%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU636^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 03:28:44 EDT 2024
% Result : Timeout 300.11s 150.28s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 367
% Syntax : Number of formulae : 399 ( 5 unt; 214 typ; 0 def)
% Number of atoms : 1557 ( 218 equ; 0 cnn)
% Maximal formula atoms : 454 ( 8 avg)
% Number of connectives : 5323 ( 381 ~; 355 |; 283 &;3336 @)
% ( 210 <=>; 758 =>; 0 <=; 0 <~>)
% Maximal formula depth : 583 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 261 ( 261 >; 0 *; 0 +; 0 <<)
% Number of symbols : 217 ( 214 usr; 158 con; 0-4 aty)
% Number of variables : 1317 ( 59 ^1187 !; 71 ?;1317 :)
% 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_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
epred1_0: $o ).
thf(decl_198,type,
esk1_2: $i > $i > $i ).
thf(decl_199,type,
esk2_2: $i > $i > $i ).
thf(decl_200,type,
esk3_2: $i > $i > $i ).
thf(decl_201,type,
esk4_1: $i > $i ).
thf(decl_202,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_203,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_204,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_205,type,
esk8_1: $i > $i ).
thf(decl_206,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_207,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_208,type,
esk11_2: $i > $i > $i ).
thf(decl_209,type,
esk12_2: $i > $i > $i ).
thf(decl_210,type,
esk13_1: $i > $i ).
thf(decl_211,type,
esk14_1: $i > $i ).
thf(decl_212,type,
esk15_1: $i > $i ).
thf(decl_213,type,
esk16_2: $i > $i > $i ).
thf(decl_214,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_215,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_216,type,
esk19_1: $i > $i ).
thf(decl_217,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_218,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_219,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_220,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_221,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_222,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_223,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_224,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_225,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_226,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_227,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_228,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_229,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_230,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_231,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_232,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_233,type,
esk36_2: $i > $i > $i ).
thf(decl_234,type,
esk37_2: $i > $i > $i ).
thf(decl_235,type,
esk38_2: $i > $i > $i ).
thf(decl_236,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_237,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_238,type,
esk41_2: $i > $i > $i ).
thf(decl_239,type,
esk42_0: $i ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/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(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(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(setunionsingleton,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
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(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
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(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
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(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(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(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(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(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(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(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(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(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(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
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(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
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(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(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(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(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(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(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(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
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(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(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(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(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(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(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(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(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
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(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(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(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(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(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_152,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_153,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_154,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_155,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_156,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_157,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_158,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_159,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_160,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_161,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_162,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_163,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_164,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_165,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_166,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_167,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_168,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_169,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_170,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_171,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_172,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_173,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_174,plain,
( epred1_0
<=> ! [X460: $i] :
? [X461: $i] :
( ! [X462: $i] :
( ( in @ X462 @ X461 )
=> ! [X463: $i] :
( ( in @ X463 @ X462 )
=> ( in @ X463 @ X460 ) ) )
& ! [X464: $i,X465: $i] :
( ( ( in @ X464 @ X460 )
& ( in @ X465 @ X460 ) )
=> ( ! [X466: $i] :
( ( in @ X466 @ X461 )
=> ( ( in @ X464 @ X466 )
<=> ( in @ X465 @ X466 ) ) )
=> ( X464 = X465 ) ) )
& ! [X467: $i,X468: $i] :
( ( ( in @ X467 @ X461 )
& ( in @ X468 @ X461 ) )
=> ( ! [X469: $i] :
( ( in @ X469 @ X467 )
=> ( in @ X469 @ X468 ) )
| ! [X470: $i] :
( ( in @ X470 @ X468 )
=> ( in @ X470 @ X467 ) ) ) )
& ! [X471: $i] :
( ( ! [X472: $i] :
( ( in @ X472 @ X471 )
=> ( in @ X472 @ X460 ) )
& ? [X473: $i] : ( in @ X473 @ X471 ) )
=> ? [X474: $i,X475: $i] :
( ( in @ X474 @ X461 )
& ( in @ X475 @ X471 )
& ~ ? [X476: $i] :
( ( in @ X476 @ X474 )
& ( in @ X476 @ X471 ) )
& ! [X477: $i] :
( ( in @ X477 @ X461 )
=> ( ! [X478: $i] :
( ( in @ X478 @ X477 )
=> ( in @ X478 @ X474 ) )
| ( in @ X475 @ X477 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_175,negated_conjecture,
~ ( ! [X433: $i,X434: $i] :
( ! [X435: $i] :
( ( in @ X435 @ X433 )
<=> ( in @ X435 @ X434 ) )
=> ( X433 = X434 ) )
=> ( ! [X436: $i] :
~ ( in @ X436 @ emptyset )
=> ( ! [X437: $i,X438: $i,X439: $i] :
( ( in @ X439 @ ( setadjoin @ X437 @ X438 ) )
<=> ( ( X439 = X437 )
| ( in @ X439 @ X438 ) ) )
=> ( ! [X440: $i,X441: $i] :
( ( in @ X441 @ ( powerset @ X440 ) )
<=> ! [X442: $i] :
( ( in @ X442 @ X441 )
=> ( in @ X442 @ X440 ) ) )
=> ( ! [X443: $i,X444: $i] :
( ( in @ X444 @ ( setunion @ X443 ) )
<=> ? [X445: $i] :
( ( in @ X444 @ X445 )
& ( in @ X445 @ X443 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X446: $i] :
( ( in @ X446 @ omega )
=> ( in @ ( setadjoin @ X446 @ X446 ) @ omega ) )
=> ( ! [X447: $i] :
( ( ( in @ emptyset @ X447 )
& ! [X448: $i] :
( ( ( in @ X448 @ omega )
& ( in @ X448 @ X447 ) )
=> ( in @ ( setadjoin @ X448 @ X448 ) @ X447 ) ) )
=> ! [X449: $i] :
( ( in @ X449 @ omega )
=> ( in @ X449 @ X447 ) ) )
=> ( ! [X450: $i > $i > $o,X451: $i] :
( ! [X452: $i] :
( ( in @ X452 @ X451 )
=> ( exu @ ( X450 @ X452 ) ) )
=> ? [X453: $i] :
! [X454: $i] :
( ( in @ X454 @ X453 )
<=> ? [X455: $i] :
( ( in @ X455 @ X451 )
& ( X450 @ X455 @ X454 ) ) ) )
=> ( ! [X456: $i] :
( ? [X457: $i] : ( in @ X457 @ X456 )
=> ? [X458: $i] :
( ( in @ X458 @ X456 )
& ~ ? [X459: $i] :
( ( in @ X459 @ X458 )
& ( in @ X459 @ X456 ) ) ) )
=> ( epred1_0
=> ( ! [X479: $i > $o] :
( ( exu @ X479 )
=> ( X479
@ ( descr
@ ^ [Z0: $i] : ( X479 @ Z0 ) ) ) )
=> ( ! [X480: $i,X481: $i > $o,X482: $i] :
( ( in @ X482 @ X480 )
=> ( ( X481 @ X482 )
=> ( in @ X482 @ ( dsetconstr @ X480 @ X481 ) ) ) )
=> ( ! [X483: $i,X484: $i > $o,X485: $i] :
( ( in @ X485 @ ( dsetconstr @ X483 @ X484 ) )
=> ( in @ X485 @ X483 ) )
=> ( ! [X486: $i,X487: $i > $o,X488: $i] :
( ( in @ X488 @ ( dsetconstr @ X486 @ X487 ) )
=> ( X487 @ X488 ) )
=> ( ! [X489: $i > $o] :
( ( exu @ X489 )
=> ? [X490: $i] :
( ( X489 @ X490 )
& ! [X491: $i] :
( ( X489 @ X491 )
=> ( X490 = X491 ) ) ) )
=> ( ! [X492: $o,X493: $i] :
( ( in @ X493 @ ( prop2set @ X492 ) )
=> X492 )
=> ( ! [X494: $i] :
( ( in @ X494 @ emptyset )
=> ! [X495: $o] : X495 )
=> ( ! [X496: $i] :
( ( in @ X496 @ emptyset )
=> ~ $true )
=> ( ! [X497: $i] :
~ ( in @ X497 @ emptyset )
=> ( ! [X498: $i > $o] :
( ( exu @ X498 )
=> ? [X499: $i] : ( X498 @ X499 ) )
=> ( ! [X500: $i,X501: $i] :
( ! [X502: $i] :
( ( in @ X502 @ X500 )
=> ( in @ X502 @ X501 ) )
=> ( ! [X503: $i] :
( ( in @ X503 @ X501 )
=> ( in @ X503 @ X500 ) )
=> ( X500 = X501 ) ) )
=> ( ! [X504: $i] :
( ! [X505: $i] :
~ ( in @ X505 @ X504 )
=> ( X504 = emptyset ) )
=> ( ! [X506: $i] :
( ! [X507: $i] :
~ ( in @ X507 @ X506 )
=> ( X506 = emptyset ) )
=> ( ! [X508: $i,X509: $i > $o,X510: $i] :
( ( in @ X510 @ X508 )
=> ( ( in @ X510 @ ( dsetconstr @ X508 @ X509 ) )
<=> ( X509 @ X510 ) ) )
=> ( ! [X511: $i] :
( ( nonempty @ X511 )
=> ? [X512: $i] : ( in @ X512 @ X511 ) )
=> ( ! [X513: $i,X514: $i > $o,X515: $i] :
( ( in @ X515 @ X513 )
=> ( ( X514 @ X515 )
=> ( nonempty @ ( dsetconstr @ X513 @ X514 ) ) ) )
=> ( ! [X516: $i] :
( ? [X517: $i] : ( in @ X517 @ X516 )
=> ( nonempty @ X516 ) )
=> ( ! [X518: $i,X519: $i] : ( in @ X518 @ ( setadjoin @ X518 @ X519 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X520: $i,X521: $i,X522: $i] :
( ( in @ X522 @ X521 )
=> ( in @ X522 @ ( setadjoin @ X520 @ X521 ) ) )
=> ( ! [X523: $i,X524: $i,X525: $i] :
( ( in @ X525 @ ( setadjoin @ X523 @ X524 ) )
=> ! [X526: $o] :
( ( ( X525 = X523 )
=> X526 )
=> ( ( ( in @ X525 @ X524 )
=> X526 )
=> X526 ) ) )
=> ( ! [X527: $i,X528: $i,X529: $i] :
( ( in @ X529 @ ( setadjoin @ X527 @ X528 ) )
=> ( ( X529 = X527 )
| ( in @ X529 @ X528 ) ) )
=> ( ! [X530: $i] :
( ( dsetconstr @ X530
@ ^ [Z0: $i] : $true )
= X530 )
=> ( ! [X531: $i,X532: $i] :
( ! [X533: $i] :
( ( in @ X533 @ X532 )
=> ( in @ X533 @ X531 ) )
=> ( in @ X532 @ ( powerset @ X531 ) ) )
=> ( ! [X534: $i] : ( in @ emptyset @ ( powerset @ X534 ) )
=> ( ! [X535: $i] : ( in @ emptyset @ ( powerset @ X535 ) )
=> ( ! [X536: $i,X537: $i,X538: $i] :
( ( in @ X537 @ ( powerset @ X536 ) )
=> ( ( in @ X538 @ X537 )
=> ( in @ X538 @ X536 ) ) )
=> ( ! [X539: $i,X540: $i,X541: $i] :
( ( in @ X540 @ X541 )
=> ( ( in @ X541 @ X539 )
=> ( in @ X540 @ ( setunion @ X539 ) ) ) )
=> ( ! [X542: $i,X543: $i] :
( ( in @ X543 @ ( setunion @ X542 ) )
=> ! [X544: $o] :
( ! [X545: $i] :
( ( in @ X543 @ X545 )
=> ( ( in @ X545 @ X542 )
=> X544 ) )
=> X544 ) )
=> ( ! [X546: $i,X547: $i] :
( ( in @ X547 @ X546 )
=> ( in @ X547 @ ( powerset @ ( setunion @ X546 ) ) ) )
=> ( ! [X548: $i > $o] :
( ( exu @ X548 )
=> ? [X549: $i] :
! [X550: $i] :
( ( X548 @ X550 )
<=> ( X550 = X549 ) ) )
=> ( ! [X551: $i] :
( ( nonempty @ X551 )
=> ? [X552: $i] :
( ( in @ X552 @ X551 )
& $true ) )
=> ( ! [X553: $i,X554: $i] :
( ( in @ X553 @ ( setadjoin @ X554 @ emptyset ) )
=> ( X553 = X554 ) )
=> ( ! [X555: $i,X556: $i] :
( ( X555 != X556 )
=> ~ ( in @ X556 @ ( setadjoin @ X555 @ emptyset ) ) )
=> ( ! [X557: $i,X558: $i] :
( ( X557 = X558 )
=> ( in @ X557 @ ( setadjoin @ X558 @ emptyset ) ) )
=> ( ! [X559: $i,X560: $i] :
( ( in @ X559 @ ( setadjoin @ X560 @ emptyset ) )
=> ( in @ X560 @ ( setadjoin @ X559 @ emptyset ) ) )
=> ( ! [X561: $i,X562: $i,X563: $i] :
( ( in @ X563 @ ( setadjoin @ X561 @ ( setadjoin @ X562 @ emptyset ) ) )
=> ( ( X563 = X561 )
| ( X563 = X562 ) ) )
=> ( ! [X564: $i,X565: $i] : ( in @ X564 @ ( setadjoin @ X564 @ ( setadjoin @ X565 @ emptyset ) ) )
=> ( ! [X566: $i,X567: $i] : ( in @ X567 @ ( setadjoin @ X566 @ ( setadjoin @ X567 @ emptyset ) ) )
=> ( ! [X568: $i,X569: $i > $o] :
( ? [X570: $i] :
( ( in @ X570 @ X568 )
& ( X569 @ X570 ) )
=> ( ( ( dsetconstr @ X568 @ X569 )
= emptyset )
=> ~ $true ) )
=> ( ! [X571: $i > $o,X572: $i] :
( ( in @ X572 @ emptyset )
=> ( X571 @ X572 ) )
=> ( ! [X573: $i,X574: $i > $o] :
( ~ ! [X575: $i] :
( ( in @ X575 @ X573 )
=> ( X574 @ X575 ) )
=> ? [X576: $i] :
( ( in @ X576 @ X573 )
& ~ ( X574 @ X576 ) ) )
=> ( ! [X577: $i,X578: $i > $o] :
( ! [X579: $i] :
( ( in @ X579 @ X577 )
=> ~ ( X578 @ X579 ) )
=> ~ ? [X580: $i] :
( ( in @ X580 @ X577 )
& ( X578 @ X580 ) ) )
=> ( ! [X581: $i,X582: $i > $o] :
( ~ ? [X583: $i] :
( ( in @ X583 @ X581 )
& ( X582 @ X583 ) )
=> ! [X584: $i] :
( ( in @ X584 @ X581 )
=> ~ ( X582 @ X584 ) ) )
=> ( ! [X585: $i,X586: $i > $o] :
( ? [X587: $i] :
( ( in @ X587 @ X585 )
& ~ ( X586 @ X587 ) )
=> ~ ! [X588: $i] :
( ( in @ X588 @ X585 )
=> ( X586 @ X588 ) ) )
=> ( ! [X589: $o] :
( X589
=> ( in @ emptyset @ ( prop2set @ X589 ) ) )
=> ( prop2set2propI
=> ( ! [X590: $i,X591: $i > $o] :
( ~ ? [X592: $i] :
( ( in @ X592 @ X590 )
& ( X591 @ X592 ) )
=> ! [X593: $i] :
( ( in @ X593 @ X590 )
=> ~ ( X591 @ X593 ) ) )
=> ( ! [X594: $i,X595: $i > $o] :
( ~ ! [X596: $i] :
( ( in @ X596 @ X594 )
=> ( X595 @ X596 ) )
=> ? [X597: $i] :
( ( in @ X597 @ X594 )
& ~ ( X595 @ X597 ) ) )
=> ( ! [X598: $i > $o] :
( ? [X599: $i] :
( ( X598 @ X599 )
& ! [X600: $i] :
( ( X598 @ X600 )
=> ( X599 = X600 ) ) )
=> ( exu @ X598 ) )
=> ( ! [X601: $i > $o] :
( ? [X602: $i] : ( X601 @ X602 )
=> ( ! [X603: $i,X604: $i] :
( ( X601 @ X603 )
=> ( ( X601 @ X604 )
=> ( X603 = X604 ) ) )
=> ( exu @ X601 ) ) )
=> ( ! [X605: $i > $o] :
( ? [X606: $i] :
! [X607: $i] :
( ( X605 @ X607 )
<=> ( X607 = X606 ) )
=> ( exu @ X605 ) )
=> ( ! [X608: $i,X609: $i] :
( ( X608 = X609 )
=> ! [X610: $i,X611: $i] :
( ( X610 = X611 )
=> ( ( in @ X610 @ X608 )
=> ( in @ X611 @ X609 ) ) ) )
=> ( ! [X612: $i,X613: $i] :
( ( X612 = X613 )
=> ! [X614: $i,X615: $i] :
( ( X614 = X615 )
=> ( ( in @ X614 @ X612 )
<=> ( in @ X615 @ X613 ) ) ) )
=> ( ! [X616: $i > $o] :
( ( exu @ X616 )
=> ! [X617: $i,X618: $i] :
( ( X616 @ X617 )
=> ( ( X616 @ X618 )
=> ( X617 = X618 ) ) ) )
=> ( ! [X619: $i > $o,X620: $i > $o] :
( ! [X621: $i,X622: $i] :
( ( X621 = X622 )
=> ( ( X619 @ X621 )
<=> ( X620 @ X622 ) ) )
=> ( ( exu @ X619 )
<=> ( exu @ X620 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X623: $i,X624: $i] :
( ( X623 = X624 )
=> ! [X625: $i,X626: $i] :
( ( X625 = X626 )
=> ( ( setadjoin @ X623 @ X625 )
= ( setadjoin @ X624 @ X626 ) ) ) )
=> ( ! [X627: $i,X628: $i] :
( ( X627 = X628 )
=> ( ( powerset @ X627 )
= ( powerset @ X628 ) ) )
=> ( ! [X629: $i,X630: $i] :
( ( X629 = X630 )
=> ( ( setunion @ X629 )
= ( setunion @ X630 ) ) )
=> ( ( omega = omega )
=> ( ! [X631: $i > $o] :
( ( exu @ X631 )
=> ! [X632: $i,X633: $i] :
( ( X631 @ X632 )
=> ( ( X631 @ X633 )
=> ( X632 = X633 ) ) ) )
=> ( ! [X634: $i > $o,X635: $i > $o] :
( ! [X636: $i,X637: $i] :
( ( X636 = X637 )
=> ( ( X634 @ X636 )
<=> ( X635 @ X637 ) ) )
=> ( ( exu @ X634 )
=> ( ( exu @ X635 )
=> ( ( descr @ X634 )
= ( descr @ X635 ) ) ) ) )
=> ( ! [X638: $i,X639: $i] :
( ( X638 = X639 )
=> ! [X640: $i > $o,X641: $i > $o] :
( ! [X642: $i] :
( ( in @ X642 @ X638 )
=> ! [X643: $i] :
( ( in @ X643 @ X639 )
=> ( ( X642 = X643 )
=> ( ( X640 @ X642 )
<=> ( X641 @ X643 ) ) ) ) )
=> ( ( dsetconstr @ X638 @ X640 )
= ( dsetconstr @ X639 @ X641 ) ) ) )
=> ( ! [X644: $i,X645: $i] :
( ! [X646: $i] :
( ( in @ X646 @ X644 )
=> ( in @ X646 @ X645 ) )
=> ( subset @ X644 @ X645 ) )
=> ( ! [X647: $i,X648: $i] :
( ( X647 = X648 )
=> ( subset @ X648 @ X647 ) )
=> ( ! [X649: $i,X650: $i] :
( ( X649 = X650 )
=> ( subset @ X649 @ X650 ) )
=> ( ! [X651: $i,X652: $i] :
( ! [X653: $i] :
( ( in @ X653 @ X651 )
=> ( in @ X653 @ X652 ) )
=> ( subset @ X651 @ X652 ) )
=> ( ! [X654: $i] : ( subset @ emptyset @ X654 )
=> ( ! [X655: $i,X656: $i,X657: $i] :
( ( subset @ X655 @ X656 )
=> ( ( in @ X657 @ X655 )
=> ( in @ X657 @ X656 ) ) )
=> ( ! [X658: $i,X659: $i,X660: $i] :
( ( subset @ X658 @ X659 )
=> ( ~ ( in @ X660 @ X659 )
=> ~ ( in @ X660 @ X658 ) ) )
=> ( ! [X661: $i,X662: $i,X663: $i] :
( ( in @ X663 @ X661 )
=> ( ~ ( in @ X663 @ X662 )
=> ~ ( subset @ X661 @ X662 ) ) )
=> ( ! [X664: $i,X665: $i] :
( ~ ( subset @ X664 @ X665 )
=> ( X664 != X665 ) )
=> ( ! [X666: $i,X667: $i,X668: $i] :
( ( in @ X668 @ X666 )
=> ( ~ ( in @ X668 @ X667 )
=> ( X666 != X667 ) ) )
=> ( ! [X669: $i] : ( subset @ X669 @ X669 )
=> ( ! [X670: $i,X671: $i,X672: $i] :
( ( subset @ X670 @ X671 )
=> ( ( subset @ X671 @ X672 )
=> ( subset @ X670 @ X672 ) ) )
=> ( ! [X673: $i,X674: $i] : ( subset @ X674 @ ( setadjoin @ X673 @ X674 ) )
=> ( ! [X675: $i,X676: $i,X677: $i] :
( ( subset @ X675 @ X677 )
=> ( subset @ X675 @ ( setadjoin @ X676 @ X677 ) ) )
=> ( ! [X678: $i,X679: $i] :
( ( subset @ X678 @ X679 )
=> ( in @ X678 @ ( powerset @ X679 ) ) )
=> ( ! [X680: $i,X681: $i] :
( ( subset @ X680 @ X681 )
=> ( ( subset @ X681 @ X680 )
=> ( X680 = X681 ) ) )
=> ( ! [X682: $i] :
( ( subset @ X682 @ emptyset )
=> ( X682 = emptyset ) )
=> ( ! [X683: $i,X684: $i] :
( ( subset @ X684 @ X683 )
=> ( in @ X684 @ ( powerset @ X683 ) ) )
=> ( ! [X685: $i,X686: $i] :
( ( in @ X686 @ ( powerset @ X685 ) )
=> ( subset @ X686 @ X685 ) )
=> ( ! [X687: $i] : ( in @ X687 @ ( powerset @ X687 ) )
=> ( ! [X688: $i,X689: $i] :
( ( subset @ X688 @ X689 )
=> ( subset @ ( powerset @ X688 ) @ ( powerset @ X689 ) ) )
=> ( ! [X690: $i,X691: $i > $o] : ( in @ ( dsetconstr @ X690 @ X691 ) @ ( powerset @ X690 ) )
=> ( ! [X692: $i,X693: $i > $o] : ( subset @ ( dsetconstr @ X692 @ X693 ) @ X692 )
=> ( ! [X694: $i,X695: $i,X696: $i] :
( ( in @ X696 @ X694 )
=> ( in @ X696 @ ( binunion @ X694 @ X695 ) ) )
=> ( ! [X697: $i,X698: $i] : ( in @ X698 @ ( setadjoin @ X697 @ ( setadjoin @ X698 @ emptyset ) ) )
=> ( ! [X699: $i,X700: $i,X701: $i] :
( ( in @ X701 @ X700 )
=> ( in @ X701 @ ( binunion @ X699 @ X700 ) ) )
=> ( ! [X702: $i,X703: $i,X704: $i,X705: $o] :
( ( in @ X704 @ ( binunion @ X702 @ X703 ) )
=> ( ( ( in @ X704 @ X702 )
=> X705 )
=> ( ( ( in @ X704 @ X703 )
=> X705 )
=> X705 ) ) )
=> ( ! [X706: $i,X707: $i,X708: $i] :
( ( in @ X708 @ ( binunion @ X706 @ X707 ) )
=> ( ( in @ X708 @ X706 )
| ( in @ X708 @ X707 ) ) )
=> ( ! [X709: $i,X710: $i] : ( subset @ X709 @ ( binunion @ X709 @ X710 ) )
=> ( ! [X711: $i,X712: $i] : ( subset @ X712 @ ( binunion @ X711 @ X712 ) )
=> ( ! [X713: $i,X714: $i,X715: $i] :
( ( in @ X715 @ X713 )
=> ( ( in @ X715 @ X714 )
=> ( in @ X715 @ ( binintersect @ X713 @ X714 ) ) ) )
=> ( ! [X716: $i,X717: $i,X718: $i] :
( ( subset @ X718 @ X716 )
=> ( ( subset @ X718 @ X717 )
=> ( subset @ X718 @ ( binintersect @ X716 @ X717 ) ) ) )
=> ( ! [X719: $i,X720: $i,X721: $i] :
( ( in @ X721 @ ( binintersect @ X719 @ X720 ) )
=> ( in @ X721 @ X719 ) )
=> ( ! [X722: $i,X723: $i] : ( subset @ ( binintersect @ X722 @ X723 ) @ X722 )
=> ( ! [X724: $i,X725: $i] :
( ( subset @ X724 @ X725 )
=> ( ( binintersect @ X724 @ X725 )
= X724 ) )
=> ( ! [X726: $i,X727: $i] :
( ( ( binintersect @ X726 @ X727 )
= X727 )
=> ( subset @ X727 @ X726 ) )
=> ( ! [X728: $i,X729: $i,X730: $i] :
( ( in @ X730 @ ( binintersect @ X728 @ X729 ) )
=> ( in @ X730 @ X729 ) )
=> ( ! [X731: $i,X732: $i] :
( ~ ? [X733: $i] :
( ( in @ X733 @ X731 )
& ( in @ X733 @ X732 ) )
=> ( ( binintersect @ X731 @ X732 )
= emptyset ) )
=> ( ! [X734: $i,X735: $i] : ( subset @ ( binintersect @ X734 @ X735 ) @ X735 )
=> ( ! [X736: $i,X737: $i] :
( ( subset @ X737 @ X736 )
=> ( ( binintersect @ X736 @ X737 )
= X737 ) )
=> ( ! [X738: $i,X739: $i] :
( ( ( binintersect @ X738 @ X739 )
= X738 )
=> ( subset @ X738 @ X739 ) )
=> ( ! [X740: $i,X741: $i,X742: $i] :
( ( binintersect @ X740 @ ( binunion @ X741 @ X742 ) )
= ( binunion @ ( binintersect @ X740 @ X741 ) @ ( binintersect @ X740 @ X742 ) ) )
=> ( ! [X743: $i,X744: $i,X745: $i] :
( ( in @ X745 @ X743 )
=> ( ~ ( in @ X745 @ X744 )
=> ( in @ X745 @ ( setminus @ X743 @ X744 ) ) ) )
=> ( ! [X746: $i,X747: $i,X748: $i] :
( ( in @ X748 @ ( setminus @ X746 @ X747 ) )
=> ( in @ X748 @ X746 ) )
=> ( ! [X749: $i,X750: $i,X751: $i] :
( ( in @ X751 @ ( setminus @ X749 @ X750 ) )
=> ~ ( in @ X751 @ X750 ) )
=> ( ! [X752: $i,X753: $i] :
( ( subset @ X752 @ X753 )
=> ( ( setminus @ X752 @ X753 )
= emptyset ) )
=> ( ! [X754: $i,X755: $i,X756: $i] :
( ~ ( in @ X756 @ ( setminus @ X754 @ X755 ) )
=> ( ( in @ X756 @ X754 )
=> ( in @ X756 @ X755 ) ) )
=> ( ! [X757: $i,X758: $i,X759: $i] :
( ~ ( in @ X759 @ ( setminus @ X757 @ X758 ) )
=> ( ~ ( in @ X759 @ X758 )
=> ~ ( in @ X759 @ X757 ) ) )
=> ( ! [X760: $i,X761: $i,X762: $i] :
( ~ ( in @ X762 @ X760 )
=> ~ ( in @ X762 @ ( setminus @ X760 @ X761 ) ) )
=> ( ! [X763: $i,X764: $i,X765: $i] :
( ( in @ X765 @ X764 )
=> ~ ( in @ X765 @ ( setminus @ X763 @ X764 ) ) )
=> ( ! [X766: $i,X767: $i] : ( subset @ ( setminus @ X766 @ X767 ) @ X766 )
=> ( ! [X768: $i,X769: $i] :
( ( ( setminus @ X768 @ X769 )
= emptyset )
=> ( subset @ X768 @ X769 ) )
=> ( ! [X770: $i,X771: $i,X772: $i] :
( ( in @ X772 @ ( symdiff @ X770 @ X771 ) )
=> ! [X773: $o] :
( ( ( in @ X772 @ X770 )
=> ( ~ ( in @ X772 @ X771 )
=> X773 ) )
=> ( ( ~ ( in @ X772 @ X770 )
=> ( ( in @ X772 @ X771 )
=> X773 ) )
=> X773 ) ) )
=> ( ! [X774: $i,X775: $i,X776: $i] :
( ( in @ X776 @ X774 )
=> ( ~ ( in @ X776 @ X775 )
=> ( in @ X776 @ ( symdiff @ X774 @ X775 ) ) ) )
=> ( ! [X777: $i,X778: $i,X779: $i] :
( ~ ( in @ X779 @ X777 )
=> ( ( in @ X779 @ X778 )
=> ( in @ X779 @ ( symdiff @ X777 @ X778 ) ) ) )
=> ( ! [X780: $i,X781: $i,X782: $i] :
( ( in @ X782 @ X780 )
=> ( ( in @ X782 @ X781 )
=> ~ ( in @ X782 @ ( symdiff @ X780 @ X781 ) ) ) )
=> ( ! [X783: $i,X784: $i,X785: $i] :
( ~ ( in @ X785 @ X783 )
=> ( ~ ( in @ X785 @ X784 )
=> ~ ( in @ X785 @ ( symdiff @ X783 @ X784 ) ) ) )
=> ( ! [X786: $i,X787: $i] : ( in @ X787 @ ( setadjoin @ X786 @ ( setadjoin @ X787 @ emptyset ) ) )
=> ( ! [X788: $i,X789: $i] : ( in @ X788 @ ( setunion @ ( setadjoin @ ( setadjoin @ X788 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X788 @ ( setadjoin @ X789 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X790: $i,X791: $i] : ( in @ X791 @ ( setunion @ ( setadjoin @ ( setadjoin @ X790 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X790 @ ( setadjoin @ X791 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X792: $i,X793: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X792 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X792 @ ( setadjoin @ X793 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X794: $i,X795: $i] : ( iskpair @ ( kpair @ X794 @ X795 ) )
=> ( ! [X796: $i,X797: $i] :
( ( in @ X797 @ X796 )
=> ( subset @ ( setadjoin @ X797 @ emptyset ) @ X796 ) )
=> ( ! [X798: $i,X799: $i] :
( ( in @ X799 @ X798 )
=> ( in @ ( setadjoin @ X799 @ emptyset ) @ ( powerset @ X798 ) ) )
=> ( ! [X800: $i,X801: $i,X802: $i] :
( ( in @ X802 @ X800 )
=> ( in @ ( setadjoin @ X802 @ emptyset ) @ ( powerset @ ( binunion @ X800 @ X801 ) ) ) )
=> ( ! [X803: $i,X804: $i,X805: $i] :
( ( in @ X805 @ ( setadjoin @ X803 @ ( setadjoin @ X804 @ emptyset ) ) )
=> ( ( X805 = X803 )
| ( X805 = X804 ) ) )
=> ( ! [X806: $i,X807: $i,X808: $i] :
( ( in @ X808 @ X806 )
=> ! [X809: $i] :
( ( in @ X809 @ X807 )
=> ( subset @ ( setadjoin @ X808 @ ( setadjoin @ X809 @ emptyset ) ) @ ( binunion @ X806 @ X807 ) ) ) )
=> ( ! [X810: $i,X811: $i,X812: $i] :
( ( in @ X812 @ X810 )
=> ! [X813: $i] :
( ( in @ X813 @ X811 )
=> ( in @ ( setadjoin @ X812 @ ( setadjoin @ X813 @ emptyset ) ) @ ( powerset @ ( binunion @ X810 @ X811 ) ) ) ) )
=> ( ! [X814: $i,X815: $i,X816: $i] :
( ( in @ X816 @ X814 )
=> ! [X817: $i] :
( ( in @ X817 @ X815 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X816 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X816 @ ( setadjoin @ X817 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X814 @ X815 ) ) ) ) )
=> ( ! [X818: $i,X819: $i,X820: $i] :
( ( in @ X820 @ X818 )
=> ! [X821: $i] :
( ( in @ X821 @ X819 )
=> ( in @ ( setadjoin @ ( setadjoin @ X820 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X820 @ ( setadjoin @ X821 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X818 @ X819 ) ) ) ) ) )
=> ( ! [X822: $i,X823: $i,X824: $i] :
( ( in @ X824 @ X822 )
=> ! [X825: $i] :
( ( in @ X825 @ X823 )
=> ( in @ ( kpair @ X824 @ X825 ) @ ( powerset @ ( powerset @ ( binunion @ X822 @ X823 ) ) ) ) ) )
=> ( ! [X826: $i,X827: $i,X828: $i] :
( ( in @ X828 @ X826 )
=> ! [X829: $i] :
( ( in @ X829 @ X827 )
=> ( in @ ( kpair @ X828 @ X829 ) @ ( cartprod @ X826 @ X827 ) ) ) )
=> ( ! [X830: $i,X831: $i,X832: $i] :
( ( in @ X832 @ ( cartprod @ X830 @ X831 ) )
=> ? [X833: $i] :
( ( in @ X833 @ X830 )
& ? [X834: $i] :
( ( in @ X834 @ X831 )
& ( X832
= ( kpair @ X833 @ X834 ) ) ) ) )
=> ( ! [X835: $i,X836: $i,X837: $i] :
( ( in @ X837 @ ( cartprod @ X835 @ X836 ) )
=> ( iskpair @ X837 ) )
=> ( ! [X838: $i,X839: $i] :
( ( in @ X839 @ ( setunion @ X838 ) )
=> ? [X840: $i] :
( ( in @ X840 @ X838 )
& ( in @ X839 @ X840 ) ) )
=> ( ! [X841: $i] : ( subset @ ( setunion @ ( setadjoin @ X841 @ emptyset ) ) @ X841 )
=> ( ! [X842: $i] : ( subset @ X842 @ ( setunion @ ( setadjoin @ X842 @ emptyset ) ) )
=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[setunionsingleton]),ubforcartprodlem1]),setunionsingleton2]),setminusELneg]),upairsetIR]),setminusILneg]),setminusIRneg]),setminusLsub]),c_0_152]),setminusSubset1]),symdiffE]),vacuousDall]),symdiffI1]),symdiffI2]),quantDeMorgan1]),symdiffIneg1]),symdiffIneg2]),quantDeMorgan2]),secondinupair]),setukpairIL]),quantDeMorgan3]),setukpairIR]),kpairiskpair]),quantDeMorgan4]),kpairp]),prop2setI]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),notdexE]),upairset2E]),upairsubunion]),upairinpowunion]),notdallE]),subsetI2]),ubforcartprodlem2]),ubforcartprodlem3]),c_0_153]),cartprodpairin]),cartprodmempair1]),c_0_154]),cartprodmempair]),setunionE2]),c_0_155]),setunionsingleton1]),inCongP]),in__Cong]),c_0_156]),c_0_157]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_158]),c_0_159]),c_0_160]),subsetI1]),eqimpsubset2]),eqimpsubset1]),binintersectSubset4]),binintersectSubset1]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_161]),c_0_162]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),eqinunit]),binintersectLsub]),singletonsswitch]),binintersectSubset2]),binintersectSubset3]),upairsetE]),binintersectER]),disjointsetsI1]),binintersectRsub]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),upairsetIL]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_163]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_164]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_165]),nonemptyE1]),c_0_166]),noeltsimpempty]),emptyI]),setext]),c_0_167]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_168]),c_0_169]),c_0_170]),c_0_171]),c_0_172]),wellorderingAx]),foundationAx]),c_0_173]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_174]) ).
thf(c_0_176,negated_conjecture,
! [X843: $i,X844: $i,X846: $i,X847: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X856: $i,X857: $i,X859: $i,X860: $i,X861: $i,X862: $i,X863: $i,X865: $i,X866: $i > $i > $o,X867: $i,X870: $i,X872: $i,X873: $i,X874: $i,X875: $i,X877: $i,X878: $i > $o,X879: $i,X880: $i > $o,X881: $i,X882: $i,X883: $i > $o,X884: $i,X885: $i,X886: $i > $o,X887: $i,X888: $i > $o,X890: $i,X891: $o,X892: $i,X893: $i,X894: $o,X895: $i,X896: $i,X897: $i > $o,X899: $i,X900: $i,X903: $i,X905: $i,X907: $i,X908: $i > $o,X909: $i,X910: $i,X912: $i,X913: $i > $o,X914: $i,X915: $i,X916: $i,X917: $i,X918: $i,X919: $i,X920: $i,X921: $i,X922: $i,X923: $i,X924: $i,X925: $o,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i,X933: $i,X934: $i,X935: $i,X936: $i,X937: $i,X938: $i,X939: $i,X940: $i,X941: $i,X942: $i,X943: $o,X945: $i,X946: $i,X947: $i > $o,X949: $i,X950: $i,X951: $i,X953: $i,X954: $i,X955: $i,X956: $i,X957: $i,X958: $i,X959: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X968: $i,X969: $i > $o,X970: $i,X971: $i > $o,X972: $i,X973: $i,X974: $i > $o,X975: $i,X977: $i,X978: $i > $o,X980: $i,X981: $i,X982: $i > $o,X984: $i,X985: $i,X986: $i > $o,X987: $i,X989: $o,X990: $i,X991: $i > $o,X993: $i,X994: $i,X995: $i > $o,X996: $i,X998: $i > $o,X999: $i,X1001: $i > $o,X1002: $i,X1005: $i > $o,X1006: $i,X1008: $i,X1009: $i,X1010: $i,X1011: $i,X1012: $i,X1013: $i,X1014: $i,X1015: $i,X1016: $i > $o,X1017: $i,X1018: $i,X1019: $i > $o,X1020: $i > $o,X1023: $i,X1024: $i,X1025: $i,X1026: $i,X1027: $i,X1028: $i,X1029: $i,X1030: $i,X1031: $i > $o,X1032: $i,X1033: $i,X1034: $i > $o,X1035: $i > $o,X1038: $i,X1039: $i,X1040: $i > $o,X1041: $i > $o,X1044: $i,X1045: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $i,X1054: $i,X1055: $i,X1056: $i,X1057: $i,X1058: $i,X1059: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i,X1081: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $i,X1089: $i,X1090: $i,X1091: $i > $o,X1092: $i,X1093: $i > $o,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i,X1105: $o,X1106: $i,X1107: $i,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i,X1115: $i,X1116: $i,X1117: $i,X1118: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,X1134: $i,X1135: $i,X1136: $i,X1137: $i,X1138: $i,X1139: $i,X1140: $i,X1141: $i,X1142: $i,X1143: $i,X1144: $i,X1145: $i,X1146: $i,X1147: $i,X1148: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1164: $i,X1165: $i,X1166: $i,X1167: $i,X1168: $i,X1169: $i,X1170: $i,X1171: $i,X1172: $i,X1173: $o,X1174: $i,X1175: $i,X1176: $i,X1177: $i,X1178: $i,X1179: $i,X1180: $i,X1181: $i,X1182: $i,X1183: $i,X1184: $i,X1185: $i,X1186: $i,X1187: $i,X1188: $i,X1189: $i,X1190: $i,X1191: $i,X1192: $i,X1193: $i,X1194: $i,X1195: $i,X1196: $i,X1197: $i,X1198: $i,X1199: $i,X1200: $i,X1201: $i,X1202: $i,X1203: $i,X1204: $i,X1205: $i,X1206: $i,X1207: $i,X1208: $i,X1209: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $i,X1217: $i,X1218: $i,X1219: $i,X1220: $i,X1221: $i,X1222: $i,X1223: $i,X1224: $i,X1225: $i,X1226: $i,X1227: $i,X1228: $i,X1229: $i,X1230: $i,X1231: $i,X1232: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1241: $i,X1242: $i] :
( ( ~ ( in @ ( esk1_2 @ X843 @ X844 ) @ X843 )
| ~ ( in @ ( esk1_2 @ X843 @ X844 ) @ X844 )
| ( X843 = X844 ) )
& ( ( in @ ( esk1_2 @ X843 @ X844 ) @ X843 )
| ( in @ ( esk1_2 @ X843 @ X844 ) @ X844 )
| ( X843 = X844 ) )
& ~ ( in @ X846 @ emptyset )
& ( ~ ( in @ X849 @ ( setadjoin @ X847 @ X848 ) )
| ( X849 = X847 )
| ( in @ X849 @ X848 ) )
& ( ( X849 != X847 )
| ( in @ X849 @ ( setadjoin @ X847 @ X848 ) ) )
& ( ~ ( in @ X849 @ X848 )
| ( in @ X849 @ ( setadjoin @ X847 @ X848 ) ) )
& ( ~ ( in @ X851 @ ( powerset @ X850 ) )
| ~ ( in @ X852 @ X851 )
| ( in @ X852 @ X850 ) )
& ( ( in @ ( esk2_2 @ X853 @ X854 ) @ X854 )
| ( in @ X854 @ ( powerset @ X853 ) ) )
& ( ~ ( in @ ( esk2_2 @ X853 @ X854 ) @ X853 )
| ( in @ X854 @ ( powerset @ X853 ) ) )
& ( ( in @ X857 @ ( esk3_2 @ X856 @ X857 ) )
| ~ ( in @ X857 @ ( setunion @ X856 ) ) )
& ( ( in @ ( esk3_2 @ X856 @ X857 ) @ X856 )
| ~ ( in @ X857 @ ( setunion @ X856 ) ) )
& ( ~ ( in @ X860 @ X861 )
| ~ ( in @ X861 @ X859 )
| ( in @ X860 @ ( setunion @ X859 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X862 @ omega )
| ( in @ ( setadjoin @ X862 @ X862 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X863 ) @ omega )
| ~ ( in @ emptyset @ X863 )
| ~ ( in @ X865 @ omega )
| ( in @ X865 @ X863 ) )
& ( ( in @ ( esk4_1 @ X863 ) @ X863 )
| ~ ( in @ emptyset @ X863 )
| ~ ( in @ X865 @ omega )
| ( in @ X865 @ X863 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X863 ) @ ( esk4_1 @ X863 ) ) @ X863 )
| ~ ( in @ emptyset @ X863 )
| ~ ( in @ X865 @ omega )
| ( in @ X865 @ X863 ) )
& ( ( in @ ( esk7_3 @ X866 @ X867 @ X870 ) @ X867 )
| ~ ( in @ X870 @ ( esk6_2 @ X866 @ X867 ) )
| ( in @ ( esk5_2 @ X866 @ X867 ) @ X867 ) )
& ( ( X866 @ ( esk7_3 @ X866 @ X867 @ X870 ) @ X870 )
| ~ ( in @ X870 @ ( esk6_2 @ X866 @ X867 ) )
| ( in @ ( esk5_2 @ X866 @ X867 ) @ X867 ) )
& ( ~ ( in @ X873 @ X867 )
| ~ ( X866 @ X873 @ X872 )
| ( in @ X872 @ ( esk6_2 @ X866 @ X867 ) )
| ( in @ ( esk5_2 @ X866 @ X867 ) @ X867 ) )
& ( ( in @ ( esk7_3 @ X866 @ X867 @ X870 ) @ X867 )
| ~ ( in @ X870 @ ( esk6_2 @ X866 @ X867 ) )
| ~ ( exu @ ( X866 @ ( esk5_2 @ X866 @ X867 ) ) ) )
& ( ( X866 @ ( esk7_3 @ X866 @ X867 @ X870 ) @ X870 )
| ~ ( in @ X870 @ ( esk6_2 @ X866 @ X867 ) )
| ~ ( exu @ ( X866 @ ( esk5_2 @ X866 @ X867 ) ) ) )
& ( ~ ( in @ X873 @ X867 )
| ~ ( X866 @ X873 @ X872 )
| ( in @ X872 @ ( esk6_2 @ X866 @ X867 ) )
| ~ ( exu @ ( X866 @ ( esk5_2 @ X866 @ X867 ) ) ) )
& ( ( in @ ( esk8_1 @ X874 ) @ X874 )
| ~ ( in @ X875 @ X874 ) )
& ( ~ ( in @ X877 @ ( esk8_1 @ X874 ) )
| ~ ( in @ X877 @ X874 )
| ~ ( in @ X875 @ X874 ) )
& epred1_0
& ( ~ ( exu @ X878 )
| ( X878 @ ( descr @ X878 ) ) )
& ( ~ ( in @ X881 @ X879 )
| ~ ( X880 @ X881 )
| ( in @ X881 @ ( dsetconstr @ X879 @ X880 ) ) )
& ( ~ ( in @ X884 @ ( dsetconstr @ X882 @ X883 ) )
| ( in @ X884 @ X882 ) )
& ( ~ ( in @ X887 @ ( dsetconstr @ X885 @ X886 ) )
| ( X886 @ X887 ) )
& ( ( X888 @ ( esk9_1 @ X888 ) )
| ~ ( exu @ X888 ) )
& ( ~ ( X888 @ X890 )
| ( ( esk9_1 @ X888 )
= X890 )
| ~ ( exu @ X888 ) )
& ( ~ ( in @ X892 @ ( prop2set @ X891 ) )
| X891 )
& ( ~ ( in @ X893 @ emptyset )
| X894 )
& ( ~ ( in @ X895 @ emptyset )
| ~ $true )
& ~ ( in @ X896 @ emptyset )
& ( ~ ( exu @ X897 )
| ( X897 @ ( esk10_1 @ X897 ) ) )
& ( ( in @ ( esk12_2 @ X899 @ X900 ) @ X900 )
| ( X899 = X900 )
| ( in @ ( esk11_2 @ X899 @ X900 ) @ X899 ) )
& ( ~ ( in @ ( esk12_2 @ X899 @ X900 ) @ X899 )
| ( X899 = X900 )
| ( in @ ( esk11_2 @ X899 @ X900 ) @ X899 ) )
& ( ( in @ ( esk12_2 @ X899 @ X900 ) @ X900 )
| ( X899 = X900 )
| ~ ( in @ ( esk11_2 @ X899 @ X900 ) @ X900 ) )
& ( ~ ( in @ ( esk12_2 @ X899 @ X900 ) @ X899 )
| ( X899 = X900 )
| ~ ( in @ ( esk11_2 @ X899 @ X900 ) @ X900 ) )
& ( ( in @ ( esk13_1 @ X903 ) @ X903 )
| ( X903 = emptyset ) )
& ( ( in @ ( esk14_1 @ X905 ) @ X905 )
| ( X905 = emptyset ) )
& ( ~ ( in @ X909 @ ( dsetconstr @ X907 @ X908 ) )
| ( X908 @ X909 )
| ~ ( in @ X909 @ X907 ) )
& ( ~ ( X908 @ X909 )
| ( in @ X909 @ ( dsetconstr @ X907 @ X908 ) )
| ~ ( in @ X909 @ X907 ) )
& ( ~ ( nonempty @ X910 )
| ( in @ ( esk15_1 @ X910 ) @ X910 ) )
& ( ~ ( in @ X914 @ X912 )
| ~ ( X913 @ X914 )
| ( nonempty @ ( dsetconstr @ X912 @ X913 ) ) )
& ( ~ ( in @ X916 @ X915 )
| ( nonempty @ X915 ) )
& ( in @ X917 @ ( setadjoin @ X917 @ X918 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X921 @ X920 )
| ( in @ X921 @ ( setadjoin @ X919 @ X920 ) ) )
& ( ( in @ X924 @ X923 )
| X925
| ( X924 = X922 )
| ~ ( in @ X924 @ ( setadjoin @ X922 @ X923 ) ) )
& ( ~ X925
| X925
| ( X924 = X922 )
| ~ ( in @ X924 @ ( setadjoin @ X922 @ X923 ) ) )
& ( ( in @ X924 @ X923 )
| X925
| ~ X925
| ~ ( in @ X924 @ ( setadjoin @ X922 @ X923 ) ) )
& ( ~ X925
| X925
| ~ X925
| ~ ( in @ X924 @ ( setadjoin @ X922 @ X923 ) ) )
& ( ~ ( in @ X928 @ ( setadjoin @ X926 @ X927 ) )
| ( X928 = X926 )
| ( in @ X928 @ X927 ) )
& ( ( dsetconstr @ X929
@ ^ [Z0: $i] : $true )
= X929 )
& ( ( in @ ( esk16_2 @ X930 @ X931 ) @ X931 )
| ( in @ X931 @ ( powerset @ X930 ) ) )
& ( ~ ( in @ ( esk16_2 @ X930 @ X931 ) @ X930 )
| ( in @ X931 @ ( powerset @ X930 ) ) )
& ( in @ emptyset @ ( powerset @ X933 ) )
& ( in @ emptyset @ ( powerset @ X934 ) )
& ( ~ ( in @ X936 @ ( powerset @ X935 ) )
| ~ ( in @ X937 @ X936 )
| ( in @ X937 @ X935 ) )
& ( ~ ( in @ X939 @ X940 )
| ~ ( in @ X940 @ X938 )
| ( in @ X939 @ ( setunion @ X938 ) ) )
& ( ( in @ X942 @ ( esk17_3 @ X941 @ X942 @ X943 ) )
| X943
| ~ ( in @ X942 @ ( setunion @ X941 ) ) )
& ( ( in @ ( esk17_3 @ X941 @ X942 @ X943 ) @ X941 )
| X943
| ~ ( in @ X942 @ ( setunion @ X941 ) ) )
& ( ~ X943
| X943
| ~ ( in @ X942 @ ( setunion @ X941 ) ) )
& ( ~ ( in @ X946 @ X945 )
| ( in @ X946 @ ( powerset @ ( setunion @ X945 ) ) ) )
& ( ~ ( X947 @ X949 )
| ( X949
= ( esk18_1 @ X947 ) )
| ~ ( exu @ X947 ) )
& ( ( X950
!= ( esk18_1 @ X947 ) )
| ( X947 @ X950 )
| ~ ( exu @ X947 ) )
& ( ( in @ ( esk19_1 @ X951 ) @ X951 )
| ~ ( nonempty @ X951 ) )
& ( $true
| ~ ( nonempty @ X951 ) )
& ( ~ ( in @ X953 @ ( setadjoin @ X954 @ emptyset ) )
| ( X953 = X954 ) )
& ( ( X955 = X956 )
| ~ ( in @ X956 @ ( setadjoin @ X955 @ emptyset ) ) )
& ( ( X957 != X958 )
| ( in @ X957 @ ( setadjoin @ X958 @ emptyset ) ) )
& ( ~ ( in @ X959 @ ( setadjoin @ X960 @ emptyset ) )
| ( in @ X960 @ ( setadjoin @ X959 @ emptyset ) ) )
& ( ~ ( in @ X963 @ ( setadjoin @ X961 @ ( setadjoin @ X962 @ emptyset ) ) )
| ( X963 = X961 )
| ( X963 = X962 ) )
& ( in @ X964 @ ( setadjoin @ X964 @ ( setadjoin @ X965 @ emptyset ) ) )
& ( in @ X967 @ ( setadjoin @ X966 @ ( setadjoin @ X967 @ emptyset ) ) )
& ( ~ ( in @ X970 @ X968 )
| ~ ( X969 @ X970 )
| ( ( dsetconstr @ X968 @ X969 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X972 @ emptyset )
| ( X971 @ X972 ) )
& ( ( in @ ( esk20_2 @ X973 @ X974 ) @ X973 )
| ~ ( in @ X975 @ X973 )
| ( X974 @ X975 ) )
& ( ~ ( X974 @ ( esk20_2 @ X973 @ X974 ) )
| ~ ( in @ X975 @ X973 )
| ( X974 @ X975 ) )
& ( ( in @ ( esk21_2 @ X977 @ X978 ) @ X977 )
| ~ ( in @ X980 @ X977 )
| ~ ( X978 @ X980 ) )
& ( ( X978 @ ( esk21_2 @ X977 @ X978 ) )
| ~ ( in @ X980 @ X977 )
| ~ ( X978 @ X980 ) )
& ( ( in @ ( esk22_2 @ X981 @ X982 ) @ X981 )
| ~ ( in @ X984 @ X981 )
| ~ ( X982 @ X984 ) )
& ( ( X982 @ ( esk22_2 @ X981 @ X982 ) )
| ~ ( in @ X984 @ X981 )
| ~ ( X982 @ X984 ) )
& ( ( in @ ( esk23_2 @ X985 @ X986 ) @ X985 )
| ~ ( in @ X987 @ X985 )
| ( X986 @ X987 ) )
& ( ~ ( X986 @ ( esk23_2 @ X985 @ X986 ) )
| ~ ( in @ X987 @ X985 )
| ( X986 @ X987 ) )
& ( ~ X989
| ( in @ emptyset @ ( prop2set @ X989 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X990 @ X991 ) @ X990 )
| ~ ( in @ X993 @ X990 )
| ~ ( X991 @ X993 ) )
& ( ( X991 @ ( esk24_2 @ X990 @ X991 ) )
| ~ ( in @ X993 @ X990 )
| ~ ( X991 @ X993 ) )
& ( ( in @ ( esk25_2 @ X994 @ X995 ) @ X994 )
| ~ ( in @ X996 @ X994 )
| ( X995 @ X996 ) )
& ( ~ ( X995 @ ( esk25_2 @ X994 @ X995 ) )
| ~ ( in @ X996 @ X994 )
| ( X995 @ X996 ) )
& ( ( X998 @ ( esk26_2 @ X998 @ X999 ) )
| ~ ( X998 @ X999 )
| ( exu @ X998 ) )
& ( ( X999
!= ( esk26_2 @ X998 @ X999 ) )
| ~ ( X998 @ X999 )
| ( exu @ X998 ) )
& ( ( X1001 @ ( esk27_1 @ X1001 ) )
| ( exu @ X1001 )
| ~ ( X1001 @ X1002 ) )
& ( ( X1001 @ ( esk28_1 @ X1001 ) )
| ( exu @ X1001 )
| ~ ( X1001 @ X1002 ) )
& ( ( ( esk27_1 @ X1001 )
!= ( esk28_1 @ X1001 ) )
| ( exu @ X1001 )
| ~ ( X1001 @ X1002 ) )
& ( ~ ( X1005 @ ( esk29_2 @ X1005 @ X1006 ) )
| ( ( esk29_2 @ X1005 @ X1006 )
!= X1006 )
| ( exu @ X1005 ) )
& ( ( X1005 @ ( esk29_2 @ X1005 @ X1006 ) )
| ( ( esk29_2 @ X1005 @ X1006 )
= X1006 )
| ( exu @ X1005 ) )
& ( ( X1008 != X1009 )
| ( X1010 != X1011 )
| ~ ( in @ X1010 @ X1008 )
| ( in @ X1011 @ X1009 ) )
& ( ~ ( in @ X1014 @ X1012 )
| ( in @ X1015 @ X1013 )
| ( X1014 != X1015 )
| ( X1012 != X1013 ) )
& ( ~ ( in @ X1015 @ X1013 )
| ( in @ X1014 @ X1012 )
| ( X1014 != X1015 )
| ( X1012 != X1013 ) )
& ( ~ ( exu @ X1016 )
| ~ ( X1016 @ X1017 )
| ~ ( X1016 @ X1018 )
| ( X1017 = X1018 ) )
& ( ~ ( exu @ X1019 )
| ( exu @ X1020 )
| ( ( esk30_2 @ X1019 @ X1020 )
= ( esk31_2 @ X1019 @ X1020 ) ) )
& ( ~ ( exu @ X1020 )
| ( exu @ X1019 )
| ( ( esk30_2 @ X1019 @ X1020 )
= ( esk31_2 @ X1019 @ X1020 ) ) )
& ( ~ ( exu @ X1019 )
| ( exu @ X1020 )
| ~ ( X1019 @ ( esk30_2 @ X1019 @ X1020 ) )
| ~ ( X1020 @ ( esk31_2 @ X1019 @ X1020 ) ) )
& ( ~ ( exu @ X1020 )
| ( exu @ X1019 )
| ~ ( X1019 @ ( esk30_2 @ X1019 @ X1020 ) )
| ~ ( X1020 @ ( esk31_2 @ X1019 @ X1020 ) ) )
& ( ~ ( exu @ X1019 )
| ( exu @ X1020 )
| ( X1019 @ ( esk30_2 @ X1019 @ X1020 ) )
| ( X1020 @ ( esk31_2 @ X1019 @ X1020 ) ) )
& ( ~ ( exu @ X1020 )
| ( exu @ X1019 )
| ( X1019 @ ( esk30_2 @ X1019 @ X1020 ) )
| ( X1020 @ ( esk31_2 @ X1019 @ X1020 ) ) )
& ( emptyset = emptyset )
& ( ( X1023 != X1024 )
| ( X1025 != X1026 )
| ( ( setadjoin @ X1023 @ X1025 )
= ( setadjoin @ X1024 @ X1026 ) ) )
& ( ( X1027 != X1028 )
| ( ( powerset @ X1027 )
= ( powerset @ X1028 ) ) )
& ( ( X1029 != X1030 )
| ( ( setunion @ X1029 )
= ( setunion @ X1030 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1031 )
| ~ ( X1031 @ X1032 )
| ~ ( X1031 @ X1033 )
| ( X1032 = X1033 ) )
& ( ( ( esk32_2 @ X1034 @ X1035 )
= ( esk33_2 @ X1034 @ X1035 ) )
| ~ ( exu @ X1034 )
| ~ ( exu @ X1035 )
| ( ( descr @ X1034 )
= ( descr @ X1035 ) ) )
& ( ~ ( X1034 @ ( esk32_2 @ X1034 @ X1035 ) )
| ~ ( X1035 @ ( esk33_2 @ X1034 @ X1035 ) )
| ~ ( exu @ X1034 )
| ~ ( exu @ X1035 )
| ( ( descr @ X1034 )
= ( descr @ X1035 ) ) )
& ( ( X1034 @ ( esk32_2 @ X1034 @ X1035 ) )
| ( X1035 @ ( esk33_2 @ X1034 @ X1035 ) )
| ~ ( exu @ X1034 )
| ~ ( exu @ X1035 )
| ( ( descr @ X1034 )
= ( descr @ X1035 ) ) )
& ( ( in @ ( esk34_4 @ X1038 @ X1039 @ X1040 @ X1041 ) @ X1038 )
| ( ( dsetconstr @ X1038 @ X1040 )
= ( dsetconstr @ X1039 @ X1041 ) )
| ( X1038 != X1039 ) )
& ( ( in @ ( esk35_4 @ X1038 @ X1039 @ X1040 @ X1041 ) @ X1039 )
| ( ( dsetconstr @ X1038 @ X1040 )
= ( dsetconstr @ X1039 @ X1041 ) )
| ( X1038 != X1039 ) )
& ( ( ( esk34_4 @ X1038 @ X1039 @ X1040 @ X1041 )
= ( esk35_4 @ X1038 @ X1039 @ X1040 @ X1041 ) )
| ( ( dsetconstr @ X1038 @ X1040 )
= ( dsetconstr @ X1039 @ X1041 ) )
| ( X1038 != X1039 ) )
& ( ~ ( X1040 @ ( esk34_4 @ X1038 @ X1039 @ X1040 @ X1041 ) )
| ~ ( X1041 @ ( esk35_4 @ X1038 @ X1039 @ X1040 @ X1041 ) )
| ( ( dsetconstr @ X1038 @ X1040 )
= ( dsetconstr @ X1039 @ X1041 ) )
| ( X1038 != X1039 ) )
& ( ( X1040 @ ( esk34_4 @ X1038 @ X1039 @ X1040 @ X1041 ) )
| ( X1041 @ ( esk35_4 @ X1038 @ X1039 @ X1040 @ X1041 ) )
| ( ( dsetconstr @ X1038 @ X1040 )
= ( dsetconstr @ X1039 @ X1041 ) )
| ( X1038 != X1039 ) )
& ( ( in @ ( esk36_2 @ X1044 @ X1045 ) @ X1044 )
| ( subset @ X1044 @ X1045 ) )
& ( ~ ( in @ ( esk36_2 @ X1044 @ X1045 ) @ X1045 )
| ( subset @ X1044 @ X1045 ) )
& ( ( X1047 != X1048 )
| ( subset @ X1048 @ X1047 ) )
& ( ( X1049 != X1050 )
| ( subset @ X1049 @ X1050 ) )
& ( ( in @ ( esk37_2 @ X1051 @ X1052 ) @ X1051 )
| ( subset @ X1051 @ X1052 ) )
& ( ~ ( in @ ( esk37_2 @ X1051 @ X1052 ) @ X1052 )
| ( subset @ X1051 @ X1052 ) )
& ( subset @ emptyset @ X1054 )
& ( ~ ( subset @ X1055 @ X1056 )
| ~ ( in @ X1057 @ X1055 )
| ( in @ X1057 @ X1056 ) )
& ( ~ ( subset @ X1058 @ X1059 )
| ( in @ X1060 @ X1059 )
| ~ ( in @ X1060 @ X1058 ) )
& ( ~ ( in @ X1063 @ X1061 )
| ( in @ X1063 @ X1062 )
| ~ ( subset @ X1061 @ X1062 ) )
& ( ( subset @ X1064 @ X1065 )
| ( X1064 != X1065 ) )
& ( ~ ( in @ X1068 @ X1066 )
| ( in @ X1068 @ X1067 )
| ( X1066 != X1067 ) )
& ( subset @ X1069 @ X1069 )
& ( ~ ( subset @ X1070 @ X1071 )
| ~ ( subset @ X1071 @ X1072 )
| ( subset @ X1070 @ X1072 ) )
& ( subset @ X1074 @ ( setadjoin @ X1073 @ X1074 ) )
& ( ~ ( subset @ X1075 @ X1077 )
| ( subset @ X1075 @ ( setadjoin @ X1076 @ X1077 ) ) )
& ( ~ ( subset @ X1078 @ X1079 )
| ( in @ X1078 @ ( powerset @ X1079 ) ) )
& ( ~ ( subset @ X1080 @ X1081 )
| ~ ( subset @ X1081 @ X1080 )
| ( X1080 = X1081 ) )
& ( ~ ( subset @ X1082 @ emptyset )
| ( X1082 = emptyset ) )
& ( ~ ( subset @ X1084 @ X1083 )
| ( in @ X1084 @ ( powerset @ X1083 ) ) )
& ( ~ ( in @ X1086 @ ( powerset @ X1085 ) )
| ( subset @ X1086 @ X1085 ) )
& ( in @ X1087 @ ( powerset @ X1087 ) )
& ( ~ ( subset @ X1088 @ X1089 )
| ( subset @ ( powerset @ X1088 ) @ ( powerset @ X1089 ) ) )
& ( in @ ( dsetconstr @ X1090 @ X1091 ) @ ( powerset @ X1090 ) )
& ( subset @ ( dsetconstr @ X1092 @ X1093 ) @ X1092 )
& ( ~ ( in @ X1096 @ X1094 )
| ( in @ X1096 @ ( binunion @ X1094 @ X1095 ) ) )
& ( in @ X1098 @ ( setadjoin @ X1097 @ ( setadjoin @ X1098 @ emptyset ) ) )
& ( ~ ( in @ X1101 @ X1100 )
| ( in @ X1101 @ ( binunion @ X1099 @ X1100 ) ) )
& ( ( in @ X1104 @ X1103 )
| X1105
| ( in @ X1104 @ X1102 )
| ~ ( in @ X1104 @ ( binunion @ X1102 @ X1103 ) ) )
& ( ~ X1105
| X1105
| ( in @ X1104 @ X1102 )
| ~ ( in @ X1104 @ ( binunion @ X1102 @ X1103 ) ) )
& ( ( in @ X1104 @ X1103 )
| X1105
| ~ X1105
| ~ ( in @ X1104 @ ( binunion @ X1102 @ X1103 ) ) )
& ( ~ X1105
| X1105
| ~ X1105
| ~ ( in @ X1104 @ ( binunion @ X1102 @ X1103 ) ) )
& ( ~ ( in @ X1108 @ ( binunion @ X1106 @ X1107 ) )
| ( in @ X1108 @ X1106 )
| ( in @ X1108 @ X1107 ) )
& ( subset @ X1109 @ ( binunion @ X1109 @ X1110 ) )
& ( subset @ X1112 @ ( binunion @ X1111 @ X1112 ) )
& ( ~ ( in @ X1115 @ X1113 )
| ~ ( in @ X1115 @ X1114 )
| ( in @ X1115 @ ( binintersect @ X1113 @ X1114 ) ) )
& ( ~ ( subset @ X1118 @ X1116 )
| ~ ( subset @ X1118 @ X1117 )
| ( subset @ X1118 @ ( binintersect @ X1116 @ X1117 ) ) )
& ( ~ ( in @ X1121 @ ( binintersect @ X1119 @ X1120 ) )
| ( in @ X1121 @ X1119 ) )
& ( subset @ ( binintersect @ X1122 @ X1123 ) @ X1122 )
& ( ~ ( subset @ X1124 @ X1125 )
| ( ( binintersect @ X1124 @ X1125 )
= X1124 ) )
& ( ( ( binintersect @ X1126 @ X1127 )
!= X1127 )
| ( subset @ X1127 @ X1126 ) )
& ( ~ ( in @ X1130 @ ( binintersect @ X1128 @ X1129 ) )
| ( in @ X1130 @ X1129 ) )
& ( ( in @ ( esk38_2 @ X1131 @ X1132 ) @ X1131 )
| ( ( binintersect @ X1131 @ X1132 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1131 @ X1132 ) @ X1132 )
| ( ( binintersect @ X1131 @ X1132 )
= emptyset ) )
& ( subset @ ( binintersect @ X1134 @ X1135 ) @ X1135 )
& ( ~ ( subset @ X1137 @ X1136 )
| ( ( binintersect @ X1136 @ X1137 )
= X1137 ) )
& ( ( ( binintersect @ X1138 @ X1139 )
!= X1138 )
| ( subset @ X1138 @ X1139 ) )
& ( ( binintersect @ X1140 @ ( binunion @ X1141 @ X1142 ) )
= ( binunion @ ( binintersect @ X1140 @ X1141 ) @ ( binintersect @ X1140 @ X1142 ) ) )
& ( ~ ( in @ X1145 @ X1143 )
| ( in @ X1145 @ X1144 )
| ( in @ X1145 @ ( setminus @ X1143 @ X1144 ) ) )
& ( ~ ( in @ X1148 @ ( setminus @ X1146 @ X1147 ) )
| ( in @ X1148 @ X1146 ) )
& ( ~ ( in @ X1151 @ ( setminus @ X1149 @ X1150 ) )
| ~ ( in @ X1151 @ X1150 ) )
& ( ~ ( subset @ X1152 @ X1153 )
| ( ( setminus @ X1152 @ X1153 )
= emptyset ) )
& ( ( in @ X1156 @ ( setminus @ X1154 @ X1155 ) )
| ~ ( in @ X1156 @ X1154 )
| ( in @ X1156 @ X1155 ) )
& ( ( in @ X1159 @ ( setminus @ X1157 @ X1158 ) )
| ( in @ X1159 @ X1158 )
| ~ ( in @ X1159 @ X1157 ) )
& ( ( in @ X1162 @ X1160 )
| ~ ( in @ X1162 @ ( setminus @ X1160 @ X1161 ) ) )
& ( ~ ( in @ X1165 @ X1164 )
| ~ ( in @ X1165 @ ( setminus @ X1163 @ X1164 ) ) )
& ( subset @ ( setminus @ X1166 @ X1167 ) @ X1166 )
& ( ( ( setminus @ X1168 @ X1169 )
!= emptyset )
| ( subset @ X1168 @ X1169 ) )
& ( ~ ( in @ X1172 @ X1170 )
| X1173
| ( in @ X1172 @ X1170 )
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ( in @ X1172 @ X1171 )
| X1173
| ( in @ X1172 @ X1170 )
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ~ X1173
| X1173
| ( in @ X1172 @ X1170 )
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ~ ( in @ X1172 @ X1170 )
| X1173
| ~ ( in @ X1172 @ X1171 )
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ( in @ X1172 @ X1171 )
| X1173
| ~ ( in @ X1172 @ X1171 )
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ~ X1173
| X1173
| ~ ( in @ X1172 @ X1171 )
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ~ ( in @ X1172 @ X1170 )
| X1173
| ~ X1173
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ( in @ X1172 @ X1171 )
| X1173
| ~ X1173
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ~ X1173
| X1173
| ~ X1173
| ~ ( in @ X1172 @ ( symdiff @ X1170 @ X1171 ) ) )
& ( ~ ( in @ X1176 @ X1174 )
| ( in @ X1176 @ X1175 )
| ( in @ X1176 @ ( symdiff @ X1174 @ X1175 ) ) )
& ( ( in @ X1179 @ X1177 )
| ~ ( in @ X1179 @ X1178 )
| ( in @ X1179 @ ( symdiff @ X1177 @ X1178 ) ) )
& ( ~ ( in @ X1182 @ X1180 )
| ~ ( in @ X1182 @ X1181 )
| ~ ( in @ X1182 @ ( symdiff @ X1180 @ X1181 ) ) )
& ( ( in @ X1185 @ X1183 )
| ( in @ X1185 @ X1184 )
| ~ ( in @ X1185 @ ( symdiff @ X1183 @ X1184 ) ) )
& ( in @ X1187 @ ( setadjoin @ X1186 @ ( setadjoin @ X1187 @ emptyset ) ) )
& ( in @ X1188 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1188 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1188 @ ( setadjoin @ X1189 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1191 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1190 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1190 @ ( setadjoin @ X1191 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1192 @ ( setadjoin @ X1193 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1194 @ X1195 ) )
& ( ~ ( in @ X1197 @ X1196 )
| ( subset @ ( setadjoin @ X1197 @ emptyset ) @ X1196 ) )
& ( ~ ( in @ X1199 @ X1198 )
| ( in @ ( setadjoin @ X1199 @ emptyset ) @ ( powerset @ X1198 ) ) )
& ( ~ ( in @ X1202 @ X1200 )
| ( in @ ( setadjoin @ X1202 @ emptyset ) @ ( powerset @ ( binunion @ X1200 @ X1201 ) ) ) )
& ( ~ ( in @ X1205 @ ( setadjoin @ X1203 @ ( setadjoin @ X1204 @ emptyset ) ) )
| ( X1205 = X1203 )
| ( X1205 = X1204 ) )
& ( ~ ( in @ X1208 @ X1206 )
| ~ ( in @ X1209 @ X1207 )
| ( subset @ ( setadjoin @ X1208 @ ( setadjoin @ X1209 @ emptyset ) ) @ ( binunion @ X1206 @ X1207 ) ) )
& ( ~ ( in @ X1212 @ X1210 )
| ~ ( in @ X1213 @ X1211 )
| ( in @ ( setadjoin @ X1212 @ ( setadjoin @ X1213 @ emptyset ) ) @ ( powerset @ ( binunion @ X1210 @ X1211 ) ) ) )
& ( ~ ( in @ X1216 @ X1214 )
| ~ ( in @ X1217 @ X1215 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1216 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1216 @ ( setadjoin @ X1217 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1214 @ X1215 ) ) ) )
& ( ~ ( in @ X1220 @ X1218 )
| ~ ( in @ X1221 @ X1219 )
| ( in @ ( setadjoin @ ( setadjoin @ X1220 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1220 @ ( setadjoin @ X1221 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1218 @ X1219 ) ) ) ) )
& ( ~ ( in @ X1224 @ X1222 )
| ~ ( in @ X1225 @ X1223 )
| ( in @ ( kpair @ X1224 @ X1225 ) @ ( powerset @ ( powerset @ ( binunion @ X1222 @ X1223 ) ) ) ) )
& ( ~ ( in @ X1228 @ X1226 )
| ~ ( in @ X1229 @ X1227 )
| ( in @ ( kpair @ X1228 @ X1229 ) @ ( cartprod @ X1226 @ X1227 ) ) )
& ( ( in @ ( esk39_3 @ X1230 @ X1231 @ X1232 ) @ X1230 )
| ~ ( in @ X1232 @ ( cartprod @ X1230 @ X1231 ) ) )
& ( ( in @ ( esk40_3 @ X1230 @ X1231 @ X1232 ) @ X1231 )
| ~ ( in @ X1232 @ ( cartprod @ X1230 @ X1231 ) ) )
& ( ( X1232
= ( kpair @ ( esk39_3 @ X1230 @ X1231 @ X1232 ) @ ( esk40_3 @ X1230 @ X1231 @ X1232 ) ) )
| ~ ( in @ X1232 @ ( cartprod @ X1230 @ X1231 ) ) )
& ( ~ ( in @ X1237 @ ( cartprod @ X1235 @ X1236 ) )
| ( iskpair @ X1237 ) )
& ( ( in @ ( esk41_2 @ X1238 @ X1239 ) @ X1238 )
| ~ ( in @ X1239 @ ( setunion @ X1238 ) ) )
& ( ( in @ X1239 @ ( esk41_2 @ X1238 @ X1239 ) )
| ~ ( in @ X1239 @ ( setunion @ X1238 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1241 @ emptyset ) ) @ X1241 )
& ( subset @ X1242 @ ( setunion @ ( setadjoin @ X1242 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ esk42_0 @ emptyset ) )
!= esk42_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_175])])])])])])]) ).
thf(c_0_177,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X3 @ X2 )
= X2 )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_178,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X2 )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_179,negated_conjecture,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ ( subset @ X3 @ X2 )
| ~ ( subset @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
thf(c_0_180,negated_conjecture,
! [X2: $i] : ( subset @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_181,negated_conjecture,
! [X2: $i] : ( subset @ X2 @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_182,negated_conjecture,
( ( setunion @ ( setadjoin @ esk42_0 @ emptyset ) )
!= esk42_0 ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_183,negated_conjecture,
! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181])]) ).
thf(c_0_184,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU636^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:54:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 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
% 300.11/150.28 # Version: 3.1.0-ho
% 300.11/150.28 # Preprocessing class: HSLMSLSSLLLCHFA.
% 300.11/150.28 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 300.11/150.28 # Starting ehoh_best5 with 300s (1) cores
% 300.11/150.28 # Starting almost_fo_3_lam with 300s (1) cores
% 300.11/150.28 # Starting new_bool_5 with 300s (1) cores
% 300.11/150.28 # Starting pre_casc_3 with 300s (1) cores
% 300.11/150.28 # Starting ho_unfolding_8 with 300s (1) cores
% 300.11/150.28 # Starting new_ho_10_cnf2 with 300s (1) cores
% 300.11/150.28 # Starting new_bool_3 with 300s (1) cores
% 300.11/150.28 # Starting new_ho_5 with 300s (1) cores
% 300.11/150.28 # new_bool_5 with pid 12404 completed with status 0
% 300.11/150.28 # Result found by new_bool_5
% 300.11/150.28 # Preprocessing class: HSLMSLSSLLLCHFA.
% 300.11/150.28 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 300.11/150.28 # Starting ehoh_best5 with 300s (1) cores
% 300.11/150.28 # Starting almost_fo_3_lam with 300s (1) cores
% 300.11/150.28 # Starting new_bool_5 with 300s (1) cores
% 300.11/150.28 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 300.11/150.28 # Search class: HGHSM-FSLS31-MHFMMSBN
% 300.11/150.28 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 300.11/150.28 # Starting pre_casc_7 with 163s (1) cores
% 300.11/150.28 # pre_casc_7 with pid 12412 completed with status 0
% 300.11/150.28 # Result found by pre_casc_7
% 300.11/150.28 # Preprocessing class: HSLMSLSSLLLCHFA.
% 300.11/150.28 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 300.11/150.28 # Starting ehoh_best5 with 300s (1) cores
% 300.11/150.28 # Starting almost_fo_3_lam with 300s (1) cores
% 300.11/150.28 # Starting new_bool_5 with 300s (1) cores
% 300.11/150.28 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 300.11/150.28 # Search class: HGHSM-FSLS31-MHFMMSBN
% 300.11/150.28 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 300.11/150.28 # Starting pre_casc_7 with 163s (1) cores
% 300.11/150.28 # Preprocessing time : 0.004 s
% 300.11/150.28
% 300.11/150.28 # Proof found!
% 300.11/150.28 # SZS status Theorem
% 300.11/150.28 # SZS output start CNFRefutation
% See solution above
% 300.11/150.29 # Parsed axioms : 332
% 300.11/150.29 # Removed by relevancy pruning/SinE : 180
% 300.11/150.29 # Initial clauses : 235
% 300.11/150.29 # Removed in clause preprocessing : 25
% 300.11/150.29 # Initial clauses in saturation : 210
% 300.11/150.29 # Processed clauses : 179
% 300.11/150.29 # ...of these trivial : 5
% 300.11/150.29 # ...subsumed : 71
% 300.11/150.29 # ...remaining for further processing : 103
% 300.11/150.29 # Other redundant clauses eliminated : 5
% 300.11/150.29 # Clauses deleted for lack of memory : 0
% 300.11/150.29 # Backward-subsumed : 4
% 300.11/150.29 # Backward-rewritten : 6
% 300.11/150.29 # Generated clauses : 243
% 300.11/150.29 # ...of the previous two non-redundant : 200
% 300.11/150.29 # ...aggressively subsumed : 0
% 300.11/150.29 # Contextual simplify-reflections : 0
% 300.11/150.29 # Paramodulations : 237
% 300.11/150.29 # Factorizations : 0
% 300.11/150.29 # NegExts : 0
% 300.11/150.29 # Equation resolutions : 5
% 300.11/150.29 # Disequality decompositions : 0
% 300.11/150.29 # Total rewrite steps : 46
% 300.11/150.29 # ...of those cached : 22
% 300.11/150.29 # Propositional unsat checks : 0
% 300.11/150.29 # Propositional check models : 0
% 300.11/150.29 # Propositional check unsatisfiable : 0
% 300.11/150.29 # Propositional clauses : 0
% 300.11/150.29 # Propositional clauses after purity: 0
% 300.11/150.29 # Propositional unsat core size : 0
% 300.11/150.29 # Propositional preprocessing time : 0.000
% 300.11/150.29 # Propositional encoding time : 0.000
% 300.11/150.29 # Propositional solver time : 0.000
% 300.11/150.29 # Success case prop preproc time : 0.000
% 300.11/150.29 # Success case prop encoding time : 0.000
% 300.11/150.29 # Success case prop solver time : 0.000
% 300.11/150.29 # Current number of processed clauses : 89
% 300.11/150.29 # Positive orientable unit clauses : 31
% 300.11/150.29 # Positive unorientable unit clauses: 0
% 300.11/150.29 # Negative unit clauses : 2
% 300.11/150.29 # Non-unit-clauses : 56
% 300.11/150.29 # Current number of unprocessed clauses: 228
% 300.11/150.29 # ...number of literals in the above : 635
% 300.11/150.29 # Current number of archived formulas : 0
% 300.11/150.29 # Current number of archived clauses : 10
% 300.11/150.29 # Clause-clause subsumption calls (NU) : 566
% 300.11/150.29 # Rec. Clause-clause subsumption calls : 494
% 300.11/150.29 # Non-unit clause-clause subsumptions : 63
% 300.11/150.29 # Unit Clause-clause subsumption calls : 5
% 300.11/150.29 # Rewrite failures with RHS unbound : 0
% 300.11/150.29 # BW rewrite match attempts : 9
% 300.11/150.29 # BW rewrite match successes : 5
% 300.11/150.29 # Condensation attempts : 179
% 300.11/150.29 # Condensation successes : 3
% 300.11/150.29 # Termbank termtop insertions : 34193
% 300.11/150.29 # Search garbage collected termcells : 13076
% 300.11/150.29
% 300.11/150.29 # -------------------------------------------------
% 300.11/150.29 # User time : 0.051 s
% 300.11/150.29 # System time : 0.009 s
% 300.11/150.29 # Total time : 0.060 s
% 300.11/150.29 # Maximum resident set size: 5080 pages
% 300.11/150.29
% 300.11/150.29 # -------------------------------------------------
% 300.11/150.29 # User time : 0.059 s
% 300.11/150.29 # System time : 0.012 s
% 300.11/150.29 # Total time : 0.071 s
% 300.11/150.29 # Maximum resident set size: 2164 pages
% 300.11/150.29 % E---3.1 exiting
% 300.11/150.29 % E exiting
%------------------------------------------------------------------------------