) ) ) ) )
=> ( ! [X410: $i > $o] :
( ? [X411: $i] :
! [X412: $i] :
( ( X410 @ X412 )
<=> ( X412 = X411 ) )
=> ? [X413: $i] :
( ( X410 @ X413 )
& ! [X414: $i] :
( ( X410 @ X414 )
=> ( X413 = X414 ) ) ) )
=> ( ! [X415: $i,X416: $i] :
( ( X415 = X416 )
=> ! [X417: $i,X418: $i] :
( ( X417 = X418 )
=> ( ( in @ X417 @ X415 )
=> ( in @ X418 @ X416 ) ) ) )
=> ( ! [X419: $i,X420: $i] :
( ( X419 = X420 )
=> ! [X421: $i,X422: $i] :
( ( X421 = X422 )
=> ( ( in @ X421 @ X419 )
<=> ( in @ X422 @ X420 ) ) ) )
=> ( ! [X423: $i > $o] :
( ? [X424: $i] :
( ( X423 @ X424 )
& ! [X425: $i] :
( ( X423 @ X425 )
=> ( X424 = X425 ) ) )
=> ! [X426: $i,X427: $i] :
( ( X423 @ X426 )
=> ( ( X423 @ X427 )
=> ( X426 = X427 ) ) ) )
=> ( ! [X428: $i > $o,X429: $i > $o] :
( ! [X430: $i,X431: $i] :
( ( X430 = X431 )
=> ( ( X428 @ X430 )
<=> ( X429 @ X431 ) ) )
=> ( ? [X432: $i] :
( ( X428 @ X432 )
& ! [X433: $i] :
( ( X428 @ X433 )
=> ( X432 = X433 ) ) )
<=> ? [X434: $i] :
( ( X429 @ X434 )
& ! [X435: $i] :
( ( X429 @ X435 )
=> ( X434 = X435 ) ) ) ) )
=> ( emptyset = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[emptyset__Cong]),c_0_80]),c_0_81]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),emptysetimpfalse]),quantDeMorgan3]),quantDeMorgan4]),notinemptyset]),prop2setI]),notdexE]),c_0_82]),notdallE]),c_0_83]),setext]),c_0_84]),c_0_85]),emptyI]),inCongP]),in__Cong]),noeltsimpempty]),c_0_86]),c_0_87]),c_0_88]),c_0_89]),eqinunit]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_90]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_91]),c_0_92]),uniqinunit]),notinsingleton]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_93]),emptysetE]),prop2setE]),c_0_94]),c_0_95]),c_0_96]),c_0_97]),wellorderingAx]),foundationAx]),c_0_98]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_99]) ).
thf(c_0_101,negated_conjecture,
! [X436: $i,X437: $i,X439: $i,X440: $i,X441: $i,X442: $i,X443: $i,X444: $i,X445: $i,X446: $i,X447: $i,X449: $i,X450: $i,X452: $i,X453: $i,X454: $i,X455: $i,X456: $i,X458: $i,X459: $i > $i > $o,X460: $i,X462: $i,X465: $i,X467: $i,X468: $i,X469: $i,X470: $i,X472: $i,X473: $i,X474: $i > $o,X475: $i,X476: $i,X477: $i > $o,X478: $i,X479: $i,X480: $i > $o,X481: $i,X482: $i > $o,X483: $i,X486: $i,X487: $o,X488: $i,X489: $i,X490: $o,X491: $i,X492: $i,X493: $i > $o,X494: $i,X497: $i,X498: $i,X501: $i,X503: $i,X505: $i,X506: $i > $o,X507: $i,X508: $i,X510: $i,X511: $i > $o,X512: $i,X513: $i,X514: $i,X515: $i,X516: $i,X517: $i,X518: $i,X519: $i,X520: $i,X521: $i,X522: $i,X523: $o,X524: $i,X525: $i,X526: $i,X527: $i,X528: $i,X529: $i,X531: $i,X532: $i,X533: $i,X534: $i,X535: $i,X536: $i,X537: $i,X538: $i,X539: $i,X540: $i,X541: $o,X543: $i,X544: $i,X545: $i > $o,X546: $i,X549: $i,X550: $i,X551: $i,X553: $i,X554: $i,X555: $i,X556: $i,X557: $i,X558: $i,X559: $i,X560: $i,X561: $i,X562: $i,X563: $i,X564: $i,X565: $i,X566: $i,X567: $i,X568: $i,X569: $i > $o,X570: $i,X571: $i > $o,X572: $i,X573: $i,X574: $i > $o,X575: $i,X577: $i,X578: $i > $o,X580: $i,X581: $i,X582: $i > $o,X584: $i,X585: $i,X586: $i > $o,X587: $i,X589: $o,X590: $i,X591: $i > $o,X593: $i,X594: $i,X595: $i > $o,X596: $i,X598: $i > $o,X599: $i,X602: $i,X603: $i > $o,X604: $i,X608: $i,X609: $i > $o,X610: $i,X613: $i,X614: $i,X615: $i,X616: $i,X617: $i,X618: $i,X619: $i,X620: $i,X621: $i,X622: $i > $o,X623: $i,X625: $i,X626: $i,X627: $i > $o,X628: $i > $o,X631: $i,X634: $i,X635: $i,X638: $i] :
( ( ~ ( in @ ( esk1_2 @ X436 @ X437 ) @ X436 )
| ~ ( in @ ( esk1_2 @ X436 @ X437 ) @ X437 )
| ( X436 = X437 ) )
& ( ( in @ ( esk1_2 @ X436 @ X437 ) @ X436 )
| ( in @ ( esk1_2 @ X436 @ X437 ) @ X437 )
| ( X436 = X437 ) )
& ~ ( in @ X439 @ emptyset )
& ( ~ ( in @ X442 @ ( setadjoin @ X440 @ X441 ) )
| ( X442 = X440 )
| ( in @ X442 @ X441 ) )
& ( ( X442 != X440 )
| ( in @ X442 @ ( setadjoin @ X440 @ X441 ) ) )
& ( ~ ( in @ X442 @ X441 )
| ( in @ X442 @ ( setadjoin @ X440 @ X441 ) ) )
& ( ~ ( in @ X444 @ ( powerset @ X443 ) )
| ~ ( in @ X445 @ X444 )
| ( in @ X445 @ X443 ) )
& ( ( in @ ( esk2_2 @ X446 @ X447 ) @ X447 )
| ( in @ X447 @ ( powerset @ X446 ) ) )
& ( ~ ( in @ ( esk2_2 @ X446 @ X447 ) @ X446 )
| ( in @ X447 @ ( powerset @ X446 ) ) )
& ( ( in @ X450 @ ( esk3_2 @ X449 @ X450 ) )
| ~ ( in @ X450 @ ( setunion @ X449 ) ) )
& ( ( in @ ( esk3_2 @ X449 @ X450 ) @ X449 )
| ~ ( in @ X450 @ ( setunion @ X449 ) ) )
& ( ~ ( in @ X453 @ X454 )
| ~ ( in @ X454 @ X452 )
| ( in @ X453 @ ( setunion @ X452 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X455 @ omega )
| ( in @ ( setadjoin @ X455 @ X455 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X456 ) @ omega )
| ~ ( in @ emptyset @ X456 )
| ~ ( in @ X458 @ omega )
| ( in @ X458 @ X456 ) )
& ( ( in @ ( esk4_1 @ X456 ) @ X456 )
| ~ ( in @ emptyset @ X456 )
| ~ ( in @ X458 @ omega )
| ( in @ X458 @ X456 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X456 ) @ ( esk4_1 @ X456 ) ) @ X456 )
| ~ ( in @ emptyset @ X456 )
| ~ ( in @ X458 @ omega )
| ( in @ X458 @ X456 ) )
& ( ( in @ ( esk8_3 @ X459 @ X460 @ X465 ) @ X460 )
| ~ ( in @ X465 @ ( esk7_2 @ X459 @ X460 ) )
| ( in @ ( esk5_2 @ X459 @ X460 ) @ X460 ) )
& ( ( X459 @ ( esk8_3 @ X459 @ X460 @ X465 ) @ X465 )
| ~ ( in @ X465 @ ( esk7_2 @ X459 @ X460 ) )
| ( in @ ( esk5_2 @ X459 @ X460 ) @ X460 ) )
& ( ~ ( in @ X468 @ X460 )
| ~ ( X459 @ X468 @ X467 )
| ( in @ X467 @ ( esk7_2 @ X459 @ X460 ) )
| ( in @ ( esk5_2 @ X459 @ X460 ) @ X460 ) )
& ( ( in @ ( esk8_3 @ X459 @ X460 @ X465 ) @ X460 )
| ~ ( in @ X465 @ ( esk7_2 @ X459 @ X460 ) )
| ( X459 @ ( esk5_2 @ X459 @ X460 ) @ ( esk6_3 @ X459 @ X460 @ X462 ) )
| ~ ( X459 @ ( esk5_2 @ X459 @ X460 ) @ X462 ) )
& ( ( X459 @ ( esk8_3 @ X459 @ X460 @ X465 ) @ X465 )
| ~ ( in @ X465 @ ( esk7_2 @ X459 @ X460 ) )
| ( X459 @ ( esk5_2 @ X459 @ X460 ) @ ( esk6_3 @ X459 @ X460 @ X462 ) )
| ~ ( X459 @ ( esk5_2 @ X459 @ X460 ) @ X462 ) )
& ( ~ ( in @ X468 @ X460 )
| ~ ( X459 @ X468 @ X467 )
| ( in @ X467 @ ( esk7_2 @ X459 @ X460 ) )
| ( X459 @ ( esk5_2 @ X459 @ X460 ) @ ( esk6_3 @ X459 @ X460 @ X462 ) )
| ~ ( X459 @ ( esk5_2 @ X459 @ X460 ) @ X462 ) )
& ( ( in @ ( esk8_3 @ X459 @ X460 @ X465 ) @ X460 )
| ~ ( in @ X465 @ ( esk7_2 @ X459 @ X460 ) )
| ( X462
!= ( esk6_3 @ X459 @ X460 @ X462 ) )
| ~ ( X459 @ ( esk5_2 @ X459 @ X460 ) @ X462 ) )
& ( ( X459 @ ( esk8_3 @ X459 @ X460 @ X465 ) @ X465 )
| ~ ( in @ X465 @ ( esk7_2 @ X459 @ X460 ) )
| ( X462
!= ( esk6_3 @ X459 @ X460 @ X462 ) )
| ~ ( X459 @ ( esk5_2 @ X459 @ X460 ) @ X462 ) )
& ( ~ ( in @ X468 @ X460 )
| ~ ( X459 @ X468 @ X467 )
| ( in @ X467 @ ( esk7_2 @ X459 @ X460 ) )
| ( X462
!= ( esk6_3 @ X459 @ X460 @ X462 ) )
| ~ ( X459 @ ( esk5_2 @ X459 @ X460 ) @ X462 ) )
& ( ( in @ ( esk9_1 @ X469 ) @ X469 )
| ~ ( in @ X470 @ X469 ) )
& ( ~ ( in @ X472 @ ( esk9_1 @ X469 ) )
| ~ ( in @ X472 @ X469 )
| ~ ( in @ X470 @ X469 ) )
& epred1_0
& descrp
& ( ~ ( in @ X475 @ X473 )
| ~ ( X474 @ X475 )
| ( in @ X475
@ ( dsetconstr @ X473
@ ^ [Z0: $i] : ( X474 @ Z0 ) ) ) )
& ( ~ ( in @ X478
@ ( dsetconstr @ X476
@ ^ [Z0: $i] : ( X477 @ Z0 ) ) )
| ( in @ X478 @ X476 ) )
& ( ~ ( in @ X481
@ ( dsetconstr @ X479
@ ^ [Z0: $i] : ( X480 @ Z0 ) ) )
| ( X480 @ X481 ) )
& ( ( X482 @ ( esk11_1 @ X482 ) )
| ( X482 @ ( esk10_2 @ X482 @ X483 ) )
| ~ ( X482 @ X483 ) )
& ( ~ ( X482 @ X486 )
| ( ( esk11_1 @ X482 )
= X486 )
| ( X482 @ ( esk10_2 @ X482 @ X483 ) )
| ~ ( X482 @ X483 ) )
& ( ( X482 @ ( esk11_1 @ X482 ) )
| ( X483
!= ( esk10_2 @ X482 @ X483 ) )
| ~ ( X482 @ X483 ) )
& ( ~ ( X482 @ X486 )
| ( ( esk11_1 @ X482 )
= X486 )
| ( X483
!= ( esk10_2 @ X482 @ X483 ) )
| ~ ( X482 @ X483 ) )
& ( ~ ( in @ X488 @ ( prop2set @ X487 ) )
| X487 )
& ( ~ ( in @ X489 @ emptyset )
| X490 )
& ~ ( in @ X491 @ emptyset )
& ~ ( in @ X492 @ emptyset )
& ( ( X493 @ ( esk12_2 @ X493 @ X494 ) )
| ~ ( X493 @ X494 )
| ( X493 @ ( esk13_1 @ X493 ) ) )
& ( ( X494
!= ( esk12_2 @ X493 @ X494 ) )
| ~ ( X493 @ X494 )
| ( X493 @ ( esk13_1 @ X493 ) ) )
& ( ( in @ ( esk15_2 @ X497 @ X498 ) @ X498 )
| ( X497 = X498 )
| ( in @ ( esk14_2 @ X497 @ X498 ) @ X497 ) )
& ( ~ ( in @ ( esk15_2 @ X497 @ X498 ) @ X497 )
| ( X497 = X498 )
| ( in @ ( esk14_2 @ X497 @ X498 ) @ X497 ) )
& ( ( in @ ( esk15_2 @ X497 @ X498 ) @ X498 )
| ( X497 = X498 )
| ~ ( in @ ( esk14_2 @ X497 @ X498 ) @ X498 ) )
& ( ~ ( in @ ( esk15_2 @ X497 @ X498 ) @ X497 )
| ( X497 = X498 )
| ~ ( in @ ( esk14_2 @ X497 @ X498 ) @ X498 ) )
& ( ( in @ ( esk16_1 @ X501 ) @ X501 )
| ( X501 = emptyset ) )
& ( ( in @ ( esk17_1 @ X503 ) @ X503 )
| ( X503 = emptyset ) )
& ( ~ ( in @ X507
@ ( dsetconstr @ X505
@ ^ [Z0: $i] : ( X506 @ Z0 ) ) )
| ( X506 @ X507 )
| ~ ( in @ X507 @ X505 ) )
& ( ~ ( X506 @ X507 )
| ( in @ X507
@ ( dsetconstr @ X505
@ ^ [Z0: $i] : ( X506 @ Z0 ) ) )
| ~ ( in @ X507 @ X505 ) )
& ( ( X508 = emptyset )
| ( in @ ( esk18_1 @ X508 ) @ X508 ) )
& ( ~ ( in @ X512 @ X510 )
| ~ ( X511 @ X512 )
| ( ( dsetconstr @ X510
@ ^ [Z0: $i] : ( X511 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X514 @ X513 )
| ( X513 != emptyset ) )
& ( in @ X515 @ ( setadjoin @ X515 @ X516 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X519 @ X518 )
| ( in @ X519 @ ( setadjoin @ X517 @ X518 ) ) )
& ( ( in @ X522 @ X521 )
| X523
| ( X522 = X520 )
| ~ ( in @ X522 @ ( setadjoin @ X520 @ X521 ) ) )
& ( ~ X523
| X523
| ( X522 = X520 )
| ~ ( in @ X522 @ ( setadjoin @ X520 @ X521 ) ) )
& ( ( in @ X522 @ X521 )
| X523
| ~ X523
| ~ ( in @ X522 @ ( setadjoin @ X520 @ X521 ) ) )
& ( ~ X523
| X523
| ~ X523
| ~ ( in @ X522 @ ( setadjoin @ X520 @ X521 ) ) )
& ( ~ ( in @ X526 @ ( setadjoin @ X524 @ X525 ) )
| ( X526 = X524 )
| ( in @ X526 @ X525 ) )
& ( ( dsetconstr @ X527
@ ^ [Z0: $i] : $true )
= X527 )
& ( ( in @ ( esk19_2 @ X528 @ X529 ) @ X529 )
| ( in @ X529 @ ( powerset @ X528 ) ) )
& ( ~ ( in @ ( esk19_2 @ X528 @ X529 ) @ X528 )
| ( in @ X529 @ ( powerset @ X528 ) ) )
& ( in @ emptyset @ ( powerset @ X531 ) )
& ( in @ emptyset @ ( powerset @ X532 ) )
& ( ~ ( in @ X534 @ ( powerset @ X533 ) )
| ~ ( in @ X535 @ X534 )
| ( in @ X535 @ X533 ) )
& ( ~ ( in @ X537 @ X538 )
| ~ ( in @ X538 @ X536 )
| ( in @ X537 @ ( setunion @ X536 ) ) )
& ( ( in @ X540 @ ( esk20_3 @ X539 @ X540 @ X541 ) )
| X541
| ~ ( in @ X540 @ ( setunion @ X539 ) ) )
& ( ( in @ ( esk20_3 @ X539 @ X540 @ X541 ) @ X539 )
| X541
| ~ ( in @ X540 @ ( setunion @ X539 ) ) )
& ( ~ X541
| X541
| ~ ( in @ X540 @ ( setunion @ X539 ) ) )
& ( ~ ( in @ X544 @ X543 )
| ( in @ X544 @ ( powerset @ ( setunion @ X543 ) ) ) )
& ( ~ ( X545 @ X549 )
| ( X549
= ( esk22_1 @ X545 ) )
| ( X545 @ ( esk21_2 @ X545 @ X546 ) )
| ~ ( X545 @ X546 ) )
& ( ( X550
!= ( esk22_1 @ X545 ) )
| ( X545 @ X550 )
| ( X545 @ ( esk21_2 @ X545 @ X546 ) )
| ~ ( X545 @ X546 ) )
& ( ~ ( X545 @ X549 )
| ( X549
= ( esk22_1 @ X545 ) )
| ( X546
!= ( esk21_2 @ X545 @ X546 ) )
| ~ ( X545 @ X546 ) )
& ( ( X550
!= ( esk22_1 @ X545 ) )
| ( X545 @ X550 )
| ( X546
!= ( esk21_2 @ X545 @ X546 ) )
| ~ ( X545 @ X546 ) )
& ( ( X551 = emptyset )
| ( in @ ( esk23_1 @ X551 ) @ X551 ) )
& ( ~ ( in @ X553 @ ( setadjoin @ X554 @ emptyset ) )
| ( X553 = X554 ) )
& ( ( X555 = X556 )
| ~ ( in @ X556 @ ( setadjoin @ X555 @ emptyset ) ) )
& ( ( X557 != X558 )
| ( in @ X557 @ ( setadjoin @ X558 @ emptyset ) ) )
& ( ~ ( in @ X559 @ ( setadjoin @ X560 @ emptyset ) )
| ( in @ X560 @ ( setadjoin @ X559 @ emptyset ) ) )
& ( ~ ( in @ X563 @ ( setadjoin @ X561 @ ( setadjoin @ X562 @ emptyset ) ) )
| ( X563 = X561 )
| ( X563 = X562 ) )
& ( in @ X564 @ ( setadjoin @ X564 @ ( setadjoin @ X565 @ emptyset ) ) )
& ( in @ X567 @ ( setadjoin @ X566 @ ( setadjoin @ X567 @ emptyset ) ) )
& ( ~ ( in @ X570 @ X568 )
| ~ ( X569 @ X570 )
| ( ( dsetconstr @ X568
@ ^ [Z0: $i] : ( X569 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X572 @ emptyset )
| ( X571 @ X572 ) )
& ( ( in @ ( esk24_2 @ X573 @ X574 ) @ X573 )
| ~ ( in @ X575 @ X573 )
| ( X574 @ X575 ) )
& ( ~ ( X574 @ ( esk24_2 @ X573 @ X574 ) )
| ~ ( in @ X575 @ X573 )
| ( X574 @ X575 ) )
& ( ( in @ ( esk25_2 @ X577 @ X578 ) @ X577 )
| ~ ( in @ X580 @ X577 )
| ~ ( X578 @ X580 ) )
& ( ( X578 @ ( esk25_2 @ X577 @ X578 ) )
| ~ ( in @ X580 @ X577 )
| ~ ( X578 @ X580 ) )
& ( ( in @ ( esk26_2 @ X581 @ X582 ) @ X581 )
| ~ ( in @ X584 @ X581 )
| ~ ( X582 @ X584 ) )
& ( ( X582 @ ( esk26_2 @ X581 @ X582 ) )
| ~ ( in @ X584 @ X581 )
| ~ ( X582 @ X584 ) )
& ( ( in @ ( esk27_2 @ X585 @ X586 ) @ X585 )
| ~ ( in @ X587 @ X585 )
| ( X586 @ X587 ) )
& ( ~ ( X586 @ ( esk27_2 @ X585 @ X586 ) )
| ~ ( in @ X587 @ X585 )
| ( X586 @ X587 ) )
& ( ~ X589
| ( in @ emptyset @ ( prop2set @ X589 ) ) )
& prop2set2propI
& ( ( in @ ( esk28_2 @ X590 @ X591 ) @ X590 )
| ~ ( in @ X593 @ X590 )
| ~ ( X591 @ X593 ) )
& ( ( X591 @ ( esk28_2 @ X590 @ X591 ) )
| ~ ( in @ X593 @ X590 )
| ~ ( X591 @ X593 ) )
& ( ( in @ ( esk29_2 @ X594 @ X595 ) @ X594 )
| ~ ( in @ X596 @ X594 )
| ( X595 @ X596 ) )
& ( ~ ( X595 @ ( esk29_2 @ X594 @ X595 ) )
| ~ ( in @ X596 @ X594 )
| ( X595 @ X596 ) )
& ( ( X598 @ ( esk31_1 @ X598 ) )
| ( X598 @ ( esk30_2 @ X598 @ X599 ) )
| ~ ( X598 @ X599 ) )
& ( ~ ( X598 @ X602 )
| ( ( esk31_1 @ X598 )
= X602 )
| ( X598 @ ( esk30_2 @ X598 @ X599 ) )
| ~ ( X598 @ X599 ) )
& ( ( X598 @ ( esk31_1 @ X598 ) )
| ( X599
!= ( esk30_2 @ X598 @ X599 ) )
| ~ ( X598 @ X599 ) )
& ( ~ ( X598 @ X602 )
| ( ( esk31_1 @ X598 )
= X602 )
| ( X599
!= ( esk30_2 @ X598 @ X599 ) )
| ~ ( X598 @ X599 ) )
& ( ( X603 @ ( esk34_1 @ X603 ) )
| ( X603 @ ( esk32_1 @ X603 ) )
| ~ ( X603 @ X604 ) )
& ( ~ ( X603 @ X608 )
| ( ( esk34_1 @ X603 )
= X608 )
| ( X603 @ ( esk32_1 @ X603 ) )
| ~ ( X603 @ X604 ) )
& ( ( X603 @ ( esk34_1 @ X603 ) )
| ( X603 @ ( esk33_1 @ X603 ) )
| ~ ( X603 @ X604 ) )
& ( ~ ( X603 @ X608 )
| ( ( esk34_1 @ X603 )
= X608 )
| ( X603 @ ( esk33_1 @ X603 ) )
| ~ ( X603 @ X604 ) )
& ( ( X603 @ ( esk34_1 @ X603 ) )
| ( ( esk32_1 @ X603 )
!= ( esk33_1 @ X603 ) )
| ~ ( X603 @ X604 ) )
& ( ~ ( X603 @ X608 )
| ( ( esk34_1 @ X603 )
= X608 )
| ( ( esk32_1 @ X603 )
!= ( esk33_1 @ X603 ) )
| ~ ( X603 @ X604 ) )
& ( ( X609 @ ( esk36_1 @ X609 ) )
| ~ ( X609 @ ( esk35_2 @ X609 @ X610 ) )
| ( ( esk35_2 @ X609 @ X610 )
!= X610 ) )
& ( ~ ( X609 @ X613 )
| ( ( esk36_1 @ X609 )
= X613 )
| ~ ( X609 @ ( esk35_2 @ X609 @ X610 ) )
| ( ( esk35_2 @ X609 @ X610 )
!= X610 ) )
& ( ( X609 @ ( esk36_1 @ X609 ) )
| ( X609 @ ( esk35_2 @ X609 @ X610 ) )
| ( ( esk35_2 @ X609 @ X610 )
= X610 ) )
& ( ~ ( X609 @ X613 )
| ( ( esk36_1 @ X609 )
= X613 )
| ( X609 @ ( esk35_2 @ X609 @ X610 ) )
| ( ( esk35_2 @ X609 @ X610 )
= X610 ) )
& ( ( X614 != X615 )
| ( X616 != X617 )
| ~ ( in @ X616 @ X614 )
| ( in @ X617 @ X615 ) )
& ( ~ ( in @ X620 @ X618 )
| ( in @ X621 @ X619 )
| ( X620 != X621 )
| ( X618 != X619 ) )
& ( ~ ( in @ X621 @ X619 )
| ( in @ X620 @ X618 )
| ( X620 != X621 )
| ( X618 != X619 ) )
& ( ( X622 @ ( esk37_2 @ X622 @ X623 ) )
| ~ ( X622 @ X623 )
| ~ ( X622 @ X625 )
| ~ ( X622 @ X626 )
| ( X625 = X626 ) )
& ( ( X623
!= ( esk37_2 @ X622 @ X623 ) )
| ~ ( X622 @ X623 )
| ~ ( X622 @ X625 )
| ~ ( X622 @ X626 )
| ( X625 = X626 ) )
& ( ( X628 @ ( esk41_2 @ X627 @ X628 ) )
| ( X627 @ ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X628 @ X634 )
| ( ( esk41_2 @ X627 @ X628 )
= X634 )
| ( X627 @ ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X628 @ ( esk41_2 @ X627 @ X628 ) )
| ( X631
!= ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X628 @ X634 )
| ( ( esk41_2 @ X627 @ X628 )
= X634 )
| ( X631
!= ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X627 @ ( esk43_2 @ X627 @ X628 ) )
| ( X628 @ ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X627 @ X638 )
| ( ( esk43_2 @ X627 @ X628 )
= X638 )
| ( X628 @ ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X627 @ ( esk43_2 @ X627 @ X628 ) )
| ( X635
!= ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X627 @ X638 )
| ( ( esk43_2 @ X627 @ X628 )
= X638 )
| ( X635
!= ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( ( esk38_2 @ X627 @ X628 )
= ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X628 @ ( esk41_2 @ X627 @ X628 ) )
| ( X627 @ ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X628 @ X634 )
| ( ( esk41_2 @ X627 @ X628 )
= X634 )
| ( X627 @ ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X628 @ ( esk41_2 @ X627 @ X628 ) )
| ( X631
!= ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X628 @ X634 )
| ( ( esk41_2 @ X627 @ X628 )
= X634 )
| ( X631
!= ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X627 @ ( esk43_2 @ X627 @ X628 ) )
| ( X628 @ ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X627 @ X638 )
| ( ( esk43_2 @ X627 @ X628 )
= X638 )
| ( X628 @ ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X627 @ ( esk43_2 @ X627 @ X628 ) )
| ( X635
!= ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X627 @ X638 )
| ( ( esk43_2 @ X627 @ X628 )
= X638 )
| ( X635
!= ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ~ ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ~ ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X628 @ ( esk41_2 @ X627 @ X628 ) )
| ( X627 @ ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X628 @ X634 )
| ( ( esk41_2 @ X627 @ X628 )
= X634 )
| ( X627 @ ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X628 @ ( esk41_2 @ X627 @ X628 ) )
| ( X631
!= ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X628 @ X634 )
| ( ( esk41_2 @ X627 @ X628 )
= X634 )
| ( X631
!= ( esk40_3 @ X627 @ X628 @ X631 ) )
| ~ ( X627 @ X631 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X627 @ ( esk43_2 @ X627 @ X628 ) )
| ( X628 @ ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X627 @ X638 )
| ( ( esk43_2 @ X627 @ X628 )
= X638 )
| ( X628 @ ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ( X627 @ ( esk43_2 @ X627 @ X628 ) )
| ( X635
!= ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( ~ ( X627 @ X638 )
| ( ( esk43_2 @ X627 @ X628 )
= X638 )
| ( X635
!= ( esk42_3 @ X627 @ X628 @ X635 ) )
| ~ ( X628 @ X635 )
| ( X627 @ ( esk38_2 @ X627 @ X628 ) )
| ( X628 @ ( esk39_2 @ X627 @ X628 ) ) )
& ( emptyset != emptyset ) ),
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_100])])])])])]) ).
thf(c_0_102,negated_conjecture,
emptyset != emptyset,
inference(split_conjunct,[status(thm)],[c_0_101]) ).
thf(c_0_103,negated_conjecture,
$false,
inference(cn,[status(thm)],[c_0_102]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU551^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.09/0.09 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n029.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun May 19 16:58:22 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.14/0.39 Running higher-order theorem proving
% 0.14/0.39 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/benchmark/theBenchmark.p
% 0.14/0.42 # Version: 3.1.0-ho
% 0.14/0.42 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.14/0.42 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 # Starting new_ho_10 with 1500s (5) cores
% 0.14/0.42 # Starting sh5l with 300s (1) cores
% 0.14/0.42 # Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 # Starting new_bool_2 with 300s (1) cores
% 0.14/0.42 # new_bool_2 with pid 20250 completed with status 0
% 0.14/0.42 # Result found by new_bool_2
% 0.14/0.42 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.14/0.42 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 # Starting new_ho_10 with 1500s (5) cores
% 0.14/0.42 # Starting sh5l with 300s (1) cores
% 0.14/0.42 # Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 # Starting new_bool_2 with 300s (1) cores
% 0.14/0.42 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.14/0.42 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 # Starting ho_unfolding_3 with 163s (1) cores
% 0.14/0.42 # ho_unfolding_3 with pid 20251 completed with status 0
% 0.14/0.42 # Result found by ho_unfolding_3
% 0.14/0.42 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.14/0.42 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 # Starting new_ho_10 with 1500s (5) cores
% 0.14/0.42 # Starting sh5l with 300s (1) cores
% 0.14/0.42 # Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 # Starting new_bool_2 with 300s (1) cores
% 0.14/0.42 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.14/0.42 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 # Starting ho_unfolding_3 with 163s (1) cores
% 0.14/0.42 # Preprocessing time : 0.003 s
% 0.14/0.42 # Presaturation interreduction done
% 0.14/0.42
% 0.14/0.42 # Proof found!
% 0.14/0.42 # SZS status Theorem
% 0.14/0.42 # SZS output start CNFRefutation
% See solution above
% 0.14/0.42 # Parsed axioms : 149
% 0.14/0.42 # Removed by relevancy pruning/SinE : 81
% 0.14/0.42 # Initial clauses : 158
% 0.14/0.42 # Removed in clause preprocessing : 7
% 0.14/0.42 # Initial clauses in saturation : 151
% 0.14/0.42 # Processed clauses : 1
% 0.14/0.42 # ...of these trivial : 0
% 0.14/0.42 # ...subsumed : 0
% 0.14/0.42 # ...remaining for further processing : 0
% 0.14/0.42 # Other redundant clauses eliminated : 0
% 0.14/0.42 # Clauses deleted for lack of memory : 0
% 0.14/0.42 # Backward-subsumed : 0
% 0.14/0.42 # Backward-rewritten : 0
% 0.14/0.42 # Generated clauses : 0
% 0.14/0.42 # ...of the previous two non-redundant : 0
% 0.14/0.42 # ...aggressively subsumed : 0
% 0.14/0.42 # Contextual simplify-reflections : 0
% 0.14/0.42 # Paramodulations : 0
% 0.14/0.42 # Factorizations : 0
% 0.14/0.42 # NegExts : 0
% 0.14/0.42 # Equation resolutions : 0
% 0.14/0.42 # Disequality decompositions : 0
% 0.14/0.42 # Total rewrite steps : 0
% 0.14/0.42 # ...of those cached : 0
% 0.14/0.42 # Propositional unsat checks : 0
% 0.14/0.42 # Propositional check models : 0
% 0.14/0.42 # Propositional check unsatisfiable : 0
% 0.14/0.42 # Propositional clauses : 0
% 0.14/0.42 # Propositional clauses after purity: 0
% 0.14/0.42 # Propositional unsat core size : 0
% 0.14/0.42 # Propositional preprocessing time : 0.000
% 0.14/0.42 # Propositional encoding time : 0.000
% 0.14/0.42 # Propositional solver time : 0.000
% 0.14/0.42 # Success case prop preproc time : 0.000
% 0.14/0.42 # Success case prop encoding time : 0.000
% 0.14/0.42 # Success case prop solver time : 0.000
% 0.14/0.42 # Current number of processed clauses : 0
% 0.14/0.42 # Positive orientable unit clauses : 0
% 0.14/0.42 # Positive unorientable unit clauses: 0
% 0.14/0.42 # Negative unit clauses : 0
% 0.14/0.42 # Non-unit-clauses : 0
% 0.14/0.42 # Current number of unprocessed clauses: 150
% 0.14/0.42 # ...number of literals in the above : 500
% 0.14/0.42 # Current number of archived formulas : 0
% 0.14/0.42 # Current number of archived clauses : 0
% 0.14/0.42 # Clause-clause subsumption calls (NU) : 0
% 0.14/0.42 # Rec. Clause-clause subsumption calls : 0
% 0.14/0.42 # Non-unit clause-clause subsumptions : 0
% 0.14/0.42 # Unit Clause-clause subsumption calls : 0
% 0.14/0.42 # Rewrite failures with RHS unbound : 0
% 0.14/0.42 # BW rewrite match attempts : 0
% 0.14/0.42 # BW rewrite match successes : 0
% 0.14/0.42 # Condensation attempts : 1
% 0.14/0.42 # Condensation successes : 0
% 0.14/0.42 # Termbank termtop insertions : 17391
% 0.14/0.42 # Search garbage collected termcells : 6329
% 0.14/0.42
% 0.14/0.42 # -------------------------------------------------
% 0.14/0.42 # User time : 0.013 s
% 0.14/0.42 # System time : 0.005 s
% 0.14/0.42 # Total time : 0.019 s
% 0.14/0.42 # Maximum resident set size: 3920 pages
% 0.14/0.42
% 0.14/0.42 # -------------------------------------------------
% 0.14/0.42 # User time : 0.017 s
% 0.14/0.42 # System time : 0.008 s
% 0.14/0.42 # Total time : 0.024 s
% 0.14/0.42 # Maximum resident set size: 1920 pages
% 0.14/0.42 % E---3.1 exiting
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------