TSTP Solution File: SEU554^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU554^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 03:28:09 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 198
% Syntax : Number of formulae : 234 ( 20 unt; 126 typ; 0 def)
% Number of atoms : 872 ( 237 equ; 0 cnn)
% Maximal formula atoms : 260 ( 8 avg)
% Number of connectives : 3393 ( 305 ~; 334 |; 229 &;1987 @)
% ( 120 <=>; 418 =>; 0 <=; 0 <~>)
% Maximal formula depth : 319 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 233 ( 233 >; 0 *; 0 +; 0 <<)
% Number of symbols : 129 ( 126 usr; 77 con; 0-3 aty)
% Number of variables : 748 ( 54 ^ 598 !; 96 ?; 748 :)
% 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,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
epred1_0: $o ).
thf(decl_105,type,
esk1_2: $i > $i > $i ).
thf(decl_106,type,
esk2_2: $i > $i > $i ).
thf(decl_107,type,
esk3_2: $i > $i > $i ).
thf(decl_108,type,
esk4_1: $i > $i ).
thf(decl_109,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_110,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_111,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_112,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_113,type,
esk9_1: $i > $i ).
thf(decl_114,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_115,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_116,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_117,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_118,type,
esk14_2: $i > $i > $i ).
thf(decl_119,type,
esk15_2: $i > $i > $i ).
thf(decl_120,type,
esk16_1: $i > $i ).
thf(decl_121,type,
esk17_1: $i > $i ).
thf(decl_122,type,
esk18_1: $i > $i ).
thf(decl_123,type,
esk19_2: $i > $i > $i ).
thf(decl_124,type,
esk20_3: $i > $i > $o > $i ).
thf(decl_125,type,
esk21_2: ( $i > $o ) > $i > $i ).
thf(decl_126,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_127,type,
esk23_1: $i > $i ).
thf(decl_128,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_129,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_130,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_131,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_132,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_133,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_134,type,
esk30_2: ( $i > $o ) > $i > $i ).
thf(decl_135,type,
esk31_1: ( $i > $o ) > $i ).
thf(decl_136,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_137,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_138,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_139,type,
esk35_2: ( $i > $o ) > $i > $i ).
thf(decl_140,type,
esk36_1: ( $i > $o ) > $i ).
thf(decl_141,type,
esk37_2: ( $i > $o ) > $i > $i ).
thf(decl_142,type,
esk38_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_143,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_144,type,
esk40_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_145,type,
esk41_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_146,type,
esk42_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_147,type,
esk43_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_148,type,
esk44_0: $i ).
thf(decl_149,type,
esk45_0: $i ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
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/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',replAx) ).
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/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(setunion__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__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
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/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setextAx) ).
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,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_73,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_74,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_75,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_76,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_77,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_78,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_79,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_80,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_81,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_82,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_83,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X220: $i] :
( ( X1 @ X220 )
& ! [X221: $i] :
( ( X1 @ X221 )
=> ( X220 = X221 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_84,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X224: $i] :
( ( X1 @ X224 )
& ! [X225: $i] :
( ( X1 @ X225 )
=> ( X224 = X225 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_73,c_0_72]) ).
thf(c_0_85,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X226: $i] :
( ( X1 @ X226 )
& ! [X227: $i] :
( ( X1 @ X227 )
=> ( X226 = X227 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_74,c_0_72]) ).
thf(c_0_86,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X228: $i] :
( ( X1 @ X228 )
& ! [X229: $i] :
( ( X1 @ X229 )
=> ( X228 = X229 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_75,c_0_72]) ).
thf(c_0_87,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X230: $i] :
( ( X1 @ X230 )
& ! [X231: $i] :
( ( X1 @ X231 )
=> ( X230 = X231 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_76,c_0_72]) ).
thf(c_0_88,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_89,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X232: $i] :
( ( X1 @ X232 )
& ! [X233: $i] :
( ( X1 @ X233 )
=> ( X232 = X233 ) ) )
<=> ? [X234: $i] :
( ( X17 @ X234 )
& ! [X235: $i] :
( ( X17 @ X235 )
=> ( X234 = X235 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_77,c_0_72]) ).
thf(c_0_90,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_78]) ).
thf(c_0_91,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_79,c_0_78]) ).
thf(c_0_92,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_78]) ).
thf(c_0_93,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_94,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X222: $i] :
( ( X1 @ X222 )
& ! [X223: $i] :
( ( X1 @ X223 )
=> ( X222 = X223 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_80,c_0_72]) ).
thf(c_0_95,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_78]) ).
thf(c_0_96,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_97,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X218: $i] :
( ( X1 @ X218 )
& ! [X219: $i] :
( ( X1 @ X219 )
=> ( X218 = X219 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_81,c_0_72]) ).
thf(c_0_98,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_99,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_100,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_101,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X216: $i] :
( ( X6 @ X2 @ X216 )
& ! [X217: $i] :
( ( X6 @ X2 @ X217 )
=> ( X216 = X217 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_82,c_0_72]) ).
thf(c_0_102,plain,
( epred1_0
<=> ! [X265: $i] :
? [X266: $i] :
( ! [X267: $i] :
( ( in @ X267 @ X266 )
=> ! [X268: $i] :
( ( in @ X268 @ X267 )
=> ( in @ X268 @ X265 ) ) )
& ! [X269: $i,X270: $i] :
( ( ( in @ X269 @ X265 )
& ( in @ X270 @ X265 ) )
=> ( ! [X271: $i] :
( ( in @ X271 @ X266 )
=> ( ( in @ X269 @ X271 )
<=> ( in @ X270 @ X271 ) ) )
=> ( X269 = X270 ) ) )
& ! [X272: $i,X273: $i] :
( ( ( in @ X272 @ X266 )
& ( in @ X273 @ X266 ) )
=> ( ! [X274: $i] :
( ( in @ X274 @ X272 )
=> ( in @ X274 @ X273 ) )
| ! [X275: $i] :
( ( in @ X275 @ X273 )
=> ( in @ X275 @ X272 ) ) ) )
& ! [X276: $i] :
( ( ! [X277: $i] :
( ( in @ X277 @ X276 )
=> ( in @ X277 @ X265 ) )
& ? [X278: $i] : ( in @ X278 @ X276 ) )
=> ? [X279: $i,X280: $i] :
( ( in @ X279 @ X266 )
& ( in @ X280 @ X276 )
& ~ ? [X281: $i] :
( ( in @ X281 @ X279 )
& ( in @ X281 @ X276 ) )
& ! [X282: $i] :
( ( in @ X282 @ X266 )
=> ( ! [X283: $i] :
( ( in @ X283 @ X282 )
=> ( in @ X283 @ X279 ) )
| ( in @ X280 @ X282 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_103,negated_conjecture,
~ ( ! [X236: $i,X237: $i] :
( ! [X238: $i] :
( ( in @ X238 @ X236 )
<=> ( in @ X238 @ X237 ) )
=> ( X236 = X237 ) )
=> ( ! [X239: $i] :
~ ( in @ X239 @ emptyset )
=> ( ! [X240: $i,X241: $i,X242: $i] :
( ( in @ X242 @ ( setadjoin @ X240 @ X241 ) )
<=> ( ( X242 = X240 )
| ( in @ X242 @ X241 ) ) )
=> ( ! [X243: $i,X244: $i] :
( ( in @ X244 @ ( powerset @ X243 ) )
<=> ! [X245: $i] :
( ( in @ X245 @ X244 )
=> ( in @ X245 @ X243 ) ) )
=> ( ! [X246: $i,X247: $i] :
( ( in @ X247 @ ( setunion @ X246 ) )
<=> ? [X248: $i] :
( ( in @ X247 @ X248 )
& ( in @ X248 @ X246 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X249: $i] :
( ( in @ X249 @ omega )
=> ( in @ ( setadjoin @ X249 @ X249 ) @ omega ) )
=> ( ! [X250: $i] :
( ( ( in @ emptyset @ X250 )
& ! [X251: $i] :
( ( ( in @ X251 @ omega )
& ( in @ X251 @ X250 ) )
=> ( in @ ( setadjoin @ X251 @ X251 ) @ X250 ) ) )
=> ! [X252: $i] :
( ( in @ X252 @ omega )
=> ( in @ X252 @ X250 ) ) )
=> ( ! [X253: $i > $i > $o,X254: $i] :
( ! [X255: $i] :
( ( in @ X255 @ X254 )
=> ? [X256: $i] :
( ( X253 @ X255 @ X256 )
& ! [X257: $i] :
( ( X253 @ X255 @ X257 )
=> ( X256 = X257 ) ) ) )
=> ? [X258: $i] :
! [X259: $i] :
( ( in @ X259 @ X258 )
<=> ? [X260: $i] :
( ( in @ X260 @ X254 )
& ( X253 @ X260 @ X259 ) ) ) )
=> ( ! [X261: $i] :
( ? [X262: $i] : ( in @ X262 @ X261 )
=> ? [X263: $i] :
( ( in @ X263 @ X261 )
& ~ ? [X264: $i] :
( ( in @ X264 @ X263 )
& ( in @ X264 @ X261 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X284: $i,X285: $i > $o,X286: $i] :
( ( in @ X286 @ X284 )
=> ( ( X285 @ X286 )
=> ( in @ X286
@ ( dsetconstr @ X284
@ ^ [Z0: $i] : ( X285 @ Z0 ) ) ) ) )
=> ( ! [X287: $i,X288: $i > $o,X289: $i] :
( ( in @ X289
@ ( dsetconstr @ X287
@ ^ [Z0: $i] : ( X288 @ Z0 ) ) )
=> ( in @ X289 @ X287 ) )
=> ( ! [X290: $i,X291: $i > $o,X292: $i] :
( ( in @ X292
@ ( dsetconstr @ X290
@ ^ [Z0: $i] : ( X291 @ Z0 ) ) )
=> ( X291 @ X292 ) )
=> ( ! [X293: $i > $o] :
( ? [X294: $i] :
( ( X293 @ X294 )
& ! [X295: $i] :
( ( X293 @ X295 )
=> ( X294 = X295 ) ) )
=> ? [X296: $i] :
( ( X293 @ X296 )
& ! [X297: $i] :
( ( X293 @ X297 )
=> ( X296 = X297 ) ) ) )
=> ( ! [X298: $o,X299: $i] :
( ( in @ X299 @ ( prop2set @ X298 ) )
=> X298 )
=> ( ! [X300: $i] :
( ( in @ X300 @ emptyset )
=> ! [X301: $o] : X301 )
=> ( ! [X302: $i] :
~ ( in @ X302 @ emptyset )
=> ( ! [X303: $i] :
~ ( in @ X303 @ emptyset )
=> ( ! [X304: $i > $o] :
( ? [X305: $i] :
( ( X304 @ X305 )
& ! [X306: $i] :
( ( X304 @ X306 )
=> ( X305 = X306 ) ) )
=> ? [X307: $i] : ( X304 @ X307 ) )
=> ( ! [X308: $i,X309: $i] :
( ! [X310: $i] :
( ( in @ X310 @ X308 )
=> ( in @ X310 @ X309 ) )
=> ( ! [X311: $i] :
( ( in @ X311 @ X309 )
=> ( in @ X311 @ X308 ) )
=> ( X308 = X309 ) ) )
=> ( ! [X312: $i] :
( ! [X313: $i] :
~ ( in @ X313 @ X312 )
=> ( X312 = emptyset ) )
=> ( ! [X314: $i] :
( ! [X315: $i] :
~ ( in @ X315 @ X314 )
=> ( X314 = emptyset ) )
=> ( ! [X316: $i,X317: $i > $o,X318: $i] :
( ( in @ X318 @ X316 )
=> ( ( in @ X318
@ ( dsetconstr @ X316
@ ^ [Z0: $i] : ( X317 @ Z0 ) ) )
<=> ( X317 @ X318 ) ) )
=> ( ! [X319: $i] :
( ( X319 != emptyset )
=> ? [X320: $i] : ( in @ X320 @ X319 ) )
=> ( ! [X321: $i,X322: $i > $o,X323: $i] :
( ( in @ X323 @ X321 )
=> ( ( X322 @ X323 )
=> ( ( dsetconstr @ X321
@ ^ [Z0: $i] : ( X322 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X324: $i] :
( ? [X325: $i] : ( in @ X325 @ X324 )
=> ( X324 != emptyset ) )
=> ( ! [X326: $i,X327: $i] : ( in @ X326 @ ( setadjoin @ X326 @ X327 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X328: $i,X329: $i,X330: $i] :
( ( in @ X330 @ X329 )
=> ( in @ X330 @ ( setadjoin @ X328 @ X329 ) ) )
=> ( ! [X331: $i,X332: $i,X333: $i] :
( ( in @ X333 @ ( setadjoin @ X331 @ X332 ) )
=> ! [X334: $o] :
( ( ( X333 = X331 )
=> X334 )
=> ( ( ( in @ X333 @ X332 )
=> X334 )
=> X334 ) ) )
=> ( ! [X335: $i,X336: $i,X337: $i] :
( ( in @ X337 @ ( setadjoin @ X335 @ X336 ) )
=> ( ( X337 = X335 )
| ( in @ X337 @ X336 ) ) )
=> ( ! [X338: $i] :
( ( dsetconstr @ X338
@ ^ [Z0: $i] : $true )
= X338 )
=> ( ! [X339: $i,X340: $i] :
( ! [X341: $i] :
( ( in @ X341 @ X340 )
=> ( in @ X341 @ X339 ) )
=> ( in @ X340 @ ( powerset @ X339 ) ) )
=> ( ! [X342: $i] : ( in @ emptyset @ ( powerset @ X342 ) )
=> ( ! [X343: $i] : ( in @ emptyset @ ( powerset @ X343 ) )
=> ( ! [X344: $i,X345: $i,X346: $i] :
( ( in @ X345 @ ( powerset @ X344 ) )
=> ( ( in @ X346 @ X345 )
=> ( in @ X346 @ X344 ) ) )
=> ( ! [X347: $i,X348: $i,X349: $i] :
( ( in @ X348 @ X349 )
=> ( ( in @ X349 @ X347 )
=> ( in @ X348 @ ( setunion @ X347 ) ) ) )
=> ( ! [X350: $i,X351: $i] :
( ( in @ X351 @ ( setunion @ X350 ) )
=> ! [X352: $o] :
( ! [X353: $i] :
( ( in @ X351 @ X353 )
=> ( ( in @ X353 @ X350 )
=> X352 ) )
=> X352 ) )
=> ( ! [X354: $i,X355: $i] :
( ( in @ X355 @ X354 )
=> ( in @ X355 @ ( powerset @ ( setunion @ X354 ) ) ) )
=> ( ! [X356: $i > $o] :
( ? [X357: $i] :
( ( X356 @ X357 )
& ! [X358: $i] :
( ( X356 @ X358 )
=> ( X357 = X358 ) ) )
=> ? [X359: $i] :
! [X360: $i] :
( ( X356 @ X360 )
<=> ( X360 = X359 ) ) )
=> ( ! [X361: $i] :
( ( X361 != emptyset )
=> ? [X362: $i] : ( in @ X362 @ X361 ) )
=> ( ! [X363: $i,X364: $i] :
( ( in @ X363 @ ( setadjoin @ X364 @ emptyset ) )
=> ( X363 = X364 ) )
=> ( ! [X365: $i,X366: $i] :
( ( X365 != X366 )
=> ~ ( in @ X366 @ ( setadjoin @ X365 @ emptyset ) ) )
=> ( ! [X367: $i,X368: $i] :
( ( X367 = X368 )
=> ( in @ X367 @ ( setadjoin @ X368 @ emptyset ) ) )
=> ( ! [X369: $i,X370: $i] :
( ( in @ X369 @ ( setadjoin @ X370 @ emptyset ) )
=> ( in @ X370 @ ( setadjoin @ X369 @ emptyset ) ) )
=> ( ! [X371: $i,X372: $i,X373: $i] :
( ( in @ X373 @ ( setadjoin @ X371 @ ( setadjoin @ X372 @ emptyset ) ) )
=> ( ( X373 = X371 )
| ( X373 = X372 ) ) )
=> ( ! [X374: $i,X375: $i] : ( in @ X374 @ ( setadjoin @ X374 @ ( setadjoin @ X375 @ emptyset ) ) )
=> ( ! [X376: $i,X377: $i] : ( in @ X377 @ ( setadjoin @ X376 @ ( setadjoin @ X377 @ emptyset ) ) )
=> ( ! [X378: $i,X379: $i > $o] :
( ? [X380: $i] :
( ( in @ X380 @ X378 )
& ( X379 @ X380 ) )
=> ( ( dsetconstr @ X378
@ ^ [Z0: $i] : ( X379 @ Z0 ) )
!= emptyset ) )
=> ( ! [X381: $i > $o,X382: $i] :
( ( in @ X382 @ emptyset )
=> ( X381 @ X382 ) )
=> ( ! [X383: $i,X384: $i > $o] :
( ~ ! [X385: $i] :
( ( in @ X385 @ X383 )
=> ( X384 @ X385 ) )
=> ? [X386: $i] :
( ( in @ X386 @ X383 )
& ~ ( X384 @ X386 ) ) )
=> ( ! [X387: $i,X388: $i > $o] :
( ! [X389: $i] :
( ( in @ X389 @ X387 )
=> ~ ( X388 @ X389 ) )
=> ~ ? [X390: $i] :
( ( in @ X390 @ X387 )
& ( X388 @ X390 ) ) )
=> ( ! [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: $o] :
( X399
=> ( in @ emptyset @ ( prop2set @ X399 ) ) )
=> ( prop2set2propI
=> ( ! [X400: $i,X401: $i > $o] :
( ~ ? [X402: $i] :
( ( in @ X402 @ X400 )
& ( X401 @ X402 ) )
=> ! [X403: $i] :
( ( in @ X403 @ X400 )
=> ~ ( X401 @ X403 ) ) )
=> ( ! [X404: $i,X405: $i > $o] :
( ~ ! [X406: $i] :
( ( in @ X406 @ X404 )
=> ( X405 @ X406 ) )
=> ? [X407: $i] :
( ( in @ X407 @ X404 )
& ~ ( X405 @ X407 ) ) )
=> ( ! [X408: $i > $o] :
( ? [X409: $i] :
( ( X408 @ X409 )
& ! [X410: $i] :
( ( X408 @ X410 )
=> ( X409 = X410 ) ) )
=> ? [X411: $i] :
( ( X408 @ X411 )
& ! [X412: $i] :
( ( X408 @ X412 )
=> ( X411 = X412 ) ) ) )
=> ( ! [X413: $i > $o] :
( ? [X414: $i] : ( X413 @ X414 )
=> ( ! [X415: $i,X416: $i] :
( ( X413 @ X415 )
=> ( ( X413 @ X416 )
=> ( X415 = X416 ) ) )
=> ? [X417: $i] :
( ( X413 @ X417 )
& ! [X418: $i] :
( ( X413 @ X418 )
=> ( X417 = X418 ) ) ) ) )
=> ( ! [X419: $i > $o] :
( ? [X420: $i] :
! [X421: $i] :
( ( X419 @ X421 )
<=> ( X421 = X420 ) )
=> ? [X422: $i] :
( ( X419 @ X422 )
& ! [X423: $i] :
( ( X419 @ X423 )
=> ( X422 = X423 ) ) ) )
=> ( ! [X424: $i,X425: $i] :
( ( X424 = X425 )
=> ! [X426: $i,X427: $i] :
( ( X426 = X427 )
=> ( ( in @ X426 @ X424 )
=> ( in @ X427 @ X425 ) ) ) )
=> ( ! [X428: $i,X429: $i] :
( ( X428 = X429 )
=> ! [X430: $i,X431: $i] :
( ( X430 = X431 )
=> ( ( in @ X430 @ X428 )
<=> ( in @ X431 @ X429 ) ) ) )
=> ( ! [X432: $i > $o] :
( ? [X433: $i] :
( ( X432 @ X433 )
& ! [X434: $i] :
( ( X432 @ X434 )
=> ( X433 = X434 ) ) )
=> ! [X435: $i,X436: $i] :
( ( X432 @ X435 )
=> ( ( X432 @ X436 )
=> ( X435 = X436 ) ) ) )
=> ( ! [X437: $i > $o,X438: $i > $o] :
( ! [X439: $i,X440: $i] :
( ( X439 = X440 )
=> ( ( X437 @ X439 )
<=> ( X438 @ X440 ) ) )
=> ( ? [X441: $i] :
( ( X437 @ X441 )
& ! [X442: $i] :
( ( X437 @ X442 )
=> ( X441 = X442 ) ) )
<=> ? [X443: $i] :
( ( X438 @ X443 )
& ! [X444: $i] :
( ( X438 @ X444 )
=> ( X443 = X444 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X445: $i,X446: $i] :
( ( X445 = X446 )
=> ! [X447: $i,X448: $i] :
( ( X447 = X448 )
=> ( ( setadjoin @ X445 @ X447 )
= ( setadjoin @ X446 @ X448 ) ) ) )
=> ( ! [X449: $i,X450: $i] :
( ( X449 = X450 )
=> ( ( powerset @ X449 )
= ( powerset @ X450 ) ) )
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setunion__Cong]),emptyinunitempty]),powerset__Cong]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),c_0_83]),notdexE]),notdallE]),setext]),c_0_84]),c_0_85]),emptyI]),c_0_86]),inCongP]),noeltsimpempty]),in__Cong]),c_0_87]),c_0_88]),c_0_89]),emptyset__Cong]),c_0_90]),setadjoin__Cong]),c_0_91]),c_0_92]),setadjoinIL]),upairsetE]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_93]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_94]),c_0_95]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetIL]),upairsetIR]),c_0_96]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_97]),c_0_98]),c_0_99]),c_0_100]),wellorderingAx]),foundationAx]),c_0_101]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_102]) ).
thf(c_0_104,negated_conjecture,
! [X451: $i,X452: $i,X454: $i,X455: $i,X456: $i,X457: $i,X458: $i,X459: $i,X460: $i,X461: $i,X462: $i,X464: $i,X465: $i,X467: $i,X468: $i,X469: $i,X470: $i,X471: $i,X473: $i,X474: $i > $i > $o,X475: $i,X477: $i,X480: $i,X482: $i,X483: $i,X484: $i,X485: $i,X487: $i,X488: $i,X489: $i > $o,X490: $i,X491: $i,X492: $i > $o,X493: $i,X494: $i,X495: $i > $o,X496: $i,X497: $i > $o,X498: $i,X501: $i,X502: $o,X503: $i,X504: $i,X505: $o,X506: $i,X507: $i,X508: $i > $o,X509: $i,X512: $i,X513: $i,X516: $i,X518: $i,X520: $i,X521: $i > $o,X522: $i,X523: $i,X525: $i,X526: $i > $o,X527: $i,X528: $i,X529: $i,X530: $i,X531: $i,X532: $i,X533: $i,X534: $i,X535: $i,X536: $i,X537: $i,X538: $o,X539: $i,X540: $i,X541: $i,X542: $i,X543: $i,X544: $i,X546: $i,X547: $i,X548: $i,X549: $i,X550: $i,X551: $i,X552: $i,X553: $i,X554: $i,X555: $i,X556: $o,X558: $i,X559: $i,X560: $i > $o,X561: $i,X564: $i,X565: $i,X566: $i,X568: $i,X569: $i,X570: $i,X571: $i,X572: $i,X573: $i,X574: $i,X575: $i,X576: $i,X577: $i,X578: $i,X579: $i,X580: $i,X581: $i,X582: $i,X583: $i,X584: $i > $o,X585: $i,X586: $i > $o,X587: $i,X588: $i,X589: $i > $o,X590: $i,X592: $i,X593: $i > $o,X595: $i,X596: $i,X597: $i > $o,X599: $i,X600: $i,X601: $i > $o,X602: $i,X604: $o,X605: $i,X606: $i > $o,X608: $i,X609: $i,X610: $i > $o,X611: $i,X613: $i > $o,X614: $i,X617: $i,X618: $i > $o,X619: $i,X623: $i,X624: $i > $o,X625: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i > $o,X638: $i,X640: $i,X641: $i,X642: $i > $o,X643: $i > $o,X646: $i,X649: $i,X650: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i] :
( ( ~ ( in @ ( esk1_2 @ X451 @ X452 ) @ X451 )
| ~ ( in @ ( esk1_2 @ X451 @ X452 ) @ X452 )
| ( X451 = X452 ) )
& ( ( in @ ( esk1_2 @ X451 @ X452 ) @ X451 )
| ( in @ ( esk1_2 @ X451 @ X452 ) @ X452 )
| ( X451 = X452 ) )
& ~ ( in @ X454 @ emptyset )
& ( ~ ( in @ X457 @ ( setadjoin @ X455 @ X456 ) )
| ( X457 = X455 )
| ( in @ X457 @ X456 ) )
& ( ( X457 != X455 )
| ( in @ X457 @ ( setadjoin @ X455 @ X456 ) ) )
& ( ~ ( in @ X457 @ X456 )
| ( in @ X457 @ ( setadjoin @ X455 @ X456 ) ) )
& ( ~ ( in @ X459 @ ( powerset @ X458 ) )
| ~ ( in @ X460 @ X459 )
| ( in @ X460 @ X458 ) )
& ( ( in @ ( esk2_2 @ X461 @ X462 ) @ X462 )
| ( in @ X462 @ ( powerset @ X461 ) ) )
& ( ~ ( in @ ( esk2_2 @ X461 @ X462 ) @ X461 )
| ( in @ X462 @ ( powerset @ X461 ) ) )
& ( ( in @ X465 @ ( esk3_2 @ X464 @ X465 ) )
| ~ ( in @ X465 @ ( setunion @ X464 ) ) )
& ( ( in @ ( esk3_2 @ X464 @ X465 ) @ X464 )
| ~ ( in @ X465 @ ( setunion @ X464 ) ) )
& ( ~ ( in @ X468 @ X469 )
| ~ ( in @ X469 @ X467 )
| ( in @ X468 @ ( setunion @ X467 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X470 @ omega )
| ( in @ ( setadjoin @ X470 @ X470 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X471 ) @ omega )
| ~ ( in @ emptyset @ X471 )
| ~ ( in @ X473 @ omega )
| ( in @ X473 @ X471 ) )
& ( ( in @ ( esk4_1 @ X471 ) @ X471 )
| ~ ( in @ emptyset @ X471 )
| ~ ( in @ X473 @ omega )
| ( in @ X473 @ X471 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X471 ) @ ( esk4_1 @ X471 ) ) @ X471 )
| ~ ( in @ emptyset @ X471 )
| ~ ( in @ X473 @ omega )
| ( in @ X473 @ X471 ) )
& ( ( in @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X475 )
| ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
| ( in @ ( esk5_2 @ X474 @ X475 ) @ X475 ) )
& ( ( X474 @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X480 )
| ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
| ( in @ ( esk5_2 @ X474 @ X475 ) @ X475 ) )
& ( ~ ( in @ X483 @ X475 )
| ~ ( X474 @ X483 @ X482 )
| ( in @ X482 @ ( esk7_2 @ X474 @ X475 ) )
| ( in @ ( esk5_2 @ X474 @ X475 ) @ X475 ) )
& ( ( in @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X475 )
| ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
| ( X474 @ ( esk5_2 @ X474 @ X475 ) @ ( esk6_3 @ X474 @ X475 @ X477 ) )
| ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
& ( ( X474 @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X480 )
| ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
| ( X474 @ ( esk5_2 @ X474 @ X475 ) @ ( esk6_3 @ X474 @ X475 @ X477 ) )
| ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
& ( ~ ( in @ X483 @ X475 )
| ~ ( X474 @ X483 @ X482 )
| ( in @ X482 @ ( esk7_2 @ X474 @ X475 ) )
| ( X474 @ ( esk5_2 @ X474 @ X475 ) @ ( esk6_3 @ X474 @ X475 @ X477 ) )
| ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
& ( ( in @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X475 )
| ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
| ( X477
!= ( esk6_3 @ X474 @ X475 @ X477 ) )
| ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
& ( ( X474 @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X480 )
| ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
| ( X477
!= ( esk6_3 @ X474 @ X475 @ X477 ) )
| ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
& ( ~ ( in @ X483 @ X475 )
| ~ ( X474 @ X483 @ X482 )
| ( in @ X482 @ ( esk7_2 @ X474 @ X475 ) )
| ( X477
!= ( esk6_3 @ X474 @ X475 @ X477 ) )
| ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
& ( ( in @ ( esk9_1 @ X484 ) @ X484 )
| ~ ( in @ X485 @ X484 ) )
& ( ~ ( in @ X487 @ ( esk9_1 @ X484 ) )
| ~ ( in @ X487 @ X484 )
| ~ ( in @ X485 @ X484 ) )
& epred1_0
& descrp
& ( ~ ( in @ X490 @ X488 )
| ~ ( X489 @ X490 )
| ( in @ X490
@ ( dsetconstr @ X488
@ ^ [Z0: $i] : ( X489 @ Z0 ) ) ) )
& ( ~ ( in @ X493
@ ( dsetconstr @ X491
@ ^ [Z0: $i] : ( X492 @ Z0 ) ) )
| ( in @ X493 @ X491 ) )
& ( ~ ( in @ X496
@ ( dsetconstr @ X494
@ ^ [Z0: $i] : ( X495 @ Z0 ) ) )
| ( X495 @ X496 ) )
& ( ( X497 @ ( esk11_1 @ X497 ) )
| ( X497 @ ( esk10_2 @ X497 @ X498 ) )
| ~ ( X497 @ X498 ) )
& ( ~ ( X497 @ X501 )
| ( ( esk11_1 @ X497 )
= X501 )
| ( X497 @ ( esk10_2 @ X497 @ X498 ) )
| ~ ( X497 @ X498 ) )
& ( ( X497 @ ( esk11_1 @ X497 ) )
| ( X498
!= ( esk10_2 @ X497 @ X498 ) )
| ~ ( X497 @ X498 ) )
& ( ~ ( X497 @ X501 )
| ( ( esk11_1 @ X497 )
= X501 )
| ( X498
!= ( esk10_2 @ X497 @ X498 ) )
| ~ ( X497 @ X498 ) )
& ( ~ ( in @ X503 @ ( prop2set @ X502 ) )
| X502 )
& ( ~ ( in @ X504 @ emptyset )
| X505 )
& ~ ( in @ X506 @ emptyset )
& ~ ( in @ X507 @ emptyset )
& ( ( X508 @ ( esk12_2 @ X508 @ X509 ) )
| ~ ( X508 @ X509 )
| ( X508 @ ( esk13_1 @ X508 ) ) )
& ( ( X509
!= ( esk12_2 @ X508 @ X509 ) )
| ~ ( X508 @ X509 )
| ( X508 @ ( esk13_1 @ X508 ) ) )
& ( ( in @ ( esk15_2 @ X512 @ X513 ) @ X513 )
| ( X512 = X513 )
| ( in @ ( esk14_2 @ X512 @ X513 ) @ X512 ) )
& ( ~ ( in @ ( esk15_2 @ X512 @ X513 ) @ X512 )
| ( X512 = X513 )
| ( in @ ( esk14_2 @ X512 @ X513 ) @ X512 ) )
& ( ( in @ ( esk15_2 @ X512 @ X513 ) @ X513 )
| ( X512 = X513 )
| ~ ( in @ ( esk14_2 @ X512 @ X513 ) @ X513 ) )
& ( ~ ( in @ ( esk15_2 @ X512 @ X513 ) @ X512 )
| ( X512 = X513 )
| ~ ( in @ ( esk14_2 @ X512 @ X513 ) @ X513 ) )
& ( ( in @ ( esk16_1 @ X516 ) @ X516 )
| ( X516 = emptyset ) )
& ( ( in @ ( esk17_1 @ X518 ) @ X518 )
| ( X518 = emptyset ) )
& ( ~ ( in @ X522
@ ( dsetconstr @ X520
@ ^ [Z0: $i] : ( X521 @ Z0 ) ) )
| ( X521 @ X522 )
| ~ ( in @ X522 @ X520 ) )
& ( ~ ( X521 @ X522 )
| ( in @ X522
@ ( dsetconstr @ X520
@ ^ [Z0: $i] : ( X521 @ Z0 ) ) )
| ~ ( in @ X522 @ X520 ) )
& ( ( X523 = emptyset )
| ( in @ ( esk18_1 @ X523 ) @ X523 ) )
& ( ~ ( in @ X527 @ X525 )
| ~ ( X526 @ X527 )
| ( ( dsetconstr @ X525
@ ^ [Z0: $i] : ( X526 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X529 @ X528 )
| ( X528 != emptyset ) )
& ( in @ X530 @ ( setadjoin @ X530 @ X531 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X534 @ X533 )
| ( in @ X534 @ ( setadjoin @ X532 @ X533 ) ) )
& ( ( in @ X537 @ X536 )
| X538
| ( X537 = X535 )
| ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
& ( ~ X538
| X538
| ( X537 = X535 )
| ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
& ( ( in @ X537 @ X536 )
| X538
| ~ X538
| ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
& ( ~ X538
| X538
| ~ X538
| ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
& ( ~ ( in @ X541 @ ( setadjoin @ X539 @ X540 ) )
| ( X541 = X539 )
| ( in @ X541 @ X540 ) )
& ( ( dsetconstr @ X542
@ ^ [Z0: $i] : $true )
= X542 )
& ( ( in @ ( esk19_2 @ X543 @ X544 ) @ X544 )
| ( in @ X544 @ ( powerset @ X543 ) ) )
& ( ~ ( in @ ( esk19_2 @ X543 @ X544 ) @ X543 )
| ( in @ X544 @ ( powerset @ X543 ) ) )
& ( in @ emptyset @ ( powerset @ X546 ) )
& ( in @ emptyset @ ( powerset @ X547 ) )
& ( ~ ( in @ X549 @ ( powerset @ X548 ) )
| ~ ( in @ X550 @ X549 )
| ( in @ X550 @ X548 ) )
& ( ~ ( in @ X552 @ X553 )
| ~ ( in @ X553 @ X551 )
| ( in @ X552 @ ( setunion @ X551 ) ) )
& ( ( in @ X555 @ ( esk20_3 @ X554 @ X555 @ X556 ) )
| X556
| ~ ( in @ X555 @ ( setunion @ X554 ) ) )
& ( ( in @ ( esk20_3 @ X554 @ X555 @ X556 ) @ X554 )
| X556
| ~ ( in @ X555 @ ( setunion @ X554 ) ) )
& ( ~ X556
| X556
| ~ ( in @ X555 @ ( setunion @ X554 ) ) )
& ( ~ ( in @ X559 @ X558 )
| ( in @ X559 @ ( powerset @ ( setunion @ X558 ) ) ) )
& ( ~ ( X560 @ X564 )
| ( X564
= ( esk22_1 @ X560 ) )
| ( X560 @ ( esk21_2 @ X560 @ X561 ) )
| ~ ( X560 @ X561 ) )
& ( ( X565
!= ( esk22_1 @ X560 ) )
| ( X560 @ X565 )
| ( X560 @ ( esk21_2 @ X560 @ X561 ) )
| ~ ( X560 @ X561 ) )
& ( ~ ( X560 @ X564 )
| ( X564
= ( esk22_1 @ X560 ) )
| ( X561
!= ( esk21_2 @ X560 @ X561 ) )
| ~ ( X560 @ X561 ) )
& ( ( X565
!= ( esk22_1 @ X560 ) )
| ( X560 @ X565 )
| ( X561
!= ( esk21_2 @ X560 @ X561 ) )
| ~ ( X560 @ X561 ) )
& ( ( X566 = emptyset )
| ( in @ ( esk23_1 @ X566 ) @ X566 ) )
& ( ~ ( in @ X568 @ ( setadjoin @ X569 @ emptyset ) )
| ( X568 = X569 ) )
& ( ( X570 = X571 )
| ~ ( in @ X571 @ ( setadjoin @ X570 @ emptyset ) ) )
& ( ( X572 != X573 )
| ( in @ X572 @ ( setadjoin @ X573 @ emptyset ) ) )
& ( ~ ( in @ X574 @ ( setadjoin @ X575 @ emptyset ) )
| ( in @ X575 @ ( setadjoin @ X574 @ emptyset ) ) )
& ( ~ ( in @ X578 @ ( setadjoin @ X576 @ ( setadjoin @ X577 @ emptyset ) ) )
| ( X578 = X576 )
| ( X578 = X577 ) )
& ( in @ X579 @ ( setadjoin @ X579 @ ( setadjoin @ X580 @ emptyset ) ) )
& ( in @ X582 @ ( setadjoin @ X581 @ ( setadjoin @ X582 @ emptyset ) ) )
& ( ~ ( in @ X585 @ X583 )
| ~ ( X584 @ X585 )
| ( ( dsetconstr @ X583
@ ^ [Z0: $i] : ( X584 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X587 @ emptyset )
| ( X586 @ X587 ) )
& ( ( in @ ( esk24_2 @ X588 @ X589 ) @ X588 )
| ~ ( in @ X590 @ X588 )
| ( X589 @ X590 ) )
& ( ~ ( X589 @ ( esk24_2 @ X588 @ X589 ) )
| ~ ( in @ X590 @ X588 )
| ( X589 @ X590 ) )
& ( ( in @ ( esk25_2 @ X592 @ X593 ) @ X592 )
| ~ ( in @ X595 @ X592 )
| ~ ( X593 @ X595 ) )
& ( ( X593 @ ( esk25_2 @ X592 @ X593 ) )
| ~ ( in @ X595 @ X592 )
| ~ ( X593 @ X595 ) )
& ( ( in @ ( esk26_2 @ X596 @ X597 ) @ X596 )
| ~ ( in @ X599 @ X596 )
| ~ ( X597 @ X599 ) )
& ( ( X597 @ ( esk26_2 @ X596 @ X597 ) )
| ~ ( in @ X599 @ X596 )
| ~ ( X597 @ X599 ) )
& ( ( in @ ( esk27_2 @ X600 @ X601 ) @ X600 )
| ~ ( in @ X602 @ X600 )
| ( X601 @ X602 ) )
& ( ~ ( X601 @ ( esk27_2 @ X600 @ X601 ) )
| ~ ( in @ X602 @ X600 )
| ( X601 @ X602 ) )
& ( ~ X604
| ( in @ emptyset @ ( prop2set @ X604 ) ) )
& prop2set2propI
& ( ( in @ ( esk28_2 @ X605 @ X606 ) @ X605 )
| ~ ( in @ X608 @ X605 )
| ~ ( X606 @ X608 ) )
& ( ( X606 @ ( esk28_2 @ X605 @ X606 ) )
| ~ ( in @ X608 @ X605 )
| ~ ( X606 @ X608 ) )
& ( ( in @ ( esk29_2 @ X609 @ X610 ) @ X609 )
| ~ ( in @ X611 @ X609 )
| ( X610 @ X611 ) )
& ( ~ ( X610 @ ( esk29_2 @ X609 @ X610 ) )
| ~ ( in @ X611 @ X609 )
| ( X610 @ X611 ) )
& ( ( X613 @ ( esk31_1 @ X613 ) )
| ( X613 @ ( esk30_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ~ ( X613 @ X617 )
| ( ( esk31_1 @ X613 )
= X617 )
| ( X613 @ ( esk30_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ( X613 @ ( esk31_1 @ X613 ) )
| ( X614
!= ( esk30_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ~ ( X613 @ X617 )
| ( ( esk31_1 @ X613 )
= X617 )
| ( X614
!= ( esk30_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ( X618 @ ( esk34_1 @ X618 ) )
| ( X618 @ ( esk32_1 @ X618 ) )
| ~ ( X618 @ X619 ) )
& ( ~ ( X618 @ X623 )
| ( ( esk34_1 @ X618 )
= X623 )
| ( X618 @ ( esk32_1 @ X618 ) )
| ~ ( X618 @ X619 ) )
& ( ( X618 @ ( esk34_1 @ X618 ) )
| ( X618 @ ( esk33_1 @ X618 ) )
| ~ ( X618 @ X619 ) )
& ( ~ ( X618 @ X623 )
| ( ( esk34_1 @ X618 )
= X623 )
| ( X618 @ ( esk33_1 @ X618 ) )
| ~ ( X618 @ X619 ) )
& ( ( X618 @ ( esk34_1 @ X618 ) )
| ( ( esk32_1 @ X618 )
!= ( esk33_1 @ X618 ) )
| ~ ( X618 @ X619 ) )
& ( ~ ( X618 @ X623 )
| ( ( esk34_1 @ X618 )
= X623 )
| ( ( esk32_1 @ X618 )
!= ( esk33_1 @ X618 ) )
| ~ ( X618 @ X619 ) )
& ( ( X624 @ ( esk36_1 @ X624 ) )
| ~ ( X624 @ ( esk35_2 @ X624 @ X625 ) )
| ( ( esk35_2 @ X624 @ X625 )
!= X625 ) )
& ( ~ ( X624 @ X628 )
| ( ( esk36_1 @ X624 )
= X628 )
| ~ ( X624 @ ( esk35_2 @ X624 @ X625 ) )
| ( ( esk35_2 @ X624 @ X625 )
!= X625 ) )
& ( ( X624 @ ( esk36_1 @ X624 ) )
| ( X624 @ ( esk35_2 @ X624 @ X625 ) )
| ( ( esk35_2 @ X624 @ X625 )
= X625 ) )
& ( ~ ( X624 @ X628 )
| ( ( esk36_1 @ X624 )
= X628 )
| ( X624 @ ( esk35_2 @ X624 @ X625 ) )
| ( ( esk35_2 @ X624 @ X625 )
= X625 ) )
& ( ( X629 != X630 )
| ( X631 != X632 )
| ~ ( in @ X631 @ X629 )
| ( in @ X632 @ X630 ) )
& ( ~ ( in @ X635 @ X633 )
| ( in @ X636 @ X634 )
| ( X635 != X636 )
| ( X633 != X634 ) )
& ( ~ ( in @ X636 @ X634 )
| ( in @ X635 @ X633 )
| ( X635 != X636 )
| ( X633 != X634 ) )
& ( ( X637 @ ( esk37_2 @ X637 @ X638 ) )
| ~ ( X637 @ X638 )
| ~ ( X637 @ X640 )
| ~ ( X637 @ X641 )
| ( X640 = X641 ) )
& ( ( X638
!= ( esk37_2 @ X637 @ X638 ) )
| ~ ( X637 @ X638 )
| ~ ( X637 @ X640 )
| ~ ( X637 @ X641 )
| ( X640 = X641 ) )
& ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
| ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X643 @ X649 )
| ( ( esk41_2 @ X642 @ X643 )
= X649 )
| ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
| ( X646
!= ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X643 @ X649 )
| ( ( esk41_2 @ X642 @ X643 )
= X649 )
| ( X646
!= ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
| ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X642 @ X653 )
| ( ( esk43_2 @ X642 @ X643 )
= X653 )
| ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
| ( X650
!= ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X642 @ X653 )
| ( ( esk43_2 @ X642 @ X643 )
= X653 )
| ( X650
!= ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( ( esk38_2 @ X642 @ X643 )
= ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
| ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X643 @ X649 )
| ( ( esk41_2 @ X642 @ X643 )
= X649 )
| ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
| ( X646
!= ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X643 @ X649 )
| ( ( esk41_2 @ X642 @ X643 )
= X649 )
| ( X646
!= ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
| ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X642 @ X653 )
| ( ( esk43_2 @ X642 @ X643 )
= X653 )
| ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
| ( X650
!= ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X642 @ X653 )
| ( ( esk43_2 @ X642 @ X643 )
= X653 )
| ( X650
!= ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
| ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X643 @ X649 )
| ( ( esk41_2 @ X642 @ X643 )
= X649 )
| ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
| ( X646
!= ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X643 @ X649 )
| ( ( esk41_2 @ X642 @ X643 )
= X649 )
| ( X646
!= ( esk40_3 @ X642 @ X643 @ X646 ) )
| ~ ( X642 @ X646 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
| ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X642 @ X653 )
| ( ( esk43_2 @ X642 @ X643 )
= X653 )
| ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
| ( X650
!= ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( ~ ( X642 @ X653 )
| ( ( esk43_2 @ X642 @ X643 )
= X653 )
| ( X650
!= ( esk42_3 @ X642 @ X643 @ X650 ) )
| ~ ( X643 @ X650 )
| ( X642 @ ( esk38_2 @ X642 @ X643 ) )
| ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
& ( emptyset = emptyset )
& ( ( X654 != X655 )
| ( X656 != X657 )
| ( ( setadjoin @ X654 @ X656 )
= ( setadjoin @ X655 @ X657 ) ) )
& ( ( X658 != X659 )
| ( ( powerset @ X658 )
= ( powerset @ X659 ) ) )
& ( esk44_0 = esk45_0 )
& ( ( setunion @ esk44_0 )
!= ( setunion @ esk45_0 ) ) ),
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_103])])])])])]) ).
thf(c_0_105,negated_conjecture,
( ( setunion @ esk44_0 )
!= ( setunion @ esk45_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
thf(c_0_106,negated_conjecture,
esk44_0 = esk45_0,
inference(split_conjunct,[status(thm)],[c_0_104]) ).
thf(c_0_107,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU554^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 18:07:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.49 Running higher-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.53 # Version: 3.1.0-ho
% 0.20/0.53 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # new_bool_2 with pid 4210 completed with status 0
% 0.20/0.53 # Result found by new_bool_2
% 0.20/0.53 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.20/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.53 # ho_unfolding_3 with pid 4211 completed with status 0
% 0.20/0.53 # Result found by ho_unfolding_3
% 0.20/0.53 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.20/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.53 # Preprocessing time : 0.004 s
% 0.20/0.53 # Presaturation interreduction done
% 0.20/0.53
% 0.20/0.53 # Proof found!
% 0.20/0.53 # SZS status Theorem
% 0.20/0.53 # SZS output start CNFRefutation
% See solution above
% 0.20/0.53 # Parsed axioms : 155
% 0.20/0.53 # Removed by relevancy pruning/SinE : 84
% 0.20/0.53 # Initial clauses : 162
% 0.20/0.53 # Removed in clause preprocessing : 10
% 0.20/0.53 # Initial clauses in saturation : 152
% 0.20/0.53 # Processed clauses : 5
% 0.20/0.53 # ...of these trivial : 0
% 0.20/0.53 # ...subsumed : 0
% 0.20/0.53 # ...remaining for further processing : 4
% 0.20/0.53 # Other redundant clauses eliminated : 0
% 0.20/0.53 # Clauses deleted for lack of memory : 0
% 0.20/0.53 # Backward-subsumed : 0
% 0.20/0.53 # Backward-rewritten : 0
% 0.20/0.53 # Generated clauses : 0
% 0.20/0.53 # ...of the previous two non-redundant : 0
% 0.20/0.53 # ...aggressively subsumed : 0
% 0.20/0.53 # Contextual simplify-reflections : 0
% 0.20/0.53 # Paramodulations : 0
% 0.20/0.53 # Factorizations : 0
% 0.20/0.53 # NegExts : 0
% 0.20/0.53 # Equation resolutions : 0
% 0.20/0.53 # Disequality decompositions : 0
% 0.20/0.53 # Total rewrite steps : 1
% 0.20/0.53 # ...of those cached : 0
% 0.20/0.53 # Propositional unsat checks : 0
% 0.20/0.53 # Propositional check models : 0
% 0.20/0.53 # Propositional check unsatisfiable : 0
% 0.20/0.53 # Propositional clauses : 0
% 0.20/0.53 # Propositional clauses after purity: 0
% 0.20/0.53 # Propositional unsat core size : 0
% 0.20/0.53 # Propositional preprocessing time : 0.000
% 0.20/0.53 # Propositional encoding time : 0.000
% 0.20/0.53 # Propositional solver time : 0.000
% 0.20/0.53 # Success case prop preproc time : 0.000
% 0.20/0.53 # Success case prop encoding time : 0.000
% 0.20/0.53 # Success case prop solver time : 0.000
% 0.20/0.53 # Current number of processed clauses : 4
% 0.20/0.53 # Positive orientable unit clauses : 4
% 0.20/0.53 # Positive unorientable unit clauses: 0
% 0.20/0.53 # Negative unit clauses : 0
% 0.20/0.53 # Non-unit-clauses : 0
% 0.20/0.53 # Current number of unprocessed clauses: 147
% 0.20/0.53 # ...number of literals in the above : 497
% 0.20/0.53 # Current number of archived formulas : 0
% 0.20/0.53 # Current number of archived clauses : 0
% 0.20/0.53 # Clause-clause subsumption calls (NU) : 0
% 0.20/0.53 # Rec. Clause-clause subsumption calls : 0
% 0.20/0.53 # Non-unit clause-clause subsumptions : 0
% 0.20/0.53 # Unit Clause-clause subsumption calls : 0
% 0.20/0.53 # Rewrite failures with RHS unbound : 0
% 0.20/0.53 # BW rewrite match attempts : 0
% 0.20/0.53 # BW rewrite match successes : 0
% 0.20/0.53 # Condensation attempts : 5
% 0.20/0.53 # Condensation successes : 0
% 0.20/0.53 # Termbank termtop insertions : 17757
% 0.20/0.53 # Search garbage collected termcells : 6568
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.018 s
% 0.20/0.53 # System time : 0.007 s
% 0.20/0.53 # Total time : 0.025 s
% 0.20/0.53 # Maximum resident set size: 3864 pages
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.023 s
% 0.20/0.53 # System time : 0.010 s
% 0.20/0.53 # Total time : 0.032 s
% 0.20/0.53 # Maximum resident set size: 1920 pages
% 0.20/0.53 % E---3.1 exiting
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------