%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU621^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 135.83s 20.01s
% Output : CNFRefutation 135.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 334
% Syntax : Number of formulae : 366 ( 3 unt; 196 typ; 0 def)
% Number of atoms : 1414 ( 203 equ; 0 cnn)
% Maximal formula atoms : 414 ( 8 avg)
% Number of connectives : 4724 ( 358 ~; 331 |; 260 &;2888 @)
% ( 195 <=>; 692 =>; 0 <=; 0 <~>)
% Maximal formula depth : 523 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 251 ( 251 >; 0 *; 0 +; 0 <<)
% Number of symbols : 199 ( 196 usr; 144 con; 0-4 aty)
% Number of variables : 1182 ( 59 ^1058 !; 65 ?;1182 :)
% 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,
epred1_0: $o ).
thf(decl_183,type,
esk1_2: $i > $i > $i ).
thf(decl_184,type,
esk2_2: $i > $i > $i ).
thf(decl_185,type,
esk3_2: $i > $i > $i ).
thf(decl_186,type,
esk4_1: $i > $i ).
thf(decl_187,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_188,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_189,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_190,type,
esk8_1: $i > $i ).
thf(decl_191,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_192,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_193,type,
esk11_2: $i > $i > $i ).
thf(decl_194,type,
esk12_2: $i > $i > $i ).
thf(decl_195,type,
esk13_1: $i > $i ).
thf(decl_196,type,
esk14_1: $i > $i ).
thf(decl_197,type,
esk15_1: $i > $i ).
thf(decl_198,type,
esk16_2: $i > $i > $i ).
thf(decl_199,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_200,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_201,type,
esk19_1: $i > $i ).
thf(decl_202,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_203,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_204,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_205,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_206,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_207,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_208,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_209,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_210,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_211,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_212,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_213,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_214,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_215,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_216,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_217,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_218,type,
esk36_2: $i > $i > $i ).
thf(decl_219,type,
esk37_2: $i > $i > $i ).
thf(decl_220,type,
esk38_2: $i > $i > $i ).
thf(decl_221,type,
esk39_0: $i ).
thf(decl_222,type,
esk40_0: $i ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(singletonsubset,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
=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
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/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_137,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_138,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_139,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_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_149,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_150,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_151,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_152,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_153,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_154,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_155,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_156,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_157,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_158,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_159,plain,
( epred1_0
<=> ! [X413: $i] :
? [X414: $i] :
( ! [X415: $i] :
( ( in @ X415 @ X414 )
=> ! [X416: $i] :
( ( in @ X416 @ X415 )
=> ( in @ X416 @ X413 ) ) )
& ! [X417: $i,X418: $i] :
( ( ( in @ X417 @ X413 )
& ( in @ X418 @ X413 ) )
=> ( ! [X419: $i] :
( ( in @ X419 @ X414 )
=> ( ( in @ X417 @ X419 )
<=> ( in @ X418 @ X419 ) ) )
=> ( X417 = X418 ) ) )
& ! [X420: $i,X421: $i] :
( ( ( in @ X420 @ X414 )
& ( in @ X421 @ X414 ) )
=> ( ! [X422: $i] :
( ( in @ X422 @ X420 )
=> ( in @ X422 @ X421 ) )
| ! [X423: $i] :
( ( in @ X423 @ X421 )
=> ( in @ X423 @ X420 ) ) ) )
& ! [X424: $i] :
( ( ! [X425: $i] :
( ( in @ X425 @ X424 )
=> ( in @ X425 @ X413 ) )
& ? [X426: $i] : ( in @ X426 @ X424 ) )
=> ? [X427: $i,X428: $i] :
( ( in @ X427 @ X414 )
& ( in @ X428 @ X424 )
& ~ ? [X429: $i] :
( ( in @ X429 @ X427 )
& ( in @ X429 @ X424 ) )
& ! [X430: $i] :
( ( in @ X430 @ X414 )
=> ( ! [X431: $i] :
( ( in @ X431 @ X430 )
=> ( in @ X431 @ X427 ) )
| ( in @ X428 @ X430 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_160,negated_conjecture,
~ ( ! [X386: $i,X387: $i] :
( ! [X388: $i] :
( ( in @ X388 @ X386 )
<=> ( in @ X388 @ X387 ) )
=> ( X386 = X387 ) )
=> ( ! [X389: $i] :
~ ( in @ X389 @ emptyset )
=> ( ! [X390: $i,X391: $i,X392: $i] :
( ( in @ X392 @ ( setadjoin @ X390 @ X391 ) )
<=> ( ( X392 = X390 )
| ( in @ X392 @ X391 ) ) )
=> ( ! [X393: $i,X394: $i] :
( ( in @ X394 @ ( powerset @ X393 ) )
<=> ! [X395: $i] :
( ( in @ X395 @ X394 )
=> ( in @ X395 @ X393 ) ) )
=> ( ! [X396: $i,X397: $i] :
( ( in @ X397 @ ( setunion @ X396 ) )
<=> ? [X398: $i] :
( ( in @ X397 @ X398 )
& ( in @ X398 @ X396 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X399: $i] :
( ( in @ X399 @ omega )
=> ( in @ ( setadjoin @ X399 @ X399 ) @ omega ) )
=> ( ! [X400: $i] :
( ( ( in @ emptyset @ X400 )
& ! [X401: $i] :
( ( ( in @ X401 @ omega )
& ( in @ X401 @ X400 ) )
=> ( in @ ( setadjoin @ X401 @ X401 ) @ X400 ) ) )
=> ! [X402: $i] :
( ( in @ X402 @ omega )
=> ( in @ X402 @ X400 ) ) )
=> ( ! [X403: $i > $i > $o,X404: $i] :
( ! [X405: $i] :
( ( in @ X405 @ X404 )
=> ( exu @ ( X403 @ X405 ) ) )
=> ? [X406: $i] :
! [X407: $i] :
( ( in @ X407 @ X406 )
<=> ? [X408: $i] :
( ( in @ X408 @ X404 )
& ( X403 @ X408 @ X407 ) ) ) )
=> ( ! [X409: $i] :
( ? [X410: $i] : ( in @ X410 @ X409 )
=> ? [X411: $i] :
( ( in @ X411 @ X409 )
& ~ ? [X412: $i] :
( ( in @ X412 @ X411 )
& ( in @ X412 @ X409 ) ) ) )
=> ( epred1_0
=> ( ! [X432: $i > $o] :
( ( exu @ X432 )
=> ( X432
@ ( descr
@ ^ [Z0: $i] : ( X432 @ Z0 ) ) ) )
=> ( ! [X433: $i,X434: $i > $o,X435: $i] :
( ( in @ X435 @ X433 )
=> ( ( X434 @ X435 )
=> ( in @ X435 @ ( dsetconstr @ X433 @ X434 ) ) ) )
=> ( ! [X436: $i,X437: $i > $o,X438: $i] :
( ( in @ X438 @ ( dsetconstr @ X436 @ X437 ) )
=> ( in @ X438 @ X436 ) )
=> ( ! [X439: $i,X440: $i > $o,X441: $i] :
( ( in @ X441 @ ( dsetconstr @ X439 @ X440 ) )
=> ( X440 @ X441 ) )
=> ( ! [X442: $i > $o] :
( ( exu @ X442 )
=> ? [X443: $i] :
( ( X442 @ X443 )
& ! [X444: $i] :
( ( X442 @ X444 )
=> ( X443 = X444 ) ) ) )
=> ( ! [X445: $o,X446: $i] :
( ( in @ X446 @ ( prop2set @ X445 ) )
=> X445 )
=> ( ! [X447: $i] :
( ( in @ X447 @ emptyset )
=> ! [X448: $o] : X448 )
=> ( ! [X449: $i] :
( ( in @ X449 @ emptyset )
=> ~ $true )
=> ( ! [X450: $i] :
~ ( in @ X450 @ emptyset )
=> ( ! [X451: $i > $o] :
( ( exu @ X451 )
=> ? [X452: $i] : ( X451 @ X452 ) )
=> ( ! [X453: $i,X454: $i] :
( ! [X455: $i] :
( ( in @ X455 @ X453 )
=> ( in @ X455 @ X454 ) )
=> ( ! [X456: $i] :
( ( in @ X456 @ X454 )
=> ( in @ X456 @ X453 ) )
=> ( X453 = X454 ) ) )
=> ( ! [X457: $i] :
( ! [X458: $i] :
~ ( in @ X458 @ X457 )
=> ( X457 = emptyset ) )
=> ( ! [X459: $i] :
( ! [X460: $i] :
~ ( in @ X460 @ X459 )
=> ( X459 = emptyset ) )
=> ( ! [X461: $i,X462: $i > $o,X463: $i] :
( ( in @ X463 @ X461 )
=> ( ( in @ X463 @ ( dsetconstr @ X461 @ X462 ) )
<=> ( X462 @ X463 ) ) )
=> ( ! [X464: $i] :
( ( nonempty @ X464 )
=> ? [X465: $i] : ( in @ X465 @ X464 ) )
=> ( ! [X466: $i,X467: $i > $o,X468: $i] :
( ( in @ X468 @ X466 )
=> ( ( X467 @ X468 )
=> ( nonempty @ ( dsetconstr @ X466 @ X467 ) ) ) )
=> ( ! [X469: $i] :
( ? [X470: $i] : ( in @ X470 @ X469 )
=> ( nonempty @ X469 ) )
=> ( ! [X471: $i,X472: $i] : ( in @ X471 @ ( setadjoin @ X471 @ X472 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X473: $i,X474: $i,X475: $i] :
( ( in @ X475 @ X474 )
=> ( in @ X475 @ ( setadjoin @ X473 @ X474 ) ) )
=> ( ! [X476: $i,X477: $i,X478: $i] :
( ( in @ X478 @ ( setadjoin @ X476 @ X477 ) )
=> ! [X479: $o] :
( ( ( X478 = X476 )
=> X479 )
=> ( ( ( in @ X478 @ X477 )
=> X479 )
=> X479 ) ) )
=> ( ! [X480: $i,X481: $i,X482: $i] :
( ( in @ X482 @ ( setadjoin @ X480 @ X481 ) )
=> ( ( X482 = X480 )
| ( in @ X482 @ X481 ) ) )
=> ( ! [X483: $i] :
( ( dsetconstr @ X483
@ ^ [Z0: $i] : $true )
= X483 )
=> ( ! [X484: $i,X485: $i] :
( ! [X486: $i] :
( ( in @ X486 @ X485 )
=> ( in @ X486 @ X484 ) )
=> ( in @ X485 @ ( powerset @ X484 ) ) )
=> ( ! [X487: $i] : ( in @ emptyset @ ( powerset @ X487 ) )
=> ( ! [X488: $i] : ( in @ emptyset @ ( powerset @ X488 ) )
=> ( ! [X489: $i,X490: $i,X491: $i] :
( ( in @ X490 @ ( powerset @ X489 ) )
=> ( ( in @ X491 @ X490 )
=> ( in @ X491 @ X489 ) ) )
=> ( ! [X492: $i,X493: $i,X494: $i] :
( ( in @ X493 @ X494 )
=> ( ( in @ X494 @ X492 )
=> ( in @ X493 @ ( setunion @ X492 ) ) ) )
=> ( ! [X495: $i,X496: $i] :
( ( in @ X496 @ ( setunion @ X495 ) )
=> ! [X497: $o] :
( ! [X498: $i] :
( ( in @ X496 @ X498 )
=> ( ( in @ X498 @ X495 )
=> X497 ) )
=> X497 ) )
=> ( ! [X499: $i,X500: $i] :
( ( in @ X500 @ X499 )
=> ( in @ X500 @ ( powerset @ ( setunion @ X499 ) ) ) )
=> ( ! [X501: $i > $o] :
( ( exu @ X501 )
=> ? [X502: $i] :
! [X503: $i] :
( ( X501 @ X503 )
<=> ( X503 = X502 ) ) )
=> ( ! [X504: $i] :
( ( nonempty @ X504 )
=> ? [X505: $i] :
( ( in @ X505 @ X504 )
& $true ) )
=> ( ! [X506: $i,X507: $i] :
( ( in @ X506 @ ( setadjoin @ X507 @ emptyset ) )
=> ( X506 = X507 ) )
=> ( ! [X508: $i,X509: $i] :
( ( X508 != X509 )
=> ~ ( in @ X509 @ ( setadjoin @ X508 @ emptyset ) ) )
=> ( ! [X510: $i,X511: $i] :
( ( X510 = X511 )
=> ( in @ X510 @ ( setadjoin @ X511 @ emptyset ) ) )
=> ( ! [X512: $i,X513: $i] :
( ( in @ X512 @ ( setadjoin @ X513 @ emptyset ) )
=> ( in @ X513 @ ( setadjoin @ X512 @ emptyset ) ) )
=> ( ! [X514: $i,X515: $i,X516: $i] :
( ( in @ X516 @ ( setadjoin @ X514 @ ( setadjoin @ X515 @ emptyset ) ) )
=> ( ( X516 = X514 )
| ( X516 = X515 ) ) )
=> ( ! [X517: $i,X518: $i] : ( in @ X517 @ ( setadjoin @ X517 @ ( setadjoin @ X518 @ emptyset ) ) )
=> ( ! [X519: $i,X520: $i] : ( in @ X520 @ ( setadjoin @ X519 @ ( setadjoin @ X520 @ emptyset ) ) )
=> ( ! [X521: $i,X522: $i > $o] :
( ? [X523: $i] :
( ( in @ X523 @ X521 )
& ( X522 @ X523 ) )
=> ( ( ( dsetconstr @ X521 @ X522 )
= emptyset )
=> ~ $true ) )
=> ( ! [X524: $i > $o,X525: $i] :
( ( in @ X525 @ emptyset )
=> ( X524 @ X525 ) )
=> ( ! [X526: $i,X527: $i > $o] :
( ~ ! [X528: $i] :
( ( in @ X528 @ X526 )
=> ( X527 @ X528 ) )
=> ? [X529: $i] :
( ( in @ X529 @ X526 )
& ~ ( X527 @ X529 ) ) )
=> ( ! [X530: $i,X531: $i > $o] :
( ! [X532: $i] :
( ( in @ X532 @ X530 )
=> ~ ( X531 @ X532 ) )
=> ~ ? [X533: $i] :
( ( in @ X533 @ X530 )
& ( X531 @ X533 ) ) )
=> ( ! [X534: $i,X535: $i > $o] :
( ~ ? [X536: $i] :
( ( in @ X536 @ X534 )
& ( X535 @ X536 ) )
=> ! [X537: $i] :
( ( in @ X537 @ X534 )
=> ~ ( X535 @ X537 ) ) )
=> ( ! [X538: $i,X539: $i > $o] :
( ? [X540: $i] :
( ( in @ X540 @ X538 )
& ~ ( X539 @ X540 ) )
=> ~ ! [X541: $i] :
( ( in @ X541 @ X538 )
=> ( X539 @ X541 ) ) )
=> ( ! [X542: $o] :
( X542
=> ( in @ emptyset @ ( prop2set @ X542 ) ) )
=> ( prop2set2propI
=> ( ! [X543: $i,X544: $i > $o] :
( ~ ? [X545: $i] :
( ( in @ X545 @ X543 )
& ( X544 @ X545 ) )
=> ! [X546: $i] :
( ( in @ X546 @ X543 )
=> ~ ( X544 @ X546 ) ) )
=> ( ! [X547: $i,X548: $i > $o] :
( ~ ! [X549: $i] :
( ( in @ X549 @ X547 )
=> ( X548 @ X549 ) )
=> ? [X550: $i] :
( ( in @ X550 @ X547 )
& ~ ( X548 @ X550 ) ) )
=> ( ! [X551: $i > $o] :
( ? [X552: $i] :
( ( X551 @ X552 )
& ! [X553: $i] :
( ( X551 @ X553 )
=> ( X552 = X553 ) ) )
=> ( exu @ X551 ) )
=> ( ! [X554: $i > $o] :
( ? [X555: $i] : ( X554 @ X555 )
=> ( ! [X556: $i,X557: $i] :
( ( X554 @ X556 )
=> ( ( X554 @ X557 )
=> ( X556 = X557 ) ) )
=> ( exu @ X554 ) ) )
=> ( ! [X558: $i > $o] :
( ? [X559: $i] :
! [X560: $i] :
( ( X558 @ X560 )
<=> ( X560 = X559 ) )
=> ( exu @ X558 ) )
=> ( ! [X561: $i,X562: $i] :
( ( X561 = X562 )
=> ! [X563: $i,X564: $i] :
( ( X563 = X564 )
=> ( ( in @ X563 @ X561 )
=> ( in @ X564 @ X562 ) ) ) )
=> ( ! [X565: $i,X566: $i] :
( ( X565 = X566 )
=> ! [X567: $i,X568: $i] :
( ( X567 = X568 )
=> ( ( in @ X567 @ X565 )
<=> ( in @ X568 @ X566 ) ) ) )
=> ( ! [X569: $i > $o] :
( ( exu @ X569 )
=> ! [X570: $i,X571: $i] :
( ( X569 @ X570 )
=> ( ( X569 @ X571 )
=> ( X570 = X571 ) ) ) )
=> ( ! [X572: $i > $o,X573: $i > $o] :
( ! [X574: $i,X575: $i] :
( ( X574 = X575 )
=> ( ( X572 @ X574 )
<=> ( X573 @ X575 ) ) )
=> ( ( exu @ X572 )
<=> ( exu @ X573 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X576: $i,X577: $i] :
( ( X576 = X577 )
=> ! [X578: $i,X579: $i] :
( ( X578 = X579 )
=> ( ( setadjoin @ X576 @ X578 )
= ( setadjoin @ X577 @ X579 ) ) ) )
=> ( ! [X580: $i,X581: $i] :
( ( X580 = X581 )
=> ( ( powerset @ X580 )
= ( powerset @ X581 ) ) )
=> ( ! [X582: $i,X583: $i] :
( ( X582 = X583 )
=> ( ( setunion @ X582 )
= ( setunion @ X583 ) ) )
=> ( ( omega = omega )
=> ( ! [X584: $i > $o] :
( ( exu @ X584 )
=> ! [X585: $i,X586: $i] :
( ( X584 @ X585 )
=> ( ( X584 @ X586 )
=> ( X585 = X586 ) ) ) )
=> ( ! [X587: $i > $o,X588: $i > $o] :
( ! [X589: $i,X590: $i] :
( ( X589 = X590 )
=> ( ( X587 @ X589 )
<=> ( X588 @ X590 ) ) )
=> ( ( exu @ X587 )
=> ( ( exu @ X588 )
=> ( ( descr @ X587 )
= ( descr @ X588 ) ) ) ) )
=> ( ! [X591: $i,X592: $i] :
( ( X591 = X592 )
=> ! [X593: $i > $o,X594: $i > $o] :
( ! [X595: $i] :
( ( in @ X595 @ X591 )
=> ! [X596: $i] :
( ( in @ X596 @ X592 )
=> ( ( X595 = X596 )
=> ( ( X593 @ X595 )
<=> ( X594 @ X596 ) ) ) ) )
=> ( ( dsetconstr @ X591 @ X593 )
= ( dsetconstr @ X592 @ X594 ) ) ) )
=> ( ! [X597: $i,X598: $i] :
( ! [X599: $i] :
( ( in @ X599 @ X597 )
=> ( in @ X599 @ X598 ) )
=> ( subset @ X597 @ X598 ) )
=> ( ! [X600: $i,X601: $i] :
( ( X600 = X601 )
=> ( subset @ X601 @ X600 ) )
=> ( ! [X602: $i,X603: $i] :
( ( X602 = X603 )
=> ( subset @ X602 @ X603 ) )
=> ( ! [X604: $i,X605: $i] :
( ! [X606: $i] :
( ( in @ X606 @ X604 )
=> ( in @ X606 @ X605 ) )
=> ( subset @ X604 @ X605 ) )
=> ( ! [X607: $i] : ( subset @ emptyset @ X607 )
=> ( ! [X608: $i,X609: $i,X610: $i] :
( ( subset @ X608 @ X609 )
=> ( ( in @ X610 @ X608 )
=> ( in @ X610 @ X609 ) ) )
=> ( ! [X611: $i,X612: $i,X613: $i] :
( ( subset @ X611 @ X612 )
=> ( ~ ( in @ X613 @ X612 )
=> ~ ( in @ X613 @ X611 ) ) )
=> ( ! [X614: $i,X615: $i,X616: $i] :
( ( in @ X616 @ X614 )
=> ( ~ ( in @ X616 @ X615 )
=> ~ ( subset @ X614 @ X615 ) ) )
=> ( ! [X617: $i,X618: $i] :
( ~ ( subset @ X617 @ X618 )
=> ( X617 != X618 ) )
=> ( ! [X619: $i,X620: $i,X621: $i] :
( ( in @ X621 @ X619 )
=> ( ~ ( in @ X621 @ X620 )
=> ( X619 != X620 ) ) )
=> ( ! [X622: $i] : ( subset @ X622 @ X622 )
=> ( ! [X623: $i,X624: $i,X625: $i] :
( ( subset @ X623 @ X624 )
=> ( ( subset @ X624 @ X625 )
=> ( subset @ X623 @ X625 ) ) )
=> ( ! [X626: $i,X627: $i] : ( subset @ X627 @ ( setadjoin @ X626 @ X627 ) )
=> ( ! [X628: $i,X629: $i,X630: $i] :
( ( subset @ X628 @ X630 )
=> ( subset @ X628 @ ( setadjoin @ X629 @ X630 ) ) )
=> ( ! [X631: $i,X632: $i] :
( ( subset @ X631 @ X632 )
=> ( in @ X631 @ ( powerset @ X632 ) ) )
=> ( ! [X633: $i,X634: $i] :
( ( subset @ X633 @ X634 )
=> ( ( subset @ X634 @ X633 )
=> ( X633 = X634 ) ) )
=> ( ! [X635: $i] :
( ( subset @ X635 @ emptyset )
=> ( X635 = emptyset ) )
=> ( ! [X636: $i,X637: $i] :
( ( subset @ X637 @ X636 )
=> ( in @ X637 @ ( powerset @ X636 ) ) )
=> ( ! [X638: $i,X639: $i] :
( ( in @ X639 @ ( powerset @ X638 ) )
=> ( subset @ X639 @ X638 ) )
=> ( ! [X640: $i] : ( in @ X640 @ ( powerset @ X640 ) )
=> ( ! [X641: $i,X642: $i] :
( ( subset @ X641 @ X642 )
=> ( subset @ ( powerset @ X641 ) @ ( powerset @ X642 ) ) )
=> ( ! [X643: $i,X644: $i > $o] : ( in @ ( dsetconstr @ X643 @ X644 ) @ ( powerset @ X643 ) )
=> ( ! [X645: $i,X646: $i > $o] : ( subset @ ( dsetconstr @ X645 @ X646 ) @ X645 )
=> ( ! [X647: $i,X648: $i,X649: $i] :
( ( in @ X649 @ X647 )
=> ( in @ X649 @ ( binunion @ X647 @ X648 ) ) )
=> ( ! [X650: $i,X651: $i] : ( in @ X651 @ ( setadjoin @ X650 @ ( setadjoin @ X651 @ emptyset ) ) )
=> ( ! [X652: $i,X653: $i,X654: $i] :
( ( in @ X654 @ X653 )
=> ( in @ X654 @ ( binunion @ X652 @ X653 ) ) )
=> ( ! [X655: $i,X656: $i,X657: $i,X658: $o] :
( ( in @ X657 @ ( binunion @ X655 @ X656 ) )
=> ( ( ( in @ X657 @ X655 )
=> X658 )
=> ( ( ( in @ X657 @ X656 )
=> X658 )
=> X658 ) ) )
=> ( ! [X659: $i,X660: $i,X661: $i] :
( ( in @ X661 @ ( binunion @ X659 @ X660 ) )
=> ( ( in @ X661 @ X659 )
| ( in @ X661 @ X660 ) ) )
=> ( ! [X662: $i,X663: $i] : ( subset @ X662 @ ( binunion @ X662 @ X663 ) )
=> ( ! [X664: $i,X665: $i] : ( subset @ X665 @ ( binunion @ X664 @ X665 ) )
=> ( ! [X666: $i,X667: $i,X668: $i] :
( ( in @ X668 @ X666 )
=> ( ( in @ X668 @ X667 )
=> ( in @ X668 @ ( binintersect @ X666 @ X667 ) ) ) )
=> ( ! [X669: $i,X670: $i,X671: $i] :
( ( subset @ X671 @ X669 )
=> ( ( subset @ X671 @ X670 )
=> ( subset @ X671 @ ( binintersect @ X669 @ X670 ) ) ) )
=> ( ! [X672: $i,X673: $i,X674: $i] :
( ( in @ X674 @ ( binintersect @ X672 @ X673 ) )
=> ( in @ X674 @ X672 ) )
=> ( ! [X675: $i,X676: $i] : ( subset @ ( binintersect @ X675 @ X676 ) @ X675 )
=> ( ! [X677: $i,X678: $i] :
( ( subset @ X677 @ X678 )
=> ( ( binintersect @ X677 @ X678 )
= X677 ) )
=> ( ! [X679: $i,X680: $i] :
( ( ( binintersect @ X679 @ X680 )
= X680 )
=> ( subset @ X680 @ X679 ) )
=> ( ! [X681: $i,X682: $i,X683: $i] :
( ( in @ X683 @ ( binintersect @ X681 @ X682 ) )
=> ( in @ X683 @ X682 ) )
=> ( ! [X684: $i,X685: $i] :
( ~ ? [X686: $i] :
( ( in @ X686 @ X684 )
& ( in @ X686 @ X685 ) )
=> ( ( binintersect @ X684 @ X685 )
= emptyset ) )
=> ( ! [X687: $i,X688: $i] : ( subset @ ( binintersect @ X687 @ X688 ) @ X688 )
=> ( ! [X689: $i,X690: $i] :
( ( subset @ X690 @ X689 )
=> ( ( binintersect @ X689 @ X690 )
= X690 ) )
=> ( ! [X691: $i,X692: $i] :
( ( ( binintersect @ X691 @ X692 )
= X691 )
=> ( subset @ X691 @ X692 ) )
=> ( ! [X693: $i,X694: $i,X695: $i] :
( ( binintersect @ X693 @ ( binunion @ X694 @ X695 ) )
= ( binunion @ ( binintersect @ X693 @ X694 ) @ ( binintersect @ X693 @ X695 ) ) )
=> ( ! [X696: $i,X697: $i,X698: $i] :
( ( in @ X698 @ X696 )
=> ( ~ ( in @ X698 @ X697 )
=> ( in @ X698 @ ( setminus @ X696 @ X697 ) ) ) )
=> ( ! [X699: $i,X700: $i,X701: $i] :
( ( in @ X701 @ ( setminus @ X699 @ X700 ) )
=> ( in @ X701 @ X699 ) )
=> ( ! [X702: $i,X703: $i,X704: $i] :
( ( in @ X704 @ ( setminus @ X702 @ X703 ) )
=> ~ ( in @ X704 @ X703 ) )
=> ( ! [X705: $i,X706: $i] :
( ( subset @ X705 @ X706 )
=> ( ( setminus @ X705 @ X706 )
= emptyset ) )
=> ( ! [X707: $i,X708: $i,X709: $i] :
( ~ ( in @ X709 @ ( setminus @ X707 @ X708 ) )
=> ( ( in @ X709 @ X707 )
=> ( in @ X709 @ X708 ) ) )
=> ( ! [X710: $i,X711: $i,X712: $i] :
( ~ ( in @ X712 @ ( setminus @ X710 @ X711 ) )
=> ( ~ ( in @ X712 @ X711 )
=> ~ ( in @ X712 @ X710 ) ) )
=> ( ! [X713: $i,X714: $i,X715: $i] :
( ~ ( in @ X715 @ X713 )
=> ~ ( in @ X715 @ ( setminus @ X713 @ X714 ) ) )
=> ( ! [X716: $i,X717: $i,X718: $i] :
( ( in @ X718 @ X717 )
=> ~ ( in @ X718 @ ( setminus @ X716 @ X717 ) ) )
=> ( ! [X719: $i,X720: $i] : ( subset @ ( setminus @ X719 @ X720 ) @ X719 )
=> ( ! [X721: $i,X722: $i] :
( ( ( setminus @ X721 @ X722 )
= emptyset )
=> ( subset @ X721 @ X722 ) )
=> ( ! [X723: $i,X724: $i,X725: $i] :
( ( in @ X725 @ ( symdiff @ X723 @ X724 ) )
=> ! [X726: $o] :
( ( ( in @ X725 @ X723 )
=> ( ~ ( in @ X725 @ X724 )
=> X726 ) )
=> ( ( ~ ( in @ X725 @ X723 )
=> ( ( in @ X725 @ X724 )
=> X726 ) )
=> X726 ) ) )
=> ( ! [X727: $i,X728: $i,X729: $i] :
( ( in @ X729 @ X727 )
=> ( ~ ( in @ X729 @ X728 )
=> ( in @ X729 @ ( symdiff @ X727 @ X728 ) ) ) )
=> ( ! [X730: $i,X731: $i,X732: $i] :
( ~ ( in @ X732 @ X730 )
=> ( ( in @ X732 @ X731 )
=> ( in @ X732 @ ( symdiff @ X730 @ X731 ) ) ) )
=> ( ! [X733: $i,X734: $i,X735: $i] :
( ( in @ X735 @ X733 )
=> ( ( in @ X735 @ X734 )
=> ~ ( in @ X735 @ ( symdiff @ X733 @ X734 ) ) ) )
=> ( ! [X736: $i,X737: $i,X738: $i] :
( ~ ( in @ X738 @ X736 )
=> ( ~ ( in @ X738 @ X737 )
=> ~ ( in @ X738 @ ( symdiff @ X736 @ X737 ) ) ) )
=> ( ! [X739: $i,X740: $i] : ( in @ X740 @ ( setadjoin @ X739 @ ( setadjoin @ X740 @ emptyset ) ) )
=> ( ! [X741: $i,X742: $i] : ( in @ X741 @ ( setunion @ ( setadjoin @ ( setadjoin @ X741 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X741 @ ( setadjoin @ X742 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X743: $i,X744: $i] : ( in @ X744 @ ( setunion @ ( setadjoin @ ( setadjoin @ X743 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X743 @ ( setadjoin @ X744 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X745: $i,X746: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X745 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X745 @ ( setadjoin @ X746 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X747: $i,X748: $i] : ( iskpair @ ( kpair @ X747 @ X748 ) )
=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[singletonsubset]),upairsetIL]),symdiffE]),kpairp]),binintersectSubset5]),binintersectEL]),binintersectLsub]),setunionE]),binintersectSubset2]),binintersectSubset3]),subPowSU]),binintersectER]),disjointsetsI1]),c_0_137]),binintersectRsub]),binintersectSubset4]),nonemptyImpWitness]),binintersectSubset1]),bs114d]),uniqinunit]),setminusI]),setminusEL]),notinsingleton]),setminusER]),setminusSubset2]),eqinunit]),setminusERneg]),setminusELneg]),singletonsswitch]),setminusILneg]),setminusIRneg]),setminusLsub]),upairsetE]),setminusSubset1]),emptyset__Cong]),symdiffI1]),symdiffI2]),symdiffIneg1]),upairsetIR]),symdiffIneg2]),secondinupair]),c_0_138]),setukpairIL]),setukpairIR]),vacuousDall]),kpairiskpair]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_139]),c_0_140]),c_0_141]),inCongP]),in__Cong]),c_0_142]),c_0_143]),binunionLsub]),binunionRsub]),binintersectI]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_144]),c_0_145]),c_0_146]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_147]),c_0_148]),emptyInPowerset]),binunionIL]),powersetE]),upairset2IR]),setunionI]),binunionIR]),binunionEcases]),binunionE]),emptyinPowerset]),powersetI]),c_0_149]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_150]),nonemptyE1]),c_0_151]),noeltsimpempty]),emptyI]),setext]),c_0_152]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_153]),c_0_154]),c_0_155]),c_0_156]),c_0_157]),wellorderingAx]),foundationAx]),c_0_158]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_159]) ).
thf(c_0_161,negated_conjecture,
! [X749: $i,X750: $i,X752: $i,X753: $i,X754: $i,X755: $i,X756: $i,X757: $i,X758: $i,X759: $i,X760: $i,X762: $i,X763: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X771: $i,X772: $i > $i > $o,X773: $i,X776: $i,X778: $i,X779: $i,X780: $i,X781: $i,X783: $i,X784: $i > $o,X785: $i,X786: $i > $o,X787: $i,X788: $i,X789: $i > $o,X790: $i,X791: $i,X792: $i > $o,X793: $i,X794: $i > $o,X796: $i,X797: $o,X798: $i,X799: $i,X800: $o,X801: $i,X802: $i,X803: $i > $o,X805: $i,X806: $i,X809: $i,X811: $i,X813: $i,X814: $i > $o,X815: $i,X816: $i,X818: $i,X819: $i > $o,X820: $i,X821: $i,X822: $i,X823: $i,X824: $i,X825: $i,X826: $i,X827: $i,X828: $i,X829: $i,X830: $i,X831: $o,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X839: $i,X840: $i,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i,X849: $o,X851: $i,X852: $i,X853: $i > $o,X855: $i,X856: $i,X857: $i,X859: $i,X860: $i,X861: $i,X862: $i,X863: $i,X864: $i,X865: $i,X866: $i,X867: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i > $o,X876: $i,X877: $i > $o,X878: $i,X879: $i,X880: $i > $o,X881: $i,X883: $i,X884: $i > $o,X886: $i,X887: $i,X888: $i > $o,X890: $i,X891: $i,X892: $i > $o,X893: $i,X895: $o,X896: $i,X897: $i > $o,X899: $i,X900: $i,X901: $i > $o,X902: $i,X904: $i > $o,X905: $i,X907: $i > $o,X908: $i,X911: $i > $o,X912: $i,X914: $i,X915: $i,X916: $i,X917: $i,X918: $i,X919: $i,X920: $i,X921: $i,X922: $i > $o,X923: $i,X924: $i,X925: $i > $o,X926: $i > $o,X929: $i,X930: $i,X931: $i,X932: $i,X933: $i,X934: $i,X935: $i,X936: $i,X937: $i > $o,X938: $i,X939: $i,X940: $i > $o,X941: $i > $o,X944: $i,X945: $i,X946: $i > $o,X947: $i > $o,X950: $i,X951: $i,X953: $i,X954: $i,X955: $i,X956: $i,X957: $i,X958: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X968: $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 > $o,X998: $i,X999: $i > $o,X1000: $i,X1001: $i,X1002: $i,X1003: $i,X1004: $i,X1005: $i,X1006: $i,X1007: $i,X1008: $i,X1009: $i,X1010: $i,X1011: $o,X1012: $i,X1013: $i,X1014: $i,X1015: $i,X1016: $i,X1017: $i,X1018: $i,X1019: $i,X1020: $i,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,X1040: $i,X1041: $i,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $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: $o,X1080: $i,X1081: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $i,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] :
( ( ~ ( in @ ( esk1_2 @ X749 @ X750 ) @ X749 )
| ~ ( in @ ( esk1_2 @ X749 @ X750 ) @ X750 )
| ( X749 = X750 ) )
& ( ( in @ ( esk1_2 @ X749 @ X750 ) @ X749 )
| ( in @ ( esk1_2 @ X749 @ X750 ) @ X750 )
| ( X749 = X750 ) )
& ~ ( in @ X752 @ emptyset )
& ( ~ ( in @ X755 @ ( setadjoin @ X753 @ X754 ) )
| ( X755 = X753 )
| ( in @ X755 @ X754 ) )
& ( ( X755 != X753 )
| ( in @ X755 @ ( setadjoin @ X753 @ X754 ) ) )
& ( ~ ( in @ X755 @ X754 )
| ( in @ X755 @ ( setadjoin @ X753 @ X754 ) ) )
& ( ~ ( in @ X757 @ ( powerset @ X756 ) )
| ~ ( in @ X758 @ X757 )
| ( in @ X758 @ X756 ) )
& ( ( in @ ( esk2_2 @ X759 @ X760 ) @ X760 )
| ( in @ X760 @ ( powerset @ X759 ) ) )
& ( ~ ( in @ ( esk2_2 @ X759 @ X760 ) @ X759 )
| ( in @ X760 @ ( powerset @ X759 ) ) )
& ( ( in @ X763 @ ( esk3_2 @ X762 @ X763 ) )
| ~ ( in @ X763 @ ( setunion @ X762 ) ) )
& ( ( in @ ( esk3_2 @ X762 @ X763 ) @ X762 )
| ~ ( in @ X763 @ ( setunion @ X762 ) ) )
& ( ~ ( in @ X766 @ X767 )
| ~ ( in @ X767 @ X765 )
| ( in @ X766 @ ( setunion @ X765 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X768 @ omega )
| ( in @ ( setadjoin @ X768 @ X768 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X769 ) @ omega )
| ~ ( in @ emptyset @ X769 )
| ~ ( in @ X771 @ omega )
| ( in @ X771 @ X769 ) )
& ( ( in @ ( esk4_1 @ X769 ) @ X769 )
| ~ ( in @ emptyset @ X769 )
| ~ ( in @ X771 @ omega )
| ( in @ X771 @ X769 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X769 ) @ ( esk4_1 @ X769 ) ) @ X769 )
| ~ ( in @ emptyset @ X769 )
| ~ ( in @ X771 @ omega )
| ( in @ X771 @ X769 ) )
& ( ( in @ ( esk7_3 @ X772 @ X773 @ X776 ) @ X773 )
| ~ ( in @ X776 @ ( esk6_2 @ X772 @ X773 ) )
| ( in @ ( esk5_2 @ X772 @ X773 ) @ X773 ) )
& ( ( X772 @ ( esk7_3 @ X772 @ X773 @ X776 ) @ X776 )
| ~ ( in @ X776 @ ( esk6_2 @ X772 @ X773 ) )
| ( in @ ( esk5_2 @ X772 @ X773 ) @ X773 ) )
& ( ~ ( in @ X779 @ X773 )
| ~ ( X772 @ X779 @ X778 )
| ( in @ X778 @ ( esk6_2 @ X772 @ X773 ) )
| ( in @ ( esk5_2 @ X772 @ X773 ) @ X773 ) )
& ( ( in @ ( esk7_3 @ X772 @ X773 @ X776 ) @ X773 )
| ~ ( in @ X776 @ ( esk6_2 @ X772 @ X773 ) )
| ~ ( exu @ ( X772 @ ( esk5_2 @ X772 @ X773 ) ) ) )
& ( ( X772 @ ( esk7_3 @ X772 @ X773 @ X776 ) @ X776 )
| ~ ( in @ X776 @ ( esk6_2 @ X772 @ X773 ) )
| ~ ( exu @ ( X772 @ ( esk5_2 @ X772 @ X773 ) ) ) )
& ( ~ ( in @ X779 @ X773 )
| ~ ( X772 @ X779 @ X778 )
| ( in @ X778 @ ( esk6_2 @ X772 @ X773 ) )
| ~ ( exu @ ( X772 @ ( esk5_2 @ X772 @ X773 ) ) ) )
& ( ( in @ ( esk8_1 @ X780 ) @ X780 )
| ~ ( in @ X781 @ X780 ) )
& ( ~ ( in @ X783 @ ( esk8_1 @ X780 ) )
| ~ ( in @ X783 @ X780 )
| ~ ( in @ X781 @ X780 ) )
& epred1_0
& ( ~ ( exu @ X784 )
| ( X784 @ ( descr @ X784 ) ) )
& ( ~ ( in @ X787 @ X785 )
| ~ ( X786 @ X787 )
| ( in @ X787 @ ( dsetconstr @ X785 @ X786 ) ) )
& ( ~ ( in @ X790 @ ( dsetconstr @ X788 @ X789 ) )
| ( in @ X790 @ X788 ) )
& ( ~ ( in @ X793 @ ( dsetconstr @ X791 @ X792 ) )
| ( X792 @ X793 ) )
& ( ( X794 @ ( esk9_1 @ X794 ) )
| ~ ( exu @ X794 ) )
& ( ~ ( X794 @ X796 )
| ( ( esk9_1 @ X794 )
= X796 )
| ~ ( exu @ X794 ) )
& ( ~ ( in @ X798 @ ( prop2set @ X797 ) )
| X797 )
& ( ~ ( in @ X799 @ emptyset )
| X800 )
& ( ~ ( in @ X801 @ emptyset )
| ~ $true )
& ~ ( in @ X802 @ emptyset )
& ( ~ ( exu @ X803 )
| ( X803 @ ( esk10_1 @ X803 ) ) )
& ( ( in @ ( esk12_2 @ X805 @ X806 ) @ X806 )
| ( X805 = X806 )
| ( in @ ( esk11_2 @ X805 @ X806 ) @ X805 ) )
& ( ~ ( in @ ( esk12_2 @ X805 @ X806 ) @ X805 )
| ( X805 = X806 )
| ( in @ ( esk11_2 @ X805 @ X806 ) @ X805 ) )
& ( ( in @ ( esk12_2 @ X805 @ X806 ) @ X806 )
| ( X805 = X806 )
| ~ ( in @ ( esk11_2 @ X805 @ X806 ) @ X806 ) )
& ( ~ ( in @ ( esk12_2 @ X805 @ X806 ) @ X805 )
| ( X805 = X806 )
| ~ ( in @ ( esk11_2 @ X805 @ X806 ) @ X806 ) )
& ( ( in @ ( esk13_1 @ X809 ) @ X809 )
| ( X809 = emptyset ) )
& ( ( in @ ( esk14_1 @ X811 ) @ X811 )
| ( X811 = emptyset ) )
& ( ~ ( in @ X815 @ ( dsetconstr @ X813 @ X814 ) )
| ( X814 @ X815 )
| ~ ( in @ X815 @ X813 ) )
& ( ~ ( X814 @ X815 )
| ( in @ X815 @ ( dsetconstr @ X813 @ X814 ) )
| ~ ( in @ X815 @ X813 ) )
& ( ~ ( nonempty @ X816 )
| ( in @ ( esk15_1 @ X816 ) @ X816 ) )
& ( ~ ( in @ X820 @ X818 )
| ~ ( X819 @ X820 )
| ( nonempty @ ( dsetconstr @ X818 @ X819 ) ) )
& ( ~ ( in @ X822 @ X821 )
| ( nonempty @ X821 ) )
& ( in @ X823 @ ( setadjoin @ X823 @ X824 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X827 @ X826 )
| ( in @ X827 @ ( setadjoin @ X825 @ X826 ) ) )
& ( ( in @ X830 @ X829 )
| X831
| ( X830 = X828 )
| ~ ( in @ X830 @ ( setadjoin @ X828 @ X829 ) ) )
& ( ~ X831
| X831
| ( X830 = X828 )
| ~ ( in @ X830 @ ( setadjoin @ X828 @ X829 ) ) )
& ( ( in @ X830 @ X829 )
| X831
| ~ X831
| ~ ( in @ X830 @ ( setadjoin @ X828 @ X829 ) ) )
& ( ~ X831
| X831
| ~ X831
| ~ ( in @ X830 @ ( setadjoin @ X828 @ X829 ) ) )
& ( ~ ( in @ X834 @ ( setadjoin @ X832 @ X833 ) )
| ( X834 = X832 )
| ( in @ X834 @ X833 ) )
& ( ( dsetconstr @ X835
@ ^ [Z0: $i] : $true )
= X835 )
& ( ( in @ ( esk16_2 @ X836 @ X837 ) @ X837 )
| ( in @ X837 @ ( powerset @ X836 ) ) )
& ( ~ ( in @ ( esk16_2 @ X836 @ X837 ) @ X836 )
| ( in @ X837 @ ( powerset @ X836 ) ) )
& ( in @ emptyset @ ( powerset @ X839 ) )
& ( in @ emptyset @ ( powerset @ X840 ) )
& ( ~ ( in @ X842 @ ( powerset @ X841 ) )
| ~ ( in @ X843 @ X842 )
| ( in @ X843 @ X841 ) )
& ( ~ ( in @ X845 @ X846 )
| ~ ( in @ X846 @ X844 )
| ( in @ X845 @ ( setunion @ X844 ) ) )
& ( ( in @ X848 @ ( esk17_3 @ X847 @ X848 @ X849 ) )
| X849
| ~ ( in @ X848 @ ( setunion @ X847 ) ) )
& ( ( in @ ( esk17_3 @ X847 @ X848 @ X849 ) @ X847 )
| X849
| ~ ( in @ X848 @ ( setunion @ X847 ) ) )
& ( ~ X849
| X849
| ~ ( in @ X848 @ ( setunion @ X847 ) ) )
& ( ~ ( in @ X852 @ X851 )
| ( in @ X852 @ ( powerset @ ( setunion @ X851 ) ) ) )
& ( ~ ( X853 @ X855 )
| ( X855
= ( esk18_1 @ X853 ) )
| ~ ( exu @ X853 ) )
& ( ( X856
!= ( esk18_1 @ X853 ) )
| ( X853 @ X856 )
| ~ ( exu @ X853 ) )
& ( ( in @ ( esk19_1 @ X857 ) @ X857 )
| ~ ( nonempty @ X857 ) )
& ( $true
| ~ ( nonempty @ X857 ) )
& ( ~ ( in @ X859 @ ( setadjoin @ X860 @ emptyset ) )
| ( X859 = X860 ) )
& ( ( X861 = X862 )
| ~ ( in @ X862 @ ( setadjoin @ X861 @ emptyset ) ) )
& ( ( X863 != X864 )
| ( in @ X863 @ ( setadjoin @ X864 @ emptyset ) ) )
& ( ~ ( in @ X865 @ ( setadjoin @ X866 @ emptyset ) )
| ( in @ X866 @ ( setadjoin @ X865 @ emptyset ) ) )
& ( ~ ( in @ X869 @ ( setadjoin @ X867 @ ( setadjoin @ X868 @ emptyset ) ) )
| ( X869 = X867 )
| ( X869 = X868 ) )
& ( in @ X870 @ ( setadjoin @ X870 @ ( setadjoin @ X871 @ emptyset ) ) )
& ( in @ X873 @ ( setadjoin @ X872 @ ( setadjoin @ X873 @ emptyset ) ) )
& ( ~ ( in @ X876 @ X874 )
| ~ ( X875 @ X876 )
| ( ( dsetconstr @ X874 @ X875 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X878 @ emptyset )
| ( X877 @ X878 ) )
& ( ( in @ ( esk20_2 @ X879 @ X880 ) @ X879 )
| ~ ( in @ X881 @ X879 )
| ( X880 @ X881 ) )
& ( ~ ( X880 @ ( esk20_2 @ X879 @ X880 ) )
| ~ ( in @ X881 @ X879 )
| ( X880 @ X881 ) )
& ( ( in @ ( esk21_2 @ X883 @ X884 ) @ X883 )
| ~ ( in @ X886 @ X883 )
| ~ ( X884 @ X886 ) )
& ( ( X884 @ ( esk21_2 @ X883 @ X884 ) )
| ~ ( in @ X886 @ X883 )
| ~ ( X884 @ X886 ) )
& ( ( in @ ( esk22_2 @ X887 @ X888 ) @ X887 )
| ~ ( in @ X890 @ X887 )
| ~ ( X888 @ X890 ) )
& ( ( X888 @ ( esk22_2 @ X887 @ X888 ) )
| ~ ( in @ X890 @ X887 )
| ~ ( X888 @ X890 ) )
& ( ( in @ ( esk23_2 @ X891 @ X892 ) @ X891 )
| ~ ( in @ X893 @ X891 )
| ( X892 @ X893 ) )
& ( ~ ( X892 @ ( esk23_2 @ X891 @ X892 ) )
| ~ ( in @ X893 @ X891 )
| ( X892 @ X893 ) )
& ( ~ X895
| ( in @ emptyset @ ( prop2set @ X895 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X896 @ X897 ) @ X896 )
| ~ ( in @ X899 @ X896 )
| ~ ( X897 @ X899 ) )
& ( ( X897 @ ( esk24_2 @ X896 @ X897 ) )
| ~ ( in @ X899 @ X896 )
| ~ ( X897 @ X899 ) )
& ( ( in @ ( esk25_2 @ X900 @ X901 ) @ X900 )
| ~ ( in @ X902 @ X900 )
| ( X901 @ X902 ) )
& ( ~ ( X901 @ ( esk25_2 @ X900 @ X901 ) )
| ~ ( in @ X902 @ X900 )
| ( X901 @ X902 ) )
& ( ( X904 @ ( esk26_2 @ X904 @ X905 ) )
| ~ ( X904 @ X905 )
| ( exu @ X904 ) )
& ( ( X905
!= ( esk26_2 @ X904 @ X905 ) )
| ~ ( X904 @ X905 )
| ( exu @ X904 ) )
& ( ( X907 @ ( esk27_1 @ X907 ) )
| ( exu @ X907 )
| ~ ( X907 @ X908 ) )
& ( ( X907 @ ( esk28_1 @ X907 ) )
| ( exu @ X907 )
| ~ ( X907 @ X908 ) )
& ( ( ( esk27_1 @ X907 )
!= ( esk28_1 @ X907 ) )
| ( exu @ X907 )
| ~ ( X907 @ X908 ) )
& ( ~ ( X911 @ ( esk29_2 @ X911 @ X912 ) )
| ( ( esk29_2 @ X911 @ X912 )
!= X912 )
| ( exu @ X911 ) )
& ( ( X911 @ ( esk29_2 @ X911 @ X912 ) )
| ( ( esk29_2 @ X911 @ X912 )
= X912 )
| ( exu @ X911 ) )
& ( ( X914 != X915 )
| ( X916 != X917 )
| ~ ( in @ X916 @ X914 )
| ( in @ X917 @ X915 ) )
& ( ~ ( in @ X920 @ X918 )
| ( in @ X921 @ X919 )
| ( X920 != X921 )
| ( X918 != X919 ) )
& ( ~ ( in @ X921 @ X919 )
| ( in @ X920 @ X918 )
| ( X920 != X921 )
| ( X918 != X919 ) )
& ( ~ ( exu @ X922 )
| ~ ( X922 @ X923 )
| ~ ( X922 @ X924 )
| ( X923 = X924 ) )
& ( ~ ( exu @ X925 )
| ( exu @ X926 )
| ( ( esk30_2 @ X925 @ X926 )
= ( esk31_2 @ X925 @ X926 ) ) )
& ( ~ ( exu @ X926 )
| ( exu @ X925 )
| ( ( esk30_2 @ X925 @ X926 )
= ( esk31_2 @ X925 @ X926 ) ) )
& ( ~ ( exu @ X925 )
| ( exu @ X926 )
| ~ ( X925 @ ( esk30_2 @ X925 @ X926 ) )
| ~ ( X926 @ ( esk31_2 @ X925 @ X926 ) ) )
& ( ~ ( exu @ X926 )
| ( exu @ X925 )
| ~ ( X925 @ ( esk30_2 @ X925 @ X926 ) )
| ~ ( X926 @ ( esk31_2 @ X925 @ X926 ) ) )
& ( ~ ( exu @ X925 )
| ( exu @ X926 )
| ( X925 @ ( esk30_2 @ X925 @ X926 ) )
| ( X926 @ ( esk31_2 @ X925 @ X926 ) ) )
& ( ~ ( exu @ X926 )
| ( exu @ X925 )
| ( X925 @ ( esk30_2 @ X925 @ X926 ) )
| ( X926 @ ( esk31_2 @ X925 @ X926 ) ) )
& ( emptyset = emptyset )
& ( ( X929 != X930 )
| ( X931 != X932 )
| ( ( setadjoin @ X929 @ X931 )
= ( setadjoin @ X930 @ X932 ) ) )
& ( ( X933 != X934 )
| ( ( powerset @ X933 )
= ( powerset @ X934 ) ) )
& ( ( X935 != X936 )
| ( ( setunion @ X935 )
= ( setunion @ X936 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X937 )
| ~ ( X937 @ X938 )
| ~ ( X937 @ X939 )
| ( X938 = X939 ) )
& ( ( ( esk32_2 @ X940 @ X941 )
= ( esk33_2 @ X940 @ X941 ) )
| ~ ( exu @ X940 )
| ~ ( exu @ X941 )
| ( ( descr @ X940 )
= ( descr @ X941 ) ) )
& ( ~ ( X940 @ ( esk32_2 @ X940 @ X941 ) )
| ~ ( X941 @ ( esk33_2 @ X940 @ X941 ) )
| ~ ( exu @ X940 )
| ~ ( exu @ X941 )
| ( ( descr @ X940 )
= ( descr @ X941 ) ) )
& ( ( X940 @ ( esk32_2 @ X940 @ X941 ) )
| ( X941 @ ( esk33_2 @ X940 @ X941 ) )
| ~ ( exu @ X940 )
| ~ ( exu @ X941 )
| ( ( descr @ X940 )
= ( descr @ X941 ) ) )
& ( ( in @ ( esk34_4 @ X944 @ X945 @ X946 @ X947 ) @ X944 )
| ( ( dsetconstr @ X944 @ X946 )
= ( dsetconstr @ X945 @ X947 ) )
| ( X944 != X945 ) )
& ( ( in @ ( esk35_4 @ X944 @ X945 @ X946 @ X947 ) @ X945 )
| ( ( dsetconstr @ X944 @ X946 )
= ( dsetconstr @ X945 @ X947 ) )
| ( X944 != X945 ) )
& ( ( ( esk34_4 @ X944 @ X945 @ X946 @ X947 )
= ( esk35_4 @ X944 @ X945 @ X946 @ X947 ) )
| ( ( dsetconstr @ X944 @ X946 )
= ( dsetconstr @ X945 @ X947 ) )
| ( X944 != X945 ) )
& ( ~ ( X946 @ ( esk34_4 @ X944 @ X945 @ X946 @ X947 ) )
| ~ ( X947 @ ( esk35_4 @ X944 @ X945 @ X946 @ X947 ) )
| ( ( dsetconstr @ X944 @ X946 )
= ( dsetconstr @ X945 @ X947 ) )
| ( X944 != X945 ) )
& ( ( X946 @ ( esk34_4 @ X944 @ X945 @ X946 @ X947 ) )
| ( X947 @ ( esk35_4 @ X944 @ X945 @ X946 @ X947 ) )
| ( ( dsetconstr @ X944 @ X946 )
= ( dsetconstr @ X945 @ X947 ) )
| ( X944 != X945 ) )
& ( ( in @ ( esk36_2 @ X950 @ X951 ) @ X950 )
| ( subset @ X950 @ X951 ) )
& ( ~ ( in @ ( esk36_2 @ X950 @ X951 ) @ X951 )
| ( subset @ X950 @ X951 ) )
& ( ( X953 != X954 )
| ( subset @ X954 @ X953 ) )
& ( ( X955 != X956 )
| ( subset @ X955 @ X956 ) )
& ( ( in @ ( esk37_2 @ X957 @ X958 ) @ X957 )
| ( subset @ X957 @ X958 ) )
& ( ~ ( in @ ( esk37_2 @ X957 @ X958 ) @ X958 )
| ( subset @ X957 @ X958 ) )
& ( subset @ emptyset @ X960 )
& ( ~ ( subset @ X961 @ X962 )
| ~ ( in @ X963 @ X961 )
| ( in @ X963 @ X962 ) )
& ( ~ ( subset @ X964 @ X965 )
| ( in @ X966 @ X965 )
| ~ ( in @ X966 @ X964 ) )
& ( ~ ( in @ X969 @ X967 )
| ( in @ X969 @ X968 )
| ~ ( subset @ X967 @ X968 ) )
& ( ( subset @ X970 @ X971 )
| ( X970 != X971 ) )
& ( ~ ( in @ X974 @ X972 )
| ( in @ X974 @ X973 )
| ( X972 != X973 ) )
& ( subset @ X975 @ X975 )
& ( ~ ( subset @ X976 @ X977 )
| ~ ( subset @ X977 @ X978 )
| ( subset @ X976 @ X978 ) )
& ( subset @ X980 @ ( setadjoin @ X979 @ X980 ) )
& ( ~ ( subset @ X981 @ X983 )
| ( subset @ X981 @ ( setadjoin @ X982 @ X983 ) ) )
& ( ~ ( subset @ X984 @ X985 )
| ( in @ X984 @ ( powerset @ X985 ) ) )
& ( ~ ( subset @ X986 @ X987 )
| ~ ( subset @ X987 @ X986 )
| ( X986 = X987 ) )
& ( ~ ( subset @ X988 @ emptyset )
| ( X988 = emptyset ) )
& ( ~ ( subset @ X990 @ X989 )
| ( in @ X990 @ ( powerset @ X989 ) ) )
& ( ~ ( in @ X992 @ ( powerset @ X991 ) )
| ( subset @ X992 @ X991 ) )
& ( in @ X993 @ ( powerset @ X993 ) )
& ( ~ ( subset @ X994 @ X995 )
| ( subset @ ( powerset @ X994 ) @ ( powerset @ X995 ) ) )
& ( in @ ( dsetconstr @ X996 @ X997 ) @ ( powerset @ X996 ) )
& ( subset @ ( dsetconstr @ X998 @ X999 ) @ X998 )
& ( ~ ( in @ X1002 @ X1000 )
| ( in @ X1002 @ ( binunion @ X1000 @ X1001 ) ) )
& ( in @ X1004 @ ( setadjoin @ X1003 @ ( setadjoin @ X1004 @ emptyset ) ) )
& ( ~ ( in @ X1007 @ X1006 )
| ( in @ X1007 @ ( binunion @ X1005 @ X1006 ) ) )
& ( ( in @ X1010 @ X1009 )
| X1011
| ( in @ X1010 @ X1008 )
| ~ ( in @ X1010 @ ( binunion @ X1008 @ X1009 ) ) )
& ( ~ X1011
| X1011
| ( in @ X1010 @ X1008 )
| ~ ( in @ X1010 @ ( binunion @ X1008 @ X1009 ) ) )
& ( ( in @ X1010 @ X1009 )
| X1011
| ~ X1011
| ~ ( in @ X1010 @ ( binunion @ X1008 @ X1009 ) ) )
& ( ~ X1011
| X1011
| ~ X1011
| ~ ( in @ X1010 @ ( binunion @ X1008 @ X1009 ) ) )
& ( ~ ( in @ X1014 @ ( binunion @ X1012 @ X1013 ) )
| ( in @ X1014 @ X1012 )
| ( in @ X1014 @ X1013 ) )
& ( subset @ X1015 @ ( binunion @ X1015 @ X1016 ) )
& ( subset @ X1018 @ ( binunion @ X1017 @ X1018 ) )
& ( ~ ( in @ X1021 @ X1019 )
| ~ ( in @ X1021 @ X1020 )
| ( in @ X1021 @ ( binintersect @ X1019 @ X1020 ) ) )
& ( ~ ( subset @ X1024 @ X1022 )
| ~ ( subset @ X1024 @ X1023 )
| ( subset @ X1024 @ ( binintersect @ X1022 @ X1023 ) ) )
& ( ~ ( in @ X1027 @ ( binintersect @ X1025 @ X1026 ) )
| ( in @ X1027 @ X1025 ) )
& ( subset @ ( binintersect @ X1028 @ X1029 ) @ X1028 )
& ( ~ ( subset @ X1030 @ X1031 )
| ( ( binintersect @ X1030 @ X1031 )
= X1030 ) )
& ( ( ( binintersect @ X1032 @ X1033 )
!= X1033 )
| ( subset @ X1033 @ X1032 ) )
& ( ~ ( in @ X1036 @ ( binintersect @ X1034 @ X1035 ) )
| ( in @ X1036 @ X1035 ) )
& ( ( in @ ( esk38_2 @ X1037 @ X1038 ) @ X1037 )
| ( ( binintersect @ X1037 @ X1038 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1037 @ X1038 ) @ X1038 )
| ( ( binintersect @ X1037 @ X1038 )
= emptyset ) )
& ( subset @ ( binintersect @ X1040 @ X1041 ) @ X1041 )
& ( ~ ( subset @ X1043 @ X1042 )
| ( ( binintersect @ X1042 @ X1043 )
= X1043 ) )
& ( ( ( binintersect @ X1044 @ X1045 )
!= X1044 )
| ( subset @ X1044 @ X1045 ) )
& ( ( binintersect @ X1046 @ ( binunion @ X1047 @ X1048 ) )
= ( binunion @ ( binintersect @ X1046 @ X1047 ) @ ( binintersect @ X1046 @ X1048 ) ) )
& ( ~ ( in @ X1051 @ X1049 )
| ( in @ X1051 @ X1050 )
| ( in @ X1051 @ ( setminus @ X1049 @ X1050 ) ) )
& ( ~ ( in @ X1054 @ ( setminus @ X1052 @ X1053 ) )
| ( in @ X1054 @ X1052 ) )
& ( ~ ( in @ X1057 @ ( setminus @ X1055 @ X1056 ) )
| ~ ( in @ X1057 @ X1056 ) )
& ( ~ ( subset @ X1058 @ X1059 )
| ( ( setminus @ X1058 @ X1059 )
= emptyset ) )
& ( ( in @ X1062 @ ( setminus @ X1060 @ X1061 ) )
| ~ ( in @ X1062 @ X1060 )
| ( in @ X1062 @ X1061 ) )
& ( ( in @ X1065 @ ( setminus @ X1063 @ X1064 ) )
| ( in @ X1065 @ X1064 )
| ~ ( in @ X1065 @ X1063 ) )
& ( ( in @ X1068 @ X1066 )
| ~ ( in @ X1068 @ ( setminus @ X1066 @ X1067 ) ) )
& ( ~ ( in @ X1071 @ X1070 )
| ~ ( in @ X1071 @ ( setminus @ X1069 @ X1070 ) ) )
& ( subset @ ( setminus @ X1072 @ X1073 ) @ X1072 )
& ( ( ( setminus @ X1074 @ X1075 )
!= emptyset )
| ( subset @ X1074 @ X1075 ) )
& ( ~ ( in @ X1078 @ X1076 )
| X1079
| ( in @ X1078 @ X1076 )
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ( in @ X1078 @ X1077 )
| X1079
| ( in @ X1078 @ X1076 )
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ~ X1079
| X1079
| ( in @ X1078 @ X1076 )
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ~ ( in @ X1078 @ X1076 )
| X1079
| ~ ( in @ X1078 @ X1077 )
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ( in @ X1078 @ X1077 )
| X1079
| ~ ( in @ X1078 @ X1077 )
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ~ X1079
| X1079
| ~ ( in @ X1078 @ X1077 )
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ~ ( in @ X1078 @ X1076 )
| X1079
| ~ X1079
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ( in @ X1078 @ X1077 )
| X1079
| ~ X1079
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ~ X1079
| X1079
| ~ X1079
| ~ ( in @ X1078 @ ( symdiff @ X1076 @ X1077 ) ) )
& ( ~ ( in @ X1082 @ X1080 )
| ( in @ X1082 @ X1081 )
| ( in @ X1082 @ ( symdiff @ X1080 @ X1081 ) ) )
& ( ( in @ X1085 @ X1083 )
| ~ ( in @ X1085 @ X1084 )
| ( in @ X1085 @ ( symdiff @ X1083 @ X1084 ) ) )
& ( ~ ( in @ X1088 @ X1086 )
| ~ ( in @ X1088 @ X1087 )
| ~ ( in @ X1088 @ ( symdiff @ X1086 @ X1087 ) ) )
& ( ( in @ X1091 @ X1089 )
| ( in @ X1091 @ X1090 )
| ~ ( in @ X1091 @ ( symdiff @ X1089 @ X1090 ) ) )
& ( in @ X1093 @ ( setadjoin @ X1092 @ ( setadjoin @ X1093 @ emptyset ) ) )
& ( in @ X1094 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1094 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1094 @ ( setadjoin @ X1095 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1097 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1096 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1096 @ ( setadjoin @ X1097 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1098 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1098 @ ( setadjoin @ X1099 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1100 @ X1101 ) )
& ( in @ esk40_0 @ esk39_0 )
& ~ ( subset @ ( setadjoin @ esk40_0 @ emptyset ) @ esk39_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_160])])])])])])]) ).
thf(c_0_162,negated_conjecture,
! [X3: $i,X2: $i] :
( ( X2 = X3 )
| ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
thf(c_0_163,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk36_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
thf(c_0_164,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk36_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
thf(c_0_165,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( esk36_2 @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= X2 )
| ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
thf(c_0_166,negated_conjecture,
~ ( subset @ ( setadjoin @ esk40_0 @ emptyset ) @ esk39_0 ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
thf(c_0_167,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
thf(c_0_168,negated_conjecture,
in @ esk40_0 @ esk39_0,
inference(split_conjunct,[status(thm)],[c_0_161]) ).
thf(c_0_169,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU621^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Sun May 19 16:12:53 EDT 2024
% 0.21/0.35 % CPUTime :
% 0.22/0.47 Running higher-order theorem proving
% 0.22/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 135.83/20.01 # Version: 3.1.0-ho
% 135.83/20.01 # Preprocessing class: HSLMSLSSLLLCHFA.
% 135.83/20.01 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 135.83/20.01 # Starting ehoh_best5 with 300s (1) cores
% 135.83/20.01 # Starting almost_fo_3_lam with 300s (1) cores
% 135.83/20.01 # Starting new_bool_5 with 300s (1) cores
% 135.83/20.01 # Starting pre_casc_3 with 300s (1) cores
% 135.83/20.01 # Starting ho_unfolding_8 with 300s (1) cores
% 135.83/20.01 # Starting new_ho_10_cnf2 with 300s (1) cores
% 135.83/20.01 # Starting new_bool_3 with 300s (1) cores
% 135.83/20.01 # Starting new_ho_5 with 300s (1) cores
% 135.83/20.01 # new_ho_5 with pid 15685 completed with status 8
% 135.83/20.01 # new_bool_5 with pid 15680 completed with status 0
% 135.83/20.01 # Result found by new_bool_5
% 135.83/20.01 # Preprocessing class: HSLMSLSSLLLCHFA.
% 135.83/20.01 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 135.83/20.01 # Starting ehoh_best5 with 300s (1) cores
% 135.83/20.01 # Starting almost_fo_3_lam with 300s (1) cores
% 135.83/20.01 # Starting new_bool_5 with 300s (1) cores
% 135.83/20.01 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 135.83/20.01 # Search class: HGHSM-FSLM31-MHFMMSBN
% 135.83/20.01 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 135.83/20.01 # Starting new_ho_10_cnf2 with 163s (1) cores
% 135.83/20.01 # new_ho_10_cnf2 with pid 15692 completed with status 0
% 135.83/20.01 # Result found by new_ho_10_cnf2
% 135.83/20.01 # Preprocessing class: HSLMSLSSLLLCHFA.
% 135.83/20.01 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 135.83/20.01 # Starting ehoh_best5 with 300s (1) cores
% 135.83/20.01 # Starting almost_fo_3_lam with 300s (1) cores
% 135.83/20.01 # Starting new_bool_5 with 300s (1) cores
% 135.83/20.01 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 135.83/20.01 # Search class: HGHSM-FSLM31-MHFMMSBN
% 135.83/20.01 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 135.83/20.01 # Starting new_ho_10_cnf2 with 163s (1) cores
% 135.83/20.01 # Preprocessing time : 0.004 s
% 135.83/20.01 # Presaturation interreduction done
% 135.83/20.01
% 135.83/20.01 # Proof found!
% 135.83/20.01 # SZS status Theorem
% 135.83/20.01 # SZS output start CNFRefutation
% See solution above
% 135.83/20.01 # Parsed axioms : 303
% 135.83/20.01 # Removed by relevancy pruning/SinE : 166
% 135.83/20.01 # Initial clauses : 218
% 135.83/20.01 # Removed in clause preprocessing : 25
% 135.83/20.01 # Initial clauses in saturation : 193
% 135.83/20.01 # Processed clauses : 7744
% 135.83/20.01 # ...of these trivial : 339
% 135.83/20.01 # ...subsumed : 3163
% 135.83/20.01 # ...remaining for further processing : 4242
% 135.83/20.01 # Other redundant clauses eliminated : 103
% 135.83/20.01 # Clauses deleted for lack of memory : 0
% 135.83/20.01 # Backward-subsumed : 407
% 135.83/20.01 # Backward-rewritten : 118
% 135.83/20.01 # Generated clauses : 731394
% 135.83/20.01 # ...of the previous two non-redundant : 718007
% 135.83/20.01 # ...aggressively subsumed : 0
% 135.83/20.01 # Contextual simplify-reflections : 10
% 135.83/20.01 # Paramodulations : 731149
% 135.83/20.01 # Factorizations : 124
% 135.83/20.01 # NegExts : 0
% 135.83/20.01 # Equation resolutions : 103
% 135.83/20.01 # Disequality decompositions : 0
% 135.83/20.01 # Total rewrite steps : 25703
% 135.83/20.01 # ...of those cached : 23877
% 135.83/20.01 # Propositional unsat checks : 0
% 135.83/20.01 # Propositional check models : 0
% 135.83/20.01 # Propositional check unsatisfiable : 0
% 135.83/20.01 # Propositional clauses : 0
% 135.83/20.01 # Propositional clauses after purity: 0
% 135.83/20.01 # Propositional unsat core size : 0
% 135.83/20.01 # Propositional preprocessing time : 0.000
% 135.83/20.01 # Propositional encoding time : 0.000
% 135.83/20.01 # Propositional solver time : 0.000
% 135.83/20.01 # Success case prop preproc time : 0.000
% 135.83/20.01 # Success case prop encoding time : 0.000
% 135.83/20.01 # Success case prop solver time : 0.000
% 135.83/20.01 # Current number of processed clauses : 3528
% 135.83/20.01 # Positive orientable unit clauses : 211
% 135.83/20.01 # Positive unorientable unit clauses: 0
% 135.83/20.01 # Negative unit clauses : 259
% 135.83/20.01 # Non-unit-clauses : 3058
% 135.83/20.01 # Current number of unprocessed clauses: 706510
% 135.83/20.01 # ...number of literals in the above : 2963009
% 135.83/20.01 # Current number of archived formulas : 0
% 135.83/20.01 # Current number of archived clauses : 703
% 135.83/20.01 # Clause-clause subsumption calls (NU) : 823748
% 135.83/20.01 # Rec. Clause-clause subsumption calls : 415768
% 135.83/20.01 # Non-unit clause-clause subsumptions : 1324
% 135.83/20.01 # Unit Clause-clause subsumption calls : 28197
% 135.83/20.01 # Rewrite failures with RHS unbound : 0
% 135.83/20.01 # BW rewrite match attempts : 251
% 135.83/20.01 # BW rewrite match successes : 84
% 135.83/20.01 # Condensation attempts : 7744
% 135.83/20.01 # Condensation successes : 71
% 135.83/20.01 # Termbank termtop insertions : 15684279
% 135.83/20.01 # Search garbage collected termcells : 11941
% 135.83/20.01
% 135.83/20.01 # -------------------------------------------------
% 135.83/20.01 # User time : 18.746 s
% 135.83/20.01 # System time : 0.497 s
% 135.83/20.01 # Total time : 19.243 s
% 135.83/20.01 # Maximum resident set size: 4760 pages
% 135.83/20.01
% 135.83/20.01 # -------------------------------------------------
% 135.83/20.01 # User time : 18.817 s
% 135.83/20.01 # System time : 0.525 s
% 135.83/20.01 # Total time : 19.342 s
% 135.83/20.01 # Maximum resident set size: 2076 pages
% 135.83/20.01 % E---3.1 exiting
% 135.83/20.01 % E exiting
%------------------------------------------------------------------------------