%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU623^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 03:28:38 EDT 2024
% Result : Theorem 0.57s 0.59s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 339
% Syntax : Number of formulae : 371 ( 5 unt; 199 typ; 0 def)
% Number of atoms : 1428 ( 201 equ; 0 cnn)
% Maximal formula atoms : 418 ( 8 avg)
% Number of connectives : 4788 ( 362 ~; 331 |; 262 &;2936 @)
% ( 197 <=>; 700 =>; 0 <=; 0 <~>)
% Maximal formula depth : 529 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 251 ( 251 >; 0 *; 0 +; 0 <<)
% Number of symbols : 202 ( 199 usr; 147 con; 0-4 aty)
% Number of variables : 1193 ( 59 ^1069 !; 65 ?;1193 :)
% 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,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
epred1_0: $o ).
thf(decl_185,type,
esk1_2: $i > $i > $i ).
thf(decl_186,type,
esk2_2: $i > $i > $i ).
thf(decl_187,type,
esk3_2: $i > $i > $i ).
thf(decl_188,type,
esk4_1: $i > $i ).
thf(decl_189,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_190,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_191,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_192,type,
esk8_1: $i > $i ).
thf(decl_193,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_194,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_195,type,
esk11_2: $i > $i > $i ).
thf(decl_196,type,
esk12_2: $i > $i > $i ).
thf(decl_197,type,
esk13_1: $i > $i ).
thf(decl_198,type,
esk14_1: $i > $i ).
thf(decl_199,type,
esk15_1: $i > $i ).
thf(decl_200,type,
esk16_2: $i > $i > $i ).
thf(decl_201,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_202,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_203,type,
esk19_1: $i > $i ).
thf(decl_204,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_205,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_206,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_207,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_208,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_209,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_210,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_211,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_212,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_213,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_214,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_215,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_216,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_217,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_218,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_219,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_220,type,
esk36_2: $i > $i > $i ).
thf(decl_221,type,
esk37_2: $i > $i > $i ).
thf(decl_222,type,
esk38_2: $i > $i > $i ).
thf(decl_223,type,
esk39_0: $i ).
thf(decl_224,type,
esk40_0: $i ).
thf(decl_225,type,
esk41_0: $i ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/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/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(singletoninpowunion,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
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
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/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(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/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_139,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_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_151,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_152,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_153,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_154,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_155,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_156,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_157,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_158,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_159,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_160,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_161,plain,
( epred1_0
<=> ! [X418: $i] :
? [X419: $i] :
( ! [X420: $i] :
( ( in @ X420 @ X419 )
=> ! [X421: $i] :
( ( in @ X421 @ X420 )
=> ( in @ X421 @ X418 ) ) )
& ! [X422: $i,X423: $i] :
( ( ( in @ X422 @ X418 )
& ( in @ X423 @ X418 ) )
=> ( ! [X424: $i] :
( ( in @ X424 @ X419 )
=> ( ( in @ X422 @ X424 )
<=> ( in @ X423 @ X424 ) ) )
=> ( X422 = X423 ) ) )
& ! [X425: $i,X426: $i] :
( ( ( in @ X425 @ X419 )
& ( in @ X426 @ X419 ) )
=> ( ! [X427: $i] :
( ( in @ X427 @ X425 )
=> ( in @ X427 @ X426 ) )
| ! [X428: $i] :
( ( in @ X428 @ X426 )
=> ( in @ X428 @ X425 ) ) ) )
& ! [X429: $i] :
( ( ! [X430: $i] :
( ( in @ X430 @ X429 )
=> ( in @ X430 @ X418 ) )
& ? [X431: $i] : ( in @ X431 @ X429 ) )
=> ? [X432: $i,X433: $i] :
( ( in @ X432 @ X419 )
& ( in @ X433 @ X429 )
& ~ ? [X434: $i] :
( ( in @ X434 @ X432 )
& ( in @ X434 @ X429 ) )
& ! [X435: $i] :
( ( in @ X435 @ X419 )
=> ( ! [X436: $i] :
( ( in @ X436 @ X435 )
=> ( in @ X436 @ X432 ) )
| ( in @ X433 @ X435 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_162,negated_conjecture,
~ ( ! [X391: $i,X392: $i] :
( ! [X393: $i] :
( ( in @ X393 @ X391 )
<=> ( in @ X393 @ X392 ) )
=> ( X391 = X392 ) )
=> ( ! [X394: $i] :
~ ( in @ X394 @ emptyset )
=> ( ! [X395: $i,X396: $i,X397: $i] :
( ( in @ X397 @ ( setadjoin @ X395 @ X396 ) )
<=> ( ( X397 = X395 )
| ( in @ X397 @ X396 ) ) )
=> ( ! [X398: $i,X399: $i] :
( ( in @ X399 @ ( powerset @ X398 ) )
<=> ! [X400: $i] :
( ( in @ X400 @ X399 )
=> ( in @ X400 @ X398 ) ) )
=> ( ! [X401: $i,X402: $i] :
( ( in @ X402 @ ( setunion @ X401 ) )
<=> ? [X403: $i] :
( ( in @ X402 @ X403 )
& ( in @ X403 @ X401 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X404: $i] :
( ( in @ X404 @ omega )
=> ( in @ ( setadjoin @ X404 @ X404 ) @ omega ) )
=> ( ! [X405: $i] :
( ( ( in @ emptyset @ X405 )
& ! [X406: $i] :
( ( ( in @ X406 @ omega )
& ( in @ X406 @ X405 ) )
=> ( in @ ( setadjoin @ X406 @ X406 ) @ X405 ) ) )
=> ! [X407: $i] :
( ( in @ X407 @ omega )
=> ( in @ X407 @ X405 ) ) )
=> ( ! [X408: $i > $i > $o,X409: $i] :
( ! [X410: $i] :
( ( in @ X410 @ X409 )
=> ( exu @ ( X408 @ X410 ) ) )
=> ? [X411: $i] :
! [X412: $i] :
( ( in @ X412 @ X411 )
<=> ? [X413: $i] :
( ( in @ X413 @ X409 )
& ( X408 @ X413 @ X412 ) ) ) )
=> ( ! [X414: $i] :
( ? [X415: $i] : ( in @ X415 @ X414 )
=> ? [X416: $i] :
( ( in @ X416 @ X414 )
& ~ ? [X417: $i] :
( ( in @ X417 @ X416 )
& ( in @ X417 @ X414 ) ) ) )
=> ( epred1_0
=> ( ! [X437: $i > $o] :
( ( exu @ X437 )
=> ( X437
@ ( descr
@ ^ [Z0: $i] : ( X437 @ Z0 ) ) ) )
=> ( ! [X438: $i,X439: $i > $o,X440: $i] :
( ( in @ X440 @ X438 )
=> ( ( X439 @ X440 )
=> ( in @ X440 @ ( dsetconstr @ X438 @ X439 ) ) ) )
=> ( ! [X441: $i,X442: $i > $o,X443: $i] :
( ( in @ X443 @ ( dsetconstr @ X441 @ X442 ) )
=> ( in @ X443 @ X441 ) )
=> ( ! [X444: $i,X445: $i > $o,X446: $i] :
( ( in @ X446 @ ( dsetconstr @ X444 @ X445 ) )
=> ( X445 @ X446 ) )
=> ( ! [X447: $i > $o] :
( ( exu @ X447 )
=> ? [X448: $i] :
( ( X447 @ X448 )
& ! [X449: $i] :
( ( X447 @ X449 )
=> ( X448 = X449 ) ) ) )
=> ( ! [X450: $o,X451: $i] :
( ( in @ X451 @ ( prop2set @ X450 ) )
=> X450 )
=> ( ! [X452: $i] :
( ( in @ X452 @ emptyset )
=> ! [X453: $o] : X453 )
=> ( ! [X454: $i] :
( ( in @ X454 @ emptyset )
=> ~ $true )
=> ( ! [X455: $i] :
~ ( in @ X455 @ emptyset )
=> ( ! [X456: $i > $o] :
( ( exu @ X456 )
=> ? [X457: $i] : ( X456 @ X457 ) )
=> ( ! [X458: $i,X459: $i] :
( ! [X460: $i] :
( ( in @ X460 @ X458 )
=> ( in @ X460 @ X459 ) )
=> ( ! [X461: $i] :
( ( in @ X461 @ X459 )
=> ( in @ X461 @ X458 ) )
=> ( X458 = X459 ) ) )
=> ( ! [X462: $i] :
( ! [X463: $i] :
~ ( in @ X463 @ X462 )
=> ( X462 = emptyset ) )
=> ( ! [X464: $i] :
( ! [X465: $i] :
~ ( in @ X465 @ X464 )
=> ( X464 = emptyset ) )
=> ( ! [X466: $i,X467: $i > $o,X468: $i] :
( ( in @ X468 @ X466 )
=> ( ( in @ X468 @ ( dsetconstr @ X466 @ X467 ) )
<=> ( X467 @ X468 ) ) )
=> ( ! [X469: $i] :
( ( nonempty @ X469 )
=> ? [X470: $i] : ( in @ X470 @ X469 ) )
=> ( ! [X471: $i,X472: $i > $o,X473: $i] :
( ( in @ X473 @ X471 )
=> ( ( X472 @ X473 )
=> ( nonempty @ ( dsetconstr @ X471 @ X472 ) ) ) )
=> ( ! [X474: $i] :
( ? [X475: $i] : ( in @ X475 @ X474 )
=> ( nonempty @ X474 ) )
=> ( ! [X476: $i,X477: $i] : ( in @ X476 @ ( setadjoin @ X476 @ X477 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X478: $i,X479: $i,X480: $i] :
( ( in @ X480 @ X479 )
=> ( in @ X480 @ ( setadjoin @ X478 @ X479 ) ) )
=> ( ! [X481: $i,X482: $i,X483: $i] :
( ( in @ X483 @ ( setadjoin @ X481 @ X482 ) )
=> ! [X484: $o] :
( ( ( X483 = X481 )
=> X484 )
=> ( ( ( in @ X483 @ X482 )
=> X484 )
=> X484 ) ) )
=> ( ! [X485: $i,X486: $i,X487: $i] :
( ( in @ X487 @ ( setadjoin @ X485 @ X486 ) )
=> ( ( X487 = X485 )
| ( in @ X487 @ X486 ) ) )
=> ( ! [X488: $i] :
( ( dsetconstr @ X488
@ ^ [Z0: $i] : $true )
= X488 )
=> ( ! [X489: $i,X490: $i] :
( ! [X491: $i] :
( ( in @ X491 @ X490 )
=> ( in @ X491 @ X489 ) )
=> ( in @ X490 @ ( powerset @ X489 ) ) )
=> ( ! [X492: $i] : ( in @ emptyset @ ( powerset @ X492 ) )
=> ( ! [X493: $i] : ( in @ emptyset @ ( powerset @ X493 ) )
=> ( ! [X494: $i,X495: $i,X496: $i] :
( ( in @ X495 @ ( powerset @ X494 ) )
=> ( ( in @ X496 @ X495 )
=> ( in @ X496 @ X494 ) ) )
=> ( ! [X497: $i,X498: $i,X499: $i] :
( ( in @ X498 @ X499 )
=> ( ( in @ X499 @ X497 )
=> ( in @ X498 @ ( setunion @ X497 ) ) ) )
=> ( ! [X500: $i,X501: $i] :
( ( in @ X501 @ ( setunion @ X500 ) )
=> ! [X502: $o] :
( ! [X503: $i] :
( ( in @ X501 @ X503 )
=> ( ( in @ X503 @ X500 )
=> X502 ) )
=> X502 ) )
=> ( ! [X504: $i,X505: $i] :
( ( in @ X505 @ X504 )
=> ( in @ X505 @ ( powerset @ ( setunion @ X504 ) ) ) )
=> ( ! [X506: $i > $o] :
( ( exu @ X506 )
=> ? [X507: $i] :
! [X508: $i] :
( ( X506 @ X508 )
<=> ( X508 = X507 ) ) )
=> ( ! [X509: $i] :
( ( nonempty @ X509 )
=> ? [X510: $i] :
( ( in @ X510 @ X509 )
& $true ) )
=> ( ! [X511: $i,X512: $i] :
( ( in @ X511 @ ( setadjoin @ X512 @ emptyset ) )
=> ( X511 = X512 ) )
=> ( ! [X513: $i,X514: $i] :
( ( X513 != X514 )
=> ~ ( in @ X514 @ ( setadjoin @ X513 @ emptyset ) ) )
=> ( ! [X515: $i,X516: $i] :
( ( X515 = X516 )
=> ( in @ X515 @ ( setadjoin @ X516 @ emptyset ) ) )
=> ( ! [X517: $i,X518: $i] :
( ( in @ X517 @ ( setadjoin @ X518 @ emptyset ) )
=> ( in @ X518 @ ( setadjoin @ X517 @ emptyset ) ) )
=> ( ! [X519: $i,X520: $i,X521: $i] :
( ( in @ X521 @ ( setadjoin @ X519 @ ( setadjoin @ X520 @ emptyset ) ) )
=> ( ( X521 = X519 )
| ( X521 = X520 ) ) )
=> ( ! [X522: $i,X523: $i] : ( in @ X522 @ ( setadjoin @ X522 @ ( setadjoin @ X523 @ emptyset ) ) )
=> ( ! [X524: $i,X525: $i] : ( in @ X525 @ ( setadjoin @ X524 @ ( setadjoin @ X525 @ emptyset ) ) )
=> ( ! [X526: $i,X527: $i > $o] :
( ? [X528: $i] :
( ( in @ X528 @ X526 )
& ( X527 @ X528 ) )
=> ( ( ( dsetconstr @ X526 @ X527 )
= emptyset )
=> ~ $true ) )
=> ( ! [X529: $i > $o,X530: $i] :
( ( in @ X530 @ emptyset )
=> ( X529 @ X530 ) )
=> ( ! [X531: $i,X532: $i > $o] :
( ~ ! [X533: $i] :
( ( in @ X533 @ X531 )
=> ( X532 @ X533 ) )
=> ? [X534: $i] :
( ( in @ X534 @ X531 )
& ~ ( X532 @ X534 ) ) )
=> ( ! [X535: $i,X536: $i > $o] :
( ! [X537: $i] :
( ( in @ X537 @ X535 )
=> ~ ( X536 @ X537 ) )
=> ~ ? [X538: $i] :
( ( in @ X538 @ X535 )
& ( X536 @ X538 ) ) )
=> ( ! [X539: $i,X540: $i > $o] :
( ~ ? [X541: $i] :
( ( in @ X541 @ X539 )
& ( X540 @ X541 ) )
=> ! [X542: $i] :
( ( in @ X542 @ X539 )
=> ~ ( X540 @ X542 ) ) )
=> ( ! [X543: $i,X544: $i > $o] :
( ? [X545: $i] :
( ( in @ X545 @ X543 )
& ~ ( X544 @ X545 ) )
=> ~ ! [X546: $i] :
( ( in @ X546 @ X543 )
=> ( X544 @ X546 ) ) )
=> ( ! [X547: $o] :
( X547
=> ( in @ emptyset @ ( prop2set @ X547 ) ) )
=> ( prop2set2propI
=> ( ! [X548: $i,X549: $i > $o] :
( ~ ? [X550: $i] :
( ( in @ X550 @ X548 )
& ( X549 @ X550 ) )
=> ! [X551: $i] :
( ( in @ X551 @ X548 )
=> ~ ( X549 @ X551 ) ) )
=> ( ! [X552: $i,X553: $i > $o] :
( ~ ! [X554: $i] :
( ( in @ X554 @ X552 )
=> ( X553 @ X554 ) )
=> ? [X555: $i] :
( ( in @ X555 @ X552 )
& ~ ( X553 @ X555 ) ) )
=> ( ! [X556: $i > $o] :
( ? [X557: $i] :
( ( X556 @ X557 )
& ! [X558: $i] :
( ( X556 @ X558 )
=> ( X557 = X558 ) ) )
=> ( exu @ X556 ) )
=> ( ! [X559: $i > $o] :
( ? [X560: $i] : ( X559 @ X560 )
=> ( ! [X561: $i,X562: $i] :
( ( X559 @ X561 )
=> ( ( X559 @ X562 )
=> ( X561 = X562 ) ) )
=> ( exu @ X559 ) ) )
=> ( ! [X563: $i > $o] :
( ? [X564: $i] :
! [X565: $i] :
( ( X563 @ X565 )
<=> ( X565 = X564 ) )
=> ( exu @ X563 ) )
=> ( ! [X566: $i,X567: $i] :
( ( X566 = X567 )
=> ! [X568: $i,X569: $i] :
( ( X568 = X569 )
=> ( ( in @ X568 @ X566 )
=> ( in @ X569 @ X567 ) ) ) )
=> ( ! [X570: $i,X571: $i] :
( ( X570 = X571 )
=> ! [X572: $i,X573: $i] :
( ( X572 = X573 )
=> ( ( in @ X572 @ X570 )
<=> ( in @ X573 @ X571 ) ) ) )
=> ( ! [X574: $i > $o] :
( ( exu @ X574 )
=> ! [X575: $i,X576: $i] :
( ( X574 @ X575 )
=> ( ( X574 @ X576 )
=> ( X575 = X576 ) ) ) )
=> ( ! [X577: $i > $o,X578: $i > $o] :
( ! [X579: $i,X580: $i] :
( ( X579 = X580 )
=> ( ( X577 @ X579 )
<=> ( X578 @ X580 ) ) )
=> ( ( exu @ X577 )
<=> ( exu @ X578 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X581: $i,X582: $i] :
( ( X581 = X582 )
=> ! [X583: $i,X584: $i] :
( ( X583 = X584 )
=> ( ( setadjoin @ X581 @ X583 )
= ( setadjoin @ X582 @ X584 ) ) ) )
=> ( ! [X585: $i,X586: $i] :
( ( X585 = X586 )
=> ( ( powerset @ X585 )
= ( powerset @ X586 ) ) )
=> ( ! [X587: $i,X588: $i] :
( ( X587 = X588 )
=> ( ( setunion @ X587 )
= ( setunion @ X588 ) ) )
=> ( ( omega = omega )
=> ( ! [X589: $i > $o] :
( ( exu @ X589 )
=> ! [X590: $i,X591: $i] :
( ( X589 @ X590 )
=> ( ( X589 @ X591 )
=> ( X590 = X591 ) ) ) )
=> ( ! [X592: $i > $o,X593: $i > $o] :
( ! [X594: $i,X595: $i] :
( ( X594 = X595 )
=> ( ( X592 @ X594 )
<=> ( X593 @ X595 ) ) )
=> ( ( exu @ X592 )
=> ( ( exu @ X593 )
=> ( ( descr @ X592 )
= ( descr @ X593 ) ) ) ) )
=> ( ! [X596: $i,X597: $i] :
( ( X596 = X597 )
=> ! [X598: $i > $o,X599: $i > $o] :
( ! [X600: $i] :
( ( in @ X600 @ X596 )
=> ! [X601: $i] :
( ( in @ X601 @ X597 )
=> ( ( X600 = X601 )
=> ( ( X598 @ X600 )
<=> ( X599 @ X601 ) ) ) ) )
=> ( ( dsetconstr @ X596 @ X598 )
= ( dsetconstr @ X597 @ X599 ) ) ) )
=> ( ! [X602: $i,X603: $i] :
( ! [X604: $i] :
( ( in @ X604 @ X602 )
=> ( in @ X604 @ X603 ) )
=> ( subset @ X602 @ X603 ) )
=> ( ! [X605: $i,X606: $i] :
( ( X605 = X606 )
=> ( subset @ X606 @ X605 ) )
=> ( ! [X607: $i,X608: $i] :
( ( X607 = X608 )
=> ( subset @ X607 @ X608 ) )
=> ( ! [X609: $i,X610: $i] :
( ! [X611: $i] :
( ( in @ X611 @ X609 )
=> ( in @ X611 @ X610 ) )
=> ( subset @ X609 @ X610 ) )
=> ( ! [X612: $i] : ( subset @ emptyset @ X612 )
=> ( ! [X613: $i,X614: $i,X615: $i] :
( ( subset @ X613 @ X614 )
=> ( ( in @ X615 @ X613 )
=> ( in @ X615 @ X614 ) ) )
=> ( ! [X616: $i,X617: $i,X618: $i] :
( ( subset @ X616 @ X617 )
=> ( ~ ( in @ X618 @ X617 )
=> ~ ( in @ X618 @ X616 ) ) )
=> ( ! [X619: $i,X620: $i,X621: $i] :
( ( in @ X621 @ X619 )
=> ( ~ ( in @ X621 @ X620 )
=> ~ ( subset @ X619 @ X620 ) ) )
=> ( ! [X622: $i,X623: $i] :
( ~ ( subset @ X622 @ X623 )
=> ( X622 != X623 ) )
=> ( ! [X624: $i,X625: $i,X626: $i] :
( ( in @ X626 @ X624 )
=> ( ~ ( in @ X626 @ X625 )
=> ( X624 != X625 ) ) )
=> ( ! [X627: $i] : ( subset @ X627 @ X627 )
=> ( ! [X628: $i,X629: $i,X630: $i] :
( ( subset @ X628 @ X629 )
=> ( ( subset @ X629 @ X630 )
=> ( subset @ X628 @ X630 ) ) )
=> ( ! [X631: $i,X632: $i] : ( subset @ X632 @ ( setadjoin @ X631 @ X632 ) )
=> ( ! [X633: $i,X634: $i,X635: $i] :
( ( subset @ X633 @ X635 )
=> ( subset @ X633 @ ( setadjoin @ X634 @ X635 ) ) )
=> ( ! [X636: $i,X637: $i] :
( ( subset @ X636 @ X637 )
=> ( in @ X636 @ ( powerset @ X637 ) ) )
=> ( ! [X638: $i,X639: $i] :
( ( subset @ X638 @ X639 )
=> ( ( subset @ X639 @ X638 )
=> ( X638 = X639 ) ) )
=> ( ! [X640: $i] :
( ( subset @ X640 @ emptyset )
=> ( X640 = emptyset ) )
=> ( ! [X641: $i,X642: $i] :
( ( subset @ X642 @ X641 )
=> ( in @ X642 @ ( powerset @ X641 ) ) )
=> ( ! [X643: $i,X644: $i] :
( ( in @ X644 @ ( powerset @ X643 ) )
=> ( subset @ X644 @ X643 ) )
=> ( ! [X645: $i] : ( in @ X645 @ ( powerset @ X645 ) )
=> ( ! [X646: $i,X647: $i] :
( ( subset @ X646 @ X647 )
=> ( subset @ ( powerset @ X646 ) @ ( powerset @ X647 ) ) )
=> ( ! [X648: $i,X649: $i > $o] : ( in @ ( dsetconstr @ X648 @ X649 ) @ ( powerset @ X648 ) )
=> ( ! [X650: $i,X651: $i > $o] : ( subset @ ( dsetconstr @ X650 @ X651 ) @ X650 )
=> ( ! [X652: $i,X653: $i,X654: $i] :
( ( in @ X654 @ X652 )
=> ( in @ X654 @ ( binunion @ X652 @ X653 ) ) )
=> ( ! [X655: $i,X656: $i] : ( in @ X656 @ ( setadjoin @ X655 @ ( setadjoin @ X656 @ emptyset ) ) )
=> ( ! [X657: $i,X658: $i,X659: $i] :
( ( in @ X659 @ X658 )
=> ( in @ X659 @ ( binunion @ X657 @ X658 ) ) )
=> ( ! [X660: $i,X661: $i,X662: $i,X663: $o] :
( ( in @ X662 @ ( binunion @ X660 @ X661 ) )
=> ( ( ( in @ X662 @ X660 )
=> X663 )
=> ( ( ( in @ X662 @ X661 )
=> X663 )
=> X663 ) ) )
=> ( ! [X664: $i,X665: $i,X666: $i] :
( ( in @ X666 @ ( binunion @ X664 @ X665 ) )
=> ( ( in @ X666 @ X664 )
| ( in @ X666 @ X665 ) ) )
=> ( ! [X667: $i,X668: $i] : ( subset @ X667 @ ( binunion @ X667 @ X668 ) )
=> ( ! [X669: $i,X670: $i] : ( subset @ X670 @ ( binunion @ X669 @ X670 ) )
=> ( ! [X671: $i,X672: $i,X673: $i] :
( ( in @ X673 @ X671 )
=> ( ( in @ X673 @ X672 )
=> ( in @ X673 @ ( binintersect @ X671 @ X672 ) ) ) )
=> ( ! [X674: $i,X675: $i,X676: $i] :
( ( subset @ X676 @ X674 )
=> ( ( subset @ X676 @ X675 )
=> ( subset @ X676 @ ( binintersect @ X674 @ X675 ) ) ) )
=> ( ! [X677: $i,X678: $i,X679: $i] :
( ( in @ X679 @ ( binintersect @ X677 @ X678 ) )
=> ( in @ X679 @ X677 ) )
=> ( ! [X680: $i,X681: $i] : ( subset @ ( binintersect @ X680 @ X681 ) @ X680 )
=> ( ! [X682: $i,X683: $i] :
( ( subset @ X682 @ X683 )
=> ( ( binintersect @ X682 @ X683 )
= X682 ) )
=> ( ! [X684: $i,X685: $i] :
( ( ( binintersect @ X684 @ X685 )
= X685 )
=> ( subset @ X685 @ X684 ) )
=> ( ! [X686: $i,X687: $i,X688: $i] :
( ( in @ X688 @ ( binintersect @ X686 @ X687 ) )
=> ( in @ X688 @ X687 ) )
=> ( ! [X689: $i,X690: $i] :
( ~ ? [X691: $i] :
( ( in @ X691 @ X689 )
& ( in @ X691 @ X690 ) )
=> ( ( binintersect @ X689 @ X690 )
= emptyset ) )
=> ( ! [X692: $i,X693: $i] : ( subset @ ( binintersect @ X692 @ X693 ) @ X693 )
=> ( ! [X694: $i,X695: $i] :
( ( subset @ X695 @ X694 )
=> ( ( binintersect @ X694 @ X695 )
= X695 ) )
=> ( ! [X696: $i,X697: $i] :
( ( ( binintersect @ X696 @ X697 )
= X696 )
=> ( subset @ X696 @ X697 ) )
=> ( ! [X698: $i,X699: $i,X700: $i] :
( ( binintersect @ X698 @ ( binunion @ X699 @ X700 ) )
= ( binunion @ ( binintersect @ X698 @ X699 ) @ ( binintersect @ X698 @ X700 ) ) )
=> ( ! [X701: $i,X702: $i,X703: $i] :
( ( in @ X703 @ X701 )
=> ( ~ ( in @ X703 @ X702 )
=> ( in @ X703 @ ( setminus @ X701 @ X702 ) ) ) )
=> ( ! [X704: $i,X705: $i,X706: $i] :
( ( in @ X706 @ ( setminus @ X704 @ X705 ) )
=> ( in @ X706 @ X704 ) )
=> ( ! [X707: $i,X708: $i,X709: $i] :
( ( in @ X709 @ ( setminus @ X707 @ X708 ) )
=> ~ ( in @ X709 @ X708 ) )
=> ( ! [X710: $i,X711: $i] :
( ( subset @ X710 @ X711 )
=> ( ( setminus @ X710 @ X711 )
= emptyset ) )
=> ( ! [X712: $i,X713: $i,X714: $i] :
( ~ ( in @ X714 @ ( setminus @ X712 @ X713 ) )
=> ( ( in @ X714 @ X712 )
=> ( in @ X714 @ X713 ) ) )
=> ( ! [X715: $i,X716: $i,X717: $i] :
( ~ ( in @ X717 @ ( setminus @ X715 @ X716 ) )
=> ( ~ ( in @ X717 @ X716 )
=> ~ ( in @ X717 @ X715 ) ) )
=> ( ! [X718: $i,X719: $i,X720: $i] :
( ~ ( in @ X720 @ X718 )
=> ~ ( in @ X720 @ ( setminus @ X718 @ X719 ) ) )
=> ( ! [X721: $i,X722: $i,X723: $i] :
( ( in @ X723 @ X722 )
=> ~ ( in @ X723 @ ( setminus @ X721 @ X722 ) ) )
=> ( ! [X724: $i,X725: $i] : ( subset @ ( setminus @ X724 @ X725 ) @ X724 )
=> ( ! [X726: $i,X727: $i] :
( ( ( setminus @ X726 @ X727 )
= emptyset )
=> ( subset @ X726 @ X727 ) )
=> ( ! [X728: $i,X729: $i,X730: $i] :
( ( in @ X730 @ ( symdiff @ X728 @ X729 ) )
=> ! [X731: $o] :
( ( ( in @ X730 @ X728 )
=> ( ~ ( in @ X730 @ X729 )
=> X731 ) )
=> ( ( ~ ( in @ X730 @ X728 )
=> ( ( in @ X730 @ X729 )
=> X731 ) )
=> X731 ) ) )
=> ( ! [X732: $i,X733: $i,X734: $i] :
( ( in @ X734 @ X732 )
=> ( ~ ( in @ X734 @ X733 )
=> ( in @ X734 @ ( symdiff @ X732 @ X733 ) ) ) )
=> ( ! [X735: $i,X736: $i,X737: $i] :
( ~ ( in @ X737 @ X735 )
=> ( ( in @ X737 @ X736 )
=> ( in @ X737 @ ( symdiff @ X735 @ X736 ) ) ) )
=> ( ! [X738: $i,X739: $i,X740: $i] :
( ( in @ X740 @ X738 )
=> ( ( in @ X740 @ X739 )
=> ~ ( in @ X740 @ ( symdiff @ X738 @ X739 ) ) ) )
=> ( ! [X741: $i,X742: $i,X743: $i] :
( ~ ( in @ X743 @ X741 )
=> ( ~ ( in @ X743 @ X742 )
=> ~ ( in @ X743 @ ( symdiff @ X741 @ X742 ) ) ) )
=> ( ! [X744: $i,X745: $i] : ( in @ X745 @ ( setadjoin @ X744 @ ( setadjoin @ X745 @ emptyset ) ) )
=> ( ! [X746: $i,X747: $i] : ( in @ X746 @ ( setunion @ ( setadjoin @ ( setadjoin @ X746 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X746 @ ( setadjoin @ X747 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X748: $i,X749: $i] : ( in @ X749 @ ( setunion @ ( setadjoin @ ( setadjoin @ X748 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X748 @ ( setadjoin @ X749 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X750: $i,X751: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X750 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X750 @ ( setadjoin @ X751 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X752: $i,X753: $i] : ( iskpair @ ( kpair @ X752 @ X753 ) )
=> ( ! [X754: $i,X755: $i] :
( ( in @ X755 @ X754 )
=> ( subset @ ( setadjoin @ X755 @ emptyset ) @ X754 ) )
=> ( ! [X756: $i,X757: $i] :
( ( in @ X757 @ X756 )
=> ( in @ ( setadjoin @ X757 @ emptyset ) @ ( powerset @ X756 ) ) )
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[singletoninpowunion]),c_0_139]),symdiffI2]),singletoninpowerset]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),c_0_140]),binintersectER]),disjointsetsI1]),nonemptyImpWitness]),binintersectRsub]),binintersectSubset4]),uniqinunit]),binintersectSubset1]),bs114d]),notinsingleton]),setminusI]),setminusEL]),eqinunit]),setminusER]),setminusSubset2]),singletonsswitch]),setminusERneg]),setminusELneg]),upairsetE]),setminusILneg]),setminusIRneg]),upairsetIL]),setminusLsub]),setminusSubset1]),symdiffE]),upairsetIR]),symdiffI1]),powerset__Cong]),symdiffIneg1]),symdiffIneg2]),secondinupair]),vacuousDall]),setukpairIL]),setukpairIR]),quantDeMorgan1]),kpairiskpair]),kpairp]),quantDeMorgan2]),singletonsubset]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_141]),c_0_142]),c_0_143]),inCongP]),in__Cong]),c_0_144]),c_0_145]),emptyset__Cong]),setadjoin__Cong]),binintersectI]),binintersectSubset5]),binintersectEL]),setunion__Cong]),omega__Cong]),c_0_146]),c_0_147]),c_0_148]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetE]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_149]),c_0_150]),binunionIL]),upairset2IR]),binunionIR]),setunionI]),binunionEcases]),setunionE]),subPowSU]),binunionE]),binunionLsub]),binunionRsub]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_151]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_152]),nonemptyE1]),c_0_153]),noeltsimpempty]),emptyI]),setext]),c_0_154]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_155]),c_0_156]),c_0_157]),c_0_158]),c_0_159]),wellorderingAx]),foundationAx]),c_0_160]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_161]) ).
thf(c_0_163,negated_conjecture,
! [X758: $i,X759: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X771: $i,X772: $i,X774: $i,X775: $i,X776: $i,X777: $i,X778: $i,X780: $i,X781: $i > $i > $o,X782: $i,X785: $i,X787: $i,X788: $i,X789: $i,X790: $i,X792: $i,X793: $i > $o,X794: $i,X795: $i > $o,X796: $i,X797: $i,X798: $i > $o,X799: $i,X800: $i,X801: $i > $o,X802: $i,X803: $i > $o,X805: $i,X806: $o,X807: $i,X808: $i,X809: $o,X810: $i,X811: $i,X812: $i > $o,X814: $i,X815: $i,X818: $i,X820: $i,X822: $i,X823: $i > $o,X824: $i,X825: $i,X827: $i,X828: $i > $o,X829: $i,X830: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X838: $i,X839: $i,X840: $o,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X855: $i,X856: $i,X857: $i,X858: $o,X860: $i,X861: $i,X862: $i > $o,X864: $i,X865: $i,X866: $i,X868: $i,X869: $i,X870: $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 > $o,X885: $i,X886: $i > $o,X887: $i,X888: $i,X889: $i > $o,X890: $i,X892: $i,X893: $i > $o,X895: $i,X896: $i,X897: $i > $o,X899: $i,X900: $i,X901: $i > $o,X902: $i,X904: $o,X905: $i,X906: $i > $o,X908: $i,X909: $i,X910: $i > $o,X911: $i,X913: $i > $o,X914: $i,X916: $i > $o,X917: $i,X920: $i > $o,X921: $i,X923: $i,X924: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i > $o,X932: $i,X933: $i,X934: $i > $o,X935: $i > $o,X938: $i,X939: $i,X940: $i,X941: $i,X942: $i,X943: $i,X944: $i,X945: $i,X946: $i > $o,X947: $i,X948: $i,X949: $i > $o,X950: $i > $o,X953: $i,X954: $i,X955: $i > $o,X956: $i > $o,X959: $i,X960: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i,X975: $i,X976: $i,X977: $i,X978: $i,X979: $i,X980: $i,X981: $i,X982: $i,X983: $i,X984: $i,X985: $i,X986: $i,X987: $i,X988: $i,X989: $i,X990: $i,X991: $i,X992: $i,X993: $i,X994: $i,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i,X1004: $i,X1005: $i,X1006: $i > $o,X1007: $i,X1008: $i > $o,X1009: $i,X1010: $i,X1011: $i,X1012: $i,X1013: $i,X1014: $i,X1015: $i,X1016: $i,X1017: $i,X1018: $i,X1019: $i,X1020: $o,X1021: $i,X1022: $i,X1023: $i,X1024: $i,X1025: $i,X1026: $i,X1027: $i,X1028: $i,X1029: $i,X1030: $i,X1031: $i,X1032: $i,X1033: $i,X1034: $i,X1035: $i,X1036: $i,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1041: $i,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $i,X1053: $i,X1054: $i,X1055: $i,X1056: $i,X1057: $i,X1058: $i,X1059: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i,X1081: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $o,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i,X1105: $i,X1106: $i,X1107: $i,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i] :
( ( ~ ( in @ ( esk1_2 @ X758 @ X759 ) @ X758 )
| ~ ( in @ ( esk1_2 @ X758 @ X759 ) @ X759 )
| ( X758 = X759 ) )
& ( ( in @ ( esk1_2 @ X758 @ X759 ) @ X758 )
| ( in @ ( esk1_2 @ X758 @ X759 ) @ X759 )
| ( X758 = X759 ) )
& ~ ( in @ X761 @ emptyset )
& ( ~ ( in @ X764 @ ( setadjoin @ X762 @ X763 ) )
| ( X764 = X762 )
| ( in @ X764 @ X763 ) )
& ( ( X764 != X762 )
| ( in @ X764 @ ( setadjoin @ X762 @ X763 ) ) )
& ( ~ ( in @ X764 @ X763 )
| ( in @ X764 @ ( setadjoin @ X762 @ X763 ) ) )
& ( ~ ( in @ X766 @ ( powerset @ X765 ) )
| ~ ( in @ X767 @ X766 )
| ( in @ X767 @ X765 ) )
& ( ( in @ ( esk2_2 @ X768 @ X769 ) @ X769 )
| ( in @ X769 @ ( powerset @ X768 ) ) )
& ( ~ ( in @ ( esk2_2 @ X768 @ X769 ) @ X768 )
| ( in @ X769 @ ( powerset @ X768 ) ) )
& ( ( in @ X772 @ ( esk3_2 @ X771 @ X772 ) )
| ~ ( in @ X772 @ ( setunion @ X771 ) ) )
& ( ( in @ ( esk3_2 @ X771 @ X772 ) @ X771 )
| ~ ( in @ X772 @ ( setunion @ X771 ) ) )
& ( ~ ( in @ X775 @ X776 )
| ~ ( in @ X776 @ X774 )
| ( in @ X775 @ ( setunion @ X774 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X777 @ omega )
| ( in @ ( setadjoin @ X777 @ X777 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X778 ) @ omega )
| ~ ( in @ emptyset @ X778 )
| ~ ( in @ X780 @ omega )
| ( in @ X780 @ X778 ) )
& ( ( in @ ( esk4_1 @ X778 ) @ X778 )
| ~ ( in @ emptyset @ X778 )
| ~ ( in @ X780 @ omega )
| ( in @ X780 @ X778 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X778 ) @ ( esk4_1 @ X778 ) ) @ X778 )
| ~ ( in @ emptyset @ X778 )
| ~ ( in @ X780 @ omega )
| ( in @ X780 @ X778 ) )
& ( ( in @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X782 )
| ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
| ( in @ ( esk5_2 @ X781 @ X782 ) @ X782 ) )
& ( ( X781 @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X785 )
| ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
| ( in @ ( esk5_2 @ X781 @ X782 ) @ X782 ) )
& ( ~ ( in @ X788 @ X782 )
| ~ ( X781 @ X788 @ X787 )
| ( in @ X787 @ ( esk6_2 @ X781 @ X782 ) )
| ( in @ ( esk5_2 @ X781 @ X782 ) @ X782 ) )
& ( ( in @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X782 )
| ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
| ~ ( exu @ ( X781 @ ( esk5_2 @ X781 @ X782 ) ) ) )
& ( ( X781 @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X785 )
| ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
| ~ ( exu @ ( X781 @ ( esk5_2 @ X781 @ X782 ) ) ) )
& ( ~ ( in @ X788 @ X782 )
| ~ ( X781 @ X788 @ X787 )
| ( in @ X787 @ ( esk6_2 @ X781 @ X782 ) )
| ~ ( exu @ ( X781 @ ( esk5_2 @ X781 @ X782 ) ) ) )
& ( ( in @ ( esk8_1 @ X789 ) @ X789 )
| ~ ( in @ X790 @ X789 ) )
& ( ~ ( in @ X792 @ ( esk8_1 @ X789 ) )
| ~ ( in @ X792 @ X789 )
| ~ ( in @ X790 @ X789 ) )
& epred1_0
& ( ~ ( exu @ X793 )
| ( X793 @ ( descr @ X793 ) ) )
& ( ~ ( in @ X796 @ X794 )
| ~ ( X795 @ X796 )
| ( in @ X796 @ ( dsetconstr @ X794 @ X795 ) ) )
& ( ~ ( in @ X799 @ ( dsetconstr @ X797 @ X798 ) )
| ( in @ X799 @ X797 ) )
& ( ~ ( in @ X802 @ ( dsetconstr @ X800 @ X801 ) )
| ( X801 @ X802 ) )
& ( ( X803 @ ( esk9_1 @ X803 ) )
| ~ ( exu @ X803 ) )
& ( ~ ( X803 @ X805 )
| ( ( esk9_1 @ X803 )
= X805 )
| ~ ( exu @ X803 ) )
& ( ~ ( in @ X807 @ ( prop2set @ X806 ) )
| X806 )
& ( ~ ( in @ X808 @ emptyset )
| X809 )
& ( ~ ( in @ X810 @ emptyset )
| ~ $true )
& ~ ( in @ X811 @ emptyset )
& ( ~ ( exu @ X812 )
| ( X812 @ ( esk10_1 @ X812 ) ) )
& ( ( in @ ( esk12_2 @ X814 @ X815 ) @ X815 )
| ( X814 = X815 )
| ( in @ ( esk11_2 @ X814 @ X815 ) @ X814 ) )
& ( ~ ( in @ ( esk12_2 @ X814 @ X815 ) @ X814 )
| ( X814 = X815 )
| ( in @ ( esk11_2 @ X814 @ X815 ) @ X814 ) )
& ( ( in @ ( esk12_2 @ X814 @ X815 ) @ X815 )
| ( X814 = X815 )
| ~ ( in @ ( esk11_2 @ X814 @ X815 ) @ X815 ) )
& ( ~ ( in @ ( esk12_2 @ X814 @ X815 ) @ X814 )
| ( X814 = X815 )
| ~ ( in @ ( esk11_2 @ X814 @ X815 ) @ X815 ) )
& ( ( in @ ( esk13_1 @ X818 ) @ X818 )
| ( X818 = emptyset ) )
& ( ( in @ ( esk14_1 @ X820 ) @ X820 )
| ( X820 = emptyset ) )
& ( ~ ( in @ X824 @ ( dsetconstr @ X822 @ X823 ) )
| ( X823 @ X824 )
| ~ ( in @ X824 @ X822 ) )
& ( ~ ( X823 @ X824 )
| ( in @ X824 @ ( dsetconstr @ X822 @ X823 ) )
| ~ ( in @ X824 @ X822 ) )
& ( ~ ( nonempty @ X825 )
| ( in @ ( esk15_1 @ X825 ) @ X825 ) )
& ( ~ ( in @ X829 @ X827 )
| ~ ( X828 @ X829 )
| ( nonempty @ ( dsetconstr @ X827 @ X828 ) ) )
& ( ~ ( in @ X831 @ X830 )
| ( nonempty @ X830 ) )
& ( in @ X832 @ ( setadjoin @ X832 @ X833 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X836 @ X835 )
| ( in @ X836 @ ( setadjoin @ X834 @ X835 ) ) )
& ( ( in @ X839 @ X838 )
| X840
| ( X839 = X837 )
| ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
& ( ~ X840
| X840
| ( X839 = X837 )
| ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
& ( ( in @ X839 @ X838 )
| X840
| ~ X840
| ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
& ( ~ X840
| X840
| ~ X840
| ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
& ( ~ ( in @ X843 @ ( setadjoin @ X841 @ X842 ) )
| ( X843 = X841 )
| ( in @ X843 @ X842 ) )
& ( ( dsetconstr @ X844
@ ^ [Z0: $i] : $true )
= X844 )
& ( ( in @ ( esk16_2 @ X845 @ X846 ) @ X846 )
| ( in @ X846 @ ( powerset @ X845 ) ) )
& ( ~ ( in @ ( esk16_2 @ X845 @ X846 ) @ X845 )
| ( in @ X846 @ ( powerset @ X845 ) ) )
& ( in @ emptyset @ ( powerset @ X848 ) )
& ( in @ emptyset @ ( powerset @ X849 ) )
& ( ~ ( in @ X851 @ ( powerset @ X850 ) )
| ~ ( in @ X852 @ X851 )
| ( in @ X852 @ X850 ) )
& ( ~ ( in @ X854 @ X855 )
| ~ ( in @ X855 @ X853 )
| ( in @ X854 @ ( setunion @ X853 ) ) )
& ( ( in @ X857 @ ( esk17_3 @ X856 @ X857 @ X858 ) )
| X858
| ~ ( in @ X857 @ ( setunion @ X856 ) ) )
& ( ( in @ ( esk17_3 @ X856 @ X857 @ X858 ) @ X856 )
| X858
| ~ ( in @ X857 @ ( setunion @ X856 ) ) )
& ( ~ X858
| X858
| ~ ( in @ X857 @ ( setunion @ X856 ) ) )
& ( ~ ( in @ X861 @ X860 )
| ( in @ X861 @ ( powerset @ ( setunion @ X860 ) ) ) )
& ( ~ ( X862 @ X864 )
| ( X864
= ( esk18_1 @ X862 ) )
| ~ ( exu @ X862 ) )
& ( ( X865
!= ( esk18_1 @ X862 ) )
| ( X862 @ X865 )
| ~ ( exu @ X862 ) )
& ( ( in @ ( esk19_1 @ X866 ) @ X866 )
| ~ ( nonempty @ X866 ) )
& ( $true
| ~ ( nonempty @ X866 ) )
& ( ~ ( in @ X868 @ ( setadjoin @ X869 @ emptyset ) )
| ( X868 = X869 ) )
& ( ( X870 = X871 )
| ~ ( in @ X871 @ ( setadjoin @ X870 @ emptyset ) ) )
& ( ( X872 != X873 )
| ( in @ X872 @ ( setadjoin @ X873 @ emptyset ) ) )
& ( ~ ( in @ X874 @ ( setadjoin @ X875 @ emptyset ) )
| ( in @ X875 @ ( setadjoin @ X874 @ emptyset ) ) )
& ( ~ ( in @ X878 @ ( setadjoin @ X876 @ ( setadjoin @ X877 @ emptyset ) ) )
| ( X878 = X876 )
| ( X878 = X877 ) )
& ( in @ X879 @ ( setadjoin @ X879 @ ( setadjoin @ X880 @ emptyset ) ) )
& ( in @ X882 @ ( setadjoin @ X881 @ ( setadjoin @ X882 @ emptyset ) ) )
& ( ~ ( in @ X885 @ X883 )
| ~ ( X884 @ X885 )
| ( ( dsetconstr @ X883 @ X884 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X887 @ emptyset )
| ( X886 @ X887 ) )
& ( ( in @ ( esk20_2 @ X888 @ X889 ) @ X888 )
| ~ ( in @ X890 @ X888 )
| ( X889 @ X890 ) )
& ( ~ ( X889 @ ( esk20_2 @ X888 @ X889 ) )
| ~ ( in @ X890 @ X888 )
| ( X889 @ X890 ) )
& ( ( in @ ( esk21_2 @ X892 @ X893 ) @ X892 )
| ~ ( in @ X895 @ X892 )
| ~ ( X893 @ X895 ) )
& ( ( X893 @ ( esk21_2 @ X892 @ X893 ) )
| ~ ( in @ X895 @ X892 )
| ~ ( X893 @ X895 ) )
& ( ( in @ ( esk22_2 @ X896 @ X897 ) @ X896 )
| ~ ( in @ X899 @ X896 )
| ~ ( X897 @ X899 ) )
& ( ( X897 @ ( esk22_2 @ X896 @ X897 ) )
| ~ ( in @ X899 @ X896 )
| ~ ( X897 @ X899 ) )
& ( ( in @ ( esk23_2 @ X900 @ X901 ) @ X900 )
| ~ ( in @ X902 @ X900 )
| ( X901 @ X902 ) )
& ( ~ ( X901 @ ( esk23_2 @ X900 @ X901 ) )
| ~ ( in @ X902 @ X900 )
| ( X901 @ X902 ) )
& ( ~ X904
| ( in @ emptyset @ ( prop2set @ X904 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X905 @ X906 ) @ X905 )
| ~ ( in @ X908 @ X905 )
| ~ ( X906 @ X908 ) )
& ( ( X906 @ ( esk24_2 @ X905 @ X906 ) )
| ~ ( in @ X908 @ X905 )
| ~ ( X906 @ X908 ) )
& ( ( in @ ( esk25_2 @ X909 @ X910 ) @ X909 )
| ~ ( in @ X911 @ X909 )
| ( X910 @ X911 ) )
& ( ~ ( X910 @ ( esk25_2 @ X909 @ X910 ) )
| ~ ( in @ X911 @ X909 )
| ( X910 @ X911 ) )
& ( ( X913 @ ( esk26_2 @ X913 @ X914 ) )
| ~ ( X913 @ X914 )
| ( exu @ X913 ) )
& ( ( X914
!= ( esk26_2 @ X913 @ X914 ) )
| ~ ( X913 @ X914 )
| ( exu @ X913 ) )
& ( ( X916 @ ( esk27_1 @ X916 ) )
| ( exu @ X916 )
| ~ ( X916 @ X917 ) )
& ( ( X916 @ ( esk28_1 @ X916 ) )
| ( exu @ X916 )
| ~ ( X916 @ X917 ) )
& ( ( ( esk27_1 @ X916 )
!= ( esk28_1 @ X916 ) )
| ( exu @ X916 )
| ~ ( X916 @ X917 ) )
& ( ~ ( X920 @ ( esk29_2 @ X920 @ X921 ) )
| ( ( esk29_2 @ X920 @ X921 )
!= X921 )
| ( exu @ X920 ) )
& ( ( X920 @ ( esk29_2 @ X920 @ X921 ) )
| ( ( esk29_2 @ X920 @ X921 )
= X921 )
| ( exu @ X920 ) )
& ( ( X923 != X924 )
| ( X925 != X926 )
| ~ ( in @ X925 @ X923 )
| ( in @ X926 @ X924 ) )
& ( ~ ( in @ X929 @ X927 )
| ( in @ X930 @ X928 )
| ( X929 != X930 )
| ( X927 != X928 ) )
& ( ~ ( in @ X930 @ X928 )
| ( in @ X929 @ X927 )
| ( X929 != X930 )
| ( X927 != X928 ) )
& ( ~ ( exu @ X931 )
| ~ ( X931 @ X932 )
| ~ ( X931 @ X933 )
| ( X932 = X933 ) )
& ( ~ ( exu @ X934 )
| ( exu @ X935 )
| ( ( esk30_2 @ X934 @ X935 )
= ( esk31_2 @ X934 @ X935 ) ) )
& ( ~ ( exu @ X935 )
| ( exu @ X934 )
| ( ( esk30_2 @ X934 @ X935 )
= ( esk31_2 @ X934 @ X935 ) ) )
& ( ~ ( exu @ X934 )
| ( exu @ X935 )
| ~ ( X934 @ ( esk30_2 @ X934 @ X935 ) )
| ~ ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
& ( ~ ( exu @ X935 )
| ( exu @ X934 )
| ~ ( X934 @ ( esk30_2 @ X934 @ X935 ) )
| ~ ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
& ( ~ ( exu @ X934 )
| ( exu @ X935 )
| ( X934 @ ( esk30_2 @ X934 @ X935 ) )
| ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
& ( ~ ( exu @ X935 )
| ( exu @ X934 )
| ( X934 @ ( esk30_2 @ X934 @ X935 ) )
| ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
& ( emptyset = emptyset )
& ( ( X938 != X939 )
| ( X940 != X941 )
| ( ( setadjoin @ X938 @ X940 )
= ( setadjoin @ X939 @ X941 ) ) )
& ( ( X942 != X943 )
| ( ( powerset @ X942 )
= ( powerset @ X943 ) ) )
& ( ( X944 != X945 )
| ( ( setunion @ X944 )
= ( setunion @ X945 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X946 )
| ~ ( X946 @ X947 )
| ~ ( X946 @ X948 )
| ( X947 = X948 ) )
& ( ( ( esk32_2 @ X949 @ X950 )
= ( esk33_2 @ X949 @ X950 ) )
| ~ ( exu @ X949 )
| ~ ( exu @ X950 )
| ( ( descr @ X949 )
= ( descr @ X950 ) ) )
& ( ~ ( X949 @ ( esk32_2 @ X949 @ X950 ) )
| ~ ( X950 @ ( esk33_2 @ X949 @ X950 ) )
| ~ ( exu @ X949 )
| ~ ( exu @ X950 )
| ( ( descr @ X949 )
= ( descr @ X950 ) ) )
& ( ( X949 @ ( esk32_2 @ X949 @ X950 ) )
| ( X950 @ ( esk33_2 @ X949 @ X950 ) )
| ~ ( exu @ X949 )
| ~ ( exu @ X950 )
| ( ( descr @ X949 )
= ( descr @ X950 ) ) )
& ( ( in @ ( esk34_4 @ X953 @ X954 @ X955 @ X956 ) @ X953 )
| ( ( dsetconstr @ X953 @ X955 )
= ( dsetconstr @ X954 @ X956 ) )
| ( X953 != X954 ) )
& ( ( in @ ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) @ X954 )
| ( ( dsetconstr @ X953 @ X955 )
= ( dsetconstr @ X954 @ X956 ) )
| ( X953 != X954 ) )
& ( ( ( esk34_4 @ X953 @ X954 @ X955 @ X956 )
= ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) )
| ( ( dsetconstr @ X953 @ X955 )
= ( dsetconstr @ X954 @ X956 ) )
| ( X953 != X954 ) )
& ( ~ ( X955 @ ( esk34_4 @ X953 @ X954 @ X955 @ X956 ) )
| ~ ( X956 @ ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) )
| ( ( dsetconstr @ X953 @ X955 )
= ( dsetconstr @ X954 @ X956 ) )
| ( X953 != X954 ) )
& ( ( X955 @ ( esk34_4 @ X953 @ X954 @ X955 @ X956 ) )
| ( X956 @ ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) )
| ( ( dsetconstr @ X953 @ X955 )
= ( dsetconstr @ X954 @ X956 ) )
| ( X953 != X954 ) )
& ( ( in @ ( esk36_2 @ X959 @ X960 ) @ X959 )
| ( subset @ X959 @ X960 ) )
& ( ~ ( in @ ( esk36_2 @ X959 @ X960 ) @ X960 )
| ( subset @ X959 @ X960 ) )
& ( ( X962 != X963 )
| ( subset @ X963 @ X962 ) )
& ( ( X964 != X965 )
| ( subset @ X964 @ X965 ) )
& ( ( in @ ( esk37_2 @ X966 @ X967 ) @ X966 )
| ( subset @ X966 @ X967 ) )
& ( ~ ( in @ ( esk37_2 @ X966 @ X967 ) @ X967 )
| ( subset @ X966 @ X967 ) )
& ( subset @ emptyset @ X969 )
& ( ~ ( subset @ X970 @ X971 )
| ~ ( in @ X972 @ X970 )
| ( in @ X972 @ X971 ) )
& ( ~ ( subset @ X973 @ X974 )
| ( in @ X975 @ X974 )
| ~ ( in @ X975 @ X973 ) )
& ( ~ ( in @ X978 @ X976 )
| ( in @ X978 @ X977 )
| ~ ( subset @ X976 @ X977 ) )
& ( ( subset @ X979 @ X980 )
| ( X979 != X980 ) )
& ( ~ ( in @ X983 @ X981 )
| ( in @ X983 @ X982 )
| ( X981 != X982 ) )
& ( subset @ X984 @ X984 )
& ( ~ ( subset @ X985 @ X986 )
| ~ ( subset @ X986 @ X987 )
| ( subset @ X985 @ X987 ) )
& ( subset @ X989 @ ( setadjoin @ X988 @ X989 ) )
& ( ~ ( subset @ X990 @ X992 )
| ( subset @ X990 @ ( setadjoin @ X991 @ X992 ) ) )
& ( ~ ( subset @ X993 @ X994 )
| ( in @ X993 @ ( powerset @ X994 ) ) )
& ( ~ ( subset @ X995 @ X996 )
| ~ ( subset @ X996 @ X995 )
| ( X995 = X996 ) )
& ( ~ ( subset @ X997 @ emptyset )
| ( X997 = emptyset ) )
& ( ~ ( subset @ X999 @ X998 )
| ( in @ X999 @ ( powerset @ X998 ) ) )
& ( ~ ( in @ X1001 @ ( powerset @ X1000 ) )
| ( subset @ X1001 @ X1000 ) )
& ( in @ X1002 @ ( powerset @ X1002 ) )
& ( ~ ( subset @ X1003 @ X1004 )
| ( subset @ ( powerset @ X1003 ) @ ( powerset @ X1004 ) ) )
& ( in @ ( dsetconstr @ X1005 @ X1006 ) @ ( powerset @ X1005 ) )
& ( subset @ ( dsetconstr @ X1007 @ X1008 ) @ X1007 )
& ( ~ ( in @ X1011 @ X1009 )
| ( in @ X1011 @ ( binunion @ X1009 @ X1010 ) ) )
& ( in @ X1013 @ ( setadjoin @ X1012 @ ( setadjoin @ X1013 @ emptyset ) ) )
& ( ~ ( in @ X1016 @ X1015 )
| ( in @ X1016 @ ( binunion @ X1014 @ X1015 ) ) )
& ( ( in @ X1019 @ X1018 )
| X1020
| ( in @ X1019 @ X1017 )
| ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
& ( ~ X1020
| X1020
| ( in @ X1019 @ X1017 )
| ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
& ( ( in @ X1019 @ X1018 )
| X1020
| ~ X1020
| ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
& ( ~ X1020
| X1020
| ~ X1020
| ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
& ( ~ ( in @ X1023 @ ( binunion @ X1021 @ X1022 ) )
| ( in @ X1023 @ X1021 )
| ( in @ X1023 @ X1022 ) )
& ( subset @ X1024 @ ( binunion @ X1024 @ X1025 ) )
& ( subset @ X1027 @ ( binunion @ X1026 @ X1027 ) )
& ( ~ ( in @ X1030 @ X1028 )
| ~ ( in @ X1030 @ X1029 )
| ( in @ X1030 @ ( binintersect @ X1028 @ X1029 ) ) )
& ( ~ ( subset @ X1033 @ X1031 )
| ~ ( subset @ X1033 @ X1032 )
| ( subset @ X1033 @ ( binintersect @ X1031 @ X1032 ) ) )
& ( ~ ( in @ X1036 @ ( binintersect @ X1034 @ X1035 ) )
| ( in @ X1036 @ X1034 ) )
& ( subset @ ( binintersect @ X1037 @ X1038 ) @ X1037 )
& ( ~ ( subset @ X1039 @ X1040 )
| ( ( binintersect @ X1039 @ X1040 )
= X1039 ) )
& ( ( ( binintersect @ X1041 @ X1042 )
!= X1042 )
| ( subset @ X1042 @ X1041 ) )
& ( ~ ( in @ X1045 @ ( binintersect @ X1043 @ X1044 ) )
| ( in @ X1045 @ X1044 ) )
& ( ( in @ ( esk38_2 @ X1046 @ X1047 ) @ X1046 )
| ( ( binintersect @ X1046 @ X1047 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1046 @ X1047 ) @ X1047 )
| ( ( binintersect @ X1046 @ X1047 )
= emptyset ) )
& ( subset @ ( binintersect @ X1049 @ X1050 ) @ X1050 )
& ( ~ ( subset @ X1052 @ X1051 )
| ( ( binintersect @ X1051 @ X1052 )
= X1052 ) )
& ( ( ( binintersect @ X1053 @ X1054 )
!= X1053 )
| ( subset @ X1053 @ X1054 ) )
& ( ( binintersect @ X1055 @ ( binunion @ X1056 @ X1057 ) )
= ( binunion @ ( binintersect @ X1055 @ X1056 ) @ ( binintersect @ X1055 @ X1057 ) ) )
& ( ~ ( in @ X1060 @ X1058 )
| ( in @ X1060 @ X1059 )
| ( in @ X1060 @ ( setminus @ X1058 @ X1059 ) ) )
& ( ~ ( in @ X1063 @ ( setminus @ X1061 @ X1062 ) )
| ( in @ X1063 @ X1061 ) )
& ( ~ ( in @ X1066 @ ( setminus @ X1064 @ X1065 ) )
| ~ ( in @ X1066 @ X1065 ) )
& ( ~ ( subset @ X1067 @ X1068 )
| ( ( setminus @ X1067 @ X1068 )
= emptyset ) )
& ( ( in @ X1071 @ ( setminus @ X1069 @ X1070 ) )
| ~ ( in @ X1071 @ X1069 )
| ( in @ X1071 @ X1070 ) )
& ( ( in @ X1074 @ ( setminus @ X1072 @ X1073 ) )
| ( in @ X1074 @ X1073 )
| ~ ( in @ X1074 @ X1072 ) )
& ( ( in @ X1077 @ X1075 )
| ~ ( in @ X1077 @ ( setminus @ X1075 @ X1076 ) ) )
& ( ~ ( in @ X1080 @ X1079 )
| ~ ( in @ X1080 @ ( setminus @ X1078 @ X1079 ) ) )
& ( subset @ ( setminus @ X1081 @ X1082 ) @ X1081 )
& ( ( ( setminus @ X1083 @ X1084 )
!= emptyset )
| ( subset @ X1083 @ X1084 ) )
& ( ~ ( in @ X1087 @ X1085 )
| X1088
| ( in @ X1087 @ X1085 )
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ( in @ X1087 @ X1086 )
| X1088
| ( in @ X1087 @ X1085 )
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ~ X1088
| X1088
| ( in @ X1087 @ X1085 )
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ~ ( in @ X1087 @ X1085 )
| X1088
| ~ ( in @ X1087 @ X1086 )
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ( in @ X1087 @ X1086 )
| X1088
| ~ ( in @ X1087 @ X1086 )
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ~ X1088
| X1088
| ~ ( in @ X1087 @ X1086 )
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ~ ( in @ X1087 @ X1085 )
| X1088
| ~ X1088
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ( in @ X1087 @ X1086 )
| X1088
| ~ X1088
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ~ X1088
| X1088
| ~ X1088
| ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
& ( ~ ( in @ X1091 @ X1089 )
| ( in @ X1091 @ X1090 )
| ( in @ X1091 @ ( symdiff @ X1089 @ X1090 ) ) )
& ( ( in @ X1094 @ X1092 )
| ~ ( in @ X1094 @ X1093 )
| ( in @ X1094 @ ( symdiff @ X1092 @ X1093 ) ) )
& ( ~ ( in @ X1097 @ X1095 )
| ~ ( in @ X1097 @ X1096 )
| ~ ( in @ X1097 @ ( symdiff @ X1095 @ X1096 ) ) )
& ( ( in @ X1100 @ X1098 )
| ( in @ X1100 @ X1099 )
| ~ ( in @ X1100 @ ( symdiff @ X1098 @ X1099 ) ) )
& ( in @ X1102 @ ( setadjoin @ X1101 @ ( setadjoin @ X1102 @ emptyset ) ) )
& ( in @ X1103 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1103 @ ( setadjoin @ X1104 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1106 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1105 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1105 @ ( setadjoin @ X1106 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1107 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1107 @ ( setadjoin @ X1108 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1109 @ X1110 ) )
& ( ~ ( in @ X1112 @ X1111 )
| ( subset @ ( setadjoin @ X1112 @ emptyset ) @ X1111 ) )
& ( ~ ( in @ X1114 @ X1113 )
| ( in @ ( setadjoin @ X1114 @ emptyset ) @ ( powerset @ X1113 ) ) )
& ( in @ esk41_0 @ esk39_0 )
& ~ ( in @ ( setadjoin @ esk41_0 @ emptyset ) @ ( powerset @ ( binunion @ esk39_0 @ esk40_0 ) ) ) ),
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_162])])])])])])]) ).
thf(c_0_164,negated_conjecture,
~ ( in @ ( setadjoin @ esk41_0 @ emptyset ) @ ( powerset @ ( binunion @ esk39_0 @ esk40_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_165,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_166,negated_conjecture,
~ ( subset @ ( setadjoin @ esk41_0 @ emptyset ) @ ( binunion @ esk39_0 @ esk40_0 ) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
thf(c_0_167,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_168,negated_conjecture,
~ ( in @ esk41_0 @ ( binunion @ esk39_0 @ esk40_0 ) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
thf(c_0_169,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( binunion @ X3 @ X4 ) )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_170,negated_conjecture,
in @ esk41_0 @ esk39_0,
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_171,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU623^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:01:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.59 # Version: 3.1.0-ho
% 0.57/0.59 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.59 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.59 # Starting ehoh_best5 with 300s (1) cores
% 0.57/0.59 # Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.59 # Starting new_bool_5 with 300s (1) cores
% 0.57/0.59 # Starting pre_casc_3 with 300s (1) cores
% 0.57/0.59 # Starting ho_unfolding_8 with 300s (1) cores
% 0.57/0.59 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.57/0.59 # Starting new_bool_3 with 300s (1) cores
% 0.57/0.59 # Starting new_ho_5 with 300s (1) cores
% 0.57/0.59 # new_bool_5 with pid 20149 completed with status 0
% 0.57/0.59 # Result found by new_bool_5
% 0.57/0.59 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.59 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.59 # Starting ehoh_best5 with 300s (1) cores
% 0.57/0.59 # Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.59 # Starting new_bool_5 with 300s (1) cores
% 0.57/0.59 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.57/0.59 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.57/0.59 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.59 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.57/0.59 # new_ho_10_cnf2 with pid 20175 completed with status 0
% 0.57/0.59 # Result found by new_ho_10_cnf2
% 0.57/0.59 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.59 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.59 # Starting ehoh_best5 with 300s (1) cores
% 0.57/0.59 # Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.59 # Starting new_bool_5 with 300s (1) cores
% 0.57/0.59 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.57/0.59 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.57/0.59 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.59 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.57/0.59 # Preprocessing time : 0.005 s
% 0.57/0.59 # Presaturation interreduction done
% 0.57/0.59
% 0.57/0.59 # Proof found!
% 0.57/0.59 # SZS status Theorem
% 0.57/0.59 # SZS output start CNFRefutation
% See solution above
% 0.57/0.59 # Parsed axioms : 307
% 0.57/0.59 # Removed by relevancy pruning/SinE : 168
% 0.57/0.59 # Initial clauses : 220
% 0.57/0.59 # Removed in clause preprocessing : 25
% 0.57/0.59 # Initial clauses in saturation : 195
% 0.57/0.59 # Processed clauses : 316
% 0.57/0.59 # ...of these trivial : 6
% 0.57/0.59 # ...subsumed : 36
% 0.57/0.59 # ...remaining for further processing : 274
% 0.57/0.59 # Other redundant clauses eliminated : 16
% 0.57/0.59 # Clauses deleted for lack of memory : 0
% 0.57/0.59 # Backward-subsumed : 0
% 0.57/0.59 # Backward-rewritten : 3
% 0.57/0.59 # Generated clauses : 353
% 0.57/0.59 # ...of the previous two non-redundant : 278
% 0.57/0.59 # ...aggressively subsumed : 0
% 0.57/0.59 # Contextual simplify-reflections : 0
% 0.57/0.59 # Paramodulations : 337
% 0.57/0.59 # Factorizations : 0
% 0.57/0.59 # NegExts : 0
% 0.57/0.59 # Equation resolutions : 16
% 0.57/0.59 # Disequality decompositions : 0
% 0.57/0.59 # Total rewrite steps : 75
% 0.57/0.59 # ...of those cached : 43
% 0.57/0.59 # Propositional unsat checks : 0
% 0.57/0.59 # Propositional check models : 0
% 0.57/0.59 # Propositional check unsatisfiable : 0
% 0.57/0.59 # Propositional clauses : 0
% 0.57/0.59 # Propositional clauses after purity: 0
% 0.57/0.59 # Propositional unsat core size : 0
% 0.57/0.59 # Propositional preprocessing time : 0.000
% 0.57/0.59 # Propositional encoding time : 0.000
% 0.57/0.59 # Propositional solver time : 0.000
% 0.57/0.59 # Success case prop preproc time : 0.000
% 0.57/0.59 # Success case prop encoding time : 0.000
% 0.57/0.59 # Success case prop solver time : 0.000
% 0.57/0.59 # Current number of processed clauses : 98
% 0.57/0.59 # Positive orientable unit clauses : 40
% 0.57/0.59 # Positive unorientable unit clauses: 0
% 0.57/0.59 # Negative unit clauses : 5
% 0.57/0.59 # Non-unit-clauses : 53
% 0.57/0.59 # Current number of unprocessed clauses: 316
% 0.57/0.59 # ...number of literals in the above : 757
% 0.57/0.59 # Current number of archived formulas : 0
% 0.57/0.59 # Current number of archived clauses : 165
% 0.57/0.59 # Clause-clause subsumption calls (NU) : 3484
% 0.57/0.59 # Rec. Clause-clause subsumption calls : 1815
% 0.57/0.59 # Non-unit clause-clause subsumptions : 23
% 0.57/0.59 # Unit Clause-clause subsumption calls : 39
% 0.57/0.59 # Rewrite failures with RHS unbound : 0
% 0.57/0.59 # BW rewrite match attempts : 16
% 0.57/0.59 # BW rewrite match successes : 2
% 0.57/0.59 # Condensation attempts : 316
% 0.57/0.59 # Condensation successes : 4
% 0.57/0.59 # Termbank termtop insertions : 34972
% 0.57/0.59 # Search garbage collected termcells : 12061
% 0.57/0.59
% 0.57/0.59 # -------------------------------------------------
% 0.57/0.59 # User time : 0.056 s
% 0.57/0.59 # System time : 0.013 s
% 0.57/0.59 # Total time : 0.070 s
% 0.57/0.59 # Maximum resident set size: 4864 pages
% 0.57/0.59
% 0.57/0.59 # -------------------------------------------------
% 0.57/0.59 # User time : 0.065 s
% 0.57/0.59 # System time : 0.016 s
% 0.57/0.59 # Total time : 0.081 s
% 0.57/0.59 # Maximum resident set size: 2068 pages
% 0.57/0.59 % E---3.1 exiting
% 0.57/0.59 % E exiting
%------------------------------------------------------------------------------