TSTP Solution File: SEU553^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU553^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 03:28:08 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 196
% Syntax : Number of formulae : 232 ( 20 unt; 125 typ; 0 def)
% Number of atoms : 864 ( 231 equ; 0 cnn)
% Maximal formula atoms : 258 ( 8 avg)
% Number of connectives : 3379 ( 304 ~; 333 |; 228 &;1981 @)
% ( 119 <=>; 414 =>; 0 <=; 0 <~>)
% Maximal formula depth : 317 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 233 ( 233 >; 0 *; 0 +; 0 <<)
% Number of symbols : 128 ( 125 usr; 76 con; 0-3 aty)
% Number of variables : 742 ( 54 ^ 592 !; 96 ?; 742 :)
% 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,
epred1_0: $o ).
thf(decl_104,type,
esk1_2: $i > $i > $i ).
thf(decl_105,type,
esk2_2: $i > $i > $i ).
thf(decl_106,type,
esk3_2: $i > $i > $i ).
thf(decl_107,type,
esk4_1: $i > $i ).
thf(decl_108,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_109,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_110,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_111,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_112,type,
esk9_1: $i > $i ).
thf(decl_113,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_114,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_115,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_116,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_117,type,
esk14_2: $i > $i > $i ).
thf(decl_118,type,
esk15_2: $i > $i > $i ).
thf(decl_119,type,
esk16_1: $i > $i ).
thf(decl_120,type,
esk17_1: $i > $i ).
thf(decl_121,type,
esk18_1: $i > $i ).
thf(decl_122,type,
esk19_2: $i > $i > $i ).
thf(decl_123,type,
esk20_3: $i > $i > $o > $i ).
thf(decl_124,type,
esk21_2: ( $i > $o ) > $i > $i ).
thf(decl_125,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_126,type,
esk23_1: $i > $i ).
thf(decl_127,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_128,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_129,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_130,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_131,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_132,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_133,type,
esk30_2: ( $i > $o ) > $i > $i ).
thf(decl_134,type,
esk31_1: ( $i > $o ) > $i ).
thf(decl_135,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_136,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_137,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_138,type,
esk35_2: ( $i > $o ) > $i > $i ).
thf(decl_139,type,
esk36_1: ( $i > $o ) > $i ).
thf(decl_140,type,
esk37_2: ( $i > $o ) > $i > $i ).
thf(decl_141,type,
esk38_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_142,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_143,type,
esk40_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_144,type,
esk41_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_145,type,
esk42_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_146,type,
esk43_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_147,type,
esk44_0: $i ).
thf(decl_148,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(powerset__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
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
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(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(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(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(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/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/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(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(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(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_70,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_71,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
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,
( 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_77,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_78,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_79,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_80,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_81,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_82,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X218: $i] :
( ( X1 @ X218 )
& ! [X219: $i] :
( ( X1 @ X219 )
=> ( X218 = X219 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_83,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X222: $i] :
( ( X1 @ X222 )
& ! [X223: $i] :
( ( X1 @ X223 )
=> ( X222 = X223 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_72,c_0_71]) ).
thf(c_0_84,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X224: $i] :
( ( X1 @ X224 )
& ! [X225: $i] :
( ( X1 @ X225 )
=> ( X224 = X225 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_73,c_0_71]) ).
thf(c_0_85,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X226: $i] :
( ( X1 @ X226 )
& ! [X227: $i] :
( ( X1 @ X227 )
=> ( X226 = X227 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_74,c_0_71]) ).
thf(c_0_86,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X228: $i] :
( ( X1 @ X228 )
& ! [X229: $i] :
( ( X1 @ X229 )
=> ( X228 = X229 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_75,c_0_71]) ).
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,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X230: $i] :
( ( X1 @ X230 )
& ! [X231: $i] :
( ( X1 @ X231 )
=> ( X230 = X231 ) ) )
<=> ? [X232: $i] :
( ( X17 @ X232 )
& ! [X233: $i] :
( ( X17 @ X233 )
=> ( X232 = X233 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_76,c_0_71]) ).
thf(c_0_89,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_77]) ).
thf(c_0_90,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_78,c_0_77]) ).
thf(c_0_91,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_77]) ).
thf(c_0_92,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_93,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X220: $i] :
( ( X1 @ X220 )
& ! [X221: $i] :
( ( X1 @ X221 )
=> ( X220 = X221 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_79,c_0_71]) ).
thf(c_0_94,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_77]) ).
thf(c_0_95,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_96,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X216: $i] :
( ( X1 @ X216 )
& ! [X217: $i] :
( ( X1 @ X217 )
=> ( X216 = X217 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_80,c_0_71]) ).
thf(c_0_97,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_98,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_99,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_100,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X214: $i] :
( ( X6 @ X2 @ X214 )
& ! [X215: $i] :
( ( X6 @ X2 @ X215 )
=> ( X214 = X215 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_81,c_0_71]) ).
thf(c_0_101,plain,
( epred1_0
<=> ! [X263: $i] :
? [X264: $i] :
( ! [X265: $i] :
( ( in @ X265 @ X264 )
=> ! [X266: $i] :
( ( in @ X266 @ X265 )
=> ( in @ X266 @ X263 ) ) )
& ! [X267: $i,X268: $i] :
( ( ( in @ X267 @ X263 )
& ( in @ X268 @ X263 ) )
=> ( ! [X269: $i] :
( ( in @ X269 @ X264 )
=> ( ( in @ X267 @ X269 )
<=> ( in @ X268 @ X269 ) ) )
=> ( X267 = X268 ) ) )
& ! [X270: $i,X271: $i] :
( ( ( in @ X270 @ X264 )
& ( in @ X271 @ X264 ) )
=> ( ! [X272: $i] :
( ( in @ X272 @ X270 )
=> ( in @ X272 @ X271 ) )
| ! [X273: $i] :
( ( in @ X273 @ X271 )
=> ( in @ X273 @ X270 ) ) ) )
& ! [X274: $i] :
( ( ! [X275: $i] :
( ( in @ X275 @ X274 )
=> ( in @ X275 @ X263 ) )
& ? [X276: $i] : ( in @ X276 @ X274 ) )
=> ? [X277: $i,X278: $i] :
( ( in @ X277 @ X264 )
& ( in @ X278 @ X274 )
& ~ ? [X279: $i] :
( ( in @ X279 @ X277 )
& ( in @ X279 @ X274 ) )
& ! [X280: $i] :
( ( in @ X280 @ X264 )
=> ( ! [X281: $i] :
( ( in @ X281 @ X280 )
=> ( in @ X281 @ X277 ) )
| ( in @ X278 @ X280 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_102,negated_conjecture,
~ ( ! [X234: $i,X235: $i] :
( ! [X236: $i] :
( ( in @ X236 @ X234 )
<=> ( in @ X236 @ X235 ) )
=> ( X234 = X235 ) )
=> ( ! [X237: $i] :
~ ( in @ X237 @ emptyset )
=> ( ! [X238: $i,X239: $i,X240: $i] :
( ( in @ X240 @ ( setadjoin @ X238 @ X239 ) )
<=> ( ( X240 = X238 )
| ( in @ X240 @ X239 ) ) )
=> ( ! [X241: $i,X242: $i] :
( ( in @ X242 @ ( powerset @ X241 ) )
<=> ! [X243: $i] :
( ( in @ X243 @ X242 )
=> ( in @ X243 @ X241 ) ) )
=> ( ! [X244: $i,X245: $i] :
( ( in @ X245 @ ( setunion @ X244 ) )
<=> ? [X246: $i] :
( ( in @ X245 @ X246 )
& ( in @ X246 @ X244 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X247: $i] :
( ( in @ X247 @ omega )
=> ( in @ ( setadjoin @ X247 @ X247 ) @ omega ) )
=> ( ! [X248: $i] :
( ( ( in @ emptyset @ X248 )
& ! [X249: $i] :
( ( ( in @ X249 @ omega )
& ( in @ X249 @ X248 ) )
=> ( in @ ( setadjoin @ X249 @ X249 ) @ X248 ) ) )
=> ! [X250: $i] :
( ( in @ X250 @ omega )
=> ( in @ X250 @ X248 ) ) )
=> ( ! [X251: $i > $i > $o,X252: $i] :
( ! [X253: $i] :
( ( in @ X253 @ X252 )
=> ? [X254: $i] :
( ( X251 @ X253 @ X254 )
& ! [X255: $i] :
( ( X251 @ X253 @ X255 )
=> ( X254 = X255 ) ) ) )
=> ? [X256: $i] :
! [X257: $i] :
( ( in @ X257 @ X256 )
<=> ? [X258: $i] :
( ( in @ X258 @ X252 )
& ( X251 @ X258 @ X257 ) ) ) )
=> ( ! [X259: $i] :
( ? [X260: $i] : ( in @ X260 @ X259 )
=> ? [X261: $i] :
( ( in @ X261 @ X259 )
& ~ ? [X262: $i] :
( ( in @ X262 @ X261 )
& ( in @ X262 @ X259 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X282: $i,X283: $i > $o,X284: $i] :
( ( in @ X284 @ X282 )
=> ( ( X283 @ X284 )
=> ( in @ X284
@ ( dsetconstr @ X282
@ ^ [Z0: $i] : ( X283 @ Z0 ) ) ) ) )
=> ( ! [X285: $i,X286: $i > $o,X287: $i] :
( ( in @ X287
@ ( dsetconstr @ X285
@ ^ [Z0: $i] : ( X286 @ Z0 ) ) )
=> ( in @ X287 @ X285 ) )
=> ( ! [X288: $i,X289: $i > $o,X290: $i] :
( ( in @ X290
@ ( dsetconstr @ X288
@ ^ [Z0: $i] : ( X289 @ Z0 ) ) )
=> ( X289 @ X290 ) )
=> ( ! [X291: $i > $o] :
( ? [X292: $i] :
( ( X291 @ X292 )
& ! [X293: $i] :
( ( X291 @ X293 )
=> ( X292 = X293 ) ) )
=> ? [X294: $i] :
( ( X291 @ X294 )
& ! [X295: $i] :
( ( X291 @ X295 )
=> ( X294 = X295 ) ) ) )
=> ( ! [X296: $o,X297: $i] :
( ( in @ X297 @ ( prop2set @ X296 ) )
=> X296 )
=> ( ! [X298: $i] :
( ( in @ X298 @ emptyset )
=> ! [X299: $o] : X299 )
=> ( ! [X300: $i] :
~ ( in @ X300 @ emptyset )
=> ( ! [X301: $i] :
~ ( in @ X301 @ emptyset )
=> ( ! [X302: $i > $o] :
( ? [X303: $i] :
( ( X302 @ X303 )
& ! [X304: $i] :
( ( X302 @ X304 )
=> ( X303 = X304 ) ) )
=> ? [X305: $i] : ( X302 @ X305 ) )
=> ( ! [X306: $i,X307: $i] :
( ! [X308: $i] :
( ( in @ X308 @ X306 )
=> ( in @ X308 @ X307 ) )
=> ( ! [X309: $i] :
( ( in @ X309 @ X307 )
=> ( in @ X309 @ X306 ) )
=> ( X306 = X307 ) ) )
=> ( ! [X310: $i] :
( ! [X311: $i] :
~ ( in @ X311 @ X310 )
=> ( X310 = emptyset ) )
=> ( ! [X312: $i] :
( ! [X313: $i] :
~ ( in @ X313 @ X312 )
=> ( X312 = emptyset ) )
=> ( ! [X314: $i,X315: $i > $o,X316: $i] :
( ( in @ X316 @ X314 )
=> ( ( in @ X316
@ ( dsetconstr @ X314
@ ^ [Z0: $i] : ( X315 @ Z0 ) ) )
<=> ( X315 @ X316 ) ) )
=> ( ! [X317: $i] :
( ( X317 != emptyset )
=> ? [X318: $i] : ( in @ X318 @ X317 ) )
=> ( ! [X319: $i,X320: $i > $o,X321: $i] :
( ( in @ X321 @ X319 )
=> ( ( X320 @ X321 )
=> ( ( dsetconstr @ X319
@ ^ [Z0: $i] : ( X320 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X322: $i] :
( ? [X323: $i] : ( in @ X323 @ X322 )
=> ( X322 != emptyset ) )
=> ( ! [X324: $i,X325: $i] : ( in @ X324 @ ( setadjoin @ X324 @ X325 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X326: $i,X327: $i,X328: $i] :
( ( in @ X328 @ X327 )
=> ( in @ X328 @ ( setadjoin @ X326 @ X327 ) ) )
=> ( ! [X329: $i,X330: $i,X331: $i] :
( ( in @ X331 @ ( setadjoin @ X329 @ X330 ) )
=> ! [X332: $o] :
( ( ( X331 = X329 )
=> X332 )
=> ( ( ( in @ X331 @ X330 )
=> X332 )
=> X332 ) ) )
=> ( ! [X333: $i,X334: $i,X335: $i] :
( ( in @ X335 @ ( setadjoin @ X333 @ X334 ) )
=> ( ( X335 = X333 )
| ( in @ X335 @ X334 ) ) )
=> ( ! [X336: $i] :
( ( dsetconstr @ X336
@ ^ [Z0: $i] : $true )
= X336 )
=> ( ! [X337: $i,X338: $i] :
( ! [X339: $i] :
( ( in @ X339 @ X338 )
=> ( in @ X339 @ X337 ) )
=> ( in @ X338 @ ( powerset @ X337 ) ) )
=> ( ! [X340: $i] : ( in @ emptyset @ ( powerset @ X340 ) )
=> ( ! [X341: $i] : ( in @ emptyset @ ( powerset @ X341 ) )
=> ( ! [X342: $i,X343: $i,X344: $i] :
( ( in @ X343 @ ( powerset @ X342 ) )
=> ( ( in @ X344 @ X343 )
=> ( in @ X344 @ X342 ) ) )
=> ( ! [X345: $i,X346: $i,X347: $i] :
( ( in @ X346 @ X347 )
=> ( ( in @ X347 @ X345 )
=> ( in @ X346 @ ( setunion @ X345 ) ) ) )
=> ( ! [X348: $i,X349: $i] :
( ( in @ X349 @ ( setunion @ X348 ) )
=> ! [X350: $o] :
( ! [X351: $i] :
( ( in @ X349 @ X351 )
=> ( ( in @ X351 @ X348 )
=> X350 ) )
=> X350 ) )
=> ( ! [X352: $i,X353: $i] :
( ( in @ X353 @ X352 )
=> ( in @ X353 @ ( powerset @ ( setunion @ X352 ) ) ) )
=> ( ! [X354: $i > $o] :
( ? [X355: $i] :
( ( X354 @ X355 )
& ! [X356: $i] :
( ( X354 @ X356 )
=> ( X355 = X356 ) ) )
=> ? [X357: $i] :
! [X358: $i] :
( ( X354 @ X358 )
<=> ( X358 = X357 ) ) )
=> ( ! [X359: $i] :
( ( X359 != emptyset )
=> ? [X360: $i] : ( in @ X360 @ X359 ) )
=> ( ! [X361: $i,X362: $i] :
( ( in @ X361 @ ( setadjoin @ X362 @ emptyset ) )
=> ( X361 = X362 ) )
=> ( ! [X363: $i,X364: $i] :
( ( X363 != X364 )
=> ~ ( in @ X364 @ ( setadjoin @ X363 @ emptyset ) ) )
=> ( ! [X365: $i,X366: $i] :
( ( X365 = X366 )
=> ( in @ X365 @ ( setadjoin @ X366 @ emptyset ) ) )
=> ( ! [X367: $i,X368: $i] :
( ( in @ X367 @ ( setadjoin @ X368 @ emptyset ) )
=> ( in @ X368 @ ( setadjoin @ X367 @ emptyset ) ) )
=> ( ! [X369: $i,X370: $i,X371: $i] :
( ( in @ X371 @ ( setadjoin @ X369 @ ( setadjoin @ X370 @ emptyset ) ) )
=> ( ( X371 = X369 )
| ( X371 = X370 ) ) )
=> ( ! [X372: $i,X373: $i] : ( in @ X372 @ ( setadjoin @ X372 @ ( setadjoin @ X373 @ emptyset ) ) )
=> ( ! [X374: $i,X375: $i] : ( in @ X375 @ ( setadjoin @ X374 @ ( setadjoin @ X375 @ emptyset ) ) )
=> ( ! [X376: $i,X377: $i > $o] :
( ? [X378: $i] :
( ( in @ X378 @ X376 )
& ( X377 @ X378 ) )
=> ( ( dsetconstr @ X376
@ ^ [Z0: $i] : ( X377 @ Z0 ) )
!= emptyset ) )
=> ( ! [X379: $i > $o,X380: $i] :
( ( in @ X380 @ emptyset )
=> ( X379 @ X380 ) )
=> ( ! [X381: $i,X382: $i > $o] :
( ~ ! [X383: $i] :
( ( in @ X383 @ X381 )
=> ( X382 @ X383 ) )
=> ? [X384: $i] :
( ( in @ X384 @ X381 )
& ~ ( X382 @ X384 ) ) )
=> ( ! [X385: $i,X386: $i > $o] :
( ! [X387: $i] :
( ( in @ X387 @ X385 )
=> ~ ( X386 @ X387 ) )
=> ~ ? [X388: $i] :
( ( in @ X388 @ X385 )
& ( X386 @ X388 ) ) )
=> ( ! [X389: $i,X390: $i > $o] :
( ~ ? [X391: $i] :
( ( in @ X391 @ X389 )
& ( X390 @ X391 ) )
=> ! [X392: $i] :
( ( in @ X392 @ X389 )
=> ~ ( X390 @ X392 ) ) )
=> ( ! [X393: $i,X394: $i > $o] :
( ? [X395: $i] :
( ( in @ X395 @ X393 )
& ~ ( X394 @ X395 ) )
=> ~ ! [X396: $i] :
( ( in @ X396 @ X393 )
=> ( X394 @ X396 ) ) )
=> ( ! [X397: $o] :
( X397
=> ( in @ emptyset @ ( prop2set @ X397 ) ) )
=> ( prop2set2propI
=> ( ! [X398: $i,X399: $i > $o] :
( ~ ? [X400: $i] :
( ( in @ X400 @ X398 )
& ( X399 @ X400 ) )
=> ! [X401: $i] :
( ( in @ X401 @ X398 )
=> ~ ( X399 @ X401 ) ) )
=> ( ! [X402: $i,X403: $i > $o] :
( ~ ! [X404: $i] :
( ( in @ X404 @ X402 )
=> ( X403 @ X404 ) )
=> ? [X405: $i] :
( ( in @ X405 @ X402 )
& ~ ( X403 @ X405 ) ) )
=> ( ! [X406: $i > $o] :
( ? [X407: $i] :
( ( X406 @ X407 )
& ! [X408: $i] :
( ( X406 @ X408 )
=> ( X407 = X408 ) ) )
=> ? [X409: $i] :
( ( X406 @ X409 )
& ! [X410: $i] :
( ( X406 @ X410 )
=> ( X409 = X410 ) ) ) )
=> ( ! [X411: $i > $o] :
( ? [X412: $i] : ( X411 @ X412 )
=> ( ! [X413: $i,X414: $i] :
( ( X411 @ X413 )
=> ( ( X411 @ X414 )
=> ( X413 = X414 ) ) )
=> ? [X415: $i] :
( ( X411 @ X415 )
& ! [X416: $i] :
( ( X411 @ X416 )
=> ( X415 = X416 ) ) ) ) )
=> ( ! [X417: $i > $o] :
( ? [X418: $i] :
! [X419: $i] :
( ( X417 @ X419 )
<=> ( X419 = X418 ) )
=> ? [X420: $i] :
( ( X417 @ X420 )
& ! [X421: $i] :
( ( X417 @ X421 )
=> ( X420 = X421 ) ) ) )
=> ( ! [X422: $i,X423: $i] :
( ( X422 = X423 )
=> ! [X424: $i,X425: $i] :
( ( X424 = X425 )
=> ( ( in @ X424 @ X422 )
=> ( in @ X425 @ X423 ) ) ) )
=> ( ! [X426: $i,X427: $i] :
( ( X426 = X427 )
=> ! [X428: $i,X429: $i] :
( ( X428 = X429 )
=> ( ( in @ X428 @ X426 )
<=> ( in @ X429 @ X427 ) ) ) )
=> ( ! [X430: $i > $o] :
( ? [X431: $i] :
( ( X430 @ X431 )
& ! [X432: $i] :
( ( X430 @ X432 )
=> ( X431 = X432 ) ) )
=> ! [X433: $i,X434: $i] :
( ( X430 @ X433 )
=> ( ( X430 @ X434 )
=> ( X433 = X434 ) ) ) )
=> ( ! [X435: $i > $o,X436: $i > $o] :
( ! [X437: $i,X438: $i] :
( ( X437 = X438 )
=> ( ( X435 @ X437 )
<=> ( X436 @ X438 ) ) )
=> ( ? [X439: $i] :
( ( X435 @ X439 )
& ! [X440: $i] :
( ( X435 @ X440 )
=> ( X439 = X440 ) ) )
<=> ? [X441: $i] :
( ( X436 @ X441 )
& ! [X442: $i] :
( ( X436 @ X442 )
=> ( X441 = X442 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X443: $i,X444: $i] :
( ( X443 = X444 )
=> ! [X445: $i,X446: $i] :
( ( X445 = X446 )
=> ( ( setadjoin @ X443 @ X445 )
= ( setadjoin @ X444 @ X446 ) ) ) )
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ 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(assume_negation,[status(cth)],[powerset__Cong]),setadjoinIL]),setadjoin__Cong]),quantDeMorgan2]),notinemptyset]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),c_0_82]),notdexE]),notdallE]),setext]),c_0_83]),c_0_84]),emptyI]),c_0_85]),inCongP]),noeltsimpempty]),in__Cong]),c_0_86]),c_0_87]),c_0_88]),emptyset__Cong]),c_0_89]),c_0_90]),c_0_91]),singletonsswitch]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_92]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_93]),c_0_94]),uniqinunit]),notinsingleton]),eqinunit]),upairsetE]),upairsetIL]),upairsetIR]),c_0_95]),vacuousDall]),quantDeMorgan1]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_96]),c_0_97]),c_0_98]),c_0_99]),wellorderingAx]),foundationAx]),c_0_100]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_101]) ).
thf(c_0_103,negated_conjecture,
! [X447: $i,X448: $i,X450: $i,X451: $i,X452: $i,X453: $i,X454: $i,X455: $i,X456: $i,X457: $i,X458: $i,X460: $i,X461: $i,X463: $i,X464: $i,X465: $i,X466: $i,X467: $i,X469: $i,X470: $i > $i > $o,X471: $i,X473: $i,X476: $i,X478: $i,X479: $i,X480: $i,X481: $i,X483: $i,X484: $i,X485: $i > $o,X486: $i,X487: $i,X488: $i > $o,X489: $i,X490: $i,X491: $i > $o,X492: $i,X493: $i > $o,X494: $i,X497: $i,X498: $o,X499: $i,X500: $i,X501: $o,X502: $i,X503: $i,X504: $i > $o,X505: $i,X508: $i,X509: $i,X512: $i,X514: $i,X516: $i,X517: $i > $o,X518: $i,X519: $i,X521: $i,X522: $i > $o,X523: $i,X524: $i,X525: $i,X526: $i,X527: $i,X528: $i,X529: $i,X530: $i,X531: $i,X532: $i,X533: $i,X534: $o,X535: $i,X536: $i,X537: $i,X538: $i,X539: $i,X540: $i,X542: $i,X543: $i,X544: $i,X545: $i,X546: $i,X547: $i,X548: $i,X549: $i,X550: $i,X551: $i,X552: $o,X554: $i,X555: $i,X556: $i > $o,X557: $i,X560: $i,X561: $i,X562: $i,X564: $i,X565: $i,X566: $i,X567: $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 > $o,X581: $i,X582: $i > $o,X583: $i,X584: $i,X585: $i > $o,X586: $i,X588: $i,X589: $i > $o,X591: $i,X592: $i,X593: $i > $o,X595: $i,X596: $i,X597: $i > $o,X598: $i,X600: $o,X601: $i,X602: $i > $o,X604: $i,X605: $i,X606: $i > $o,X607: $i,X609: $i > $o,X610: $i,X613: $i,X614: $i > $o,X615: $i,X619: $i,X620: $i > $o,X621: $i,X624: $i,X625: $i,X626: $i,X627: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i > $o,X634: $i,X636: $i,X637: $i,X638: $i > $o,X639: $i > $o,X642: $i,X645: $i,X646: $i,X649: $i,X650: $i,X651: $i,X652: $i,X653: $i] :
( ( ~ ( in @ ( esk1_2 @ X447 @ X448 ) @ X447 )
| ~ ( in @ ( esk1_2 @ X447 @ X448 ) @ X448 )
| ( X447 = X448 ) )
& ( ( in @ ( esk1_2 @ X447 @ X448 ) @ X447 )
| ( in @ ( esk1_2 @ X447 @ X448 ) @ X448 )
| ( X447 = X448 ) )
& ~ ( in @ X450 @ emptyset )
& ( ~ ( in @ X453 @ ( setadjoin @ X451 @ X452 ) )
| ( X453 = X451 )
| ( in @ X453 @ X452 ) )
& ( ( X453 != X451 )
| ( in @ X453 @ ( setadjoin @ X451 @ X452 ) ) )
& ( ~ ( in @ X453 @ X452 )
| ( in @ X453 @ ( setadjoin @ X451 @ X452 ) ) )
& ( ~ ( in @ X455 @ ( powerset @ X454 ) )
| ~ ( in @ X456 @ X455 )
| ( in @ X456 @ X454 ) )
& ( ( in @ ( esk2_2 @ X457 @ X458 ) @ X458 )
| ( in @ X458 @ ( powerset @ X457 ) ) )
& ( ~ ( in @ ( esk2_2 @ X457 @ X458 ) @ X457 )
| ( in @ X458 @ ( powerset @ X457 ) ) )
& ( ( in @ X461 @ ( esk3_2 @ X460 @ X461 ) )
| ~ ( in @ X461 @ ( setunion @ X460 ) ) )
& ( ( in @ ( esk3_2 @ X460 @ X461 ) @ X460 )
| ~ ( in @ X461 @ ( setunion @ X460 ) ) )
& ( ~ ( in @ X464 @ X465 )
| ~ ( in @ X465 @ X463 )
| ( in @ X464 @ ( setunion @ X463 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X466 @ omega )
| ( in @ ( setadjoin @ X466 @ X466 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X467 ) @ omega )
| ~ ( in @ emptyset @ X467 )
| ~ ( in @ X469 @ omega )
| ( in @ X469 @ X467 ) )
& ( ( in @ ( esk4_1 @ X467 ) @ X467 )
| ~ ( in @ emptyset @ X467 )
| ~ ( in @ X469 @ omega )
| ( in @ X469 @ X467 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X467 ) @ ( esk4_1 @ X467 ) ) @ X467 )
| ~ ( in @ emptyset @ X467 )
| ~ ( in @ X469 @ omega )
| ( in @ X469 @ X467 ) )
& ( ( in @ ( esk8_3 @ X470 @ X471 @ X476 ) @ X471 )
| ~ ( in @ X476 @ ( esk7_2 @ X470 @ X471 ) )
| ( in @ ( esk5_2 @ X470 @ X471 ) @ X471 ) )
& ( ( X470 @ ( esk8_3 @ X470 @ X471 @ X476 ) @ X476 )
| ~ ( in @ X476 @ ( esk7_2 @ X470 @ X471 ) )
| ( in @ ( esk5_2 @ X470 @ X471 ) @ X471 ) )
& ( ~ ( in @ X479 @ X471 )
| ~ ( X470 @ X479 @ X478 )
| ( in @ X478 @ ( esk7_2 @ X470 @ X471 ) )
| ( in @ ( esk5_2 @ X470 @ X471 ) @ X471 ) )
& ( ( in @ ( esk8_3 @ X470 @ X471 @ X476 ) @ X471 )
| ~ ( in @ X476 @ ( esk7_2 @ X470 @ X471 ) )
| ( X470 @ ( esk5_2 @ X470 @ X471 ) @ ( esk6_3 @ X470 @ X471 @ X473 ) )
| ~ ( X470 @ ( esk5_2 @ X470 @ X471 ) @ X473 ) )
& ( ( X470 @ ( esk8_3 @ X470 @ X471 @ X476 ) @ X476 )
| ~ ( in @ X476 @ ( esk7_2 @ X470 @ X471 ) )
| ( X470 @ ( esk5_2 @ X470 @ X471 ) @ ( esk6_3 @ X470 @ X471 @ X473 ) )
| ~ ( X470 @ ( esk5_2 @ X470 @ X471 ) @ X473 ) )
& ( ~ ( in @ X479 @ X471 )
| ~ ( X470 @ X479 @ X478 )
| ( in @ X478 @ ( esk7_2 @ X470 @ X471 ) )
| ( X470 @ ( esk5_2 @ X470 @ X471 ) @ ( esk6_3 @ X470 @ X471 @ X473 ) )
| ~ ( X470 @ ( esk5_2 @ X470 @ X471 ) @ X473 ) )
& ( ( in @ ( esk8_3 @ X470 @ X471 @ X476 ) @ X471 )
| ~ ( in @ X476 @ ( esk7_2 @ X470 @ X471 ) )
| ( X473
!= ( esk6_3 @ X470 @ X471 @ X473 ) )
| ~ ( X470 @ ( esk5_2 @ X470 @ X471 ) @ X473 ) )
& ( ( X470 @ ( esk8_3 @ X470 @ X471 @ X476 ) @ X476 )
| ~ ( in @ X476 @ ( esk7_2 @ X470 @ X471 ) )
| ( X473
!= ( esk6_3 @ X470 @ X471 @ X473 ) )
| ~ ( X470 @ ( esk5_2 @ X470 @ X471 ) @ X473 ) )
& ( ~ ( in @ X479 @ X471 )
| ~ ( X470 @ X479 @ X478 )
| ( in @ X478 @ ( esk7_2 @ X470 @ X471 ) )
| ( X473
!= ( esk6_3 @ X470 @ X471 @ X473 ) )
| ~ ( X470 @ ( esk5_2 @ X470 @ X471 ) @ X473 ) )
& ( ( in @ ( esk9_1 @ X480 ) @ X480 )
| ~ ( in @ X481 @ X480 ) )
& ( ~ ( in @ X483 @ ( esk9_1 @ X480 ) )
| ~ ( in @ X483 @ X480 )
| ~ ( in @ X481 @ X480 ) )
& epred1_0
& descrp
& ( ~ ( in @ X486 @ X484 )
| ~ ( X485 @ X486 )
| ( in @ X486
@ ( dsetconstr @ X484
@ ^ [Z0: $i] : ( X485 @ Z0 ) ) ) )
& ( ~ ( in @ X489
@ ( dsetconstr @ X487
@ ^ [Z0: $i] : ( X488 @ Z0 ) ) )
| ( in @ X489 @ X487 ) )
& ( ~ ( in @ X492
@ ( dsetconstr @ X490
@ ^ [Z0: $i] : ( X491 @ Z0 ) ) )
| ( X491 @ X492 ) )
& ( ( X493 @ ( esk11_1 @ X493 ) )
| ( X493 @ ( esk10_2 @ X493 @ X494 ) )
| ~ ( X493 @ X494 ) )
& ( ~ ( X493 @ X497 )
| ( ( esk11_1 @ X493 )
= X497 )
| ( X493 @ ( esk10_2 @ X493 @ X494 ) )
| ~ ( X493 @ X494 ) )
& ( ( X493 @ ( esk11_1 @ X493 ) )
| ( X494
!= ( esk10_2 @ X493 @ X494 ) )
| ~ ( X493 @ X494 ) )
& ( ~ ( X493 @ X497 )
| ( ( esk11_1 @ X493 )
= X497 )
| ( X494
!= ( esk10_2 @ X493 @ X494 ) )
| ~ ( X493 @ X494 ) )
& ( ~ ( in @ X499 @ ( prop2set @ X498 ) )
| X498 )
& ( ~ ( in @ X500 @ emptyset )
| X501 )
& ~ ( in @ X502 @ emptyset )
& ~ ( in @ X503 @ emptyset )
& ( ( X504 @ ( esk12_2 @ X504 @ X505 ) )
| ~ ( X504 @ X505 )
| ( X504 @ ( esk13_1 @ X504 ) ) )
& ( ( X505
!= ( esk12_2 @ X504 @ X505 ) )
| ~ ( X504 @ X505 )
| ( X504 @ ( esk13_1 @ X504 ) ) )
& ( ( in @ ( esk15_2 @ X508 @ X509 ) @ X509 )
| ( X508 = X509 )
| ( in @ ( esk14_2 @ X508 @ X509 ) @ X508 ) )
& ( ~ ( in @ ( esk15_2 @ X508 @ X509 ) @ X508 )
| ( X508 = X509 )
| ( in @ ( esk14_2 @ X508 @ X509 ) @ X508 ) )
& ( ( in @ ( esk15_2 @ X508 @ X509 ) @ X509 )
| ( X508 = X509 )
| ~ ( in @ ( esk14_2 @ X508 @ X509 ) @ X509 ) )
& ( ~ ( in @ ( esk15_2 @ X508 @ X509 ) @ X508 )
| ( X508 = X509 )
| ~ ( in @ ( esk14_2 @ X508 @ X509 ) @ X509 ) )
& ( ( in @ ( esk16_1 @ X512 ) @ X512 )
| ( X512 = emptyset ) )
& ( ( in @ ( esk17_1 @ X514 ) @ X514 )
| ( X514 = emptyset ) )
& ( ~ ( in @ X518
@ ( dsetconstr @ X516
@ ^ [Z0: $i] : ( X517 @ Z0 ) ) )
| ( X517 @ X518 )
| ~ ( in @ X518 @ X516 ) )
& ( ~ ( X517 @ X518 )
| ( in @ X518
@ ( dsetconstr @ X516
@ ^ [Z0: $i] : ( X517 @ Z0 ) ) )
| ~ ( in @ X518 @ X516 ) )
& ( ( X519 = emptyset )
| ( in @ ( esk18_1 @ X519 ) @ X519 ) )
& ( ~ ( in @ X523 @ X521 )
| ~ ( X522 @ X523 )
| ( ( dsetconstr @ X521
@ ^ [Z0: $i] : ( X522 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X525 @ X524 )
| ( X524 != emptyset ) )
& ( in @ X526 @ ( setadjoin @ X526 @ X527 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X530 @ X529 )
| ( in @ X530 @ ( setadjoin @ X528 @ X529 ) ) )
& ( ( in @ X533 @ X532 )
| X534
| ( X533 = X531 )
| ~ ( in @ X533 @ ( setadjoin @ X531 @ X532 ) ) )
& ( ~ X534
| X534
| ( X533 = X531 )
| ~ ( in @ X533 @ ( setadjoin @ X531 @ X532 ) ) )
& ( ( in @ X533 @ X532 )
| X534
| ~ X534
| ~ ( in @ X533 @ ( setadjoin @ X531 @ X532 ) ) )
& ( ~ X534
| X534
| ~ X534
| ~ ( in @ X533 @ ( setadjoin @ X531 @ X532 ) ) )
& ( ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) )
| ( X537 = X535 )
| ( in @ X537 @ X536 ) )
& ( ( dsetconstr @ X538
@ ^ [Z0: $i] : $true )
= X538 )
& ( ( in @ ( esk19_2 @ X539 @ X540 ) @ X540 )
| ( in @ X540 @ ( powerset @ X539 ) ) )
& ( ~ ( in @ ( esk19_2 @ X539 @ X540 ) @ X539 )
| ( in @ X540 @ ( powerset @ X539 ) ) )
& ( in @ emptyset @ ( powerset @ X542 ) )
& ( in @ emptyset @ ( powerset @ X543 ) )
& ( ~ ( in @ X545 @ ( powerset @ X544 ) )
| ~ ( in @ X546 @ X545 )
| ( in @ X546 @ X544 ) )
& ( ~ ( in @ X548 @ X549 )
| ~ ( in @ X549 @ X547 )
| ( in @ X548 @ ( setunion @ X547 ) ) )
& ( ( in @ X551 @ ( esk20_3 @ X550 @ X551 @ X552 ) )
| X552
| ~ ( in @ X551 @ ( setunion @ X550 ) ) )
& ( ( in @ ( esk20_3 @ X550 @ X551 @ X552 ) @ X550 )
| X552
| ~ ( in @ X551 @ ( setunion @ X550 ) ) )
& ( ~ X552
| X552
| ~ ( in @ X551 @ ( setunion @ X550 ) ) )
& ( ~ ( in @ X555 @ X554 )
| ( in @ X555 @ ( powerset @ ( setunion @ X554 ) ) ) )
& ( ~ ( X556 @ X560 )
| ( X560
= ( esk22_1 @ X556 ) )
| ( X556 @ ( esk21_2 @ X556 @ X557 ) )
| ~ ( X556 @ X557 ) )
& ( ( X561
!= ( esk22_1 @ X556 ) )
| ( X556 @ X561 )
| ( X556 @ ( esk21_2 @ X556 @ X557 ) )
| ~ ( X556 @ X557 ) )
& ( ~ ( X556 @ X560 )
| ( X560
= ( esk22_1 @ X556 ) )
| ( X557
!= ( esk21_2 @ X556 @ X557 ) )
| ~ ( X556 @ X557 ) )
& ( ( X561
!= ( esk22_1 @ X556 ) )
| ( X556 @ X561 )
| ( X557
!= ( esk21_2 @ X556 @ X557 ) )
| ~ ( X556 @ X557 ) )
& ( ( X562 = emptyset )
| ( in @ ( esk23_1 @ X562 ) @ X562 ) )
& ( ~ ( in @ X564 @ ( setadjoin @ X565 @ emptyset ) )
| ( X564 = X565 ) )
& ( ( X566 = X567 )
| ~ ( in @ X567 @ ( setadjoin @ X566 @ emptyset ) ) )
& ( ( X568 != X569 )
| ( in @ X568 @ ( setadjoin @ X569 @ emptyset ) ) )
& ( ~ ( in @ X570 @ ( setadjoin @ X571 @ emptyset ) )
| ( in @ X571 @ ( setadjoin @ X570 @ emptyset ) ) )
& ( ~ ( in @ X574 @ ( setadjoin @ X572 @ ( setadjoin @ X573 @ emptyset ) ) )
| ( X574 = X572 )
| ( X574 = X573 ) )
& ( in @ X575 @ ( setadjoin @ X575 @ ( setadjoin @ X576 @ emptyset ) ) )
& ( in @ X578 @ ( setadjoin @ X577 @ ( setadjoin @ X578 @ emptyset ) ) )
& ( ~ ( in @ X581 @ X579 )
| ~ ( X580 @ X581 )
| ( ( dsetconstr @ X579
@ ^ [Z0: $i] : ( X580 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X583 @ emptyset )
| ( X582 @ X583 ) )
& ( ( in @ ( esk24_2 @ X584 @ X585 ) @ X584 )
| ~ ( in @ X586 @ X584 )
| ( X585 @ X586 ) )
& ( ~ ( X585 @ ( esk24_2 @ X584 @ X585 ) )
| ~ ( in @ X586 @ X584 )
| ( X585 @ X586 ) )
& ( ( in @ ( esk25_2 @ X588 @ X589 ) @ X588 )
| ~ ( in @ X591 @ X588 )
| ~ ( X589 @ X591 ) )
& ( ( X589 @ ( esk25_2 @ X588 @ X589 ) )
| ~ ( in @ X591 @ X588 )
| ~ ( X589 @ X591 ) )
& ( ( in @ ( esk26_2 @ X592 @ X593 ) @ X592 )
| ~ ( in @ X595 @ X592 )
| ~ ( X593 @ X595 ) )
& ( ( X593 @ ( esk26_2 @ X592 @ X593 ) )
| ~ ( in @ X595 @ X592 )
| ~ ( X593 @ X595 ) )
& ( ( in @ ( esk27_2 @ X596 @ X597 ) @ X596 )
| ~ ( in @ X598 @ X596 )
| ( X597 @ X598 ) )
& ( ~ ( X597 @ ( esk27_2 @ X596 @ X597 ) )
| ~ ( in @ X598 @ X596 )
| ( X597 @ X598 ) )
& ( ~ X600
| ( in @ emptyset @ ( prop2set @ X600 ) ) )
& prop2set2propI
& ( ( in @ ( esk28_2 @ X601 @ X602 ) @ X601 )
| ~ ( in @ X604 @ X601 )
| ~ ( X602 @ X604 ) )
& ( ( X602 @ ( esk28_2 @ X601 @ X602 ) )
| ~ ( in @ X604 @ X601 )
| ~ ( X602 @ X604 ) )
& ( ( in @ ( esk29_2 @ X605 @ X606 ) @ X605 )
| ~ ( in @ X607 @ X605 )
| ( X606 @ X607 ) )
& ( ~ ( X606 @ ( esk29_2 @ X605 @ X606 ) )
| ~ ( in @ X607 @ X605 )
| ( X606 @ X607 ) )
& ( ( X609 @ ( esk31_1 @ X609 ) )
| ( X609 @ ( esk30_2 @ X609 @ X610 ) )
| ~ ( X609 @ X610 ) )
& ( ~ ( X609 @ X613 )
| ( ( esk31_1 @ X609 )
= X613 )
| ( X609 @ ( esk30_2 @ X609 @ X610 ) )
| ~ ( X609 @ X610 ) )
& ( ( X609 @ ( esk31_1 @ X609 ) )
| ( X610
!= ( esk30_2 @ X609 @ X610 ) )
| ~ ( X609 @ X610 ) )
& ( ~ ( X609 @ X613 )
| ( ( esk31_1 @ X609 )
= X613 )
| ( X610
!= ( esk30_2 @ X609 @ X610 ) )
| ~ ( X609 @ X610 ) )
& ( ( X614 @ ( esk34_1 @ X614 ) )
| ( X614 @ ( esk32_1 @ X614 ) )
| ~ ( X614 @ X615 ) )
& ( ~ ( X614 @ X619 )
| ( ( esk34_1 @ X614 )
= X619 )
| ( X614 @ ( esk32_1 @ X614 ) )
| ~ ( X614 @ X615 ) )
& ( ( X614 @ ( esk34_1 @ X614 ) )
| ( X614 @ ( esk33_1 @ X614 ) )
| ~ ( X614 @ X615 ) )
& ( ~ ( X614 @ X619 )
| ( ( esk34_1 @ X614 )
= X619 )
| ( X614 @ ( esk33_1 @ X614 ) )
| ~ ( X614 @ X615 ) )
& ( ( X614 @ ( esk34_1 @ X614 ) )
| ( ( esk32_1 @ X614 )
!= ( esk33_1 @ X614 ) )
| ~ ( X614 @ X615 ) )
& ( ~ ( X614 @ X619 )
| ( ( esk34_1 @ X614 )
= X619 )
| ( ( esk32_1 @ X614 )
!= ( esk33_1 @ X614 ) )
| ~ ( X614 @ X615 ) )
& ( ( X620 @ ( esk36_1 @ X620 ) )
| ~ ( X620 @ ( esk35_2 @ X620 @ X621 ) )
| ( ( esk35_2 @ X620 @ X621 )
!= X621 ) )
& ( ~ ( X620 @ X624 )
| ( ( esk36_1 @ X620 )
= X624 )
| ~ ( X620 @ ( esk35_2 @ X620 @ X621 ) )
| ( ( esk35_2 @ X620 @ X621 )
!= X621 ) )
& ( ( X620 @ ( esk36_1 @ X620 ) )
| ( X620 @ ( esk35_2 @ X620 @ X621 ) )
| ( ( esk35_2 @ X620 @ X621 )
= X621 ) )
& ( ~ ( X620 @ X624 )
| ( ( esk36_1 @ X620 )
= X624 )
| ( X620 @ ( esk35_2 @ X620 @ X621 ) )
| ( ( esk35_2 @ X620 @ X621 )
= X621 ) )
& ( ( X625 != X626 )
| ( X627 != X628 )
| ~ ( in @ X627 @ X625 )
| ( in @ X628 @ X626 ) )
& ( ~ ( in @ X631 @ X629 )
| ( in @ X632 @ X630 )
| ( X631 != X632 )
| ( X629 != X630 ) )
& ( ~ ( in @ X632 @ X630 )
| ( in @ X631 @ X629 )
| ( X631 != X632 )
| ( X629 != X630 ) )
& ( ( X633 @ ( esk37_2 @ X633 @ X634 ) )
| ~ ( X633 @ X634 )
| ~ ( X633 @ X636 )
| ~ ( X633 @ X637 )
| ( X636 = X637 ) )
& ( ( X634
!= ( esk37_2 @ X633 @ X634 ) )
| ~ ( X633 @ X634 )
| ~ ( X633 @ X636 )
| ~ ( X633 @ X637 )
| ( X636 = X637 ) )
& ( ( X639 @ ( esk41_2 @ X638 @ X639 ) )
| ( X638 @ ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X639 @ X645 )
| ( ( esk41_2 @ X638 @ X639 )
= X645 )
| ( X638 @ ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X639 @ ( esk41_2 @ X638 @ X639 ) )
| ( X642
!= ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X639 @ X645 )
| ( ( esk41_2 @ X638 @ X639 )
= X645 )
| ( X642
!= ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X638 @ ( esk43_2 @ X638 @ X639 ) )
| ( X639 @ ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X638 @ X649 )
| ( ( esk43_2 @ X638 @ X639 )
= X649 )
| ( X639 @ ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X638 @ ( esk43_2 @ X638 @ X639 ) )
| ( X646
!= ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X638 @ X649 )
| ( ( esk43_2 @ X638 @ X639 )
= X649 )
| ( X646
!= ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( ( esk38_2 @ X638 @ X639 )
= ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X639 @ ( esk41_2 @ X638 @ X639 ) )
| ( X638 @ ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X639 @ X645 )
| ( ( esk41_2 @ X638 @ X639 )
= X645 )
| ( X638 @ ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X639 @ ( esk41_2 @ X638 @ X639 ) )
| ( X642
!= ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X639 @ X645 )
| ( ( esk41_2 @ X638 @ X639 )
= X645 )
| ( X642
!= ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X638 @ ( esk43_2 @ X638 @ X639 ) )
| ( X639 @ ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X638 @ X649 )
| ( ( esk43_2 @ X638 @ X639 )
= X649 )
| ( X639 @ ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X638 @ ( esk43_2 @ X638 @ X639 ) )
| ( X646
!= ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X638 @ X649 )
| ( ( esk43_2 @ X638 @ X639 )
= X649 )
| ( X646
!= ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ~ ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ~ ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X639 @ ( esk41_2 @ X638 @ X639 ) )
| ( X638 @ ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X639 @ X645 )
| ( ( esk41_2 @ X638 @ X639 )
= X645 )
| ( X638 @ ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X639 @ ( esk41_2 @ X638 @ X639 ) )
| ( X642
!= ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X639 @ X645 )
| ( ( esk41_2 @ X638 @ X639 )
= X645 )
| ( X642
!= ( esk40_3 @ X638 @ X639 @ X642 ) )
| ~ ( X638 @ X642 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X638 @ ( esk43_2 @ X638 @ X639 ) )
| ( X639 @ ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X638 @ X649 )
| ( ( esk43_2 @ X638 @ X639 )
= X649 )
| ( X639 @ ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ( X638 @ ( esk43_2 @ X638 @ X639 ) )
| ( X646
!= ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( ~ ( X638 @ X649 )
| ( ( esk43_2 @ X638 @ X639 )
= X649 )
| ( X646
!= ( esk42_3 @ X638 @ X639 @ X646 ) )
| ~ ( X639 @ X646 )
| ( X638 @ ( esk38_2 @ X638 @ X639 ) )
| ( X639 @ ( esk39_2 @ X638 @ X639 ) ) )
& ( emptyset = emptyset )
& ( ( X650 != X651 )
| ( X652 != X653 )
| ( ( setadjoin @ X650 @ X652 )
= ( setadjoin @ X651 @ X653 ) ) )
& ( esk44_0 = esk45_0 )
& ( ( powerset @ esk44_0 )
!= ( powerset @ 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_102])])])])])]) ).
thf(c_0_104,negated_conjecture,
( ( powerset @ esk44_0 )
!= ( powerset @ esk45_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_105,negated_conjecture,
esk44_0 = esk45_0,
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_106,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU553^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:09:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running higher-order theorem proving
% 0.21/0.47 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
% 0.21/0.51 # Version: 3.1.0-ho
% 0.21/0.51 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51 # new_bool_2 with pid 7889 completed with status 0
% 0.21/0.51 # Result found by new_bool_2
% 0.21/0.51 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 163s (1) cores
% 0.21/0.51 # ho_unfolding_3 with pid 7890 completed with status 0
% 0.21/0.51 # Result found by ho_unfolding_3
% 0.21/0.51 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 163s (1) cores
% 0.21/0.51 # Preprocessing time : 0.004 s
% 0.21/0.51 # Presaturation interreduction done
% 0.21/0.51
% 0.21/0.51 # Proof found!
% 0.21/0.51 # SZS status Theorem
% 0.21/0.51 # SZS output start CNFRefutation
% See solution above
% 0.21/0.51 # Parsed axioms : 153
% 0.21/0.51 # Removed by relevancy pruning/SinE : 83
% 0.21/0.51 # Initial clauses : 161
% 0.21/0.51 # Removed in clause preprocessing : 9
% 0.21/0.51 # Initial clauses in saturation : 152
% 0.21/0.51 # Processed clauses : 5
% 0.21/0.51 # ...of these trivial : 0
% 0.21/0.51 # ...subsumed : 0
% 0.21/0.51 # ...remaining for further processing : 4
% 0.21/0.51 # Other redundant clauses eliminated : 0
% 0.21/0.51 # Clauses deleted for lack of memory : 0
% 0.21/0.51 # Backward-subsumed : 0
% 0.21/0.51 # Backward-rewritten : 0
% 0.21/0.51 # Generated clauses : 0
% 0.21/0.51 # ...of the previous two non-redundant : 0
% 0.21/0.51 # ...aggressively subsumed : 0
% 0.21/0.51 # Contextual simplify-reflections : 0
% 0.21/0.51 # Paramodulations : 0
% 0.21/0.51 # Factorizations : 0
% 0.21/0.51 # NegExts : 0
% 0.21/0.51 # Equation resolutions : 0
% 0.21/0.51 # Disequality decompositions : 0
% 0.21/0.51 # Total rewrite steps : 1
% 0.21/0.51 # ...of those cached : 0
% 0.21/0.51 # Propositional unsat checks : 0
% 0.21/0.51 # Propositional check models : 0
% 0.21/0.51 # Propositional check unsatisfiable : 0
% 0.21/0.51 # Propositional clauses : 0
% 0.21/0.51 # Propositional clauses after purity: 0
% 0.21/0.51 # Propositional unsat core size : 0
% 0.21/0.51 # Propositional preprocessing time : 0.000
% 0.21/0.51 # Propositional encoding time : 0.000
% 0.21/0.51 # Propositional solver time : 0.000
% 0.21/0.51 # Success case prop preproc time : 0.000
% 0.21/0.51 # Success case prop encoding time : 0.000
% 0.21/0.51 # Success case prop solver time : 0.000
% 0.21/0.51 # Current number of processed clauses : 4
% 0.21/0.51 # Positive orientable unit clauses : 4
% 0.21/0.51 # Positive unorientable unit clauses: 0
% 0.21/0.51 # Negative unit clauses : 0
% 0.21/0.51 # Non-unit-clauses : 0
% 0.21/0.51 # Current number of unprocessed clauses: 147
% 0.21/0.51 # ...number of literals in the above : 497
% 0.21/0.51 # Current number of archived formulas : 0
% 0.21/0.51 # Current number of archived clauses : 0
% 0.21/0.51 # Clause-clause subsumption calls (NU) : 0
% 0.21/0.51 # Rec. Clause-clause subsumption calls : 0
% 0.21/0.51 # Non-unit clause-clause subsumptions : 0
% 0.21/0.51 # Unit Clause-clause subsumption calls : 0
% 0.21/0.52 # Rewrite failures with RHS unbound : 0
% 0.21/0.52 # BW rewrite match attempts : 0
% 0.21/0.52 # BW rewrite match successes : 0
% 0.21/0.52 # Condensation attempts : 5
% 0.21/0.52 # Condensation successes : 0
% 0.21/0.52 # Termbank termtop insertions : 17652
% 0.21/0.52 # Search garbage collected termcells : 6520
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.017 s
% 0.21/0.52 # System time : 0.008 s
% 0.21/0.52 # Total time : 0.025 s
% 0.21/0.52 # Maximum resident set size: 3844 pages
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.021 s
% 0.21/0.52 # System time : 0.011 s
% 0.21/0.52 # Total time : 0.032 s
% 0.21/0.52 # Maximum resident set size: 1920 pages
% 0.21/0.52 % E---3.1 exiting
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------