TSTP Solution File: SEU581^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU581^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 03:28:20 EDT 2024
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 265
% Syntax : Number of formulae : 311 ( 23 unt; 165 typ; 0 def)
% Number of atoms : 1179 ( 331 equ; 0 cnn)
% Maximal formula atoms : 356 ( 8 avg)
% Number of connectives : 4629 ( 407 ~; 453 |; 282 &;2750 @)
% ( 160 <=>; 577 =>; 0 <=; 0 <~>)
% Maximal formula depth : 428 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 314 ( 314 >; 0 *; 0 +; 0 <<)
% Number of symbols : 168 ( 165 usr; 103 con; 0-4 aty)
% Number of variables : 1053 ( 123 ^ 826 !; 104 ?;1053 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_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,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
epred1_0: $o ).
thf(decl_135,type,
esk1_2: $i > $i > $i ).
thf(decl_136,type,
esk2_2: $i > $i > $i ).
thf(decl_137,type,
esk3_2: $i > $i > $i ).
thf(decl_138,type,
esk4_1: $i > $i ).
thf(decl_139,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_140,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_141,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_142,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_143,type,
esk9_1: $i > $i ).
thf(decl_144,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_145,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_146,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_147,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_148,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_149,type,
esk15_2: $i > $i > $i ).
thf(decl_150,type,
esk16_2: $i > $i > $i ).
thf(decl_151,type,
esk17_1: $i > $i ).
thf(decl_152,type,
esk18_1: $i > $i ).
thf(decl_153,type,
esk19_1: $i > $i ).
thf(decl_154,type,
esk20_2: $i > $i > $i ).
thf(decl_155,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_156,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_157,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_158,type,
esk24_1: $i > $i ).
thf(decl_159,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_160,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_161,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_162,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_163,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_164,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_165,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_166,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_167,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_168,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_169,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_170,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_171,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_172,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_173,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_174,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_175,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_176,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_177,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_178,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_179,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_180,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_181,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_182,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_183,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_184,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_185,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_186,type,
esk52_2: $i > $i > $i ).
thf(decl_187,type,
esk53_2: $i > $i > $i ).
thf(decl_188,type,
esk54_0: $i ).
thf(decl_189,type,
epred2_0: $i > $o ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
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(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(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(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(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(exuEu,axiom,
( exuEu
<=> ! [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',exuEu) ).
thf(descr__Cong,axiom,
( descr__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 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
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(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
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(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
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(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(sepSubset,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
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
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(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
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(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
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(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
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(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
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(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(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(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(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(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(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(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
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(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(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(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
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(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_99,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_100,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_101,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_102,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_103,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_104,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_105,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_106,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_107,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu]) ).
thf(c_0_108,plain,
( descr__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 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_109,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_110,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_111,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_112,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_113,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_114,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_99]) ).
thf(c_0_115,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_116,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_117,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X288: $i] :
( ( X1 @ X288 )
& ! [X289: $i] :
( ( X1 @ X289 )
=> ( X288 = X289 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_100,c_0_101]) ).
thf(c_0_118,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X292: $i] :
( ( X1 @ X292 )
& ! [X293: $i] :
( ( X1 @ X293 )
=> ( X292 = X293 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_102,c_0_101]) ).
thf(c_0_119,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_120,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X290: $i] :
( ( X1 @ X290 )
& ! [X291: $i] :
( ( X1 @ X291 )
=> ( X290 = X291 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_103,c_0_101]) ).
thf(c_0_121,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X294: $i] :
( ( X1 @ X294 )
& ! [X295: $i] :
( ( X1 @ X295 )
=> ( X294 = X295 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_104,c_0_101]) ).
thf(c_0_122,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X296: $i] :
( ( X1 @ X296 )
& ! [X297: $i] :
( ( X1 @ X297 )
=> ( X296 = X297 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_105,c_0_101]) ).
thf(c_0_123,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X298: $i] :
( ( X1 @ X298 )
& ! [X299: $i] :
( ( X1 @ X299 )
=> ( X298 = X299 ) ) )
<=> ? [X300: $i] :
( ( X17 @ X300 )
& ! [X301: $i] :
( ( X17 @ X301 )
=> ( X300 = X301 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_106,c_0_101]) ).
thf(c_0_124,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X302: $i] :
( ( X1 @ X302 )
& ! [X303: $i] :
( ( X1 @ X303 )
=> ( X302 = X303 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_107,c_0_101]) ).
thf(c_0_125,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X304: $i] :
( ( X1 @ X304 )
& ! [X305: $i] :
( ( X1 @ X305 )
=> ( X304 = X305 ) ) )
=> ( ? [X306: $i] :
( ( X17 @ X306 )
& ! [X307: $i] :
( ( X17 @ X307 )
=> ( X306 = X307 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_108,c_0_101]) ).
thf(c_0_126,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_127,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_99]) ).
thf(c_0_128,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_109,c_0_99]) ).
thf(c_0_129,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_99]) ).
thf(c_0_130,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_131,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X286: $i] :
( ( X1 @ X286 )
& ! [X287: $i] :
( ( X1 @ X287 )
=> ( X286 = X287 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_110,c_0_101]) ).
thf(c_0_132,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X284: $i] :
( ( X1 @ X284 )
& ! [X285: $i] :
( ( X1 @ X285 )
=> ( X284 = X285 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_111,c_0_101]) ).
thf(c_0_133,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_134,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_135,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_136,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X282: $i] :
( ( X1 @ X282 )
& ! [X283: $i] :
( ( X1 @ X283 )
=> ( X282 = X283 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_112,c_0_101]) ).
thf(c_0_137,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X280: $i] :
( ( X6 @ X2 @ X280 )
& ! [X281: $i] :
( ( X6 @ X2 @ X281 )
=> ( X280 = X281 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_113,c_0_101]) ).
thf(c_0_138,plain,
( epred1_0
<=> ! [X337: $i] :
? [X338: $i] :
( ! [X339: $i] :
( ( in @ X339 @ X338 )
=> ! [X340: $i] :
( ( in @ X340 @ X339 )
=> ( in @ X340 @ X337 ) ) )
& ! [X341: $i,X342: $i] :
( ( ( in @ X341 @ X337 )
& ( in @ X342 @ X337 ) )
=> ( ! [X343: $i] :
( ( in @ X343 @ X338 )
=> ( ( in @ X341 @ X343 )
<=> ( in @ X342 @ X343 ) ) )
=> ( X341 = X342 ) ) )
& ! [X344: $i,X345: $i] :
( ( ( in @ X344 @ X338 )
& ( in @ X345 @ X338 ) )
=> ( ! [X346: $i] :
( ( in @ X346 @ X344 )
=> ( in @ X346 @ X345 ) )
| ! [X347: $i] :
( ( in @ X347 @ X345 )
=> ( in @ X347 @ X344 ) ) ) )
& ! [X348: $i] :
( ( ! [X349: $i] :
( ( in @ X349 @ X348 )
=> ( in @ X349 @ X337 ) )
& ? [X350: $i] : ( in @ X350 @ X348 ) )
=> ? [X351: $i,X352: $i] :
( ( in @ X351 @ X338 )
& ( in @ X352 @ X348 )
& ~ ? [X353: $i] :
( ( in @ X353 @ X351 )
& ( in @ X353 @ X348 ) )
& ! [X354: $i] :
( ( in @ X354 @ X338 )
=> ( ! [X355: $i] :
( ( in @ X355 @ X354 )
=> ( in @ X355 @ X351 ) )
| ( in @ X352 @ X354 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_139,negated_conjecture,
~ ( ! [X308: $i,X309: $i] :
( ! [X310: $i] :
( ( in @ X310 @ X308 )
<=> ( in @ X310 @ X309 ) )
=> ( X308 = X309 ) )
=> ( ! [X311: $i] :
~ ( in @ X311 @ emptyset )
=> ( ! [X312: $i,X313: $i,X314: $i] :
( ( in @ X314 @ ( setadjoin @ X312 @ X313 ) )
<=> ( ( X314 = X312 )
| ( in @ X314 @ X313 ) ) )
=> ( ! [X315: $i,X316: $i] :
( ( in @ X316 @ ( powerset @ X315 ) )
<=> ! [X317: $i] :
( ( in @ X317 @ X316 )
=> ( in @ X317 @ X315 ) ) )
=> ( ! [X318: $i,X319: $i] :
( ( in @ X319 @ ( setunion @ X318 ) )
<=> ? [X320: $i] :
( ( in @ X319 @ X320 )
& ( in @ X320 @ X318 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X321: $i] :
( ( in @ X321 @ omega )
=> ( in @ ( setadjoin @ X321 @ X321 ) @ omega ) )
=> ( ! [X322: $i] :
( ( ( in @ emptyset @ X322 )
& ! [X323: $i] :
( ( ( in @ X323 @ omega )
& ( in @ X323 @ X322 ) )
=> ( in @ ( setadjoin @ X323 @ X323 ) @ X322 ) ) )
=> ! [X324: $i] :
( ( in @ X324 @ omega )
=> ( in @ X324 @ X322 ) ) )
=> ( ! [X325: $i > $i > $o,X326: $i] :
( ! [X327: $i] :
( ( in @ X327 @ X326 )
=> ? [X328: $i] :
( ( X325 @ X327 @ X328 )
& ! [X329: $i] :
( ( X325 @ X327 @ X329 )
=> ( X328 = X329 ) ) ) )
=> ? [X330: $i] :
! [X331: $i] :
( ( in @ X331 @ X330 )
<=> ? [X332: $i] :
( ( in @ X332 @ X326 )
& ( X325 @ X332 @ X331 ) ) ) )
=> ( ! [X333: $i] :
( ? [X334: $i] : ( in @ X334 @ X333 )
=> ? [X335: $i] :
( ( in @ X335 @ X333 )
& ~ ? [X336: $i] :
( ( in @ X336 @ X335 )
& ( in @ X336 @ X333 ) ) ) )
=> ( epred1_0
=> ( ! [X356: $i > $o] :
( ? [X357: $i] :
( ( X356 @ X357 )
& ! [X358: $i] :
( ( X356 @ X358 )
=> ( X357 = X358 ) ) )
=> ( X356
@ ( descr
@ ^ [Z0: $i] : ( X356 @ Z0 ) ) ) )
=> ( ! [X359: $i,X360: $i > $o,X361: $i] :
( ( in @ X361 @ X359 )
=> ( ( X360 @ X361 )
=> ( in @ X361
@ ( dsetconstr @ X359
@ ^ [Z0: $i] : ( X360 @ Z0 ) ) ) ) )
=> ( ! [X362: $i,X363: $i > $o,X364: $i] :
( ( in @ X364
@ ( dsetconstr @ X362
@ ^ [Z0: $i] : ( X363 @ Z0 ) ) )
=> ( in @ X364 @ X362 ) )
=> ( ! [X365: $i,X366: $i > $o,X367: $i] :
( ( in @ X367
@ ( dsetconstr @ X365
@ ^ [Z0: $i] : ( X366 @ Z0 ) ) )
=> ( X366 @ X367 ) )
=> ( ! [X368: $i > $o] :
( ? [X369: $i] :
( ( X368 @ X369 )
& ! [X370: $i] :
( ( X368 @ X370 )
=> ( X369 = X370 ) ) )
=> ? [X371: $i] :
( ( X368 @ X371 )
& ! [X372: $i] :
( ( X368 @ X372 )
=> ( X371 = X372 ) ) ) )
=> ( ! [X373: $o,X374: $i] :
( ( in @ X374 @ ( prop2set @ X373 ) )
=> X373 )
=> ( ! [X375: $i] :
( ( in @ X375 @ emptyset )
=> ! [X376: $o] : X376 )
=> ( ! [X377: $i] :
~ ( in @ X377 @ emptyset )
=> ( ! [X378: $i] :
~ ( in @ X378 @ emptyset )
=> ( ! [X379: $i > $o] :
( ? [X380: $i] :
( ( X379 @ X380 )
& ! [X381: $i] :
( ( X379 @ X381 )
=> ( X380 = X381 ) ) )
=> ? [X382: $i] : ( X379 @ X382 ) )
=> ( ! [X383: $i,X384: $i] :
( ! [X385: $i] :
( ( in @ X385 @ X383 )
=> ( in @ X385 @ X384 ) )
=> ( ! [X386: $i] :
( ( in @ X386 @ X384 )
=> ( in @ X386 @ X383 ) )
=> ( X383 = X384 ) ) )
=> ( ! [X387: $i] :
( ! [X388: $i] :
~ ( in @ X388 @ X387 )
=> ( X387 = emptyset ) )
=> ( ! [X389: $i] :
( ! [X390: $i] :
~ ( in @ X390 @ X389 )
=> ( X389 = emptyset ) )
=> ( ! [X391: $i,X392: $i > $o,X393: $i] :
( ( in @ X393 @ X391 )
=> ( ( in @ X393
@ ( dsetconstr @ X391
@ ^ [Z0: $i] : ( X392 @ Z0 ) ) )
<=> ( X392 @ X393 ) ) )
=> ( ! [X394: $i] :
( ( X394 != emptyset )
=> ? [X395: $i] : ( in @ X395 @ X394 ) )
=> ( ! [X396: $i,X397: $i > $o,X398: $i] :
( ( in @ X398 @ X396 )
=> ( ( X397 @ X398 )
=> ( ( dsetconstr @ X396
@ ^ [Z0: $i] : ( X397 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X399: $i] :
( ? [X400: $i] : ( in @ X400 @ X399 )
=> ( X399 != emptyset ) )
=> ( ! [X401: $i,X402: $i] : ( in @ X401 @ ( setadjoin @ X401 @ X402 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X403: $i,X404: $i,X405: $i] :
( ( in @ X405 @ X404 )
=> ( in @ X405 @ ( setadjoin @ X403 @ X404 ) ) )
=> ( ! [X406: $i,X407: $i,X408: $i] :
( ( in @ X408 @ ( setadjoin @ X406 @ X407 ) )
=> ! [X409: $o] :
( ( ( X408 = X406 )
=> X409 )
=> ( ( ( in @ X408 @ X407 )
=> X409 )
=> X409 ) ) )
=> ( ! [X410: $i,X411: $i,X412: $i] :
( ( in @ X412 @ ( setadjoin @ X410 @ X411 ) )
=> ( ( X412 = X410 )
| ( in @ X412 @ X411 ) ) )
=> ( ! [X413: $i] :
( ( dsetconstr @ X413
@ ^ [Z0: $i] : $true )
= X413 )
=> ( ! [X414: $i,X415: $i] :
( ! [X416: $i] :
( ( in @ X416 @ X415 )
=> ( in @ X416 @ X414 ) )
=> ( in @ X415 @ ( powerset @ X414 ) ) )
=> ( ! [X417: $i] : ( in @ emptyset @ ( powerset @ X417 ) )
=> ( ! [X418: $i] : ( in @ emptyset @ ( powerset @ X418 ) )
=> ( ! [X419: $i,X420: $i,X421: $i] :
( ( in @ X420 @ ( powerset @ X419 ) )
=> ( ( in @ X421 @ X420 )
=> ( in @ X421 @ X419 ) ) )
=> ( ! [X422: $i,X423: $i,X424: $i] :
( ( in @ X423 @ X424 )
=> ( ( in @ X424 @ X422 )
=> ( in @ X423 @ ( setunion @ X422 ) ) ) )
=> ( ! [X425: $i,X426: $i] :
( ( in @ X426 @ ( setunion @ X425 ) )
=> ! [X427: $o] :
( ! [X428: $i] :
( ( in @ X426 @ X428 )
=> ( ( in @ X428 @ X425 )
=> X427 ) )
=> X427 ) )
=> ( ! [X429: $i,X430: $i] :
( ( in @ X430 @ X429 )
=> ( in @ X430 @ ( powerset @ ( setunion @ X429 ) ) ) )
=> ( ! [X431: $i > $o] :
( ? [X432: $i] :
( ( X431 @ X432 )
& ! [X433: $i] :
( ( X431 @ X433 )
=> ( X432 = X433 ) ) )
=> ? [X434: $i] :
! [X435: $i] :
( ( X431 @ X435 )
<=> ( X435 = X434 ) ) )
=> ( ! [X436: $i] :
( ( X436 != emptyset )
=> ? [X437: $i] : ( in @ X437 @ X436 ) )
=> ( ! [X438: $i,X439: $i] :
( ( in @ X438 @ ( setadjoin @ X439 @ emptyset ) )
=> ( X438 = X439 ) )
=> ( ! [X440: $i,X441: $i] :
( ( X440 != X441 )
=> ~ ( in @ X441 @ ( setadjoin @ X440 @ emptyset ) ) )
=> ( ! [X442: $i,X443: $i] :
( ( X442 = X443 )
=> ( in @ X442 @ ( setadjoin @ X443 @ emptyset ) ) )
=> ( ! [X444: $i,X445: $i] :
( ( in @ X444 @ ( setadjoin @ X445 @ emptyset ) )
=> ( in @ X445 @ ( setadjoin @ X444 @ emptyset ) ) )
=> ( ! [X446: $i,X447: $i,X448: $i] :
( ( in @ X448 @ ( setadjoin @ X446 @ ( setadjoin @ X447 @ emptyset ) ) )
=> ( ( X448 = X446 )
| ( X448 = X447 ) ) )
=> ( ! [X449: $i,X450: $i] : ( in @ X449 @ ( setadjoin @ X449 @ ( setadjoin @ X450 @ emptyset ) ) )
=> ( ! [X451: $i,X452: $i] : ( in @ X452 @ ( setadjoin @ X451 @ ( setadjoin @ X452 @ emptyset ) ) )
=> ( ! [X453: $i,X454: $i > $o] :
( ? [X455: $i] :
( ( in @ X455 @ X453 )
& ( X454 @ X455 ) )
=> ( ( dsetconstr @ X453
@ ^ [Z0: $i] : ( X454 @ Z0 ) )
!= emptyset ) )
=> ( ! [X456: $i > $o,X457: $i] :
( ( in @ X457 @ emptyset )
=> ( X456 @ X457 ) )
=> ( ! [X458: $i,X459: $i > $o] :
( ~ ! [X460: $i] :
( ( in @ X460 @ X458 )
=> ( X459 @ X460 ) )
=> ? [X461: $i] :
( ( in @ X461 @ X458 )
& ~ ( X459 @ X461 ) ) )
=> ( ! [X462: $i,X463: $i > $o] :
( ! [X464: $i] :
( ( in @ X464 @ X462 )
=> ~ ( X463 @ X464 ) )
=> ~ ? [X465: $i] :
( ( in @ X465 @ X462 )
& ( X463 @ X465 ) ) )
=> ( ! [X466: $i,X467: $i > $o] :
( ~ ? [X468: $i] :
( ( in @ X468 @ X466 )
& ( X467 @ X468 ) )
=> ! [X469: $i] :
( ( in @ X469 @ X466 )
=> ~ ( X467 @ X469 ) ) )
=> ( ! [X470: $i,X471: $i > $o] :
( ? [X472: $i] :
( ( in @ X472 @ X470 )
& ~ ( X471 @ X472 ) )
=> ~ ! [X473: $i] :
( ( in @ X473 @ X470 )
=> ( X471 @ X473 ) ) )
=> ( ! [X474: $o] :
( X474
=> ( in @ emptyset @ ( prop2set @ X474 ) ) )
=> ( prop2set2propI
=> ( ! [X475: $i,X476: $i > $o] :
( ~ ? [X477: $i] :
( ( in @ X477 @ X475 )
& ( X476 @ X477 ) )
=> ! [X478: $i] :
( ( in @ X478 @ X475 )
=> ~ ( X476 @ X478 ) ) )
=> ( ! [X479: $i,X480: $i > $o] :
( ~ ! [X481: $i] :
( ( in @ X481 @ X479 )
=> ( X480 @ X481 ) )
=> ? [X482: $i] :
( ( in @ X482 @ X479 )
& ~ ( X480 @ X482 ) ) )
=> ( ! [X483: $i > $o] :
( ? [X484: $i] :
( ( X483 @ X484 )
& ! [X485: $i] :
( ( X483 @ X485 )
=> ( X484 = X485 ) ) )
=> ? [X486: $i] :
( ( X483 @ X486 )
& ! [X487: $i] :
( ( X483 @ X487 )
=> ( X486 = X487 ) ) ) )
=> ( ! [X488: $i > $o] :
( ? [X489: $i] : ( X488 @ X489 )
=> ( ! [X490: $i,X491: $i] :
( ( X488 @ X490 )
=> ( ( X488 @ X491 )
=> ( X490 = X491 ) ) )
=> ? [X492: $i] :
( ( X488 @ X492 )
& ! [X493: $i] :
( ( X488 @ X493 )
=> ( X492 = X493 ) ) ) ) )
=> ( ! [X494: $i > $o] :
( ? [X495: $i] :
! [X496: $i] :
( ( X494 @ X496 )
<=> ( X496 = X495 ) )
=> ? [X497: $i] :
( ( X494 @ X497 )
& ! [X498: $i] :
( ( X494 @ X498 )
=> ( X497 = X498 ) ) ) )
=> ( ! [X499: $i,X500: $i] :
( ( X499 = X500 )
=> ! [X501: $i,X502: $i] :
( ( X501 = X502 )
=> ( ( in @ X501 @ X499 )
=> ( in @ X502 @ X500 ) ) ) )
=> ( ! [X503: $i,X504: $i] :
( ( X503 = X504 )
=> ! [X505: $i,X506: $i] :
( ( X505 = X506 )
=> ( ( in @ X505 @ X503 )
<=> ( in @ X506 @ X504 ) ) ) )
=> ( ! [X507: $i > $o] :
( ? [X508: $i] :
( ( X507 @ X508 )
& ! [X509: $i] :
( ( X507 @ X509 )
=> ( X508 = X509 ) ) )
=> ! [X510: $i,X511: $i] :
( ( X507 @ X510 )
=> ( ( X507 @ X511 )
=> ( X510 = X511 ) ) ) )
=> ( ! [X512: $i > $o,X513: $i > $o] :
( ! [X514: $i,X515: $i] :
( ( X514 = X515 )
=> ( ( X512 @ X514 )
<=> ( X513 @ X515 ) ) )
=> ( ? [X516: $i] :
( ( X512 @ X516 )
& ! [X517: $i] :
( ( X512 @ X517 )
=> ( X516 = X517 ) ) )
<=> ? [X518: $i] :
( ( X513 @ X518 )
& ! [X519: $i] :
( ( X513 @ X519 )
=> ( X518 = X519 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X520: $i,X521: $i] :
( ( X520 = X521 )
=> ! [X522: $i,X523: $i] :
( ( X522 = X523 )
=> ( ( setadjoin @ X520 @ X522 )
= ( setadjoin @ X521 @ X523 ) ) ) )
=> ( ! [X524: $i,X525: $i] :
( ( X524 = X525 )
=> ( ( powerset @ X524 )
= ( powerset @ X525 ) ) )
=> ( ! [X526: $i,X527: $i] :
( ( X526 = X527 )
=> ( ( setunion @ X526 )
= ( setunion @ X527 ) ) )
=> ( ( omega = omega )
=> ( ! [X528: $i > $o] :
( ? [X529: $i] :
( ( X528 @ X529 )
& ! [X530: $i] :
( ( X528 @ X530 )
=> ( X529 = X530 ) ) )
=> ! [X531: $i,X532: $i] :
( ( X528 @ X531 )
=> ( ( X528 @ X532 )
=> ( X531 = X532 ) ) ) )
=> ( ! [X533: $i > $o,X534: $i > $o] :
( ! [X535: $i,X536: $i] :
( ( X535 = X536 )
=> ( ( X533 @ X535 )
<=> ( X534 @ X536 ) ) )
=> ( ? [X537: $i] :
( ( X533 @ X537 )
& ! [X538: $i] :
( ( X533 @ X538 )
=> ( X537 = X538 ) ) )
=> ( ? [X539: $i] :
( ( X534 @ X539 )
& ! [X540: $i] :
( ( X534 @ X540 )
=> ( X539 = X540 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X533 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X534 @ Z0 ) ) ) ) ) )
=> ( ! [X541: $i,X542: $i] :
( ( X541 = X542 )
=> ! [X543: $i > $o,X544: $i > $o] :
( ! [X545: $i] :
( ( in @ X545 @ X541 )
=> ! [X546: $i] :
( ( in @ X546 @ X542 )
=> ( ( X545 = X546 )
=> ( ( X543 @ X545 )
<=> ( X544 @ X546 ) ) ) ) )
=> ( ( dsetconstr @ X541
@ ^ [Z0: $i] : ( X543 @ Z0 ) )
= ( dsetconstr @ X542
@ ^ [Z0: $i] : ( X544 @ Z0 ) ) ) ) )
=> ( ! [X547: $i,X548: $i] :
( ! [X549: $i] :
( ( in @ X549 @ X547 )
=> ( in @ X549 @ X548 ) )
=> ( subset @ X547 @ X548 ) )
=> ( ! [X550: $i,X551: $i] :
( ( X550 = X551 )
=> ( subset @ X551 @ X550 ) )
=> ( ! [X552: $i,X553: $i] :
( ( X552 = X553 )
=> ( subset @ X552 @ X553 ) )
=> ( ! [X554: $i,X555: $i] :
( ! [X556: $i] :
( ( in @ X556 @ X554 )
=> ( in @ X556 @ X555 ) )
=> ( subset @ X554 @ X555 ) )
=> ( ! [X557: $i] : ( subset @ emptyset @ X557 )
=> ( ! [X558: $i,X559: $i,X560: $i] :
( ( subset @ X558 @ X559 )
=> ( ( in @ X560 @ X558 )
=> ( in @ X560 @ X559 ) ) )
=> ( ! [X561: $i,X562: $i,X563: $i] :
( ( subset @ X561 @ X562 )
=> ( ~ ( in @ X563 @ X562 )
=> ~ ( in @ X563 @ X561 ) ) )
=> ( ! [X564: $i,X565: $i,X566: $i] :
( ( in @ X566 @ X564 )
=> ( ~ ( in @ X566 @ X565 )
=> ~ ( subset @ X564 @ X565 ) ) )
=> ( ! [X567: $i,X568: $i] :
( ~ ( subset @ X567 @ X568 )
=> ( X567 != X568 ) )
=> ( ! [X569: $i,X570: $i,X571: $i] :
( ( in @ X571 @ X569 )
=> ( ~ ( in @ X571 @ X570 )
=> ( X569 != X570 ) ) )
=> ( ! [X572: $i] : ( subset @ X572 @ X572 )
=> ( ! [X573: $i,X574: $i,X575: $i] :
( ( subset @ X573 @ X574 )
=> ( ( subset @ X574 @ X575 )
=> ( subset @ X573 @ X575 ) ) )
=> ( ! [X576: $i,X577: $i] : ( subset @ X577 @ ( setadjoin @ X576 @ X577 ) )
=> ( ! [X578: $i,X579: $i,X580: $i] :
( ( subset @ X578 @ X580 )
=> ( subset @ X578 @ ( setadjoin @ X579 @ X580 ) ) )
=> ( ! [X581: $i,X582: $i] :
( ( subset @ X581 @ X582 )
=> ( in @ X581 @ ( powerset @ X582 ) ) )
=> ( ! [X583: $i,X584: $i] :
( ( subset @ X583 @ X584 )
=> ( ( subset @ X584 @ X583 )
=> ( X583 = X584 ) ) )
=> ( ! [X585: $i] :
( ( subset @ X585 @ emptyset )
=> ( X585 = emptyset ) )
=> ( ! [X586: $i,X587: $i] :
( ( subset @ X587 @ X586 )
=> ( in @ X587 @ ( powerset @ X586 ) ) )
=> ( ! [X588: $i,X589: $i] :
( ( in @ X589 @ ( powerset @ X588 ) )
=> ( subset @ X589 @ X588 ) )
=> ( ! [X590: $i] : ( in @ X590 @ ( powerset @ X590 ) )
=> ( ! [X591: $i,X592: $i] :
( ( subset @ X591 @ X592 )
=> ( subset @ ( powerset @ X591 ) @ ( powerset @ X592 ) ) )
=> ( ! [X593: $i,X594: $i > $o] :
( in
@ ( dsetconstr @ X593
@ ^ [Z0: $i] : ( X594 @ Z0 ) )
@ ( powerset @ X593 ) )
=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[sepSubset])]),c_0_114]),c_0_115]),subsetE2]),c_0_116]),notsubsetI]),notequalI1]),notequalI2]),powersetI]),subsetRefl]),subsetTrans]),emptyinPowerset]),setadjoinSub]),setadjoinSub2]),emptyInPowerset]),subset2powerset]),setextsub]),powersetE]),subsetemptysetimpeq]),powersetI1]),setunionI]),powersetE1]),inPowerset]),setunionE]),powersetsubset]),subPowSU]),c_0_117]),c_0_118]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_119]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_120]),c_0_121]),inCongP]),in__Cong]),c_0_122]),c_0_123]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_124]),c_0_125]),c_0_126]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_127]),c_0_128]),c_0_129]),c_0_130]),noeltsimpempty]),emptyI]),setext]),c_0_131]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_132]),c_0_133]),c_0_134]),c_0_135]),c_0_136]),wellorderingAx]),foundationAx]),c_0_137]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_138]) ).
thf(c_0_140,negated_conjecture,
! [X595: $i,X596: $i,X598: $i,X599: $i,X600: $i,X601: $i,X602: $i,X603: $i,X604: $i,X605: $i,X606: $i,X608: $i,X609: $i,X611: $i,X612: $i,X613: $i,X614: $i,X615: $i,X617: $i,X618: $i > $i > $o,X619: $i,X621: $i,X624: $i,X626: $i,X627: $i,X628: $i,X629: $i,X631: $i,X632: $i > $o,X633: $i,X635: $i,X636: $i > $o,X637: $i,X638: $i,X639: $i > $o,X640: $i,X641: $i,X642: $i > $o,X643: $i,X644: $i > $o,X645: $i,X648: $i,X649: $o,X650: $i,X651: $i,X652: $o,X653: $i,X654: $i,X655: $i > $o,X656: $i,X659: $i,X660: $i,X663: $i,X665: $i,X667: $i,X668: $i > $o,X669: $i,X670: $i,X672: $i,X673: $i > $o,X674: $i,X675: $i,X676: $i,X677: $i,X678: $i,X679: $i,X680: $i,X681: $i,X682: $i,X683: $i,X684: $i,X685: $o,X686: $i,X687: $i,X688: $i,X689: $i,X690: $i,X691: $i,X693: $i,X694: $i,X695: $i,X696: $i,X697: $i,X698: $i,X699: $i,X700: $i,X701: $i,X702: $i,X703: $o,X705: $i,X706: $i,X707: $i > $o,X708: $i,X711: $i,X712: $i,X713: $i,X715: $i,X716: $i,X717: $i,X718: $i,X719: $i,X720: $i,X721: $i,X722: $i,X723: $i,X724: $i,X725: $i,X726: $i,X727: $i,X728: $i,X729: $i,X730: $i,X731: $i > $o,X732: $i,X733: $i > $o,X734: $i,X735: $i,X736: $i > $o,X737: $i,X739: $i,X740: $i > $o,X742: $i,X743: $i,X744: $i > $o,X746: $i,X747: $i,X748: $i > $o,X749: $i,X751: $o,X752: $i,X753: $i > $o,X755: $i,X756: $i,X757: $i > $o,X758: $i,X760: $i > $o,X761: $i,X764: $i,X765: $i > $o,X766: $i,X770: $i,X771: $i > $o,X772: $i,X775: $i,X776: $i,X777: $i,X778: $i,X779: $i,X780: $i,X781: $i,X782: $i,X783: $i,X784: $i > $o,X785: $i,X787: $i,X788: $i,X789: $i > $o,X790: $i > $o,X793: $i,X796: $i,X797: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i > $o,X810: $i,X812: $i,X813: $i,X814: $i > $o,X815: $i > $o,X818: $i,X820: $i,X822: $i,X823: $i,X824: $i > $o,X825: $i > $o,X828: $i,X829: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X838: $i,X839: $i,X840: $i,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X855: $i,X856: $i,X857: $i,X858: $i,X859: $i,X860: $i,X861: $i,X862: $i,X863: $i,X864: $i,X865: $i,X866: $i,X867: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i > $o] :
( ( ~ ( in @ ( esk1_2 @ X595 @ X596 ) @ X595 )
| ~ ( in @ ( esk1_2 @ X595 @ X596 ) @ X596 )
| ( X595 = X596 ) )
& ( ( in @ ( esk1_2 @ X595 @ X596 ) @ X595 )
| ( in @ ( esk1_2 @ X595 @ X596 ) @ X596 )
| ( X595 = X596 ) )
& ~ ( in @ X598 @ emptyset )
& ( ~ ( in @ X601 @ ( setadjoin @ X599 @ X600 ) )
| ( X601 = X599 )
| ( in @ X601 @ X600 ) )
& ( ( X601 != X599 )
| ( in @ X601 @ ( setadjoin @ X599 @ X600 ) ) )
& ( ~ ( in @ X601 @ X600 )
| ( in @ X601 @ ( setadjoin @ X599 @ X600 ) ) )
& ( ~ ( in @ X603 @ ( powerset @ X602 ) )
| ~ ( in @ X604 @ X603 )
| ( in @ X604 @ X602 ) )
& ( ( in @ ( esk2_2 @ X605 @ X606 ) @ X606 )
| ( in @ X606 @ ( powerset @ X605 ) ) )
& ( ~ ( in @ ( esk2_2 @ X605 @ X606 ) @ X605 )
| ( in @ X606 @ ( powerset @ X605 ) ) )
& ( ( in @ X609 @ ( esk3_2 @ X608 @ X609 ) )
| ~ ( in @ X609 @ ( setunion @ X608 ) ) )
& ( ( in @ ( esk3_2 @ X608 @ X609 ) @ X608 )
| ~ ( in @ X609 @ ( setunion @ X608 ) ) )
& ( ~ ( in @ X612 @ X613 )
| ~ ( in @ X613 @ X611 )
| ( in @ X612 @ ( setunion @ X611 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X614 @ omega )
| ( in @ ( setadjoin @ X614 @ X614 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X615 ) @ omega )
| ~ ( in @ emptyset @ X615 )
| ~ ( in @ X617 @ omega )
| ( in @ X617 @ X615 ) )
& ( ( in @ ( esk4_1 @ X615 ) @ X615 )
| ~ ( in @ emptyset @ X615 )
| ~ ( in @ X617 @ omega )
| ( in @ X617 @ X615 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X615 ) @ ( esk4_1 @ X615 ) ) @ X615 )
| ~ ( in @ emptyset @ X615 )
| ~ ( in @ X617 @ omega )
| ( in @ X617 @ X615 ) )
& ( ( in @ ( esk8_3 @ X618 @ X619 @ X624 ) @ X619 )
| ~ ( in @ X624 @ ( esk7_2 @ X618 @ X619 ) )
| ( in @ ( esk5_2 @ X618 @ X619 ) @ X619 ) )
& ( ( X618 @ ( esk8_3 @ X618 @ X619 @ X624 ) @ X624 )
| ~ ( in @ X624 @ ( esk7_2 @ X618 @ X619 ) )
| ( in @ ( esk5_2 @ X618 @ X619 ) @ X619 ) )
& ( ~ ( in @ X627 @ X619 )
| ~ ( X618 @ X627 @ X626 )
| ( in @ X626 @ ( esk7_2 @ X618 @ X619 ) )
| ( in @ ( esk5_2 @ X618 @ X619 ) @ X619 ) )
& ( ( in @ ( esk8_3 @ X618 @ X619 @ X624 ) @ X619 )
| ~ ( in @ X624 @ ( esk7_2 @ X618 @ X619 ) )
| ( X618 @ ( esk5_2 @ X618 @ X619 ) @ ( esk6_3 @ X618 @ X619 @ X621 ) )
| ~ ( X618 @ ( esk5_2 @ X618 @ X619 ) @ X621 ) )
& ( ( X618 @ ( esk8_3 @ X618 @ X619 @ X624 ) @ X624 )
| ~ ( in @ X624 @ ( esk7_2 @ X618 @ X619 ) )
| ( X618 @ ( esk5_2 @ X618 @ X619 ) @ ( esk6_3 @ X618 @ X619 @ X621 ) )
| ~ ( X618 @ ( esk5_2 @ X618 @ X619 ) @ X621 ) )
& ( ~ ( in @ X627 @ X619 )
| ~ ( X618 @ X627 @ X626 )
| ( in @ X626 @ ( esk7_2 @ X618 @ X619 ) )
| ( X618 @ ( esk5_2 @ X618 @ X619 ) @ ( esk6_3 @ X618 @ X619 @ X621 ) )
| ~ ( X618 @ ( esk5_2 @ X618 @ X619 ) @ X621 ) )
& ( ( in @ ( esk8_3 @ X618 @ X619 @ X624 ) @ X619 )
| ~ ( in @ X624 @ ( esk7_2 @ X618 @ X619 ) )
| ( X621
!= ( esk6_3 @ X618 @ X619 @ X621 ) )
| ~ ( X618 @ ( esk5_2 @ X618 @ X619 ) @ X621 ) )
& ( ( X618 @ ( esk8_3 @ X618 @ X619 @ X624 ) @ X624 )
| ~ ( in @ X624 @ ( esk7_2 @ X618 @ X619 ) )
| ( X621
!= ( esk6_3 @ X618 @ X619 @ X621 ) )
| ~ ( X618 @ ( esk5_2 @ X618 @ X619 ) @ X621 ) )
& ( ~ ( in @ X627 @ X619 )
| ~ ( X618 @ X627 @ X626 )
| ( in @ X626 @ ( esk7_2 @ X618 @ X619 ) )
| ( X621
!= ( esk6_3 @ X618 @ X619 @ X621 ) )
| ~ ( X618 @ ( esk5_2 @ X618 @ X619 ) @ X621 ) )
& ( ( in @ ( esk9_1 @ X628 ) @ X628 )
| ~ ( in @ X629 @ X628 ) )
& ( ~ ( in @ X631 @ ( esk9_1 @ X628 ) )
| ~ ( in @ X631 @ X628 )
| ~ ( in @ X629 @ X628 ) )
& epred1_0
& ( ( X632 @ ( esk10_2 @ X632 @ X633 ) )
| ~ ( X632 @ X633 )
| ( X632
@ ( descr
@ ^ [Z0: $i] : ( X632 @ Z0 ) ) ) )
& ( ( X633
!= ( esk10_2 @ X632 @ X633 ) )
| ~ ( X632 @ X633 )
| ( X632
@ ( descr
@ ^ [Z0: $i] : ( X632 @ Z0 ) ) ) )
& ( ~ ( in @ X637 @ X635 )
| ~ ( X636 @ X637 )
| ( in @ X637
@ ( dsetconstr @ X635
@ ^ [Z0: $i] : ( X636 @ Z0 ) ) ) )
& ( ~ ( in @ X640
@ ( dsetconstr @ X638
@ ^ [Z0: $i] : ( X639 @ Z0 ) ) )
| ( in @ X640 @ X638 ) )
& ( ~ ( in @ X643
@ ( dsetconstr @ X641
@ ^ [Z0: $i] : ( X642 @ Z0 ) ) )
| ( X642 @ X643 ) )
& ( ( X644 @ ( esk12_1 @ X644 ) )
| ( X644 @ ( esk11_2 @ X644 @ X645 ) )
| ~ ( X644 @ X645 ) )
& ( ~ ( X644 @ X648 )
| ( ( esk12_1 @ X644 )
= X648 )
| ( X644 @ ( esk11_2 @ X644 @ X645 ) )
| ~ ( X644 @ X645 ) )
& ( ( X644 @ ( esk12_1 @ X644 ) )
| ( X645
!= ( esk11_2 @ X644 @ X645 ) )
| ~ ( X644 @ X645 ) )
& ( ~ ( X644 @ X648 )
| ( ( esk12_1 @ X644 )
= X648 )
| ( X645
!= ( esk11_2 @ X644 @ X645 ) )
| ~ ( X644 @ X645 ) )
& ( ~ ( in @ X650 @ ( prop2set @ X649 ) )
| X649 )
& ( ~ ( in @ X651 @ emptyset )
| X652 )
& ~ ( in @ X653 @ emptyset )
& ~ ( in @ X654 @ emptyset )
& ( ( X655 @ ( esk13_2 @ X655 @ X656 ) )
| ~ ( X655 @ X656 )
| ( X655 @ ( esk14_1 @ X655 ) ) )
& ( ( X656
!= ( esk13_2 @ X655 @ X656 ) )
| ~ ( X655 @ X656 )
| ( X655 @ ( esk14_1 @ X655 ) ) )
& ( ( in @ ( esk16_2 @ X659 @ X660 ) @ X660 )
| ( X659 = X660 )
| ( in @ ( esk15_2 @ X659 @ X660 ) @ X659 ) )
& ( ~ ( in @ ( esk16_2 @ X659 @ X660 ) @ X659 )
| ( X659 = X660 )
| ( in @ ( esk15_2 @ X659 @ X660 ) @ X659 ) )
& ( ( in @ ( esk16_2 @ X659 @ X660 ) @ X660 )
| ( X659 = X660 )
| ~ ( in @ ( esk15_2 @ X659 @ X660 ) @ X660 ) )
& ( ~ ( in @ ( esk16_2 @ X659 @ X660 ) @ X659 )
| ( X659 = X660 )
| ~ ( in @ ( esk15_2 @ X659 @ X660 ) @ X660 ) )
& ( ( in @ ( esk17_1 @ X663 ) @ X663 )
| ( X663 = emptyset ) )
& ( ( in @ ( esk18_1 @ X665 ) @ X665 )
| ( X665 = emptyset ) )
& ( ~ ( in @ X669
@ ( dsetconstr @ X667
@ ^ [Z0: $i] : ( X668 @ Z0 ) ) )
| ( X668 @ X669 )
| ~ ( in @ X669 @ X667 ) )
& ( ~ ( X668 @ X669 )
| ( in @ X669
@ ( dsetconstr @ X667
@ ^ [Z0: $i] : ( X668 @ Z0 ) ) )
| ~ ( in @ X669 @ X667 ) )
& ( ( X670 = emptyset )
| ( in @ ( esk19_1 @ X670 ) @ X670 ) )
& ( ~ ( in @ X674 @ X672 )
| ~ ( X673 @ X674 )
| ( ( dsetconstr @ X672
@ ^ [Z0: $i] : ( X673 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X676 @ X675 )
| ( X675 != emptyset ) )
& ( in @ X677 @ ( setadjoin @ X677 @ X678 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X681 @ X680 )
| ( in @ X681 @ ( setadjoin @ X679 @ X680 ) ) )
& ( ( in @ X684 @ X683 )
| X685
| ( X684 = X682 )
| ~ ( in @ X684 @ ( setadjoin @ X682 @ X683 ) ) )
& ( ~ X685
| X685
| ( X684 = X682 )
| ~ ( in @ X684 @ ( setadjoin @ X682 @ X683 ) ) )
& ( ( in @ X684 @ X683 )
| X685
| ~ X685
| ~ ( in @ X684 @ ( setadjoin @ X682 @ X683 ) ) )
& ( ~ X685
| X685
| ~ X685
| ~ ( in @ X684 @ ( setadjoin @ X682 @ X683 ) ) )
& ( ~ ( in @ X688 @ ( setadjoin @ X686 @ X687 ) )
| ( X688 = X686 )
| ( in @ X688 @ X687 ) )
& ( ( dsetconstr @ X689
@ ^ [Z0: $i] : $true )
= X689 )
& ( ( in @ ( esk20_2 @ X690 @ X691 ) @ X691 )
| ( in @ X691 @ ( powerset @ X690 ) ) )
& ( ~ ( in @ ( esk20_2 @ X690 @ X691 ) @ X690 )
| ( in @ X691 @ ( powerset @ X690 ) ) )
& ( in @ emptyset @ ( powerset @ X693 ) )
& ( in @ emptyset @ ( powerset @ X694 ) )
& ( ~ ( in @ X696 @ ( powerset @ X695 ) )
| ~ ( in @ X697 @ X696 )
| ( in @ X697 @ X695 ) )
& ( ~ ( in @ X699 @ X700 )
| ~ ( in @ X700 @ X698 )
| ( in @ X699 @ ( setunion @ X698 ) ) )
& ( ( in @ X702 @ ( esk21_3 @ X701 @ X702 @ X703 ) )
| X703
| ~ ( in @ X702 @ ( setunion @ X701 ) ) )
& ( ( in @ ( esk21_3 @ X701 @ X702 @ X703 ) @ X701 )
| X703
| ~ ( in @ X702 @ ( setunion @ X701 ) ) )
& ( ~ X703
| X703
| ~ ( in @ X702 @ ( setunion @ X701 ) ) )
& ( ~ ( in @ X706 @ X705 )
| ( in @ X706 @ ( powerset @ ( setunion @ X705 ) ) ) )
& ( ~ ( X707 @ X711 )
| ( X711
= ( esk23_1 @ X707 ) )
| ( X707 @ ( esk22_2 @ X707 @ X708 ) )
| ~ ( X707 @ X708 ) )
& ( ( X712
!= ( esk23_1 @ X707 ) )
| ( X707 @ X712 )
| ( X707 @ ( esk22_2 @ X707 @ X708 ) )
| ~ ( X707 @ X708 ) )
& ( ~ ( X707 @ X711 )
| ( X711
= ( esk23_1 @ X707 ) )
| ( X708
!= ( esk22_2 @ X707 @ X708 ) )
| ~ ( X707 @ X708 ) )
& ( ( X712
!= ( esk23_1 @ X707 ) )
| ( X707 @ X712 )
| ( X708
!= ( esk22_2 @ X707 @ X708 ) )
| ~ ( X707 @ X708 ) )
& ( ( X713 = emptyset )
| ( in @ ( esk24_1 @ X713 ) @ X713 ) )
& ( ~ ( in @ X715 @ ( setadjoin @ X716 @ emptyset ) )
| ( X715 = X716 ) )
& ( ( X717 = X718 )
| ~ ( in @ X718 @ ( setadjoin @ X717 @ emptyset ) ) )
& ( ( X719 != X720 )
| ( in @ X719 @ ( setadjoin @ X720 @ emptyset ) ) )
& ( ~ ( in @ X721 @ ( setadjoin @ X722 @ emptyset ) )
| ( in @ X722 @ ( setadjoin @ X721 @ emptyset ) ) )
& ( ~ ( in @ X725 @ ( setadjoin @ X723 @ ( setadjoin @ X724 @ emptyset ) ) )
| ( X725 = X723 )
| ( X725 = X724 ) )
& ( in @ X726 @ ( setadjoin @ X726 @ ( setadjoin @ X727 @ emptyset ) ) )
& ( in @ X729 @ ( setadjoin @ X728 @ ( setadjoin @ X729 @ emptyset ) ) )
& ( ~ ( in @ X732 @ X730 )
| ~ ( X731 @ X732 )
| ( ( dsetconstr @ X730
@ ^ [Z0: $i] : ( X731 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X734 @ emptyset )
| ( X733 @ X734 ) )
& ( ( in @ ( esk25_2 @ X735 @ X736 ) @ X735 )
| ~ ( in @ X737 @ X735 )
| ( X736 @ X737 ) )
& ( ~ ( X736 @ ( esk25_2 @ X735 @ X736 ) )
| ~ ( in @ X737 @ X735 )
| ( X736 @ X737 ) )
& ( ( in @ ( esk26_2 @ X739 @ X740 ) @ X739 )
| ~ ( in @ X742 @ X739 )
| ~ ( X740 @ X742 ) )
& ( ( X740 @ ( esk26_2 @ X739 @ X740 ) )
| ~ ( in @ X742 @ X739 )
| ~ ( X740 @ X742 ) )
& ( ( in @ ( esk27_2 @ X743 @ X744 ) @ X743 )
| ~ ( in @ X746 @ X743 )
| ~ ( X744 @ X746 ) )
& ( ( X744 @ ( esk27_2 @ X743 @ X744 ) )
| ~ ( in @ X746 @ X743 )
| ~ ( X744 @ X746 ) )
& ( ( in @ ( esk28_2 @ X747 @ X748 ) @ X747 )
| ~ ( in @ X749 @ X747 )
| ( X748 @ X749 ) )
& ( ~ ( X748 @ ( esk28_2 @ X747 @ X748 ) )
| ~ ( in @ X749 @ X747 )
| ( X748 @ X749 ) )
& ( ~ X751
| ( in @ emptyset @ ( prop2set @ X751 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X752 @ X753 ) @ X752 )
| ~ ( in @ X755 @ X752 )
| ~ ( X753 @ X755 ) )
& ( ( X753 @ ( esk29_2 @ X752 @ X753 ) )
| ~ ( in @ X755 @ X752 )
| ~ ( X753 @ X755 ) )
& ( ( in @ ( esk30_2 @ X756 @ X757 ) @ X756 )
| ~ ( in @ X758 @ X756 )
| ( X757 @ X758 ) )
& ( ~ ( X757 @ ( esk30_2 @ X756 @ X757 ) )
| ~ ( in @ X758 @ X756 )
| ( X757 @ X758 ) )
& ( ( X760 @ ( esk32_1 @ X760 ) )
| ( X760 @ ( esk31_2 @ X760 @ X761 ) )
| ~ ( X760 @ X761 ) )
& ( ~ ( X760 @ X764 )
| ( ( esk32_1 @ X760 )
= X764 )
| ( X760 @ ( esk31_2 @ X760 @ X761 ) )
| ~ ( X760 @ X761 ) )
& ( ( X760 @ ( esk32_1 @ X760 ) )
| ( X761
!= ( esk31_2 @ X760 @ X761 ) )
| ~ ( X760 @ X761 ) )
& ( ~ ( X760 @ X764 )
| ( ( esk32_1 @ X760 )
= X764 )
| ( X761
!= ( esk31_2 @ X760 @ X761 ) )
| ~ ( X760 @ X761 ) )
& ( ( X765 @ ( esk35_1 @ X765 ) )
| ( X765 @ ( esk33_1 @ X765 ) )
| ~ ( X765 @ X766 ) )
& ( ~ ( X765 @ X770 )
| ( ( esk35_1 @ X765 )
= X770 )
| ( X765 @ ( esk33_1 @ X765 ) )
| ~ ( X765 @ X766 ) )
& ( ( X765 @ ( esk35_1 @ X765 ) )
| ( X765 @ ( esk34_1 @ X765 ) )
| ~ ( X765 @ X766 ) )
& ( ~ ( X765 @ X770 )
| ( ( esk35_1 @ X765 )
= X770 )
| ( X765 @ ( esk34_1 @ X765 ) )
| ~ ( X765 @ X766 ) )
& ( ( X765 @ ( esk35_1 @ X765 ) )
| ( ( esk33_1 @ X765 )
!= ( esk34_1 @ X765 ) )
| ~ ( X765 @ X766 ) )
& ( ~ ( X765 @ X770 )
| ( ( esk35_1 @ X765 )
= X770 )
| ( ( esk33_1 @ X765 )
!= ( esk34_1 @ X765 ) )
| ~ ( X765 @ X766 ) )
& ( ( X771 @ ( esk37_1 @ X771 ) )
| ~ ( X771 @ ( esk36_2 @ X771 @ X772 ) )
| ( ( esk36_2 @ X771 @ X772 )
!= X772 ) )
& ( ~ ( X771 @ X775 )
| ( ( esk37_1 @ X771 )
= X775 )
| ~ ( X771 @ ( esk36_2 @ X771 @ X772 ) )
| ( ( esk36_2 @ X771 @ X772 )
!= X772 ) )
& ( ( X771 @ ( esk37_1 @ X771 ) )
| ( X771 @ ( esk36_2 @ X771 @ X772 ) )
| ( ( esk36_2 @ X771 @ X772 )
= X772 ) )
& ( ~ ( X771 @ X775 )
| ( ( esk37_1 @ X771 )
= X775 )
| ( X771 @ ( esk36_2 @ X771 @ X772 ) )
| ( ( esk36_2 @ X771 @ X772 )
= X772 ) )
& ( ( X776 != X777 )
| ( X778 != X779 )
| ~ ( in @ X778 @ X776 )
| ( in @ X779 @ X777 ) )
& ( ~ ( in @ X782 @ X780 )
| ( in @ X783 @ X781 )
| ( X782 != X783 )
| ( X780 != X781 ) )
& ( ~ ( in @ X783 @ X781 )
| ( in @ X782 @ X780 )
| ( X782 != X783 )
| ( X780 != X781 ) )
& ( ( X784 @ ( esk38_2 @ X784 @ X785 ) )
| ~ ( X784 @ X785 )
| ~ ( X784 @ X787 )
| ~ ( X784 @ X788 )
| ( X787 = X788 ) )
& ( ( X785
!= ( esk38_2 @ X784 @ X785 ) )
| ~ ( X784 @ X785 )
| ~ ( X784 @ X787 )
| ~ ( X784 @ X788 )
| ( X787 = X788 ) )
& ( ( X790 @ ( esk42_2 @ X789 @ X790 ) )
| ( X789 @ ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X790 @ X796 )
| ( ( esk42_2 @ X789 @ X790 )
= X796 )
| ( X789 @ ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X790 @ ( esk42_2 @ X789 @ X790 ) )
| ( X793
!= ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X790 @ X796 )
| ( ( esk42_2 @ X789 @ X790 )
= X796 )
| ( X793
!= ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X789 @ ( esk44_2 @ X789 @ X790 ) )
| ( X790 @ ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X789 @ X800 )
| ( ( esk44_2 @ X789 @ X790 )
= X800 )
| ( X790 @ ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X789 @ ( esk44_2 @ X789 @ X790 ) )
| ( X797
!= ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X789 @ X800 )
| ( ( esk44_2 @ X789 @ X790 )
= X800 )
| ( X797
!= ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( ( esk39_2 @ X789 @ X790 )
= ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X790 @ ( esk42_2 @ X789 @ X790 ) )
| ( X789 @ ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X790 @ X796 )
| ( ( esk42_2 @ X789 @ X790 )
= X796 )
| ( X789 @ ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X790 @ ( esk42_2 @ X789 @ X790 ) )
| ( X793
!= ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X790 @ X796 )
| ( ( esk42_2 @ X789 @ X790 )
= X796 )
| ( X793
!= ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X789 @ ( esk44_2 @ X789 @ X790 ) )
| ( X790 @ ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X789 @ X800 )
| ( ( esk44_2 @ X789 @ X790 )
= X800 )
| ( X790 @ ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X789 @ ( esk44_2 @ X789 @ X790 ) )
| ( X797
!= ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X789 @ X800 )
| ( ( esk44_2 @ X789 @ X790 )
= X800 )
| ( X797
!= ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ~ ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ~ ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X790 @ ( esk42_2 @ X789 @ X790 ) )
| ( X789 @ ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X790 @ X796 )
| ( ( esk42_2 @ X789 @ X790 )
= X796 )
| ( X789 @ ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X790 @ ( esk42_2 @ X789 @ X790 ) )
| ( X793
!= ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X790 @ X796 )
| ( ( esk42_2 @ X789 @ X790 )
= X796 )
| ( X793
!= ( esk41_3 @ X789 @ X790 @ X793 ) )
| ~ ( X789 @ X793 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X789 @ ( esk44_2 @ X789 @ X790 ) )
| ( X790 @ ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X789 @ X800 )
| ( ( esk44_2 @ X789 @ X790 )
= X800 )
| ( X790 @ ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ( X789 @ ( esk44_2 @ X789 @ X790 ) )
| ( X797
!= ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( ~ ( X789 @ X800 )
| ( ( esk44_2 @ X789 @ X790 )
= X800 )
| ( X797
!= ( esk43_3 @ X789 @ X790 @ X797 ) )
| ~ ( X790 @ X797 )
| ( X789 @ ( esk39_2 @ X789 @ X790 ) )
| ( X790 @ ( esk40_2 @ X789 @ X790 ) ) )
& ( emptyset = emptyset )
& ( ( X801 != X802 )
| ( X803 != X804 )
| ( ( setadjoin @ X801 @ X803 )
= ( setadjoin @ X802 @ X804 ) ) )
& ( ( X805 != X806 )
| ( ( powerset @ X805 )
= ( powerset @ X806 ) ) )
& ( ( X807 != X808 )
| ( ( setunion @ X807 )
= ( setunion @ X808 ) ) )
& ( omega = omega )
& ( ( X809 @ ( esk45_2 @ X809 @ X810 ) )
| ~ ( X809 @ X810 )
| ~ ( X809 @ X812 )
| ~ ( X809 @ X813 )
| ( X812 = X813 ) )
& ( ( X810
!= ( esk45_2 @ X809 @ X810 ) )
| ~ ( X809 @ X810 )
| ~ ( X809 @ X812 )
| ~ ( X809 @ X813 )
| ( X812 = X813 ) )
& ( ( X815 @ ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X814 @ ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( ( esk46_2 @ X814 @ X815 )
= ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X820
!= ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X814 @ ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( ( esk46_2 @ X814 @ X815 )
= ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X815 @ ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X818
!= ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( ( esk46_2 @ X814 @ X815 )
= ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X820
!= ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X818
!= ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( ( esk46_2 @ X814 @ X815 )
= ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X815 @ ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X814 @ ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ~ ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ~ ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X820
!= ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X814 @ ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ~ ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ~ ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X815 @ ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X818
!= ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ~ ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ~ ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X820
!= ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X818
!= ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ~ ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ~ ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X815 @ ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X814 @ ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X820
!= ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X814 @ ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X815 @ ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X818
!= ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( X820
!= ( esk49_3 @ X814 @ X815 @ X820 ) )
| ~ ( X815 @ X820 )
| ( ( descr
@ ^ [Z0: $i] : ( X814 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X815 @ Z0 ) ) )
| ( X818
!= ( esk48_3 @ X814 @ X815 @ X818 ) )
| ~ ( X814 @ X818 )
| ( X814 @ ( esk46_2 @ X814 @ X815 ) )
| ( X815 @ ( esk47_2 @ X814 @ X815 ) ) )
& ( ( in @ ( esk50_4 @ X822 @ X823 @ X824 @ X825 ) @ X822 )
| ( ( dsetconstr @ X822
@ ^ [Z0: $i] : ( X824 @ Z0 ) )
= ( dsetconstr @ X823
@ ^ [Z0: $i] : ( X825 @ Z0 ) ) )
| ( X822 != X823 ) )
& ( ( in @ ( esk51_4 @ X822 @ X823 @ X824 @ X825 ) @ X823 )
| ( ( dsetconstr @ X822
@ ^ [Z0: $i] : ( X824 @ Z0 ) )
= ( dsetconstr @ X823
@ ^ [Z0: $i] : ( X825 @ Z0 ) ) )
| ( X822 != X823 ) )
& ( ( ( esk50_4 @ X822 @ X823 @ X824 @ X825 )
= ( esk51_4 @ X822 @ X823 @ X824 @ X825 ) )
| ( ( dsetconstr @ X822
@ ^ [Z0: $i] : ( X824 @ Z0 ) )
= ( dsetconstr @ X823
@ ^ [Z0: $i] : ( X825 @ Z0 ) ) )
| ( X822 != X823 ) )
& ( ~ ( X824 @ ( esk50_4 @ X822 @ X823 @ X824 @ X825 ) )
| ~ ( X825 @ ( esk51_4 @ X822 @ X823 @ X824 @ X825 ) )
| ( ( dsetconstr @ X822
@ ^ [Z0: $i] : ( X824 @ Z0 ) )
= ( dsetconstr @ X823
@ ^ [Z0: $i] : ( X825 @ Z0 ) ) )
| ( X822 != X823 ) )
& ( ( X824 @ ( esk50_4 @ X822 @ X823 @ X824 @ X825 ) )
| ( X825 @ ( esk51_4 @ X822 @ X823 @ X824 @ X825 ) )
| ( ( dsetconstr @ X822
@ ^ [Z0: $i] : ( X824 @ Z0 ) )
= ( dsetconstr @ X823
@ ^ [Z0: $i] : ( X825 @ Z0 ) ) )
| ( X822 != X823 ) )
& ( ( in @ ( esk52_2 @ X828 @ X829 ) @ X828 )
| ( subset @ X828 @ X829 ) )
& ( ~ ( in @ ( esk52_2 @ X828 @ X829 ) @ X829 )
| ( subset @ X828 @ X829 ) )
& ( ( X831 != X832 )
| ( subset @ X832 @ X831 ) )
& ( ( X833 != X834 )
| ( subset @ X833 @ X834 ) )
& ( ( in @ ( esk53_2 @ X835 @ X836 ) @ X835 )
| ( subset @ X835 @ X836 ) )
& ( ~ ( in @ ( esk53_2 @ X835 @ X836 ) @ X836 )
| ( subset @ X835 @ X836 ) )
& ( subset @ emptyset @ X838 )
& ( ~ ( subset @ X839 @ X840 )
| ~ ( in @ X841 @ X839 )
| ( in @ X841 @ X840 ) )
& ( ~ ( subset @ X842 @ X843 )
| ( in @ X844 @ X843 )
| ~ ( in @ X844 @ X842 ) )
& ( ~ ( in @ X847 @ X845 )
| ( in @ X847 @ X846 )
| ~ ( subset @ X845 @ X846 ) )
& ( ( subset @ X848 @ X849 )
| ( X848 != X849 ) )
& ( ~ ( in @ X852 @ X850 )
| ( in @ X852 @ X851 )
| ( X850 != X851 ) )
& ( subset @ X853 @ X853 )
& ( ~ ( subset @ X854 @ X855 )
| ~ ( subset @ X855 @ X856 )
| ( subset @ X854 @ X856 ) )
& ( subset @ X858 @ ( setadjoin @ X857 @ X858 ) )
& ( ~ ( subset @ X859 @ X861 )
| ( subset @ X859 @ ( setadjoin @ X860 @ X861 ) ) )
& ( ~ ( subset @ X862 @ X863 )
| ( in @ X862 @ ( powerset @ X863 ) ) )
& ( ~ ( subset @ X864 @ X865 )
| ~ ( subset @ X865 @ X864 )
| ( X864 = X865 ) )
& ( ~ ( subset @ X866 @ emptyset )
| ( X866 = emptyset ) )
& ( ~ ( subset @ X868 @ X867 )
| ( in @ X868 @ ( powerset @ X867 ) ) )
& ( ~ ( in @ X870 @ ( powerset @ X869 ) )
| ( subset @ X870 @ X869 ) )
& ( in @ X871 @ ( powerset @ X871 ) )
& ( ~ ( subset @ X872 @ X873 )
| ( subset @ ( powerset @ X872 ) @ ( powerset @ X873 ) ) )
& ( in
@ ( dsetconstr @ X874
@ ^ [Z0: $i] : ( X875 @ Z0 ) )
@ ( powerset @ X874 ) )
& ~ ( subset
@ ( dsetconstr @ esk54_0
@ ^ [Z0: $i] : ( epred2_0 @ Z0 ) )
@ esk54_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_139])])])])])]) ).
thf(c_0_141,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ X2 @ ( powerset @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
thf(c_0_142,negated_conjecture,
! [X1: $i > $o,X2: $i] : ( in @ ( dsetconstr @ X2 @ X1 ) @ ( powerset @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
thf(c_0_143,negated_conjecture,
~ ( subset @ ( dsetconstr @ esk54_0 @ epred2_0 ) @ esk54_0 ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
thf(c_0_144,negated_conjecture,
! [X1: $i > $o,X2: $i] : ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
thf(c_0_145,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU581^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 16:50:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 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
% 0.19/0.53 # Version: 3.1.0-ho
% 0.19/0.53 # Preprocessing class: HSMMSLSSLLLCHSA.
% 0.19/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.53 # Starting sh5l with 300s (1) cores
% 0.19/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.19/0.53 # new_bool_2 with pid 3304 completed with status 0
% 0.19/0.53 # Result found by new_bool_2
% 0.19/0.53 # Preprocessing class: HSMMSLSSLLLCHSA.
% 0.19/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.53 # Starting sh5l with 300s (1) cores
% 0.19/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.19/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.53 # Search class: HGHSM-FSLS31-SHSMMSBN
% 0.19/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.53 # Starting new_ho_10 with 181s (1) cores
% 0.19/0.53 # new_ho_10 with pid 3305 completed with status 0
% 0.19/0.53 # Result found by new_ho_10
% 0.19/0.53 # Preprocessing class: HSMMSLSSLLLCHSA.
% 0.19/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.53 # Starting sh5l with 300s (1) cores
% 0.19/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.19/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.53 # Search class: HGHSM-FSLS31-SHSMMSBN
% 0.19/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.53 # Starting new_ho_10 with 181s (1) cores
% 0.19/0.53 # Preprocessing time : 0.004 s
% 0.19/0.53 # Presaturation interreduction done
% 0.19/0.53
% 0.19/0.53 # Proof found!
% 0.19/0.53 # SZS status Theorem
% 0.19/0.53 # SZS output start CNFRefutation
% See solution above
% 0.19/0.53 # Parsed axioms : 212
% 0.19/0.53 # Removed by relevancy pruning/SinE : 113
% 0.19/0.53 # Initial clauses : 207
% 0.19/0.53 # Removed in clause preprocessing : 13
% 0.19/0.53 # Initial clauses in saturation : 194
% 0.19/0.53 # Processed clauses : 250
% 0.19/0.53 # ...of these trivial : 3
% 0.19/0.53 # ...subsumed : 20
% 0.19/0.53 # ...remaining for further processing : 227
% 0.19/0.53 # Other redundant clauses eliminated : 14
% 0.19/0.53 # Clauses deleted for lack of memory : 0
% 0.19/0.53 # Backward-subsumed : 0
% 0.19/0.53 # Backward-rewritten : 3
% 0.19/0.53 # Generated clauses : 94
% 0.19/0.53 # ...of the previous two non-redundant : 76
% 0.19/0.53 # ...aggressively subsumed : 0
% 0.19/0.53 # Contextual simplify-reflections : 0
% 0.19/0.53 # Paramodulations : 80
% 0.19/0.53 # Factorizations : 0
% 0.19/0.53 # NegExts : 0
% 0.19/0.53 # Equation resolutions : 14
% 0.19/0.53 # Disequality decompositions : 0
% 0.19/0.53 # Total rewrite steps : 32
% 0.19/0.53 # ...of those cached : 19
% 0.19/0.53 # Propositional unsat checks : 0
% 0.19/0.53 # Propositional check models : 0
% 0.19/0.53 # Propositional check unsatisfiable : 0
% 0.19/0.53 # Propositional clauses : 0
% 0.19/0.53 # Propositional clauses after purity: 0
% 0.19/0.53 # Propositional unsat core size : 0
% 0.19/0.53 # Propositional preprocessing time : 0.000
% 0.19/0.53 # Propositional encoding time : 0.000
% 0.19/0.53 # Propositional solver time : 0.000
% 0.19/0.53 # Success case prop preproc time : 0.000
% 0.19/0.53 # Success case prop encoding time : 0.000
% 0.19/0.53 # Success case prop solver time : 0.000
% 0.19/0.53 # Current number of processed clauses : 42
% 0.19/0.53 # Positive orientable unit clauses : 17
% 0.19/0.53 # Positive unorientable unit clauses: 0
% 0.19/0.53 # Negative unit clauses : 1
% 0.19/0.53 # Non-unit-clauses : 24
% 0.19/0.53 # Current number of unprocessed clauses: 187
% 0.19/0.53 # ...number of literals in the above : 633
% 0.19/0.53 # Current number of archived formulas : 0
% 0.19/0.53 # Current number of archived clauses : 172
% 0.19/0.53 # Clause-clause subsumption calls (NU) : 5128
% 0.19/0.53 # Rec. Clause-clause subsumption calls : 1542
% 0.19/0.53 # Non-unit clause-clause subsumptions : 16
% 0.19/0.53 # Unit Clause-clause subsumption calls : 15
% 0.19/0.53 # Rewrite failures with RHS unbound : 0
% 0.19/0.53 # BW rewrite match attempts : 12
% 0.19/0.53 # BW rewrite match successes : 3
% 0.19/0.53 # Condensation attempts : 250
% 0.19/0.53 # Condensation successes : 3
% 0.19/0.53 # Termbank termtop insertions : 28307
% 0.19/0.53 # Search garbage collected termcells : 8811
% 0.19/0.53
% 0.19/0.53 # -------------------------------------------------
% 0.19/0.53 # User time : 0.043 s
% 0.19/0.53 # System time : 0.008 s
% 0.19/0.53 # Total time : 0.051 s
% 0.19/0.53 # Maximum resident set size: 4448 pages
% 0.19/0.53
% 0.19/0.53 # -------------------------------------------------
% 0.19/0.53 # User time : 0.049 s
% 0.19/0.53 # System time : 0.010 s
% 0.19/0.53 # Total time : 0.059 s
% 0.19/0.53 # Maximum resident set size: 1936 pages
% 0.19/0.53 % E---3.1 exiting
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------