TSTP Solution File: SEU604^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU604^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 03:28:30 EDT 2024
% Result : Theorem 2.08s 0.65s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 297
% Syntax : Number of formulae : 342 ( 4 unt; 176 typ; 0 def)
% Number of atoms : 1280 ( 205 equ; 0 cnn)
% Maximal formula atoms : 361 ( 7 avg)
% Number of connectives : 4148 ( 307 ~; 302 |; 235 &;2514 @)
% ( 178 <=>; 612 =>; 0 <=; 0 <~>)
% Maximal formula depth : 453 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 246 ( 246 >; 0 *; 0 +; 0 <<)
% Number of symbols : 179 ( 176 usr; 127 con; 0-4 aty)
% Number of variables : 1077 ( 59 ^ 953 !; 65 ?;1077 :)
% 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,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
epred1_0: $o ).
thf(decl_162,type,
esk1_2: $i > $i > $i ).
thf(decl_163,type,
esk2_2: $i > $i > $i ).
thf(decl_164,type,
esk3_2: $i > $i > $i ).
thf(decl_165,type,
esk4_1: $i > $i ).
thf(decl_166,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_167,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_168,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_169,type,
esk8_1: $i > $i ).
thf(decl_170,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_171,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_172,type,
esk11_2: $i > $i > $i ).
thf(decl_173,type,
esk12_2: $i > $i > $i ).
thf(decl_174,type,
esk13_1: $i > $i ).
thf(decl_175,type,
esk14_1: $i > $i ).
thf(decl_176,type,
esk15_1: $i > $i ).
thf(decl_177,type,
esk16_2: $i > $i > $i ).
thf(decl_178,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_179,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_180,type,
esk19_1: $i > $i ).
thf(decl_181,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_182,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_183,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_184,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_185,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_186,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_187,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_188,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_189,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_190,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_191,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_192,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_193,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_194,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_195,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_196,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_197,type,
esk36_2: $i > $i > $i ).
thf(decl_198,type,
esk37_2: $i > $i > $i ).
thf(decl_199,type,
esk38_2: $i > $i > $i ).
thf(decl_200,type,
esk39_0: $i ).
thf(decl_201,type,
esk40_0: $i ).
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(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
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(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(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(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(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(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
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(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(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(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(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(setminusSubset2,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
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
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(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
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(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
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(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
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(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
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(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(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(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(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(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(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(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(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
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(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(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(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_120,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_121,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_122,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_123,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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_133,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_134,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_135,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_136,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_137,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_138,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_139,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_140,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_141,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_142,plain,
( epred1_0
<=> ! [X368: $i] :
? [X369: $i] :
( ! [X370: $i] :
( ( in @ X370 @ X369 )
=> ! [X371: $i] :
( ( in @ X371 @ X370 )
=> ( in @ X371 @ X368 ) ) )
& ! [X372: $i,X373: $i] :
( ( ( in @ X372 @ X368 )
& ( in @ X373 @ X368 ) )
=> ( ! [X374: $i] :
( ( in @ X374 @ X369 )
=> ( ( in @ X372 @ X374 )
<=> ( in @ X373 @ X374 ) ) )
=> ( X372 = X373 ) ) )
& ! [X375: $i,X376: $i] :
( ( ( in @ X375 @ X369 )
& ( in @ X376 @ X369 ) )
=> ( ! [X377: $i] :
( ( in @ X377 @ X375 )
=> ( in @ X377 @ X376 ) )
| ! [X378: $i] :
( ( in @ X378 @ X376 )
=> ( in @ X378 @ X375 ) ) ) )
& ! [X379: $i] :
( ( ! [X380: $i] :
( ( in @ X380 @ X379 )
=> ( in @ X380 @ X368 ) )
& ? [X381: $i] : ( in @ X381 @ X379 ) )
=> ? [X382: $i,X383: $i] :
( ( in @ X382 @ X369 )
& ( in @ X383 @ X379 )
& ~ ? [X384: $i] :
( ( in @ X384 @ X382 )
& ( in @ X384 @ X379 ) )
& ! [X385: $i] :
( ( in @ X385 @ X369 )
=> ( ! [X386: $i] :
( ( in @ X386 @ X385 )
=> ( in @ X386 @ X382 ) )
| ( in @ X383 @ X385 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_143,negated_conjecture,
~ ( ! [X341: $i,X342: $i] :
( ! [X343: $i] :
( ( in @ X343 @ X341 )
<=> ( in @ X343 @ X342 ) )
=> ( X341 = X342 ) )
=> ( ! [X344: $i] :
~ ( in @ X344 @ emptyset )
=> ( ! [X345: $i,X346: $i,X347: $i] :
( ( in @ X347 @ ( setadjoin @ X345 @ X346 ) )
<=> ( ( X347 = X345 )
| ( in @ X347 @ X346 ) ) )
=> ( ! [X348: $i,X349: $i] :
( ( in @ X349 @ ( powerset @ X348 ) )
<=> ! [X350: $i] :
( ( in @ X350 @ X349 )
=> ( in @ X350 @ X348 ) ) )
=> ( ! [X351: $i,X352: $i] :
( ( in @ X352 @ ( setunion @ X351 ) )
<=> ? [X353: $i] :
( ( in @ X352 @ X353 )
& ( in @ X353 @ X351 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X354: $i] :
( ( in @ X354 @ omega )
=> ( in @ ( setadjoin @ X354 @ X354 ) @ omega ) )
=> ( ! [X355: $i] :
( ( ( in @ emptyset @ X355 )
& ! [X356: $i] :
( ( ( in @ X356 @ omega )
& ( in @ X356 @ X355 ) )
=> ( in @ ( setadjoin @ X356 @ X356 ) @ X355 ) ) )
=> ! [X357: $i] :
( ( in @ X357 @ omega )
=> ( in @ X357 @ X355 ) ) )
=> ( ! [X358: $i > $i > $o,X359: $i] :
( ! [X360: $i] :
( ( in @ X360 @ X359 )
=> ( exu @ ( X358 @ X360 ) ) )
=> ? [X361: $i] :
! [X362: $i] :
( ( in @ X362 @ X361 )
<=> ? [X363: $i] :
( ( in @ X363 @ X359 )
& ( X358 @ X363 @ X362 ) ) ) )
=> ( ! [X364: $i] :
( ? [X365: $i] : ( in @ X365 @ X364 )
=> ? [X366: $i] :
( ( in @ X366 @ X364 )
& ~ ? [X367: $i] :
( ( in @ X367 @ X366 )
& ( in @ X367 @ X364 ) ) ) )
=> ( epred1_0
=> ( ! [X387: $i > $o] :
( ( exu @ X387 )
=> ( X387
@ ( descr
@ ^ [Z0: $i] : ( X387 @ Z0 ) ) ) )
=> ( ! [X388: $i,X389: $i > $o,X390: $i] :
( ( in @ X390 @ X388 )
=> ( ( X389 @ X390 )
=> ( in @ X390 @ ( dsetconstr @ X388 @ X389 ) ) ) )
=> ( ! [X391: $i,X392: $i > $o,X393: $i] :
( ( in @ X393 @ ( dsetconstr @ X391 @ X392 ) )
=> ( in @ X393 @ X391 ) )
=> ( ! [X394: $i,X395: $i > $o,X396: $i] :
( ( in @ X396 @ ( dsetconstr @ X394 @ X395 ) )
=> ( X395 @ X396 ) )
=> ( ! [X397: $i > $o] :
( ( exu @ X397 )
=> ? [X398: $i] :
( ( X397 @ X398 )
& ! [X399: $i] :
( ( X397 @ X399 )
=> ( X398 = X399 ) ) ) )
=> ( ! [X400: $o,X401: $i] :
( ( in @ X401 @ ( prop2set @ X400 ) )
=> X400 )
=> ( ! [X402: $i] :
( ( in @ X402 @ emptyset )
=> ! [X403: $o] : X403 )
=> ( ! [X404: $i] :
( ( in @ X404 @ emptyset )
=> ~ $true )
=> ( ! [X405: $i] :
~ ( in @ X405 @ emptyset )
=> ( ! [X406: $i > $o] :
( ( exu @ X406 )
=> ? [X407: $i] : ( X406 @ X407 ) )
=> ( ! [X408: $i,X409: $i] :
( ! [X410: $i] :
( ( in @ X410 @ X408 )
=> ( in @ X410 @ X409 ) )
=> ( ! [X411: $i] :
( ( in @ X411 @ X409 )
=> ( in @ X411 @ X408 ) )
=> ( X408 = X409 ) ) )
=> ( ! [X412: $i] :
( ! [X413: $i] :
~ ( in @ X413 @ X412 )
=> ( X412 = emptyset ) )
=> ( ! [X414: $i] :
( ! [X415: $i] :
~ ( in @ X415 @ X414 )
=> ( X414 = emptyset ) )
=> ( ! [X416: $i,X417: $i > $o,X418: $i] :
( ( in @ X418 @ X416 )
=> ( ( in @ X418 @ ( dsetconstr @ X416 @ X417 ) )
<=> ( X417 @ X418 ) ) )
=> ( ! [X419: $i] :
( ( nonempty @ X419 )
=> ? [X420: $i] : ( in @ X420 @ X419 ) )
=> ( ! [X421: $i,X422: $i > $o,X423: $i] :
( ( in @ X423 @ X421 )
=> ( ( X422 @ X423 )
=> ( nonempty @ ( dsetconstr @ X421 @ X422 ) ) ) )
=> ( ! [X424: $i] :
( ? [X425: $i] : ( in @ X425 @ X424 )
=> ( nonempty @ X424 ) )
=> ( ! [X426: $i,X427: $i] : ( in @ X426 @ ( setadjoin @ X426 @ X427 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X428: $i,X429: $i,X430: $i] :
( ( in @ X430 @ X429 )
=> ( in @ X430 @ ( setadjoin @ X428 @ X429 ) ) )
=> ( ! [X431: $i,X432: $i,X433: $i] :
( ( in @ X433 @ ( setadjoin @ X431 @ X432 ) )
=> ! [X434: $o] :
( ( ( X433 = X431 )
=> X434 )
=> ( ( ( in @ X433 @ X432 )
=> X434 )
=> X434 ) ) )
=> ( ! [X435: $i,X436: $i,X437: $i] :
( ( in @ X437 @ ( setadjoin @ X435 @ X436 ) )
=> ( ( X437 = X435 )
| ( in @ X437 @ X436 ) ) )
=> ( ! [X438: $i] :
( ( dsetconstr @ X438
@ ^ [Z0: $i] : $true )
= X438 )
=> ( ! [X439: $i,X440: $i] :
( ! [X441: $i] :
( ( in @ X441 @ X440 )
=> ( in @ X441 @ X439 ) )
=> ( in @ X440 @ ( powerset @ X439 ) ) )
=> ( ! [X442: $i] : ( in @ emptyset @ ( powerset @ X442 ) )
=> ( ! [X443: $i] : ( in @ emptyset @ ( powerset @ X443 ) )
=> ( ! [X444: $i,X445: $i,X446: $i] :
( ( in @ X445 @ ( powerset @ X444 ) )
=> ( ( in @ X446 @ X445 )
=> ( in @ X446 @ X444 ) ) )
=> ( ! [X447: $i,X448: $i,X449: $i] :
( ( in @ X448 @ X449 )
=> ( ( in @ X449 @ X447 )
=> ( in @ X448 @ ( setunion @ X447 ) ) ) )
=> ( ! [X450: $i,X451: $i] :
( ( in @ X451 @ ( setunion @ X450 ) )
=> ! [X452: $o] :
( ! [X453: $i] :
( ( in @ X451 @ X453 )
=> ( ( in @ X453 @ X450 )
=> X452 ) )
=> X452 ) )
=> ( ! [X454: $i,X455: $i] :
( ( in @ X455 @ X454 )
=> ( in @ X455 @ ( powerset @ ( setunion @ X454 ) ) ) )
=> ( ! [X456: $i > $o] :
( ( exu @ X456 )
=> ? [X457: $i] :
! [X458: $i] :
( ( X456 @ X458 )
<=> ( X458 = X457 ) ) )
=> ( ! [X459: $i] :
( ( nonempty @ X459 )
=> ? [X460: $i] :
( ( in @ X460 @ X459 )
& $true ) )
=> ( ! [X461: $i,X462: $i] :
( ( in @ X461 @ ( setadjoin @ X462 @ emptyset ) )
=> ( X461 = X462 ) )
=> ( ! [X463: $i,X464: $i] :
( ( X463 != X464 )
=> ~ ( in @ X464 @ ( setadjoin @ X463 @ emptyset ) ) )
=> ( ! [X465: $i,X466: $i] :
( ( X465 = X466 )
=> ( in @ X465 @ ( setadjoin @ X466 @ emptyset ) ) )
=> ( ! [X467: $i,X468: $i] :
( ( in @ X467 @ ( setadjoin @ X468 @ emptyset ) )
=> ( in @ X468 @ ( setadjoin @ X467 @ emptyset ) ) )
=> ( ! [X469: $i,X470: $i,X471: $i] :
( ( in @ X471 @ ( setadjoin @ X469 @ ( setadjoin @ X470 @ emptyset ) ) )
=> ( ( X471 = X469 )
| ( X471 = X470 ) ) )
=> ( ! [X472: $i,X473: $i] : ( in @ X472 @ ( setadjoin @ X472 @ ( setadjoin @ X473 @ emptyset ) ) )
=> ( ! [X474: $i,X475: $i] : ( in @ X475 @ ( setadjoin @ X474 @ ( setadjoin @ X475 @ emptyset ) ) )
=> ( ! [X476: $i,X477: $i > $o] :
( ? [X478: $i] :
( ( in @ X478 @ X476 )
& ( X477 @ X478 ) )
=> ( ( ( dsetconstr @ X476 @ X477 )
= emptyset )
=> ~ $true ) )
=> ( ! [X479: $i > $o,X480: $i] :
( ( in @ X480 @ emptyset )
=> ( X479 @ X480 ) )
=> ( ! [X481: $i,X482: $i > $o] :
( ~ ! [X483: $i] :
( ( in @ X483 @ X481 )
=> ( X482 @ X483 ) )
=> ? [X484: $i] :
( ( in @ X484 @ X481 )
& ~ ( X482 @ X484 ) ) )
=> ( ! [X485: $i,X486: $i > $o] :
( ! [X487: $i] :
( ( in @ X487 @ X485 )
=> ~ ( X486 @ X487 ) )
=> ~ ? [X488: $i] :
( ( in @ X488 @ X485 )
& ( X486 @ X488 ) ) )
=> ( ! [X489: $i,X490: $i > $o] :
( ~ ? [X491: $i] :
( ( in @ X491 @ X489 )
& ( X490 @ X491 ) )
=> ! [X492: $i] :
( ( in @ X492 @ X489 )
=> ~ ( X490 @ X492 ) ) )
=> ( ! [X493: $i,X494: $i > $o] :
( ? [X495: $i] :
( ( in @ X495 @ X493 )
& ~ ( X494 @ X495 ) )
=> ~ ! [X496: $i] :
( ( in @ X496 @ X493 )
=> ( X494 @ X496 ) ) )
=> ( ! [X497: $o] :
( X497
=> ( in @ emptyset @ ( prop2set @ X497 ) ) )
=> ( prop2set2propI
=> ( ! [X498: $i,X499: $i > $o] :
( ~ ? [X500: $i] :
( ( in @ X500 @ X498 )
& ( X499 @ X500 ) )
=> ! [X501: $i] :
( ( in @ X501 @ X498 )
=> ~ ( X499 @ X501 ) ) )
=> ( ! [X502: $i,X503: $i > $o] :
( ~ ! [X504: $i] :
( ( in @ X504 @ X502 )
=> ( X503 @ X504 ) )
=> ? [X505: $i] :
( ( in @ X505 @ X502 )
& ~ ( X503 @ X505 ) ) )
=> ( ! [X506: $i > $o] :
( ? [X507: $i] :
( ( X506 @ X507 )
& ! [X508: $i] :
( ( X506 @ X508 )
=> ( X507 = X508 ) ) )
=> ( exu @ X506 ) )
=> ( ! [X509: $i > $o] :
( ? [X510: $i] : ( X509 @ X510 )
=> ( ! [X511: $i,X512: $i] :
( ( X509 @ X511 )
=> ( ( X509 @ X512 )
=> ( X511 = X512 ) ) )
=> ( exu @ X509 ) ) )
=> ( ! [X513: $i > $o] :
( ? [X514: $i] :
! [X515: $i] :
( ( X513 @ X515 )
<=> ( X515 = X514 ) )
=> ( exu @ X513 ) )
=> ( ! [X516: $i,X517: $i] :
( ( X516 = X517 )
=> ! [X518: $i,X519: $i] :
( ( X518 = X519 )
=> ( ( in @ X518 @ X516 )
=> ( in @ X519 @ X517 ) ) ) )
=> ( ! [X520: $i,X521: $i] :
( ( X520 = X521 )
=> ! [X522: $i,X523: $i] :
( ( X522 = X523 )
=> ( ( in @ X522 @ X520 )
<=> ( in @ X523 @ X521 ) ) ) )
=> ( ! [X524: $i > $o] :
( ( exu @ X524 )
=> ! [X525: $i,X526: $i] :
( ( X524 @ X525 )
=> ( ( X524 @ X526 )
=> ( X525 = X526 ) ) ) )
=> ( ! [X527: $i > $o,X528: $i > $o] :
( ! [X529: $i,X530: $i] :
( ( X529 = X530 )
=> ( ( X527 @ X529 )
<=> ( X528 @ X530 ) ) )
=> ( ( exu @ X527 )
<=> ( exu @ X528 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X531: $i,X532: $i] :
( ( X531 = X532 )
=> ! [X533: $i,X534: $i] :
( ( X533 = X534 )
=> ( ( setadjoin @ X531 @ X533 )
= ( setadjoin @ X532 @ X534 ) ) ) )
=> ( ! [X535: $i,X536: $i] :
( ( X535 = X536 )
=> ( ( powerset @ X535 )
= ( powerset @ X536 ) ) )
=> ( ! [X537: $i,X538: $i] :
( ( X537 = X538 )
=> ( ( setunion @ X537 )
= ( setunion @ X538 ) ) )
=> ( ( omega = omega )
=> ( ! [X539: $i > $o] :
( ( exu @ X539 )
=> ! [X540: $i,X541: $i] :
( ( X539 @ X540 )
=> ( ( X539 @ X541 )
=> ( X540 = X541 ) ) ) )
=> ( ! [X542: $i > $o,X543: $i > $o] :
( ! [X544: $i,X545: $i] :
( ( X544 = X545 )
=> ( ( X542 @ X544 )
<=> ( X543 @ X545 ) ) )
=> ( ( exu @ X542 )
=> ( ( exu @ X543 )
=> ( ( descr @ X542 )
= ( descr @ X543 ) ) ) ) )
=> ( ! [X546: $i,X547: $i] :
( ( X546 = X547 )
=> ! [X548: $i > $o,X549: $i > $o] :
( ! [X550: $i] :
( ( in @ X550 @ X546 )
=> ! [X551: $i] :
( ( in @ X551 @ X547 )
=> ( ( X550 = X551 )
=> ( ( X548 @ X550 )
<=> ( X549 @ X551 ) ) ) ) )
=> ( ( dsetconstr @ X546 @ X548 )
= ( dsetconstr @ X547 @ X549 ) ) ) )
=> ( ! [X552: $i,X553: $i] :
( ! [X554: $i] :
( ( in @ X554 @ X552 )
=> ( in @ X554 @ X553 ) )
=> ( subset @ X552 @ X553 ) )
=> ( ! [X555: $i,X556: $i] :
( ( X555 = X556 )
=> ( subset @ X556 @ X555 ) )
=> ( ! [X557: $i,X558: $i] :
( ( X557 = X558 )
=> ( subset @ X557 @ X558 ) )
=> ( ! [X559: $i,X560: $i] :
( ! [X561: $i] :
( ( in @ X561 @ X559 )
=> ( in @ X561 @ X560 ) )
=> ( subset @ X559 @ X560 ) )
=> ( ! [X562: $i] : ( subset @ emptyset @ X562 )
=> ( ! [X563: $i,X564: $i,X565: $i] :
( ( subset @ X563 @ X564 )
=> ( ( in @ X565 @ X563 )
=> ( in @ X565 @ X564 ) ) )
=> ( ! [X566: $i,X567: $i,X568: $i] :
( ( subset @ X566 @ X567 )
=> ( ~ ( in @ X568 @ X567 )
=> ~ ( in @ X568 @ X566 ) ) )
=> ( ! [X569: $i,X570: $i,X571: $i] :
( ( in @ X571 @ X569 )
=> ( ~ ( in @ X571 @ X570 )
=> ~ ( subset @ X569 @ X570 ) ) )
=> ( ! [X572: $i,X573: $i] :
( ~ ( subset @ X572 @ X573 )
=> ( X572 != X573 ) )
=> ( ! [X574: $i,X575: $i,X576: $i] :
( ( in @ X576 @ X574 )
=> ( ~ ( in @ X576 @ X575 )
=> ( X574 != X575 ) ) )
=> ( ! [X577: $i] : ( subset @ X577 @ X577 )
=> ( ! [X578: $i,X579: $i,X580: $i] :
( ( subset @ X578 @ X579 )
=> ( ( subset @ X579 @ X580 )
=> ( subset @ X578 @ X580 ) ) )
=> ( ! [X581: $i,X582: $i] : ( subset @ X582 @ ( setadjoin @ X581 @ X582 ) )
=> ( ! [X583: $i,X584: $i,X585: $i] :
( ( subset @ X583 @ X585 )
=> ( subset @ X583 @ ( setadjoin @ X584 @ X585 ) ) )
=> ( ! [X586: $i,X587: $i] :
( ( subset @ X586 @ X587 )
=> ( in @ X586 @ ( powerset @ X587 ) ) )
=> ( ! [X588: $i,X589: $i] :
( ( subset @ X588 @ X589 )
=> ( ( subset @ X589 @ X588 )
=> ( X588 = X589 ) ) )
=> ( ! [X590: $i] :
( ( subset @ X590 @ emptyset )
=> ( X590 = emptyset ) )
=> ( ! [X591: $i,X592: $i] :
( ( subset @ X592 @ X591 )
=> ( in @ X592 @ ( powerset @ X591 ) ) )
=> ( ! [X593: $i,X594: $i] :
( ( in @ X594 @ ( powerset @ X593 ) )
=> ( subset @ X594 @ X593 ) )
=> ( ! [X595: $i] : ( in @ X595 @ ( powerset @ X595 ) )
=> ( ! [X596: $i,X597: $i] :
( ( subset @ X596 @ X597 )
=> ( subset @ ( powerset @ X596 ) @ ( powerset @ X597 ) ) )
=> ( ! [X598: $i,X599: $i > $o] : ( in @ ( dsetconstr @ X598 @ X599 ) @ ( powerset @ X598 ) )
=> ( ! [X600: $i,X601: $i > $o] : ( subset @ ( dsetconstr @ X600 @ X601 ) @ X600 )
=> ( ! [X602: $i,X603: $i,X604: $i] :
( ( in @ X604 @ X602 )
=> ( in @ X604 @ ( binunion @ X602 @ X603 ) ) )
=> ( ! [X605: $i,X606: $i] : ( in @ X606 @ ( setadjoin @ X605 @ ( setadjoin @ X606 @ emptyset ) ) )
=> ( ! [X607: $i,X608: $i,X609: $i] :
( ( in @ X609 @ X608 )
=> ( in @ X609 @ ( binunion @ X607 @ X608 ) ) )
=> ( ! [X610: $i,X611: $i,X612: $i,X613: $o] :
( ( in @ X612 @ ( binunion @ X610 @ X611 ) )
=> ( ( ( in @ X612 @ X610 )
=> X613 )
=> ( ( ( in @ X612 @ X611 )
=> X613 )
=> X613 ) ) )
=> ( ! [X614: $i,X615: $i,X616: $i] :
( ( in @ X616 @ ( binunion @ X614 @ X615 ) )
=> ( ( in @ X616 @ X614 )
| ( in @ X616 @ X615 ) ) )
=> ( ! [X617: $i,X618: $i] : ( subset @ X617 @ ( binunion @ X617 @ X618 ) )
=> ( ! [X619: $i,X620: $i] : ( subset @ X620 @ ( binunion @ X619 @ X620 ) )
=> ( ! [X621: $i,X622: $i,X623: $i] :
( ( in @ X623 @ X621 )
=> ( ( in @ X623 @ X622 )
=> ( in @ X623 @ ( binintersect @ X621 @ X622 ) ) ) )
=> ( ! [X624: $i,X625: $i,X626: $i] :
( ( subset @ X626 @ X624 )
=> ( ( subset @ X626 @ X625 )
=> ( subset @ X626 @ ( binintersect @ X624 @ X625 ) ) ) )
=> ( ! [X627: $i,X628: $i,X629: $i] :
( ( in @ X629 @ ( binintersect @ X627 @ X628 ) )
=> ( in @ X629 @ X627 ) )
=> ( ! [X630: $i,X631: $i] : ( subset @ ( binintersect @ X630 @ X631 ) @ X630 )
=> ( ! [X632: $i,X633: $i] :
( ( subset @ X632 @ X633 )
=> ( ( binintersect @ X632 @ X633 )
= X632 ) )
=> ( ! [X634: $i,X635: $i] :
( ( ( binintersect @ X634 @ X635 )
= X635 )
=> ( subset @ X635 @ X634 ) )
=> ( ! [X636: $i,X637: $i,X638: $i] :
( ( in @ X638 @ ( binintersect @ X636 @ X637 ) )
=> ( in @ X638 @ X637 ) )
=> ( ! [X639: $i,X640: $i] :
( ~ ? [X641: $i] :
( ( in @ X641 @ X639 )
& ( in @ X641 @ X640 ) )
=> ( ( binintersect @ X639 @ X640 )
= emptyset ) )
=> ( ! [X642: $i,X643: $i] : ( subset @ ( binintersect @ X642 @ X643 ) @ X643 )
=> ( ! [X644: $i,X645: $i] :
( ( subset @ X645 @ X644 )
=> ( ( binintersect @ X644 @ X645 )
= X645 ) )
=> ( ! [X646: $i,X647: $i] :
( ( ( binintersect @ X646 @ X647 )
= X646 )
=> ( subset @ X646 @ X647 ) )
=> ( ! [X648: $i,X649: $i,X650: $i] :
( ( binintersect @ X648 @ ( binunion @ X649 @ X650 ) )
= ( binunion @ ( binintersect @ X648 @ X649 ) @ ( binintersect @ X648 @ X650 ) ) )
=> ( ! [X651: $i,X652: $i,X653: $i] :
( ( in @ X653 @ X651 )
=> ( ~ ( in @ X653 @ X652 )
=> ( in @ X653 @ ( setminus @ X651 @ X652 ) ) ) )
=> ( ! [X654: $i,X655: $i,X656: $i] :
( ( in @ X656 @ ( setminus @ X654 @ X655 ) )
=> ( in @ X656 @ X654 ) )
=> ( ! [X657: $i,X658: $i,X659: $i] :
( ( in @ X659 @ ( setminus @ X657 @ X658 ) )
=> ~ ( in @ X659 @ X658 ) )
=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setminusSubset2]),upairsetIL]),setminusI]),setminusER]),c_0_120]),c_0_121]),binunionIL]),setunionE]),upairset2IR]),binunionIR]),subPowSU]),binunionEcases]),binunionE]),c_0_122]),binunionLsub]),binunionRsub]),nonemptyImpWitness]),binintersectI]),binintersectSubset5]),uniqinunit]),binintersectEL]),binintersectLsub]),notinsingleton]),binintersectSubset2]),binintersectSubset3]),eqinunit]),binintersectER]),disjointsetsI1]),singletonsswitch]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),upairsetE]),bs114d]),emptyset__Cong]),setminusEL]),upairsetIR]),c_0_123]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_124]),c_0_125]),c_0_126]),inCongP]),in__Cong]),c_0_127]),c_0_128]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_129]),c_0_130]),c_0_131]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),emptyInPowerset]),powersetE]),setunionI]),emptyinPowerset]),powersetI]),c_0_132]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_133]),nonemptyE1]),c_0_134]),noeltsimpempty]),emptyI]),setext]),c_0_135]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_136]),c_0_137]),c_0_138]),c_0_139]),c_0_140]),wellorderingAx]),foundationAx]),c_0_141]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_142]) ).
thf(c_0_144,negated_conjecture,
! [X660: $i,X661: $i,X663: $i,X664: $i,X665: $i,X666: $i,X667: $i,X668: $i,X669: $i,X670: $i,X671: $i,X673: $i,X674: $i,X676: $i,X677: $i,X678: $i,X679: $i,X680: $i,X682: $i,X683: $i > $i > $o,X684: $i,X687: $i,X689: $i,X690: $i,X691: $i,X692: $i,X694: $i,X695: $i > $o,X696: $i,X697: $i > $o,X698: $i,X699: $i,X700: $i > $o,X701: $i,X702: $i,X703: $i > $o,X704: $i,X705: $i > $o,X707: $i,X708: $o,X709: $i,X710: $i,X711: $o,X712: $i,X713: $i,X714: $i > $o,X716: $i,X717: $i,X720: $i,X722: $i,X724: $i,X725: $i > $o,X726: $i,X727: $i,X729: $i,X730: $i > $o,X731: $i,X732: $i,X733: $i,X734: $i,X735: $i,X736: $i,X737: $i,X738: $i,X739: $i,X740: $i,X741: $i,X742: $o,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X750: $i,X751: $i,X752: $i,X753: $i,X754: $i,X755: $i,X756: $i,X757: $i,X758: $i,X759: $i,X760: $o,X762: $i,X763: $i,X764: $i > $o,X766: $i,X767: $i,X768: $i,X770: $i,X771: $i,X772: $i,X773: $i,X774: $i,X775: $i,X776: $i,X777: $i,X778: $i,X779: $i,X780: $i,X781: $i,X782: $i,X783: $i,X784: $i,X785: $i,X786: $i > $o,X787: $i,X788: $i > $o,X789: $i,X790: $i,X791: $i > $o,X792: $i,X794: $i,X795: $i > $o,X797: $i,X798: $i,X799: $i > $o,X801: $i,X802: $i,X803: $i > $o,X804: $i,X806: $o,X807: $i,X808: $i > $o,X810: $i,X811: $i,X812: $i > $o,X813: $i,X815: $i > $o,X816: $i,X818: $i > $o,X819: $i,X822: $i > $o,X823: $i,X825: $i,X826: $i,X827: $i,X828: $i,X829: $i,X830: $i,X831: $i,X832: $i,X833: $i > $o,X834: $i,X835: $i,X836: $i > $o,X837: $i > $o,X840: $i,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i > $o,X849: $i,X850: $i,X851: $i > $o,X852: $i > $o,X855: $i,X856: $i,X857: $i > $o,X858: $i > $o,X861: $i,X862: $i,X864: $i,X865: $i,X866: $i,X867: $i,X868: $i,X869: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i,X878: $i,X879: $i,X880: $i,X881: $i,X882: $i,X883: $i,X884: $i,X885: $i,X886: $i,X887: $i,X888: $i,X889: $i,X890: $i,X891: $i,X892: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $i,X898: $i,X899: $i,X900: $i,X901: $i,X902: $i,X903: $i,X904: $i,X905: $i,X906: $i,X907: $i,X908: $i > $o,X909: $i,X910: $i > $o,X911: $i,X912: $i,X913: $i,X914: $i,X915: $i,X916: $i,X917: $i,X918: $i,X919: $i,X920: $i,X921: $i,X922: $o,X923: $i,X924: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i,X932: $i,X933: $i,X934: $i,X935: $i,X936: $i,X937: $i,X938: $i,X939: $i,X940: $i,X941: $i,X942: $i,X943: $i,X944: $i,X945: $i,X946: $i,X947: $i,X948: $i,X949: $i,X951: $i,X952: $i,X953: $i,X954: $i,X955: $i,X956: $i,X957: $i,X958: $i,X959: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X968: $i] :
( ( ~ ( in @ ( esk1_2 @ X660 @ X661 ) @ X660 )
| ~ ( in @ ( esk1_2 @ X660 @ X661 ) @ X661 )
| ( X660 = X661 ) )
& ( ( in @ ( esk1_2 @ X660 @ X661 ) @ X660 )
| ( in @ ( esk1_2 @ X660 @ X661 ) @ X661 )
| ( X660 = X661 ) )
& ~ ( in @ X663 @ emptyset )
& ( ~ ( in @ X666 @ ( setadjoin @ X664 @ X665 ) )
| ( X666 = X664 )
| ( in @ X666 @ X665 ) )
& ( ( X666 != X664 )
| ( in @ X666 @ ( setadjoin @ X664 @ X665 ) ) )
& ( ~ ( in @ X666 @ X665 )
| ( in @ X666 @ ( setadjoin @ X664 @ X665 ) ) )
& ( ~ ( in @ X668 @ ( powerset @ X667 ) )
| ~ ( in @ X669 @ X668 )
| ( in @ X669 @ X667 ) )
& ( ( in @ ( esk2_2 @ X670 @ X671 ) @ X671 )
| ( in @ X671 @ ( powerset @ X670 ) ) )
& ( ~ ( in @ ( esk2_2 @ X670 @ X671 ) @ X670 )
| ( in @ X671 @ ( powerset @ X670 ) ) )
& ( ( in @ X674 @ ( esk3_2 @ X673 @ X674 ) )
| ~ ( in @ X674 @ ( setunion @ X673 ) ) )
& ( ( in @ ( esk3_2 @ X673 @ X674 ) @ X673 )
| ~ ( in @ X674 @ ( setunion @ X673 ) ) )
& ( ~ ( in @ X677 @ X678 )
| ~ ( in @ X678 @ X676 )
| ( in @ X677 @ ( setunion @ X676 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X679 @ omega )
| ( in @ ( setadjoin @ X679 @ X679 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X680 ) @ omega )
| ~ ( in @ emptyset @ X680 )
| ~ ( in @ X682 @ omega )
| ( in @ X682 @ X680 ) )
& ( ( in @ ( esk4_1 @ X680 ) @ X680 )
| ~ ( in @ emptyset @ X680 )
| ~ ( in @ X682 @ omega )
| ( in @ X682 @ X680 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X680 ) @ ( esk4_1 @ X680 ) ) @ X680 )
| ~ ( in @ emptyset @ X680 )
| ~ ( in @ X682 @ omega )
| ( in @ X682 @ X680 ) )
& ( ( in @ ( esk7_3 @ X683 @ X684 @ X687 ) @ X684 )
| ~ ( in @ X687 @ ( esk6_2 @ X683 @ X684 ) )
| ( in @ ( esk5_2 @ X683 @ X684 ) @ X684 ) )
& ( ( X683 @ ( esk7_3 @ X683 @ X684 @ X687 ) @ X687 )
| ~ ( in @ X687 @ ( esk6_2 @ X683 @ X684 ) )
| ( in @ ( esk5_2 @ X683 @ X684 ) @ X684 ) )
& ( ~ ( in @ X690 @ X684 )
| ~ ( X683 @ X690 @ X689 )
| ( in @ X689 @ ( esk6_2 @ X683 @ X684 ) )
| ( in @ ( esk5_2 @ X683 @ X684 ) @ X684 ) )
& ( ( in @ ( esk7_3 @ X683 @ X684 @ X687 ) @ X684 )
| ~ ( in @ X687 @ ( esk6_2 @ X683 @ X684 ) )
| ~ ( exu @ ( X683 @ ( esk5_2 @ X683 @ X684 ) ) ) )
& ( ( X683 @ ( esk7_3 @ X683 @ X684 @ X687 ) @ X687 )
| ~ ( in @ X687 @ ( esk6_2 @ X683 @ X684 ) )
| ~ ( exu @ ( X683 @ ( esk5_2 @ X683 @ X684 ) ) ) )
& ( ~ ( in @ X690 @ X684 )
| ~ ( X683 @ X690 @ X689 )
| ( in @ X689 @ ( esk6_2 @ X683 @ X684 ) )
| ~ ( exu @ ( X683 @ ( esk5_2 @ X683 @ X684 ) ) ) )
& ( ( in @ ( esk8_1 @ X691 ) @ X691 )
| ~ ( in @ X692 @ X691 ) )
& ( ~ ( in @ X694 @ ( esk8_1 @ X691 ) )
| ~ ( in @ X694 @ X691 )
| ~ ( in @ X692 @ X691 ) )
& epred1_0
& ( ~ ( exu @ X695 )
| ( X695 @ ( descr @ X695 ) ) )
& ( ~ ( in @ X698 @ X696 )
| ~ ( X697 @ X698 )
| ( in @ X698 @ ( dsetconstr @ X696 @ X697 ) ) )
& ( ~ ( in @ X701 @ ( dsetconstr @ X699 @ X700 ) )
| ( in @ X701 @ X699 ) )
& ( ~ ( in @ X704 @ ( dsetconstr @ X702 @ X703 ) )
| ( X703 @ X704 ) )
& ( ( X705 @ ( esk9_1 @ X705 ) )
| ~ ( exu @ X705 ) )
& ( ~ ( X705 @ X707 )
| ( ( esk9_1 @ X705 )
= X707 )
| ~ ( exu @ X705 ) )
& ( ~ ( in @ X709 @ ( prop2set @ X708 ) )
| X708 )
& ( ~ ( in @ X710 @ emptyset )
| X711 )
& ( ~ ( in @ X712 @ emptyset )
| ~ $true )
& ~ ( in @ X713 @ emptyset )
& ( ~ ( exu @ X714 )
| ( X714 @ ( esk10_1 @ X714 ) ) )
& ( ( in @ ( esk12_2 @ X716 @ X717 ) @ X717 )
| ( X716 = X717 )
| ( in @ ( esk11_2 @ X716 @ X717 ) @ X716 ) )
& ( ~ ( in @ ( esk12_2 @ X716 @ X717 ) @ X716 )
| ( X716 = X717 )
| ( in @ ( esk11_2 @ X716 @ X717 ) @ X716 ) )
& ( ( in @ ( esk12_2 @ X716 @ X717 ) @ X717 )
| ( X716 = X717 )
| ~ ( in @ ( esk11_2 @ X716 @ X717 ) @ X717 ) )
& ( ~ ( in @ ( esk12_2 @ X716 @ X717 ) @ X716 )
| ( X716 = X717 )
| ~ ( in @ ( esk11_2 @ X716 @ X717 ) @ X717 ) )
& ( ( in @ ( esk13_1 @ X720 ) @ X720 )
| ( X720 = emptyset ) )
& ( ( in @ ( esk14_1 @ X722 ) @ X722 )
| ( X722 = emptyset ) )
& ( ~ ( in @ X726 @ ( dsetconstr @ X724 @ X725 ) )
| ( X725 @ X726 )
| ~ ( in @ X726 @ X724 ) )
& ( ~ ( X725 @ X726 )
| ( in @ X726 @ ( dsetconstr @ X724 @ X725 ) )
| ~ ( in @ X726 @ X724 ) )
& ( ~ ( nonempty @ X727 )
| ( in @ ( esk15_1 @ X727 ) @ X727 ) )
& ( ~ ( in @ X731 @ X729 )
| ~ ( X730 @ X731 )
| ( nonempty @ ( dsetconstr @ X729 @ X730 ) ) )
& ( ~ ( in @ X733 @ X732 )
| ( nonempty @ X732 ) )
& ( in @ X734 @ ( setadjoin @ X734 @ X735 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X738 @ X737 )
| ( in @ X738 @ ( setadjoin @ X736 @ X737 ) ) )
& ( ( in @ X741 @ X740 )
| X742
| ( X741 = X739 )
| ~ ( in @ X741 @ ( setadjoin @ X739 @ X740 ) ) )
& ( ~ X742
| X742
| ( X741 = X739 )
| ~ ( in @ X741 @ ( setadjoin @ X739 @ X740 ) ) )
& ( ( in @ X741 @ X740 )
| X742
| ~ X742
| ~ ( in @ X741 @ ( setadjoin @ X739 @ X740 ) ) )
& ( ~ X742
| X742
| ~ X742
| ~ ( in @ X741 @ ( setadjoin @ X739 @ X740 ) ) )
& ( ~ ( in @ X745 @ ( setadjoin @ X743 @ X744 ) )
| ( X745 = X743 )
| ( in @ X745 @ X744 ) )
& ( ( dsetconstr @ X746
@ ^ [Z0: $i] : $true )
= X746 )
& ( ( in @ ( esk16_2 @ X747 @ X748 ) @ X748 )
| ( in @ X748 @ ( powerset @ X747 ) ) )
& ( ~ ( in @ ( esk16_2 @ X747 @ X748 ) @ X747 )
| ( in @ X748 @ ( powerset @ X747 ) ) )
& ( in @ emptyset @ ( powerset @ X750 ) )
& ( in @ emptyset @ ( powerset @ X751 ) )
& ( ~ ( in @ X753 @ ( powerset @ X752 ) )
| ~ ( in @ X754 @ X753 )
| ( in @ X754 @ X752 ) )
& ( ~ ( in @ X756 @ X757 )
| ~ ( in @ X757 @ X755 )
| ( in @ X756 @ ( setunion @ X755 ) ) )
& ( ( in @ X759 @ ( esk17_3 @ X758 @ X759 @ X760 ) )
| X760
| ~ ( in @ X759 @ ( setunion @ X758 ) ) )
& ( ( in @ ( esk17_3 @ X758 @ X759 @ X760 ) @ X758 )
| X760
| ~ ( in @ X759 @ ( setunion @ X758 ) ) )
& ( ~ X760
| X760
| ~ ( in @ X759 @ ( setunion @ X758 ) ) )
& ( ~ ( in @ X763 @ X762 )
| ( in @ X763 @ ( powerset @ ( setunion @ X762 ) ) ) )
& ( ~ ( X764 @ X766 )
| ( X766
= ( esk18_1 @ X764 ) )
| ~ ( exu @ X764 ) )
& ( ( X767
!= ( esk18_1 @ X764 ) )
| ( X764 @ X767 )
| ~ ( exu @ X764 ) )
& ( ( in @ ( esk19_1 @ X768 ) @ X768 )
| ~ ( nonempty @ X768 ) )
& ( $true
| ~ ( nonempty @ X768 ) )
& ( ~ ( in @ X770 @ ( setadjoin @ X771 @ emptyset ) )
| ( X770 = X771 ) )
& ( ( X772 = X773 )
| ~ ( in @ X773 @ ( setadjoin @ X772 @ emptyset ) ) )
& ( ( X774 != X775 )
| ( in @ X774 @ ( setadjoin @ X775 @ emptyset ) ) )
& ( ~ ( in @ X776 @ ( setadjoin @ X777 @ emptyset ) )
| ( in @ X777 @ ( setadjoin @ X776 @ emptyset ) ) )
& ( ~ ( in @ X780 @ ( setadjoin @ X778 @ ( setadjoin @ X779 @ emptyset ) ) )
| ( X780 = X778 )
| ( X780 = X779 ) )
& ( in @ X781 @ ( setadjoin @ X781 @ ( setadjoin @ X782 @ emptyset ) ) )
& ( in @ X784 @ ( setadjoin @ X783 @ ( setadjoin @ X784 @ emptyset ) ) )
& ( ~ ( in @ X787 @ X785 )
| ~ ( X786 @ X787 )
| ( ( dsetconstr @ X785 @ X786 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X789 @ emptyset )
| ( X788 @ X789 ) )
& ( ( in @ ( esk20_2 @ X790 @ X791 ) @ X790 )
| ~ ( in @ X792 @ X790 )
| ( X791 @ X792 ) )
& ( ~ ( X791 @ ( esk20_2 @ X790 @ X791 ) )
| ~ ( in @ X792 @ X790 )
| ( X791 @ X792 ) )
& ( ( in @ ( esk21_2 @ X794 @ X795 ) @ X794 )
| ~ ( in @ X797 @ X794 )
| ~ ( X795 @ X797 ) )
& ( ( X795 @ ( esk21_2 @ X794 @ X795 ) )
| ~ ( in @ X797 @ X794 )
| ~ ( X795 @ X797 ) )
& ( ( in @ ( esk22_2 @ X798 @ X799 ) @ X798 )
| ~ ( in @ X801 @ X798 )
| ~ ( X799 @ X801 ) )
& ( ( X799 @ ( esk22_2 @ X798 @ X799 ) )
| ~ ( in @ X801 @ X798 )
| ~ ( X799 @ X801 ) )
& ( ( in @ ( esk23_2 @ X802 @ X803 ) @ X802 )
| ~ ( in @ X804 @ X802 )
| ( X803 @ X804 ) )
& ( ~ ( X803 @ ( esk23_2 @ X802 @ X803 ) )
| ~ ( in @ X804 @ X802 )
| ( X803 @ X804 ) )
& ( ~ X806
| ( in @ emptyset @ ( prop2set @ X806 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X807 @ X808 ) @ X807 )
| ~ ( in @ X810 @ X807 )
| ~ ( X808 @ X810 ) )
& ( ( X808 @ ( esk24_2 @ X807 @ X808 ) )
| ~ ( in @ X810 @ X807 )
| ~ ( X808 @ X810 ) )
& ( ( in @ ( esk25_2 @ X811 @ X812 ) @ X811 )
| ~ ( in @ X813 @ X811 )
| ( X812 @ X813 ) )
& ( ~ ( X812 @ ( esk25_2 @ X811 @ X812 ) )
| ~ ( in @ X813 @ X811 )
| ( X812 @ X813 ) )
& ( ( X815 @ ( esk26_2 @ X815 @ X816 ) )
| ~ ( X815 @ X816 )
| ( exu @ X815 ) )
& ( ( X816
!= ( esk26_2 @ X815 @ X816 ) )
| ~ ( X815 @ X816 )
| ( exu @ X815 ) )
& ( ( X818 @ ( esk27_1 @ X818 ) )
| ( exu @ X818 )
| ~ ( X818 @ X819 ) )
& ( ( X818 @ ( esk28_1 @ X818 ) )
| ( exu @ X818 )
| ~ ( X818 @ X819 ) )
& ( ( ( esk27_1 @ X818 )
!= ( esk28_1 @ X818 ) )
| ( exu @ X818 )
| ~ ( X818 @ X819 ) )
& ( ~ ( X822 @ ( esk29_2 @ X822 @ X823 ) )
| ( ( esk29_2 @ X822 @ X823 )
!= X823 )
| ( exu @ X822 ) )
& ( ( X822 @ ( esk29_2 @ X822 @ X823 ) )
| ( ( esk29_2 @ X822 @ X823 )
= X823 )
| ( exu @ X822 ) )
& ( ( X825 != X826 )
| ( X827 != X828 )
| ~ ( in @ X827 @ X825 )
| ( in @ X828 @ X826 ) )
& ( ~ ( in @ X831 @ X829 )
| ( in @ X832 @ X830 )
| ( X831 != X832 )
| ( X829 != X830 ) )
& ( ~ ( in @ X832 @ X830 )
| ( in @ X831 @ X829 )
| ( X831 != X832 )
| ( X829 != X830 ) )
& ( ~ ( exu @ X833 )
| ~ ( X833 @ X834 )
| ~ ( X833 @ X835 )
| ( X834 = X835 ) )
& ( ~ ( exu @ X836 )
| ( exu @ X837 )
| ( ( esk30_2 @ X836 @ X837 )
= ( esk31_2 @ X836 @ X837 ) ) )
& ( ~ ( exu @ X837 )
| ( exu @ X836 )
| ( ( esk30_2 @ X836 @ X837 )
= ( esk31_2 @ X836 @ X837 ) ) )
& ( ~ ( exu @ X836 )
| ( exu @ X837 )
| ~ ( X836 @ ( esk30_2 @ X836 @ X837 ) )
| ~ ( X837 @ ( esk31_2 @ X836 @ X837 ) ) )
& ( ~ ( exu @ X837 )
| ( exu @ X836 )
| ~ ( X836 @ ( esk30_2 @ X836 @ X837 ) )
| ~ ( X837 @ ( esk31_2 @ X836 @ X837 ) ) )
& ( ~ ( exu @ X836 )
| ( exu @ X837 )
| ( X836 @ ( esk30_2 @ X836 @ X837 ) )
| ( X837 @ ( esk31_2 @ X836 @ X837 ) ) )
& ( ~ ( exu @ X837 )
| ( exu @ X836 )
| ( X836 @ ( esk30_2 @ X836 @ X837 ) )
| ( X837 @ ( esk31_2 @ X836 @ X837 ) ) )
& ( emptyset = emptyset )
& ( ( X840 != X841 )
| ( X842 != X843 )
| ( ( setadjoin @ X840 @ X842 )
= ( setadjoin @ X841 @ X843 ) ) )
& ( ( X844 != X845 )
| ( ( powerset @ X844 )
= ( powerset @ X845 ) ) )
& ( ( X846 != X847 )
| ( ( setunion @ X846 )
= ( setunion @ X847 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X848 )
| ~ ( X848 @ X849 )
| ~ ( X848 @ X850 )
| ( X849 = X850 ) )
& ( ( ( esk32_2 @ X851 @ X852 )
= ( esk33_2 @ X851 @ X852 ) )
| ~ ( exu @ X851 )
| ~ ( exu @ X852 )
| ( ( descr @ X851 )
= ( descr @ X852 ) ) )
& ( ~ ( X851 @ ( esk32_2 @ X851 @ X852 ) )
| ~ ( X852 @ ( esk33_2 @ X851 @ X852 ) )
| ~ ( exu @ X851 )
| ~ ( exu @ X852 )
| ( ( descr @ X851 )
= ( descr @ X852 ) ) )
& ( ( X851 @ ( esk32_2 @ X851 @ X852 ) )
| ( X852 @ ( esk33_2 @ X851 @ X852 ) )
| ~ ( exu @ X851 )
| ~ ( exu @ X852 )
| ( ( descr @ X851 )
= ( descr @ X852 ) ) )
& ( ( in @ ( esk34_4 @ X855 @ X856 @ X857 @ X858 ) @ X855 )
| ( ( dsetconstr @ X855 @ X857 )
= ( dsetconstr @ X856 @ X858 ) )
| ( X855 != X856 ) )
& ( ( in @ ( esk35_4 @ X855 @ X856 @ X857 @ X858 ) @ X856 )
| ( ( dsetconstr @ X855 @ X857 )
= ( dsetconstr @ X856 @ X858 ) )
| ( X855 != X856 ) )
& ( ( ( esk34_4 @ X855 @ X856 @ X857 @ X858 )
= ( esk35_4 @ X855 @ X856 @ X857 @ X858 ) )
| ( ( dsetconstr @ X855 @ X857 )
= ( dsetconstr @ X856 @ X858 ) )
| ( X855 != X856 ) )
& ( ~ ( X857 @ ( esk34_4 @ X855 @ X856 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk35_4 @ X855 @ X856 @ X857 @ X858 ) )
| ( ( dsetconstr @ X855 @ X857 )
= ( dsetconstr @ X856 @ X858 ) )
| ( X855 != X856 ) )
& ( ( X857 @ ( esk34_4 @ X855 @ X856 @ X857 @ X858 ) )
| ( X858 @ ( esk35_4 @ X855 @ X856 @ X857 @ X858 ) )
| ( ( dsetconstr @ X855 @ X857 )
= ( dsetconstr @ X856 @ X858 ) )
| ( X855 != X856 ) )
& ( ( in @ ( esk36_2 @ X861 @ X862 ) @ X861 )
| ( subset @ X861 @ X862 ) )
& ( ~ ( in @ ( esk36_2 @ X861 @ X862 ) @ X862 )
| ( subset @ X861 @ X862 ) )
& ( ( X864 != X865 )
| ( subset @ X865 @ X864 ) )
& ( ( X866 != X867 )
| ( subset @ X866 @ X867 ) )
& ( ( in @ ( esk37_2 @ X868 @ X869 ) @ X868 )
| ( subset @ X868 @ X869 ) )
& ( ~ ( in @ ( esk37_2 @ X868 @ X869 ) @ X869 )
| ( subset @ X868 @ X869 ) )
& ( subset @ emptyset @ X871 )
& ( ~ ( subset @ X872 @ X873 )
| ~ ( in @ X874 @ X872 )
| ( in @ X874 @ X873 ) )
& ( ~ ( subset @ X875 @ X876 )
| ( in @ X877 @ X876 )
| ~ ( in @ X877 @ X875 ) )
& ( ~ ( in @ X880 @ X878 )
| ( in @ X880 @ X879 )
| ~ ( subset @ X878 @ X879 ) )
& ( ( subset @ X881 @ X882 )
| ( X881 != X882 ) )
& ( ~ ( in @ X885 @ X883 )
| ( in @ X885 @ X884 )
| ( X883 != X884 ) )
& ( subset @ X886 @ X886 )
& ( ~ ( subset @ X887 @ X888 )
| ~ ( subset @ X888 @ X889 )
| ( subset @ X887 @ X889 ) )
& ( subset @ X891 @ ( setadjoin @ X890 @ X891 ) )
& ( ~ ( subset @ X892 @ X894 )
| ( subset @ X892 @ ( setadjoin @ X893 @ X894 ) ) )
& ( ~ ( subset @ X895 @ X896 )
| ( in @ X895 @ ( powerset @ X896 ) ) )
& ( ~ ( subset @ X897 @ X898 )
| ~ ( subset @ X898 @ X897 )
| ( X897 = X898 ) )
& ( ~ ( subset @ X899 @ emptyset )
| ( X899 = emptyset ) )
& ( ~ ( subset @ X901 @ X900 )
| ( in @ X901 @ ( powerset @ X900 ) ) )
& ( ~ ( in @ X903 @ ( powerset @ X902 ) )
| ( subset @ X903 @ X902 ) )
& ( in @ X904 @ ( powerset @ X904 ) )
& ( ~ ( subset @ X905 @ X906 )
| ( subset @ ( powerset @ X905 ) @ ( powerset @ X906 ) ) )
& ( in @ ( dsetconstr @ X907 @ X908 ) @ ( powerset @ X907 ) )
& ( subset @ ( dsetconstr @ X909 @ X910 ) @ X909 )
& ( ~ ( in @ X913 @ X911 )
| ( in @ X913 @ ( binunion @ X911 @ X912 ) ) )
& ( in @ X915 @ ( setadjoin @ X914 @ ( setadjoin @ X915 @ emptyset ) ) )
& ( ~ ( in @ X918 @ X917 )
| ( in @ X918 @ ( binunion @ X916 @ X917 ) ) )
& ( ( in @ X921 @ X920 )
| X922
| ( in @ X921 @ X919 )
| ~ ( in @ X921 @ ( binunion @ X919 @ X920 ) ) )
& ( ~ X922
| X922
| ( in @ X921 @ X919 )
| ~ ( in @ X921 @ ( binunion @ X919 @ X920 ) ) )
& ( ( in @ X921 @ X920 )
| X922
| ~ X922
| ~ ( in @ X921 @ ( binunion @ X919 @ X920 ) ) )
& ( ~ X922
| X922
| ~ X922
| ~ ( in @ X921 @ ( binunion @ X919 @ X920 ) ) )
& ( ~ ( in @ X925 @ ( binunion @ X923 @ X924 ) )
| ( in @ X925 @ X923 )
| ( in @ X925 @ X924 ) )
& ( subset @ X926 @ ( binunion @ X926 @ X927 ) )
& ( subset @ X929 @ ( binunion @ X928 @ X929 ) )
& ( ~ ( in @ X932 @ X930 )
| ~ ( in @ X932 @ X931 )
| ( in @ X932 @ ( binintersect @ X930 @ X931 ) ) )
& ( ~ ( subset @ X935 @ X933 )
| ~ ( subset @ X935 @ X934 )
| ( subset @ X935 @ ( binintersect @ X933 @ X934 ) ) )
& ( ~ ( in @ X938 @ ( binintersect @ X936 @ X937 ) )
| ( in @ X938 @ X936 ) )
& ( subset @ ( binintersect @ X939 @ X940 ) @ X939 )
& ( ~ ( subset @ X941 @ X942 )
| ( ( binintersect @ X941 @ X942 )
= X941 ) )
& ( ( ( binintersect @ X943 @ X944 )
!= X944 )
| ( subset @ X944 @ X943 ) )
& ( ~ ( in @ X947 @ ( binintersect @ X945 @ X946 ) )
| ( in @ X947 @ X946 ) )
& ( ( in @ ( esk38_2 @ X948 @ X949 ) @ X948 )
| ( ( binintersect @ X948 @ X949 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X948 @ X949 ) @ X949 )
| ( ( binintersect @ X948 @ X949 )
= emptyset ) )
& ( subset @ ( binintersect @ X951 @ X952 ) @ X952 )
& ( ~ ( subset @ X954 @ X953 )
| ( ( binintersect @ X953 @ X954 )
= X954 ) )
& ( ( ( binintersect @ X955 @ X956 )
!= X955 )
| ( subset @ X955 @ X956 ) )
& ( ( binintersect @ X957 @ ( binunion @ X958 @ X959 ) )
= ( binunion @ ( binintersect @ X957 @ X958 ) @ ( binintersect @ X957 @ X959 ) ) )
& ( ~ ( in @ X962 @ X960 )
| ( in @ X962 @ X961 )
| ( in @ X962 @ ( setminus @ X960 @ X961 ) ) )
& ( ~ ( in @ X965 @ ( setminus @ X963 @ X964 ) )
| ( in @ X965 @ X963 ) )
& ( ~ ( in @ X968 @ ( setminus @ X966 @ X967 ) )
| ~ ( in @ X968 @ X967 ) )
& ( subset @ esk39_0 @ esk40_0 )
& ( ( setminus @ esk39_0 @ esk40_0 )
!= emptyset ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])])])])])]) ).
thf(c_0_145,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_146,negated_conjecture,
! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_147,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ X4 )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_148,negated_conjecture,
subset @ esk39_0 @ esk40_0,
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_149,negated_conjecture,
! [X3: $i,X2: $i] :
( ( X2 = X3 )
| ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_150,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk36_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_151,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ X3 )
| ~ ( subset @ ( setadjoin @ X2 @ X4 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
thf(c_0_152,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk40_0 )
| ~ ( subset @ X2 @ esk39_0 ) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
thf(c_0_153,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk36_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_154,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( esk36_2 @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= X2 )
| ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
thf(c_0_155,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ~ ( in @ X2 @ ( setminus @ X3 @ X4 ) )
| ~ ( in @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_156,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk14_1 @ X2 ) @ X2 )
| ( X2 = emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_157,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ esk40_0 )
| ~ ( subset @ ( setadjoin @ X2 @ X3 ) @ esk39_0 ) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
thf(c_0_158,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
thf(c_0_159,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( setminus @ X2 @ X3 )
= emptyset )
| ~ ( in @ ( esk14_1 @ ( setminus @ X2 @ X3 ) ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
thf(c_0_160,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk40_0 )
| ~ ( in @ X2 @ esk39_0 ) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
thf(c_0_161,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ X3 )
| ~ ( in @ X2 @ ( setminus @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_162,negated_conjecture,
! [X2: $i] :
( ( ( setminus @ X2 @ esk40_0 )
= emptyset )
| ~ ( in @ ( esk14_1 @ ( setminus @ X2 @ esk40_0 ) ) @ esk39_0 ) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
thf(c_0_163,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( setminus @ X2 @ X3 )
= emptyset )
| ( in @ ( esk14_1 @ ( setminus @ X2 @ X3 ) ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_161,c_0_156]) ).
thf(c_0_164,negated_conjecture,
( ( setminus @ esk39_0 @ esk40_0 )
!= emptyset ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_165,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SEU604^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.10 % Command : run_E %s %d THM
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Sun May 19 16:04:37 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.13/0.37 Running higher-order theorem proving
% 0.13/0.37 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
% 2.08/0.65 # Version: 3.1.0-ho
% 2.08/0.65 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.08/0.65 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.08/0.65 # Starting ehoh_best5 with 300s (1) cores
% 2.08/0.65 # Starting almost_fo_3_lam with 300s (1) cores
% 2.08/0.65 # Starting new_bool_5 with 300s (1) cores
% 2.08/0.65 # Starting pre_casc_3 with 300s (1) cores
% 2.08/0.65 # Starting ho_unfolding_8 with 300s (1) cores
% 2.08/0.65 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.08/0.65 # Starting new_bool_3 with 300s (1) cores
% 2.08/0.65 # Starting new_ho_5 with 300s (1) cores
% 2.08/0.65 # new_bool_5 with pid 10066 completed with status 0
% 2.08/0.65 # Result found by new_bool_5
% 2.08/0.65 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.08/0.65 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.08/0.65 # Starting ehoh_best5 with 300s (1) cores
% 2.08/0.65 # Starting almost_fo_3_lam with 300s (1) cores
% 2.08/0.65 # Starting new_bool_5 with 300s (1) cores
% 2.08/0.65 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.08/0.65 # Search class: HGHSM-FSLM31-SHFMMSBN
% 2.08/0.65 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.08/0.65 # Starting ehoh_best3 with 163s (1) cores
% 2.08/0.65 # ehoh_best3 with pid 10074 completed with status 0
% 2.08/0.65 # Result found by ehoh_best3
% 2.08/0.65 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.08/0.65 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.08/0.65 # Starting ehoh_best5 with 300s (1) cores
% 2.08/0.65 # Starting almost_fo_3_lam with 300s (1) cores
% 2.08/0.65 # Starting new_bool_5 with 300s (1) cores
% 2.08/0.65 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.08/0.65 # Search class: HGHSM-FSLM31-SHFMMSBN
% 2.08/0.65 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.08/0.65 # Starting ehoh_best3 with 163s (1) cores
% 2.08/0.65 # Preprocessing time : 0.002 s
% 2.08/0.65 # Presaturation interreduction done
% 2.08/0.65
% 2.08/0.65 # Proof found!
% 2.08/0.65 # SZS status Theorem
% 2.08/0.65 # SZS output start CNFRefutation
% See solution above
% 2.08/0.65 # Parsed axioms : 262
% 2.08/0.65 # Removed by relevancy pruning/SinE : 142
% 2.08/0.65 # Initial clauses : 193
% 2.08/0.65 # Removed in clause preprocessing : 18
% 2.08/0.65 # Initial clauses in saturation : 175
% 2.08/0.65 # Processed clauses : 2486
% 2.08/0.65 # ...of these trivial : 73
% 2.08/0.65 # ...subsumed : 1337
% 2.08/0.65 # ...remaining for further processing : 1076
% 2.08/0.65 # Other redundant clauses eliminated : 61
% 2.08/0.65 # Clauses deleted for lack of memory : 0
% 2.08/0.65 # Backward-subsumed : 45
% 2.08/0.65 # Backward-rewritten : 69
% 2.08/0.65 # Generated clauses : 26800
% 2.08/0.65 # ...of the previous two non-redundant : 19489
% 2.08/0.65 # ...aggressively subsumed : 0
% 2.08/0.65 # Contextual simplify-reflections : 0
% 2.08/0.65 # Paramodulations : 26736
% 2.08/0.65 # Factorizations : 2
% 2.08/0.65 # NegExts : 0
% 2.08/0.65 # Equation resolutions : 61
% 2.08/0.65 # Disequality decompositions : 0
% 2.08/0.65 # Total rewrite steps : 10950
% 2.08/0.65 # ...of those cached : 10374
% 2.08/0.65 # Propositional unsat checks : 0
% 2.08/0.65 # Propositional check models : 0
% 2.08/0.65 # Propositional check unsatisfiable : 0
% 2.08/0.65 # Propositional clauses : 0
% 2.08/0.65 # Propositional clauses after purity: 0
% 2.08/0.65 # Propositional unsat core size : 0
% 2.08/0.65 # Propositional preprocessing time : 0.000
% 2.08/0.65 # Propositional encoding time : 0.000
% 2.08/0.65 # Propositional solver time : 0.000
% 2.08/0.65 # Success case prop preproc time : 0.000
% 2.08/0.65 # Success case prop encoding time : 0.000
% 2.08/0.65 # Success case prop solver time : 0.000
% 2.08/0.65 # Current number of processed clauses : 802
% 2.08/0.65 # Positive orientable unit clauses : 188
% 2.08/0.65 # Positive unorientable unit clauses: 0
% 2.08/0.65 # Negative unit clauses : 4
% 2.08/0.65 # Non-unit-clauses : 610
% 2.08/0.65 # Current number of unprocessed clauses: 16950
% 2.08/0.65 # ...number of literals in the above : 46920
% 2.08/0.65 # Current number of archived formulas : 0
% 2.08/0.65 # Current number of archived clauses : 263
% 2.08/0.65 # Clause-clause subsumption calls (NU) : 31406
% 2.08/0.65 # Rec. Clause-clause subsumption calls : 21417
% 2.08/0.65 # Non-unit clause-clause subsumptions : 1096
% 2.08/0.65 # Unit Clause-clause subsumption calls : 1633
% 2.08/0.65 # Rewrite failures with RHS unbound : 0
% 2.08/0.65 # BW rewrite match attempts : 493
% 2.08/0.65 # BW rewrite match successes : 12
% 2.08/0.65 # Condensation attempts : 0
% 2.08/0.65 # Condensation successes : 0
% 2.08/0.65 # Termbank termtop insertions : 309629
% 2.08/0.65 # Search garbage collected termcells : 10657
% 2.08/0.65
% 2.08/0.65 # -------------------------------------------------
% 2.08/0.65 # User time : 0.235 s
% 2.08/0.65 # System time : 0.017 s
% 2.08/0.65 # Total time : 0.253 s
% 2.08/0.65 # Maximum resident set size: 4628 pages
% 2.08/0.65
% 2.08/0.65 # -------------------------------------------------
% 2.08/0.65 # User time : 0.241 s
% 2.08/0.65 # System time : 0.018 s
% 2.08/0.65 # Total time : 0.258 s
% 2.08/0.65 # Maximum resident set size: 2060 pages
% 2.08/0.65 % E---3.1 exiting
% 2.08/0.65 % E exiting
%------------------------------------------------------------------------------