%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU631^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:42 EDT 2024
% Result : Theorem 3.14s 0.89s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 383
% Syntax : Number of formulae : 441 ( 36 unt; 230 typ; 0 def)
% Number of atoms : 1720 ( 397 equ; 0 cnn)
% Maximal formula atoms : 503 ( 8 avg)
% Number of connectives : 7008 ( 524 ~; 556 |; 389 &;4519 @)
% ( 211 <=>; 809 =>; 0 <=; 0 <~>)
% Maximal formula depth : 639 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 337 ( 337 >; 0 *; 0 +; 0 <<)
% Number of symbols : 233 ( 230 usr; 157 con; 0-4 aty)
% Number of variables : 1484 ( 88 ^1254 !; 142 ?;1484 :)
% 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,
epred1_0: $o ).
thf(decl_193,type,
esk1_2: $i > $i > $i ).
thf(decl_194,type,
esk2_2: $i > $i > $i ).
thf(decl_195,type,
esk3_2: $i > $i > $i ).
thf(decl_196,type,
esk4_1: $i > $i ).
thf(decl_197,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_198,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_199,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_200,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_201,type,
esk9_1: $i > $i ).
thf(decl_202,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_203,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_204,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_205,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_206,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_207,type,
esk15_2: $i > $i > $i ).
thf(decl_208,type,
esk16_2: $i > $i > $i ).
thf(decl_209,type,
esk17_1: $i > $i ).
thf(decl_210,type,
esk18_1: $i > $i ).
thf(decl_211,type,
esk19_1: $i > $i ).
thf(decl_212,type,
esk20_2: $i > $i > $i ).
thf(decl_213,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_214,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_215,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_216,type,
esk24_1: $i > $i ).
thf(decl_217,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_218,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_219,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_220,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_221,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_222,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_223,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_224,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_225,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_226,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_227,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_228,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_229,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_230,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_231,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_232,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_233,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_234,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_235,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_236,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_237,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_238,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_239,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_240,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_241,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_242,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_243,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_244,type,
esk52_2: $i > $i > $i ).
thf(decl_245,type,
esk53_2: $i > $i > $i ).
thf(decl_246,type,
esk54_2: $i > $i > $i ).
thf(decl_247,type,
esk55_2: $i > $i > $i ).
thf(decl_248,type,
esk56_2: $i > $i > $i ).
thf(decl_249,type,
esk57_2: $i > $i > $i ).
thf(decl_250,type,
esk58_2: $i > $i > $i ).
thf(decl_251,type,
esk59_0: $i ).
thf(decl_252,type,
esk60_0: $i ).
thf(decl_253,type,
esk61_0: $i ).
thf(decl_259,type,
esk67_0: $i ).
thf(decl_260,type,
esk68_0: $i ).
thf(cartprod,axiom,
( cartprod
= ( ^ [X4: $i,X5: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ( in @ X3 @ X4 )
& ? [X14: $i] :
( ( in @ X14 @ X5 )
& ( X2
= ( kpair @ X3 @ X14 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprod) ).
thf(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X4 ) )
& ( X4
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
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(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(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(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(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(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
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(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(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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(cartprodmempair1,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
=> ! [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(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(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(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(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(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(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(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(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(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(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(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(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(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(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(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(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(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(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(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(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(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
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(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
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(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(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(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(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
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(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(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
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(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(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,
( cartprod
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Z0 @ Z1 ) ) )
@ ^ [Z2: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ? [X14: $i] :
( ( in @ X14 @ Z1 )
& ( Z2
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X14 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cartprod]) ).
thf(c_0_153,plain,
( kpair
= ( ^ [Z0: $i,Z1: $i] : ( setadjoin @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fof_simplification,[status(thm)],[kpair]) ).
thf(c_0_154,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_155,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_156,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_157,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_158,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_159,plain,
( cartprod
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Z0 @ Z1 ) ) )
@ ^ [Z2: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ? [X14: $i] :
( ( in @ X14 @ Z1 )
& ( Z2
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X14 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_152,c_0_153]) ).
thf(c_0_160,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_161,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_162,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_163,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_164,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_165,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_166,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_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,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_170,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_171,axiom,
( kpairiskpair
= ( ! [X2: $i,X3: $i] :
? [X451: $i] :
( ( in @ X451 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X452: $i] :
( ( in @ X452 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X451 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X451 @ ( setadjoin @ X452 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairiskpair,c_0_154]) ).
thf(c_0_172,axiom,
( kpairp
= ( ! [X2: $i,X3: $i] :
? [X453: $i] :
( ( in @ X453 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X454: $i] :
( ( in @ X454 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X453 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X453 @ ( setadjoin @ X454 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp,c_0_153]),c_0_154]) ).
thf(c_0_173,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X433: $i] :
( ( X1 @ X433 )
& ! [X434: $i] :
( ( X1 @ X434 )
=> ( X433 = X434 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_155,c_0_156]) ).
thf(c_0_174,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X435: $i] :
( ( X1 @ X435 )
& ! [X436: $i] :
( ( X1 @ X436 )
=> ( X435 = X436 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_157,c_0_156]) ).
thf(c_0_175,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X437: $i] :
( ( X1 @ X437 )
& ! [X438: $i] :
( ( X1 @ X438 )
=> ( X437 = X438 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_158,c_0_156]) ).
thf(c_0_176,axiom,
( ubforcartprodlem3
= ( ! [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 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[ubforcartprodlem3,c_0_153]) ).
thf(c_0_177,axiom,
( cartprodpairin
= ( ! [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 ) )
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) )
@ ^ [Z0: $i] :
? [X455: $i] :
( ( in @ X455 @ X4 )
& ? [X456: $i] :
( ( in @ X456 @ X5 )
& ( Z0
= ( setadjoin @ ( setadjoin @ X455 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X455 @ ( setadjoin @ X456 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[cartprodpairin,c_0_153]),c_0_159]) ).
thf(c_0_178,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X439: $i] :
( ( X1 @ X439 )
& ! [X440: $i] :
( ( X1 @ X440 )
=> ( X439 = X440 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_160,c_0_156]) ).
thf(c_0_179,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X441: $i] :
( ( X1 @ X441 )
& ! [X442: $i] :
( ( X1 @ X442 )
=> ( X441 = X442 ) ) )
<=> ? [X443: $i] :
( ( X17 @ X443 )
& ! [X444: $i] :
( ( X17 @ X444 )
=> ( X443 = X444 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_161,c_0_156]) ).
thf(c_0_180,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X445: $i] :
( ( X1 @ X445 )
& ! [X446: $i] :
( ( X1 @ X446 )
=> ( X445 = X446 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_162,c_0_156]) ).
thf(c_0_181,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X447: $i] :
( ( X1 @ X447 )
& ! [X448: $i] :
( ( X1 @ X448 )
=> ( X447 = X448 ) ) )
=> ( ? [X449: $i] :
( ( X17 @ X449 )
& ! [X450: $i] :
( ( X17 @ X450 )
=> ( X449 = X450 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_163,c_0_156]) ).
thf(c_0_182,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_183,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_184,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_185,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_186,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_164]) ).
thf(c_0_187,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X431: $i] :
( ( X1 @ X431 )
& ! [X432: $i] :
( ( X1 @ X432 )
=> ( X431 = X432 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_165,c_0_156]) ).
thf(c_0_188,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_189,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_164]) ).
thf(c_0_190,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_166,c_0_164]) ).
thf(c_0_191,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_164]) ).
thf(c_0_192,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_193,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X429: $i] :
( ( X1 @ X429 )
& ! [X430: $i] :
( ( X1 @ X430 )
=> ( X429 = X430 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_167,c_0_156]) ).
thf(c_0_194,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X427: $i] :
( ( X1 @ X427 )
& ! [X428: $i] :
( ( X1 @ X428 )
=> ( X427 = X428 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_168,c_0_156]) ).
thf(c_0_195,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_196,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_197,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_198,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X425: $i] :
( ( X1 @ X425 )
& ! [X426: $i] :
( ( X1 @ X426 )
=> ( X425 = X426 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_169,c_0_156]) ).
thf(c_0_199,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X423: $i] :
( ( X6 @ X2 @ X423 )
& ! [X424: $i] :
( ( X6 @ X2 @ X424 )
=> ( X423 = X424 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_170,c_0_156]) ).
thf(c_0_200,plain,
( epred1_0
<=> ! [X486: $i] :
? [X487: $i] :
( ! [X488: $i] :
( ( in @ X488 @ X487 )
=> ! [X489: $i] :
( ( in @ X489 @ X488 )
=> ( in @ X489 @ X486 ) ) )
& ! [X490: $i,X491: $i] :
( ( ( in @ X490 @ X486 )
& ( in @ X491 @ X486 ) )
=> ( ! [X492: $i] :
( ( in @ X492 @ X487 )
=> ( ( in @ X490 @ X492 )
<=> ( in @ X491 @ X492 ) ) )
=> ( X490 = X491 ) ) )
& ! [X493: $i,X494: $i] :
( ( ( in @ X493 @ X487 )
& ( in @ X494 @ X487 ) )
=> ( ! [X495: $i] :
( ( in @ X495 @ X493 )
=> ( in @ X495 @ X494 ) )
| ! [X496: $i] :
( ( in @ X496 @ X494 )
=> ( in @ X496 @ X493 ) ) ) )
& ! [X497: $i] :
( ( ! [X498: $i] :
( ( in @ X498 @ X497 )
=> ( in @ X498 @ X486 ) )
& ? [X499: $i] : ( in @ X499 @ X497 ) )
=> ? [X500: $i,X501: $i] :
( ( in @ X500 @ X487 )
& ( in @ X501 @ X497 )
& ~ ? [X502: $i] :
( ( in @ X502 @ X500 )
& ( in @ X502 @ X497 ) )
& ! [X503: $i] :
( ( in @ X503 @ X487 )
=> ( ! [X504: $i] :
( ( in @ X504 @ X503 )
=> ( in @ X504 @ X500 ) )
| ( in @ X501 @ X503 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_201,negated_conjecture,
~ ( ! [X457: $i,X458: $i] :
( ! [X459: $i] :
( ( in @ X459 @ X457 )
<=> ( in @ X459 @ X458 ) )
=> ( X457 = X458 ) )
=> ( ! [X460: $i] :
~ ( in @ X460 @ emptyset )
=> ( ! [X461: $i,X462: $i,X463: $i] :
( ( in @ X463 @ ( setadjoin @ X461 @ X462 ) )
<=> ( ( X463 = X461 )
| ( in @ X463 @ X462 ) ) )
=> ( ! [X464: $i,X465: $i] :
( ( in @ X465 @ ( powerset @ X464 ) )
<=> ! [X466: $i] :
( ( in @ X466 @ X465 )
=> ( in @ X466 @ X464 ) ) )
=> ( ! [X467: $i,X468: $i] :
( ( in @ X468 @ ( setunion @ X467 ) )
<=> ? [X469: $i] :
( ( in @ X468 @ X469 )
& ( in @ X469 @ X467 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X470: $i] :
( ( in @ X470 @ omega )
=> ( in @ ( setadjoin @ X470 @ X470 ) @ omega ) )
=> ( ! [X471: $i] :
( ( ( in @ emptyset @ X471 )
& ! [X472: $i] :
( ( ( in @ X472 @ omega )
& ( in @ X472 @ X471 ) )
=> ( in @ ( setadjoin @ X472 @ X472 ) @ X471 ) ) )
=> ! [X473: $i] :
( ( in @ X473 @ omega )
=> ( in @ X473 @ X471 ) ) )
=> ( ! [X474: $i > $i > $o,X475: $i] :
( ! [X476: $i] :
( ( in @ X476 @ X475 )
=> ? [X477: $i] :
( ( X474 @ X476 @ X477 )
& ! [X478: $i] :
( ( X474 @ X476 @ X478 )
=> ( X477 = X478 ) ) ) )
=> ? [X479: $i] :
! [X480: $i] :
( ( in @ X480 @ X479 )
<=> ? [X481: $i] :
( ( in @ X481 @ X475 )
& ( X474 @ X481 @ X480 ) ) ) )
=> ( ! [X482: $i] :
( ? [X483: $i] : ( in @ X483 @ X482 )
=> ? [X484: $i] :
( ( in @ X484 @ X482 )
& ~ ? [X485: $i] :
( ( in @ X485 @ X484 )
& ( in @ X485 @ X482 ) ) ) )
=> ( epred1_0
=> ( ! [X505: $i > $o] :
( ? [X506: $i] :
( ( X505 @ X506 )
& ! [X507: $i] :
( ( X505 @ X507 )
=> ( X506 = X507 ) ) )
=> ( X505
@ ( descr
@ ^ [Z0: $i] : ( X505 @ Z0 ) ) ) )
=> ( ! [X508: $i,X509: $i > $o,X510: $i] :
( ( in @ X510 @ X508 )
=> ( ( X509 @ X510 )
=> ( in @ X510 @ ( dsetconstr @ X508 @ X509 ) ) ) )
=> ( ! [X511: $i,X512: $i > $o,X513: $i] :
( ( in @ X513 @ ( dsetconstr @ X511 @ X512 ) )
=> ( in @ X513 @ X511 ) )
=> ( ! [X514: $i,X515: $i > $o,X516: $i] :
( ( in @ X516 @ ( dsetconstr @ X514 @ X515 ) )
=> ( X515 @ X516 ) )
=> ( ! [X517: $i > $o] :
( ? [X518: $i] :
( ( X517 @ X518 )
& ! [X519: $i] :
( ( X517 @ X519 )
=> ( X518 = X519 ) ) )
=> ? [X520: $i] :
( ( X517 @ X520 )
& ! [X521: $i] :
( ( X517 @ X521 )
=> ( X520 = X521 ) ) ) )
=> ( ! [X522: $o,X523: $i] :
( ( in @ X523 @ ( prop2set @ X522 ) )
=> X522 )
=> ( ! [X524: $i] :
( ( in @ X524 @ emptyset )
=> ! [X525: $o] : X525 )
=> ( ! [X526: $i] :
( ( in @ X526 @ emptyset )
=> ~ $true )
=> ( ! [X527: $i] :
~ ( in @ X527 @ emptyset )
=> ( ! [X528: $i > $o] :
( ? [X529: $i] :
( ( X528 @ X529 )
& ! [X530: $i] :
( ( X528 @ X530 )
=> ( X529 = X530 ) ) )
=> ? [X531: $i] : ( X528 @ X531 ) )
=> ( ! [X532: $i,X533: $i] :
( ! [X534: $i] :
( ( in @ X534 @ X532 )
=> ( in @ X534 @ X533 ) )
=> ( ! [X535: $i] :
( ( in @ X535 @ X533 )
=> ( in @ X535 @ X532 ) )
=> ( X532 = X533 ) ) )
=> ( ! [X536: $i] :
( ! [X537: $i] :
~ ( in @ X537 @ X536 )
=> ( X536 = emptyset ) )
=> ( ! [X538: $i] :
( ! [X539: $i] :
~ ( in @ X539 @ X538 )
=> ( X538 = emptyset ) )
=> ( ! [X540: $i,X541: $i > $o,X542: $i] :
( ( in @ X542 @ X540 )
=> ( ( in @ X542 @ ( dsetconstr @ X540 @ X541 ) )
<=> ( X541 @ X542 ) ) )
=> ( ! [X543: $i] :
( ( X543 != emptyset )
=> ? [X544: $i] : ( in @ X544 @ X543 ) )
=> ( ! [X545: $i,X546: $i > $o,X547: $i] :
( ( in @ X547 @ X545 )
=> ( ( X546 @ X547 )
=> ( ( dsetconstr @ X545 @ X546 )
!= emptyset ) ) )
=> ( ! [X548: $i] :
( ? [X549: $i] : ( in @ X549 @ X548 )
=> ( X548 != emptyset ) )
=> ( ! [X550: $i,X551: $i] : ( in @ X550 @ ( setadjoin @ X550 @ X551 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X552: $i,X553: $i,X554: $i] :
( ( in @ X554 @ X553 )
=> ( in @ X554 @ ( setadjoin @ X552 @ X553 ) ) )
=> ( ! [X555: $i,X556: $i,X557: $i] :
( ( in @ X557 @ ( setadjoin @ X555 @ X556 ) )
=> ! [X558: $o] :
( ( ( X557 = X555 )
=> X558 )
=> ( ( ( in @ X557 @ X556 )
=> X558 )
=> X558 ) ) )
=> ( ! [X559: $i,X560: $i,X561: $i] :
( ( in @ X561 @ ( setadjoin @ X559 @ X560 ) )
=> ( ( X561 = X559 )
| ( in @ X561 @ X560 ) ) )
=> ( ! [X562: $i] :
( ( dsetconstr @ X562
@ ^ [Z0: $i] : $true )
= X562 )
=> ( ! [X563: $i,X564: $i] :
( ! [X565: $i] :
( ( in @ X565 @ X564 )
=> ( in @ X565 @ X563 ) )
=> ( in @ X564 @ ( powerset @ X563 ) ) )
=> ( ! [X566: $i] : ( in @ emptyset @ ( powerset @ X566 ) )
=> ( ! [X567: $i] : ( in @ emptyset @ ( powerset @ X567 ) )
=> ( ! [X568: $i,X569: $i,X570: $i] :
( ( in @ X569 @ ( powerset @ X568 ) )
=> ( ( in @ X570 @ X569 )
=> ( in @ X570 @ X568 ) ) )
=> ( ! [X571: $i,X572: $i,X573: $i] :
( ( in @ X572 @ X573 )
=> ( ( in @ X573 @ X571 )
=> ( in @ X572 @ ( setunion @ X571 ) ) ) )
=> ( ! [X574: $i,X575: $i] :
( ( in @ X575 @ ( setunion @ X574 ) )
=> ! [X576: $o] :
( ! [X577: $i] :
( ( in @ X575 @ X577 )
=> ( ( in @ X577 @ X574 )
=> X576 ) )
=> X576 ) )
=> ( ! [X578: $i,X579: $i] :
( ( in @ X579 @ X578 )
=> ( in @ X579 @ ( powerset @ ( setunion @ X578 ) ) ) )
=> ( ! [X580: $i > $o] :
( ? [X581: $i] :
( ( X580 @ X581 )
& ! [X582: $i] :
( ( X580 @ X582 )
=> ( X581 = X582 ) ) )
=> ? [X583: $i] :
! [X584: $i] :
( ( X580 @ X584 )
<=> ( X584 = X583 ) ) )
=> ( ! [X585: $i] :
( ( X585 != emptyset )
=> ? [X586: $i] :
( ( in @ X586 @ X585 )
& $true ) )
=> ( ! [X587: $i,X588: $i] :
( ( in @ X587 @ ( setadjoin @ X588 @ emptyset ) )
=> ( X587 = X588 ) )
=> ( ! [X589: $i,X590: $i] :
( ( X589 != X590 )
=> ~ ( in @ X590 @ ( setadjoin @ X589 @ emptyset ) ) )
=> ( ! [X591: $i,X592: $i] :
( ( X591 = X592 )
=> ( in @ X591 @ ( setadjoin @ X592 @ emptyset ) ) )
=> ( ! [X593: $i,X594: $i] :
( ( in @ X593 @ ( setadjoin @ X594 @ emptyset ) )
=> ( in @ X594 @ ( setadjoin @ X593 @ emptyset ) ) )
=> ( ! [X595: $i,X596: $i,X597: $i] :
( ( in @ X597 @ ( setadjoin @ X595 @ ( setadjoin @ X596 @ emptyset ) ) )
=> ( ( X597 = X595 )
| ( X597 = X596 ) ) )
=> ( ! [X598: $i,X599: $i] : ( in @ X598 @ ( setadjoin @ X598 @ ( setadjoin @ X599 @ emptyset ) ) )
=> ( ! [X600: $i,X601: $i] : ( in @ X601 @ ( setadjoin @ X600 @ ( setadjoin @ X601 @ emptyset ) ) )
=> ( ! [X602: $i,X603: $i > $o] :
( ? [X604: $i] :
( ( in @ X604 @ X602 )
& ( X603 @ X604 ) )
=> ( ( ( dsetconstr @ X602 @ X603 )
= emptyset )
=> ~ $true ) )
=> ( ! [X605: $i > $o,X606: $i] :
( ( in @ X606 @ emptyset )
=> ( X605 @ X606 ) )
=> ( ! [X607: $i,X608: $i > $o] :
( ~ ! [X609: $i] :
( ( in @ X609 @ X607 )
=> ( X608 @ X609 ) )
=> ? [X610: $i] :
( ( in @ X610 @ X607 )
& ~ ( X608 @ X610 ) ) )
=> ( ! [X611: $i,X612: $i > $o] :
( ! [X613: $i] :
( ( in @ X613 @ X611 )
=> ~ ( X612 @ X613 ) )
=> ~ ? [X614: $i] :
( ( in @ X614 @ X611 )
& ( X612 @ X614 ) ) )
=> ( ! [X615: $i,X616: $i > $o] :
( ~ ? [X617: $i] :
( ( in @ X617 @ X615 )
& ( X616 @ X617 ) )
=> ! [X618: $i] :
( ( in @ X618 @ X615 )
=> ~ ( X616 @ X618 ) ) )
=> ( ! [X619: $i,X620: $i > $o] :
( ? [X621: $i] :
( ( in @ X621 @ X619 )
& ~ ( X620 @ X621 ) )
=> ~ ! [X622: $i] :
( ( in @ X622 @ X619 )
=> ( X620 @ X622 ) ) )
=> ( ! [X623: $o] :
( X623
=> ( in @ emptyset @ ( prop2set @ X623 ) ) )
=> ( prop2set2propI
=> ( ! [X624: $i,X625: $i > $o] :
( ~ ? [X626: $i] :
( ( in @ X626 @ X624 )
& ( X625 @ X626 ) )
=> ! [X627: $i] :
( ( in @ X627 @ X624 )
=> ~ ( X625 @ X627 ) ) )
=> ( ! [X628: $i,X629: $i > $o] :
( ~ ! [X630: $i] :
( ( in @ X630 @ X628 )
=> ( X629 @ X630 ) )
=> ? [X631: $i] :
( ( in @ X631 @ X628 )
& ~ ( X629 @ X631 ) ) )
=> ( ! [X632: $i > $o] :
( ? [X633: $i] :
( ( X632 @ X633 )
& ! [X634: $i] :
( ( X632 @ X634 )
=> ( X633 = X634 ) ) )
=> ? [X635: $i] :
( ( X632 @ X635 )
& ! [X636: $i] :
( ( X632 @ X636 )
=> ( X635 = X636 ) ) ) )
=> ( ! [X637: $i > $o] :
( ? [X638: $i] : ( X637 @ X638 )
=> ( ! [X639: $i,X640: $i] :
( ( X637 @ X639 )
=> ( ( X637 @ X640 )
=> ( X639 = X640 ) ) )
=> ? [X641: $i] :
( ( X637 @ X641 )
& ! [X642: $i] :
( ( X637 @ X642 )
=> ( X641 = X642 ) ) ) ) )
=> ( ! [X643: $i > $o] :
( ? [X644: $i] :
! [X645: $i] :
( ( X643 @ X645 )
<=> ( X645 = X644 ) )
=> ? [X646: $i] :
( ( X643 @ X646 )
& ! [X647: $i] :
( ( X643 @ X647 )
=> ( X646 = X647 ) ) ) )
=> ( ! [X648: $i,X649: $i] :
( ( X648 = X649 )
=> ! [X650: $i,X651: $i] :
( ( X650 = X651 )
=> ( ( in @ X650 @ X648 )
=> ( in @ X651 @ X649 ) ) ) )
=> ( ! [X652: $i,X653: $i] :
( ( X652 = X653 )
=> ! [X654: $i,X655: $i] :
( ( X654 = X655 )
=> ( ( in @ X654 @ X652 )
<=> ( in @ X655 @ X653 ) ) ) )
=> ( ! [X656: $i > $o] :
( ? [X657: $i] :
( ( X656 @ X657 )
& ! [X658: $i] :
( ( X656 @ X658 )
=> ( X657 = X658 ) ) )
=> ! [X659: $i,X660: $i] :
( ( X656 @ X659 )
=> ( ( X656 @ X660 )
=> ( X659 = X660 ) ) ) )
=> ( ! [X661: $i > $o,X662: $i > $o] :
( ! [X663: $i,X664: $i] :
( ( X663 = X664 )
=> ( ( X661 @ X663 )
<=> ( X662 @ X664 ) ) )
=> ( ? [X665: $i] :
( ( X661 @ X665 )
& ! [X666: $i] :
( ( X661 @ X666 )
=> ( X665 = X666 ) ) )
<=> ? [X667: $i] :
( ( X662 @ X667 )
& ! [X668: $i] :
( ( X662 @ X668 )
=> ( X667 = X668 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X669: $i,X670: $i] :
( ( X669 = X670 )
=> ! [X671: $i,X672: $i] :
( ( X671 = X672 )
=> ( ( setadjoin @ X669 @ X671 )
= ( setadjoin @ X670 @ X672 ) ) ) )
=> ( ! [X673: $i,X674: $i] :
( ( X673 = X674 )
=> ( ( powerset @ X673 )
= ( powerset @ X674 ) ) )
=> ( ! [X675: $i,X676: $i] :
( ( X675 = X676 )
=> ( ( setunion @ X675 )
= ( setunion @ X676 ) ) )
=> ( ( omega = omega )
=> ( ! [X677: $i > $o] :
( ? [X678: $i] :
( ( X677 @ X678 )
& ! [X679: $i] :
( ( X677 @ X679 )
=> ( X678 = X679 ) ) )
=> ! [X680: $i,X681: $i] :
( ( X677 @ X680 )
=> ( ( X677 @ X681 )
=> ( X680 = X681 ) ) ) )
=> ( ! [X682: $i > $o,X683: $i > $o] :
( ! [X684: $i,X685: $i] :
( ( X684 = X685 )
=> ( ( X682 @ X684 )
<=> ( X683 @ X685 ) ) )
=> ( ? [X686: $i] :
( ( X682 @ X686 )
& ! [X687: $i] :
( ( X682 @ X687 )
=> ( X686 = X687 ) ) )
=> ( ? [X688: $i] :
( ( X683 @ X688 )
& ! [X689: $i] :
( ( X683 @ X689 )
=> ( X688 = X689 ) ) )
=> ( ( descr @ X682 )
= ( descr @ X683 ) ) ) ) )
=> ( ! [X690: $i,X691: $i] :
( ( X690 = X691 )
=> ! [X692: $i > $o,X693: $i > $o] :
( ! [X694: $i] :
( ( in @ X694 @ X690 )
=> ! [X695: $i] :
( ( in @ X695 @ X691 )
=> ( ( X694 = X695 )
=> ( ( X692 @ X694 )
<=> ( X693 @ X695 ) ) ) ) )
=> ( ( dsetconstr @ X690 @ X692 )
= ( dsetconstr @ X691 @ X693 ) ) ) )
=> ( ! [X696: $i,X697: $i] :
( ! [X698: $i] :
( ( in @ X698 @ X696 )
=> ( in @ X698 @ X697 ) )
=> ( subset @ X696 @ X697 ) )
=> ( ! [X699: $i,X700: $i] :
( ( X699 = X700 )
=> ( subset @ X700 @ X699 ) )
=> ( ! [X701: $i,X702: $i] :
( ( X701 = X702 )
=> ( subset @ X701 @ X702 ) )
=> ( ! [X703: $i,X704: $i] :
( ! [X705: $i] :
( ( in @ X705 @ X703 )
=> ( in @ X705 @ X704 ) )
=> ( subset @ X703 @ X704 ) )
=> ( ! [X706: $i] : ( subset @ emptyset @ X706 )
=> ( ! [X707: $i,X708: $i,X709: $i] :
( ( subset @ X707 @ X708 )
=> ( ( in @ X709 @ X707 )
=> ( in @ X709 @ X708 ) ) )
=> ( ! [X710: $i,X711: $i,X712: $i] :
( ( subset @ X710 @ X711 )
=> ( ~ ( in @ X712 @ X711 )
=> ~ ( in @ X712 @ X710 ) ) )
=> ( ! [X713: $i,X714: $i,X715: $i] :
( ( in @ X715 @ X713 )
=> ( ~ ( in @ X715 @ X714 )
=> ~ ( subset @ X713 @ X714 ) ) )
=> ( ! [X716: $i,X717: $i] :
( ~ ( subset @ X716 @ X717 )
=> ( X716 != X717 ) )
=> ( ! [X718: $i,X719: $i,X720: $i] :
( ( in @ X720 @ X718 )
=> ( ~ ( in @ X720 @ X719 )
=> ( X718 != X719 ) ) )
=> ( ! [X721: $i] : ( subset @ X721 @ X721 )
=> ( ! [X722: $i,X723: $i,X724: $i] :
( ( subset @ X722 @ X723 )
=> ( ( subset @ X723 @ X724 )
=> ( subset @ X722 @ X724 ) ) )
=> ( ! [X725: $i,X726: $i] : ( subset @ X726 @ ( setadjoin @ X725 @ X726 ) )
=> ( ! [X727: $i,X728: $i,X729: $i] :
( ( subset @ X727 @ X729 )
=> ( subset @ X727 @ ( setadjoin @ X728 @ X729 ) ) )
=> ( ! [X730: $i,X731: $i] :
( ( subset @ X730 @ X731 )
=> ( in @ X730 @ ( powerset @ X731 ) ) )
=> ( ! [X732: $i,X733: $i] :
( ( subset @ X732 @ X733 )
=> ( ( subset @ X733 @ X732 )
=> ( X732 = X733 ) ) )
=> ( ! [X734: $i] :
( ( subset @ X734 @ emptyset )
=> ( X734 = emptyset ) )
=> ( ! [X735: $i,X736: $i] :
( ( subset @ X736 @ X735 )
=> ( in @ X736 @ ( powerset @ X735 ) ) )
=> ( ! [X737: $i,X738: $i] :
( ( in @ X738 @ ( powerset @ X737 ) )
=> ( subset @ X738 @ X737 ) )
=> ( ! [X739: $i] : ( in @ X739 @ ( powerset @ X739 ) )
=> ( ! [X740: $i,X741: $i] :
( ( subset @ X740 @ X741 )
=> ( subset @ ( powerset @ X740 ) @ ( powerset @ X741 ) ) )
=> ( ! [X742: $i,X743: $i > $o] : ( in @ ( dsetconstr @ X742 @ X743 ) @ ( powerset @ X742 ) )
=> ( ! [X744: $i,X745: $i > $o] : ( subset @ ( dsetconstr @ X744 @ X745 ) @ X744 )
=> ( ! [X746: $i,X747: $i,X748: $i] :
( ( in @ X748 @ X746 )
=> ( in @ X748 @ ( binunion @ X746 @ X747 ) ) )
=> ( ! [X749: $i,X750: $i] : ( in @ X750 @ ( setadjoin @ X749 @ ( setadjoin @ X750 @ emptyset ) ) )
=> ( ! [X751: $i,X752: $i,X753: $i] :
( ( in @ X753 @ X752 )
=> ( in @ X753 @ ( binunion @ X751 @ X752 ) ) )
=> ( ! [X754: $i,X755: $i,X756: $i,X757: $o] :
( ( in @ X756 @ ( binunion @ X754 @ X755 ) )
=> ( ( ( in @ X756 @ X754 )
=> X757 )
=> ( ( ( in @ X756 @ X755 )
=> X757 )
=> X757 ) ) )
=> ( ! [X758: $i,X759: $i,X760: $i] :
( ( in @ X760 @ ( binunion @ X758 @ X759 ) )
=> ( ( in @ X760 @ X758 )
| ( in @ X760 @ X759 ) ) )
=> ( ! [X761: $i,X762: $i] : ( subset @ X761 @ ( binunion @ X761 @ X762 ) )
=> ( ! [X763: $i,X764: $i] : ( subset @ X764 @ ( binunion @ X763 @ X764 ) )
=> ( ! [X765: $i,X766: $i,X767: $i] :
( ( in @ X767 @ X765 )
=> ( ( in @ X767 @ X766 )
=> ( in @ X767 @ ( binintersect @ X765 @ X766 ) ) ) )
=> ( ! [X768: $i,X769: $i,X770: $i] :
( ( subset @ X770 @ X768 )
=> ( ( subset @ X770 @ X769 )
=> ( subset @ X770 @ ( binintersect @ X768 @ X769 ) ) ) )
=> ( ! [X771: $i,X772: $i,X773: $i] :
( ( in @ X773 @ ( binintersect @ X771 @ X772 ) )
=> ( in @ X773 @ X771 ) )
=> ( ! [X774: $i,X775: $i] : ( subset @ ( binintersect @ X774 @ X775 ) @ X774 )
=> ( ! [X776: $i,X777: $i] :
( ( subset @ X776 @ X777 )
=> ( ( binintersect @ X776 @ X777 )
= X776 ) )
=> ( ! [X778: $i,X779: $i] :
( ( ( binintersect @ X778 @ X779 )
= X779 )
=> ( subset @ X779 @ X778 ) )
=> ( ! [X780: $i,X781: $i,X782: $i] :
( ( in @ X782 @ ( binintersect @ X780 @ X781 ) )
=> ( in @ X782 @ X781 ) )
=> ( ! [X783: $i,X784: $i] :
( ~ ? [X785: $i] :
( ( in @ X785 @ X783 )
& ( in @ X785 @ X784 ) )
=> ( ( binintersect @ X783 @ X784 )
= emptyset ) )
=> ( ! [X786: $i,X787: $i] : ( subset @ ( binintersect @ X786 @ X787 ) @ X787 )
=> ( ! [X788: $i,X789: $i] :
( ( subset @ X789 @ X788 )
=> ( ( binintersect @ X788 @ X789 )
= X789 ) )
=> ( ! [X790: $i,X791: $i] :
( ( ( binintersect @ X790 @ X791 )
= X790 )
=> ( subset @ X790 @ X791 ) )
=> ( ! [X792: $i,X793: $i,X794: $i] :
( ( binintersect @ X792 @ ( binunion @ X793 @ X794 ) )
= ( binunion @ ( binintersect @ X792 @ X793 ) @ ( binintersect @ X792 @ X794 ) ) )
=> ( ! [X795: $i,X796: $i,X797: $i] :
( ( in @ X797 @ X795 )
=> ( ~ ( in @ X797 @ X796 )
=> ( in @ X797 @ ( setminus @ X795 @ X796 ) ) ) )
=> ( ! [X798: $i,X799: $i,X800: $i] :
( ( in @ X800 @ ( setminus @ X798 @ X799 ) )
=> ( in @ X800 @ X798 ) )
=> ( ! [X801: $i,X802: $i,X803: $i] :
( ( in @ X803 @ ( setminus @ X801 @ X802 ) )
=> ~ ( in @ X803 @ X802 ) )
=> ( ! [X804: $i,X805: $i] :
( ( subset @ X804 @ X805 )
=> ( ( setminus @ X804 @ X805 )
= emptyset ) )
=> ( ! [X806: $i,X807: $i,X808: $i] :
( ~ ( in @ X808 @ ( setminus @ X806 @ X807 ) )
=> ( ( in @ X808 @ X806 )
=> ( in @ X808 @ X807 ) ) )
=> ( ! [X809: $i,X810: $i,X811: $i] :
( ~ ( in @ X811 @ ( setminus @ X809 @ X810 ) )
=> ( ~ ( in @ X811 @ X810 )
=> ~ ( in @ X811 @ X809 ) ) )
=> ( ! [X812: $i,X813: $i,X814: $i] :
( ~ ( in @ X814 @ X812 )
=> ~ ( in @ X814 @ ( setminus @ X812 @ X813 ) ) )
=> ( ! [X815: $i,X816: $i,X817: $i] :
( ( in @ X817 @ X816 )
=> ~ ( in @ X817 @ ( setminus @ X815 @ X816 ) ) )
=> ( ! [X818: $i,X819: $i] : ( subset @ ( setminus @ X818 @ X819 ) @ X818 )
=> ( ! [X820: $i,X821: $i] :
( ( ( setminus @ X820 @ X821 )
= emptyset )
=> ( subset @ X820 @ X821 ) )
=> ( ! [X822: $i,X823: $i,X824: $i] :
( ( in @ X824 @ ( symdiff @ X822 @ X823 ) )
=> ! [X825: $o] :
( ( ( in @ X824 @ X822 )
=> ( ~ ( in @ X824 @ X823 )
=> X825 ) )
=> ( ( ~ ( in @ X824 @ X822 )
=> ( ( in @ X824 @ X823 )
=> X825 ) )
=> X825 ) ) )
=> ( ! [X826: $i,X827: $i,X828: $i] :
( ( in @ X828 @ X826 )
=> ( ~ ( in @ X828 @ X827 )
=> ( in @ X828 @ ( symdiff @ X826 @ X827 ) ) ) )
=> ( ! [X829: $i,X830: $i,X831: $i] :
( ~ ( in @ X831 @ X829 )
=> ( ( in @ X831 @ X830 )
=> ( in @ X831 @ ( symdiff @ X829 @ X830 ) ) ) )
=> ( ! [X832: $i,X833: $i,X834: $i] :
( ( in @ X834 @ X832 )
=> ( ( in @ X834 @ X833 )
=> ~ ( in @ X834 @ ( symdiff @ X832 @ X833 ) ) ) )
=> ( ! [X835: $i,X836: $i,X837: $i] :
( ~ ( in @ X837 @ X835 )
=> ( ~ ( in @ X837 @ X836 )
=> ~ ( in @ X837 @ ( symdiff @ X835 @ X836 ) ) ) )
=> ( ! [X838: $i,X839: $i] : ( in @ X839 @ ( setadjoin @ X838 @ ( setadjoin @ X839 @ emptyset ) ) )
=> ( ! [X840: $i,X841: $i] : ( in @ X840 @ ( setunion @ ( setadjoin @ ( setadjoin @ X840 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X840 @ ( setadjoin @ X841 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X842: $i,X843: $i] : ( in @ X843 @ ( setunion @ ( setadjoin @ ( setadjoin @ X842 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X842 @ ( setadjoin @ X843 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X844: $i,X845: $i] :
? [X846: $i] :
( ( in @ X846 @ ( setunion @ ( setadjoin @ ( setadjoin @ X844 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X844 @ ( setadjoin @ X845 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X847: $i] :
( ( in @ X847 @ ( setunion @ ( setadjoin @ ( setadjoin @ X844 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X844 @ ( setadjoin @ X845 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X844 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X844 @ ( setadjoin @ X845 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X846 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X846 @ ( setadjoin @ X847 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X848: $i,X849: $i] :
? [X850: $i] :
( ( in @ X850 @ ( setunion @ ( setadjoin @ ( setadjoin @ X848 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X848 @ ( setadjoin @ X849 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X851: $i] :
( ( in @ X851 @ ( setunion @ ( setadjoin @ ( setadjoin @ X848 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X848 @ ( setadjoin @ X849 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X848 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X848 @ ( setadjoin @ X849 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X850 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X850 @ ( setadjoin @ X851 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X852: $i,X853: $i] :
( ( in @ X853 @ X852 )
=> ( subset @ ( setadjoin @ X853 @ emptyset ) @ X852 ) )
=> ( ! [X854: $i,X855: $i] :
( ( in @ X855 @ X854 )
=> ( in @ ( setadjoin @ X855 @ emptyset ) @ ( powerset @ X854 ) ) )
=> ( ! [X856: $i,X857: $i,X858: $i] :
( ( in @ X858 @ X856 )
=> ( in @ ( setadjoin @ X858 @ emptyset ) @ ( powerset @ ( binunion @ X856 @ X857 ) ) ) )
=> ( ! [X859: $i,X860: $i,X861: $i] :
( ( in @ X861 @ ( setadjoin @ X859 @ ( setadjoin @ X860 @ emptyset ) ) )
=> ( ( X861 = X859 )
| ( X861 = X860 ) ) )
=> ( ! [X862: $i,X863: $i,X864: $i] :
( ( in @ X864 @ X862 )
=> ! [X865: $i] :
( ( in @ X865 @ X863 )
=> ( subset @ ( setadjoin @ X864 @ ( setadjoin @ X865 @ emptyset ) ) @ ( binunion @ X862 @ X863 ) ) ) )
=> ( ! [X866: $i,X867: $i,X868: $i] :
( ( in @ X868 @ X866 )
=> ! [X869: $i] :
( ( in @ X869 @ X867 )
=> ( in @ ( setadjoin @ X868 @ ( setadjoin @ X869 @ emptyset ) ) @ ( powerset @ ( binunion @ X866 @ X867 ) ) ) ) )
=> ( ! [X870: $i,X871: $i,X872: $i] :
( ( in @ X872 @ X870 )
=> ! [X873: $i] :
( ( in @ X873 @ X871 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X872 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X872 @ ( setadjoin @ X873 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X870 @ X871 ) ) ) ) )
=> ( ! [X874: $i,X875: $i,X876: $i] :
( ( in @ X876 @ X874 )
=> ! [X877: $i] :
( ( in @ X877 @ X875 )
=> ( in @ ( setadjoin @ ( setadjoin @ X876 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X876 @ ( setadjoin @ X877 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X874 @ X875 ) ) ) ) ) )
=> ( ! [X878: $i,X879: $i,X880: $i] :
( ( in @ X880 @ X878 )
=> ! [X881: $i] :
( ( in @ X881 @ X879 )
=> ( in @ ( setadjoin @ ( setadjoin @ X880 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X880 @ ( setadjoin @ X881 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X878 @ X879 ) ) ) ) ) )
=> ( ! [X882: $i,X883: $i,X884: $i] :
( ( in @ X884 @ X882 )
=> ! [X885: $i] :
( ( in @ X885 @ X883 )
=> ( in @ ( setadjoin @ ( setadjoin @ X884 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X884 @ ( setadjoin @ X885 @ emptyset ) ) @ emptyset ) )
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X882 @ X883 ) ) )
@ ^ [Z0: $i] :
? [X886: $i] :
( ( in @ X886 @ X882 )
& ? [X887: $i] :
( ( in @ X887 @ X883 )
& ( Z0
= ( setadjoin @ ( setadjoin @ X886 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X886 @ ( setadjoin @ X887 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) )
=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) )
@ ^ [Z0: $i] :
? [X888: $i] :
( ( in @ X888 @ X4 )
& ? [X889: $i] :
( ( in @ X889 @ X5 )
& ( Z0
= ( setadjoin @ ( setadjoin @ X888 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X888 @ ( setadjoin @ X889 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[cartprodmempair1]),c_0_153]),symdiffI1]),symdiffI2]),symdiffIneg1]),prop2setI]),symdiffIneg2]),secondinupair]),notdexE]),setukpairIL]),setukpairIR]),notdallE]),c_0_171]),c_0_172]),c_0_173]),singletonsubset]),singletoninpowerset]),c_0_174]),singletoninpowunion]),upairset2E]),c_0_175]),upairsubunion]),inCongP]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),in__Cong]),c_0_176]),c_0_177]),c_0_159]),c_0_178]),notequalI1]),c_0_179]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_180]),c_0_181]),c_0_182]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),setminusER]),setminusSubset2]),setminusERneg]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_183]),c_0_184]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),quantDeMorgan1]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),quantDeMorgan2]),binintersectSubset4]),quantDeMorgan3]),binintersectSubset1]),quantDeMorgan4]),bs114d]),setminusI]),setminusEL]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),vacuousDall]),c_0_185]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_186]),c_0_187]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_188]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_189]),c_0_190]),c_0_191]),c_0_192]),noeltsimpempty]),emptyI]),setext]),c_0_193]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_194]),c_0_195]),c_0_196]),c_0_197]),c_0_198]),wellorderingAx]),foundationAx]),c_0_199]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_200]) ).
thf(c_0_202,negated_conjecture,
! [X890: $i,X891: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $i,X898: $i,X899: $i,X900: $i,X901: $i,X903: $i,X904: $i,X906: $i,X907: $i,X908: $i,X909: $i,X910: $i,X912: $i,X913: $i > $i > $o,X914: $i,X916: $i,X919: $i,X921: $i,X922: $i,X923: $i,X924: $i,X926: $i,X927: $i > $o,X928: $i,X930: $i,X931: $i > $o,X932: $i,X933: $i,X934: $i > $o,X935: $i,X936: $i,X937: $i > $o,X938: $i,X939: $i > $o,X940: $i,X943: $i,X944: $o,X945: $i,X946: $i,X947: $o,X948: $i,X949: $i,X950: $i > $o,X951: $i,X954: $i,X955: $i,X958: $i,X960: $i,X962: $i,X963: $i > $o,X964: $i,X965: $i,X967: $i,X968: $i > $o,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i,X975: $i,X976: $i,X977: $i,X978: $i,X979: $i,X980: $o,X981: $i,X982: $i,X983: $i,X984: $i,X985: $i,X986: $i,X988: $i,X989: $i,X990: $i,X991: $i,X992: $i,X993: $i,X994: $i,X995: $i,X996: $i,X997: $i,X998: $o,X1000: $i,X1001: $i,X1002: $i > $o,X1003: $i,X1006: $i,X1007: $i,X1008: $i,X1010: $i,X1011: $i,X1012: $i,X1013: $i,X1014: $i,X1015: $i,X1016: $i,X1017: $i,X1018: $i,X1019: $i,X1020: $i,X1021: $i,X1022: $i,X1023: $i,X1024: $i,X1025: $i,X1026: $i > $o,X1027: $i,X1028: $i > $o,X1029: $i,X1030: $i,X1031: $i > $o,X1032: $i,X1034: $i,X1035: $i > $o,X1037: $i,X1038: $i,X1039: $i > $o,X1041: $i,X1042: $i,X1043: $i > $o,X1044: $i,X1046: $o,X1047: $i,X1048: $i > $o,X1050: $i,X1051: $i,X1052: $i > $o,X1053: $i,X1055: $i > $o,X1056: $i,X1059: $i,X1060: $i > $o,X1061: $i,X1065: $i,X1066: $i > $o,X1067: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i > $o,X1080: $i,X1082: $i,X1083: $i,X1084: $i > $o,X1085: $i > $o,X1088: $i,X1091: $i,X1092: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i > $o,X1105: $i,X1107: $i,X1108: $i,X1109: $i > $o,X1110: $i > $o,X1113: $i,X1115: $i,X1117: $i,X1118: $i,X1119: $i > $o,X1120: $i > $o,X1123: $i,X1124: $i,X1126: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1133: $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 > $o,X1171: $i,X1172: $i > $o,X1173: $i,X1174: $i,X1175: $i,X1176: $i,X1177: $i,X1178: $i,X1179: $i,X1180: $i,X1181: $i,X1182: $i,X1183: $i,X1184: $o,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,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,X1233: $i,X1234: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1240: $i,X1241: $i,X1242: $i,X1243: $i,X1244: $i,X1245: $i,X1246: $i,X1247: $i,X1248: $i,X1249: $i,X1250: $i,X1251: $i,X1252: $o,X1253: $i,X1254: $i,X1255: $i,X1256: $i,X1257: $i,X1258: $i,X1259: $i,X1260: $i,X1261: $i,X1262: $i,X1263: $i,X1264: $i,X1265: $i,X1266: $i,X1267: $i,X1268: $i,X1269: $i,X1270: $i,X1271: $i,X1272: $i,X1275: $i,X1276: $i,X1279: $i,X1280: $i,X1281: $i,X1282: $i,X1283: $i,X1284: $i,X1285: $i,X1286: $i,X1287: $i,X1288: $i,X1289: $i,X1290: $i,X1291: $i,X1292: $i,X1293: $i,X1294: $i,X1295: $i,X1296: $i,X1297: $i,X1298: $i,X1299: $i,X1300: $i,X1301: $i,X1302: $i,X1303: $i,X1304: $i,X1305: $i,X1306: $i,X1307: $i,X1308: $i,X1309: $i,X1310: $i,X1311: $i,X1312: $i,X1316: $i,X1317: $i] :
( ( ~ ( in @ ( esk1_2 @ X890 @ X891 ) @ X890 )
| ~ ( in @ ( esk1_2 @ X890 @ X891 ) @ X891 )
| ( X890 = X891 ) )
& ( ( in @ ( esk1_2 @ X890 @ X891 ) @ X890 )
| ( in @ ( esk1_2 @ X890 @ X891 ) @ X891 )
| ( X890 = X891 ) )
& ~ ( in @ X893 @ emptyset )
& ( ~ ( in @ X896 @ ( setadjoin @ X894 @ X895 ) )
| ( X896 = X894 )
| ( in @ X896 @ X895 ) )
& ( ( X896 != X894 )
| ( in @ X896 @ ( setadjoin @ X894 @ X895 ) ) )
& ( ~ ( in @ X896 @ X895 )
| ( in @ X896 @ ( setadjoin @ X894 @ X895 ) ) )
& ( ~ ( in @ X898 @ ( powerset @ X897 ) )
| ~ ( in @ X899 @ X898 )
| ( in @ X899 @ X897 ) )
& ( ( in @ ( esk2_2 @ X900 @ X901 ) @ X901 )
| ( in @ X901 @ ( powerset @ X900 ) ) )
& ( ~ ( in @ ( esk2_2 @ X900 @ X901 ) @ X900 )
| ( in @ X901 @ ( powerset @ X900 ) ) )
& ( ( in @ X904 @ ( esk3_2 @ X903 @ X904 ) )
| ~ ( in @ X904 @ ( setunion @ X903 ) ) )
& ( ( in @ ( esk3_2 @ X903 @ X904 ) @ X903 )
| ~ ( in @ X904 @ ( setunion @ X903 ) ) )
& ( ~ ( in @ X907 @ X908 )
| ~ ( in @ X908 @ X906 )
| ( in @ X907 @ ( setunion @ X906 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X909 @ omega )
| ( in @ ( setadjoin @ X909 @ X909 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X910 ) @ omega )
| ~ ( in @ emptyset @ X910 )
| ~ ( in @ X912 @ omega )
| ( in @ X912 @ X910 ) )
& ( ( in @ ( esk4_1 @ X910 ) @ X910 )
| ~ ( in @ emptyset @ X910 )
| ~ ( in @ X912 @ omega )
| ( in @ X912 @ X910 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X910 ) @ ( esk4_1 @ X910 ) ) @ X910 )
| ~ ( in @ emptyset @ X910 )
| ~ ( in @ X912 @ omega )
| ( in @ X912 @ X910 ) )
& ( ( in @ ( esk8_3 @ X913 @ X914 @ X919 ) @ X914 )
| ~ ( in @ X919 @ ( esk7_2 @ X913 @ X914 ) )
| ( in @ ( esk5_2 @ X913 @ X914 ) @ X914 ) )
& ( ( X913 @ ( esk8_3 @ X913 @ X914 @ X919 ) @ X919 )
| ~ ( in @ X919 @ ( esk7_2 @ X913 @ X914 ) )
| ( in @ ( esk5_2 @ X913 @ X914 ) @ X914 ) )
& ( ~ ( in @ X922 @ X914 )
| ~ ( X913 @ X922 @ X921 )
| ( in @ X921 @ ( esk7_2 @ X913 @ X914 ) )
| ( in @ ( esk5_2 @ X913 @ X914 ) @ X914 ) )
& ( ( in @ ( esk8_3 @ X913 @ X914 @ X919 ) @ X914 )
| ~ ( in @ X919 @ ( esk7_2 @ X913 @ X914 ) )
| ( X913 @ ( esk5_2 @ X913 @ X914 ) @ ( esk6_3 @ X913 @ X914 @ X916 ) )
| ~ ( X913 @ ( esk5_2 @ X913 @ X914 ) @ X916 ) )
& ( ( X913 @ ( esk8_3 @ X913 @ X914 @ X919 ) @ X919 )
| ~ ( in @ X919 @ ( esk7_2 @ X913 @ X914 ) )
| ( X913 @ ( esk5_2 @ X913 @ X914 ) @ ( esk6_3 @ X913 @ X914 @ X916 ) )
| ~ ( X913 @ ( esk5_2 @ X913 @ X914 ) @ X916 ) )
& ( ~ ( in @ X922 @ X914 )
| ~ ( X913 @ X922 @ X921 )
| ( in @ X921 @ ( esk7_2 @ X913 @ X914 ) )
| ( X913 @ ( esk5_2 @ X913 @ X914 ) @ ( esk6_3 @ X913 @ X914 @ X916 ) )
| ~ ( X913 @ ( esk5_2 @ X913 @ X914 ) @ X916 ) )
& ( ( in @ ( esk8_3 @ X913 @ X914 @ X919 ) @ X914 )
| ~ ( in @ X919 @ ( esk7_2 @ X913 @ X914 ) )
| ( X916
!= ( esk6_3 @ X913 @ X914 @ X916 ) )
| ~ ( X913 @ ( esk5_2 @ X913 @ X914 ) @ X916 ) )
& ( ( X913 @ ( esk8_3 @ X913 @ X914 @ X919 ) @ X919 )
| ~ ( in @ X919 @ ( esk7_2 @ X913 @ X914 ) )
| ( X916
!= ( esk6_3 @ X913 @ X914 @ X916 ) )
| ~ ( X913 @ ( esk5_2 @ X913 @ X914 ) @ X916 ) )
& ( ~ ( in @ X922 @ X914 )
| ~ ( X913 @ X922 @ X921 )
| ( in @ X921 @ ( esk7_2 @ X913 @ X914 ) )
| ( X916
!= ( esk6_3 @ X913 @ X914 @ X916 ) )
| ~ ( X913 @ ( esk5_2 @ X913 @ X914 ) @ X916 ) )
& ( ( in @ ( esk9_1 @ X923 ) @ X923 )
| ~ ( in @ X924 @ X923 ) )
& ( ~ ( in @ X926 @ ( esk9_1 @ X923 ) )
| ~ ( in @ X926 @ X923 )
| ~ ( in @ X924 @ X923 ) )
& epred1_0
& ( ( X927 @ ( esk10_2 @ X927 @ X928 ) )
| ~ ( X927 @ X928 )
| ( X927 @ ( descr @ X927 ) ) )
& ( ( X928
!= ( esk10_2 @ X927 @ X928 ) )
| ~ ( X927 @ X928 )
| ( X927 @ ( descr @ X927 ) ) )
& ( ~ ( in @ X932 @ X930 )
| ~ ( X931 @ X932 )
| ( in @ X932 @ ( dsetconstr @ X930 @ X931 ) ) )
& ( ~ ( in @ X935 @ ( dsetconstr @ X933 @ X934 ) )
| ( in @ X935 @ X933 ) )
& ( ~ ( in @ X938 @ ( dsetconstr @ X936 @ X937 ) )
| ( X937 @ X938 ) )
& ( ( X939 @ ( esk12_1 @ X939 ) )
| ( X939 @ ( esk11_2 @ X939 @ X940 ) )
| ~ ( X939 @ X940 ) )
& ( ~ ( X939 @ X943 )
| ( ( esk12_1 @ X939 )
= X943 )
| ( X939 @ ( esk11_2 @ X939 @ X940 ) )
| ~ ( X939 @ X940 ) )
& ( ( X939 @ ( esk12_1 @ X939 ) )
| ( X940
!= ( esk11_2 @ X939 @ X940 ) )
| ~ ( X939 @ X940 ) )
& ( ~ ( X939 @ X943 )
| ( ( esk12_1 @ X939 )
= X943 )
| ( X940
!= ( esk11_2 @ X939 @ X940 ) )
| ~ ( X939 @ X940 ) )
& ( ~ ( in @ X945 @ ( prop2set @ X944 ) )
| X944 )
& ( ~ ( in @ X946 @ emptyset )
| X947 )
& ( ~ ( in @ X948 @ emptyset )
| ~ $true )
& ~ ( in @ X949 @ emptyset )
& ( ( X950 @ ( esk13_2 @ X950 @ X951 ) )
| ~ ( X950 @ X951 )
| ( X950 @ ( esk14_1 @ X950 ) ) )
& ( ( X951
!= ( esk13_2 @ X950 @ X951 ) )
| ~ ( X950 @ X951 )
| ( X950 @ ( esk14_1 @ X950 ) ) )
& ( ( in @ ( esk16_2 @ X954 @ X955 ) @ X955 )
| ( X954 = X955 )
| ( in @ ( esk15_2 @ X954 @ X955 ) @ X954 ) )
& ( ~ ( in @ ( esk16_2 @ X954 @ X955 ) @ X954 )
| ( X954 = X955 )
| ( in @ ( esk15_2 @ X954 @ X955 ) @ X954 ) )
& ( ( in @ ( esk16_2 @ X954 @ X955 ) @ X955 )
| ( X954 = X955 )
| ~ ( in @ ( esk15_2 @ X954 @ X955 ) @ X955 ) )
& ( ~ ( in @ ( esk16_2 @ X954 @ X955 ) @ X954 )
| ( X954 = X955 )
| ~ ( in @ ( esk15_2 @ X954 @ X955 ) @ X955 ) )
& ( ( in @ ( esk17_1 @ X958 ) @ X958 )
| ( X958 = emptyset ) )
& ( ( in @ ( esk18_1 @ X960 ) @ X960 )
| ( X960 = emptyset ) )
& ( ~ ( in @ X964 @ ( dsetconstr @ X962 @ X963 ) )
| ( X963 @ X964 )
| ~ ( in @ X964 @ X962 ) )
& ( ~ ( X963 @ X964 )
| ( in @ X964 @ ( dsetconstr @ X962 @ X963 ) )
| ~ ( in @ X964 @ X962 ) )
& ( ( X965 = emptyset )
| ( in @ ( esk19_1 @ X965 ) @ X965 ) )
& ( ~ ( in @ X969 @ X967 )
| ~ ( X968 @ X969 )
| ( ( dsetconstr @ X967 @ X968 )
!= emptyset ) )
& ( ~ ( in @ X971 @ X970 )
| ( X970 != emptyset ) )
& ( in @ X972 @ ( setadjoin @ X972 @ X973 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X976 @ X975 )
| ( in @ X976 @ ( setadjoin @ X974 @ X975 ) ) )
& ( ( in @ X979 @ X978 )
| X980
| ( X979 = X977 )
| ~ ( in @ X979 @ ( setadjoin @ X977 @ X978 ) ) )
& ( ~ X980
| X980
| ( X979 = X977 )
| ~ ( in @ X979 @ ( setadjoin @ X977 @ X978 ) ) )
& ( ( in @ X979 @ X978 )
| X980
| ~ X980
| ~ ( in @ X979 @ ( setadjoin @ X977 @ X978 ) ) )
& ( ~ X980
| X980
| ~ X980
| ~ ( in @ X979 @ ( setadjoin @ X977 @ X978 ) ) )
& ( ~ ( in @ X983 @ ( setadjoin @ X981 @ X982 ) )
| ( X983 = X981 )
| ( in @ X983 @ X982 ) )
& ( ( dsetconstr @ X984
@ ^ [Z0: $i] : $true )
= X984 )
& ( ( in @ ( esk20_2 @ X985 @ X986 ) @ X986 )
| ( in @ X986 @ ( powerset @ X985 ) ) )
& ( ~ ( in @ ( esk20_2 @ X985 @ X986 ) @ X985 )
| ( in @ X986 @ ( powerset @ X985 ) ) )
& ( in @ emptyset @ ( powerset @ X988 ) )
& ( in @ emptyset @ ( powerset @ X989 ) )
& ( ~ ( in @ X991 @ ( powerset @ X990 ) )
| ~ ( in @ X992 @ X991 )
| ( in @ X992 @ X990 ) )
& ( ~ ( in @ X994 @ X995 )
| ~ ( in @ X995 @ X993 )
| ( in @ X994 @ ( setunion @ X993 ) ) )
& ( ( in @ X997 @ ( esk21_3 @ X996 @ X997 @ X998 ) )
| X998
| ~ ( in @ X997 @ ( setunion @ X996 ) ) )
& ( ( in @ ( esk21_3 @ X996 @ X997 @ X998 ) @ X996 )
| X998
| ~ ( in @ X997 @ ( setunion @ X996 ) ) )
& ( ~ X998
| X998
| ~ ( in @ X997 @ ( setunion @ X996 ) ) )
& ( ~ ( in @ X1001 @ X1000 )
| ( in @ X1001 @ ( powerset @ ( setunion @ X1000 ) ) ) )
& ( ~ ( X1002 @ X1006 )
| ( X1006
= ( esk23_1 @ X1002 ) )
| ( X1002 @ ( esk22_2 @ X1002 @ X1003 ) )
| ~ ( X1002 @ X1003 ) )
& ( ( X1007
!= ( esk23_1 @ X1002 ) )
| ( X1002 @ X1007 )
| ( X1002 @ ( esk22_2 @ X1002 @ X1003 ) )
| ~ ( X1002 @ X1003 ) )
& ( ~ ( X1002 @ X1006 )
| ( X1006
= ( esk23_1 @ X1002 ) )
| ( X1003
!= ( esk22_2 @ X1002 @ X1003 ) )
| ~ ( X1002 @ X1003 ) )
& ( ( X1007
!= ( esk23_1 @ X1002 ) )
| ( X1002 @ X1007 )
| ( X1003
!= ( esk22_2 @ X1002 @ X1003 ) )
| ~ ( X1002 @ X1003 ) )
& ( ( in @ ( esk24_1 @ X1008 ) @ X1008 )
| ( X1008 = emptyset ) )
& ( $true
| ( X1008 = emptyset ) )
& ( ~ ( in @ X1010 @ ( setadjoin @ X1011 @ emptyset ) )
| ( X1010 = X1011 ) )
& ( ( X1012 = X1013 )
| ~ ( in @ X1013 @ ( setadjoin @ X1012 @ emptyset ) ) )
& ( ( X1014 != X1015 )
| ( in @ X1014 @ ( setadjoin @ X1015 @ emptyset ) ) )
& ( ~ ( in @ X1016 @ ( setadjoin @ X1017 @ emptyset ) )
| ( in @ X1017 @ ( setadjoin @ X1016 @ emptyset ) ) )
& ( ~ ( in @ X1020 @ ( setadjoin @ X1018 @ ( setadjoin @ X1019 @ emptyset ) ) )
| ( X1020 = X1018 )
| ( X1020 = X1019 ) )
& ( in @ X1021 @ ( setadjoin @ X1021 @ ( setadjoin @ X1022 @ emptyset ) ) )
& ( in @ X1024 @ ( setadjoin @ X1023 @ ( setadjoin @ X1024 @ emptyset ) ) )
& ( ~ ( in @ X1027 @ X1025 )
| ~ ( X1026 @ X1027 )
| ( ( dsetconstr @ X1025 @ X1026 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1029 @ emptyset )
| ( X1028 @ X1029 ) )
& ( ( in @ ( esk25_2 @ X1030 @ X1031 ) @ X1030 )
| ~ ( in @ X1032 @ X1030 )
| ( X1031 @ X1032 ) )
& ( ~ ( X1031 @ ( esk25_2 @ X1030 @ X1031 ) )
| ~ ( in @ X1032 @ X1030 )
| ( X1031 @ X1032 ) )
& ( ( in @ ( esk26_2 @ X1034 @ X1035 ) @ X1034 )
| ~ ( in @ X1037 @ X1034 )
| ~ ( X1035 @ X1037 ) )
& ( ( X1035 @ ( esk26_2 @ X1034 @ X1035 ) )
| ~ ( in @ X1037 @ X1034 )
| ~ ( X1035 @ X1037 ) )
& ( ( in @ ( esk27_2 @ X1038 @ X1039 ) @ X1038 )
| ~ ( in @ X1041 @ X1038 )
| ~ ( X1039 @ X1041 ) )
& ( ( X1039 @ ( esk27_2 @ X1038 @ X1039 ) )
| ~ ( in @ X1041 @ X1038 )
| ~ ( X1039 @ X1041 ) )
& ( ( in @ ( esk28_2 @ X1042 @ X1043 ) @ X1042 )
| ~ ( in @ X1044 @ X1042 )
| ( X1043 @ X1044 ) )
& ( ~ ( X1043 @ ( esk28_2 @ X1042 @ X1043 ) )
| ~ ( in @ X1044 @ X1042 )
| ( X1043 @ X1044 ) )
& ( ~ X1046
| ( in @ emptyset @ ( prop2set @ X1046 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X1047 @ X1048 ) @ X1047 )
| ~ ( in @ X1050 @ X1047 )
| ~ ( X1048 @ X1050 ) )
& ( ( X1048 @ ( esk29_2 @ X1047 @ X1048 ) )
| ~ ( in @ X1050 @ X1047 )
| ~ ( X1048 @ X1050 ) )
& ( ( in @ ( esk30_2 @ X1051 @ X1052 ) @ X1051 )
| ~ ( in @ X1053 @ X1051 )
| ( X1052 @ X1053 ) )
& ( ~ ( X1052 @ ( esk30_2 @ X1051 @ X1052 ) )
| ~ ( in @ X1053 @ X1051 )
| ( X1052 @ X1053 ) )
& ( ( X1055 @ ( esk32_1 @ X1055 ) )
| ( X1055 @ ( esk31_2 @ X1055 @ X1056 ) )
| ~ ( X1055 @ X1056 ) )
& ( ~ ( X1055 @ X1059 )
| ( ( esk32_1 @ X1055 )
= X1059 )
| ( X1055 @ ( esk31_2 @ X1055 @ X1056 ) )
| ~ ( X1055 @ X1056 ) )
& ( ( X1055 @ ( esk32_1 @ X1055 ) )
| ( X1056
!= ( esk31_2 @ X1055 @ X1056 ) )
| ~ ( X1055 @ X1056 ) )
& ( ~ ( X1055 @ X1059 )
| ( ( esk32_1 @ X1055 )
= X1059 )
| ( X1056
!= ( esk31_2 @ X1055 @ X1056 ) )
| ~ ( X1055 @ X1056 ) )
& ( ( X1060 @ ( esk35_1 @ X1060 ) )
| ( X1060 @ ( esk33_1 @ X1060 ) )
| ~ ( X1060 @ X1061 ) )
& ( ~ ( X1060 @ X1065 )
| ( ( esk35_1 @ X1060 )
= X1065 )
| ( X1060 @ ( esk33_1 @ X1060 ) )
| ~ ( X1060 @ X1061 ) )
& ( ( X1060 @ ( esk35_1 @ X1060 ) )
| ( X1060 @ ( esk34_1 @ X1060 ) )
| ~ ( X1060 @ X1061 ) )
& ( ~ ( X1060 @ X1065 )
| ( ( esk35_1 @ X1060 )
= X1065 )
| ( X1060 @ ( esk34_1 @ X1060 ) )
| ~ ( X1060 @ X1061 ) )
& ( ( X1060 @ ( esk35_1 @ X1060 ) )
| ( ( esk33_1 @ X1060 )
!= ( esk34_1 @ X1060 ) )
| ~ ( X1060 @ X1061 ) )
& ( ~ ( X1060 @ X1065 )
| ( ( esk35_1 @ X1060 )
= X1065 )
| ( ( esk33_1 @ X1060 )
!= ( esk34_1 @ X1060 ) )
| ~ ( X1060 @ X1061 ) )
& ( ( X1066 @ ( esk37_1 @ X1066 ) )
| ~ ( X1066 @ ( esk36_2 @ X1066 @ X1067 ) )
| ( ( esk36_2 @ X1066 @ X1067 )
!= X1067 ) )
& ( ~ ( X1066 @ X1070 )
| ( ( esk37_1 @ X1066 )
= X1070 )
| ~ ( X1066 @ ( esk36_2 @ X1066 @ X1067 ) )
| ( ( esk36_2 @ X1066 @ X1067 )
!= X1067 ) )
& ( ( X1066 @ ( esk37_1 @ X1066 ) )
| ( X1066 @ ( esk36_2 @ X1066 @ X1067 ) )
| ( ( esk36_2 @ X1066 @ X1067 )
= X1067 ) )
& ( ~ ( X1066 @ X1070 )
| ( ( esk37_1 @ X1066 )
= X1070 )
| ( X1066 @ ( esk36_2 @ X1066 @ X1067 ) )
| ( ( esk36_2 @ X1066 @ X1067 )
= X1067 ) )
& ( ( X1071 != X1072 )
| ( X1073 != X1074 )
| ~ ( in @ X1073 @ X1071 )
| ( in @ X1074 @ X1072 ) )
& ( ~ ( in @ X1077 @ X1075 )
| ( in @ X1078 @ X1076 )
| ( X1077 != X1078 )
| ( X1075 != X1076 ) )
& ( ~ ( in @ X1078 @ X1076 )
| ( in @ X1077 @ X1075 )
| ( X1077 != X1078 )
| ( X1075 != X1076 ) )
& ( ( X1079 @ ( esk38_2 @ X1079 @ X1080 ) )
| ~ ( X1079 @ X1080 )
| ~ ( X1079 @ X1082 )
| ~ ( X1079 @ X1083 )
| ( X1082 = X1083 ) )
& ( ( X1080
!= ( esk38_2 @ X1079 @ X1080 ) )
| ~ ( X1079 @ X1080 )
| ~ ( X1079 @ X1082 )
| ~ ( X1079 @ X1083 )
| ( X1082 = X1083 ) )
& ( ( X1085 @ ( esk42_2 @ X1084 @ X1085 ) )
| ( X1084 @ ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1085 @ X1091 )
| ( ( esk42_2 @ X1084 @ X1085 )
= X1091 )
| ( X1084 @ ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1085 @ ( esk42_2 @ X1084 @ X1085 ) )
| ( X1088
!= ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1085 @ X1091 )
| ( ( esk42_2 @ X1084 @ X1085 )
= X1091 )
| ( X1088
!= ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1084 @ ( esk44_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1084 @ X1095 )
| ( ( esk44_2 @ X1084 @ X1085 )
= X1095 )
| ( X1085 @ ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1084 @ ( esk44_2 @ X1084 @ X1085 ) )
| ( X1092
!= ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1084 @ X1095 )
| ( ( esk44_2 @ X1084 @ X1085 )
= X1095 )
| ( X1092
!= ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( ( esk39_2 @ X1084 @ X1085 )
= ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1085 @ ( esk42_2 @ X1084 @ X1085 ) )
| ( X1084 @ ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1085 @ X1091 )
| ( ( esk42_2 @ X1084 @ X1085 )
= X1091 )
| ( X1084 @ ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1085 @ ( esk42_2 @ X1084 @ X1085 ) )
| ( X1088
!= ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1085 @ X1091 )
| ( ( esk42_2 @ X1084 @ X1085 )
= X1091 )
| ( X1088
!= ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1084 @ ( esk44_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1084 @ X1095 )
| ( ( esk44_2 @ X1084 @ X1085 )
= X1095 )
| ( X1085 @ ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1084 @ ( esk44_2 @ X1084 @ X1085 ) )
| ( X1092
!= ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1084 @ X1095 )
| ( ( esk44_2 @ X1084 @ X1085 )
= X1095 )
| ( X1092
!= ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ~ ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ~ ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1085 @ ( esk42_2 @ X1084 @ X1085 ) )
| ( X1084 @ ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1085 @ X1091 )
| ( ( esk42_2 @ X1084 @ X1085 )
= X1091 )
| ( X1084 @ ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1085 @ ( esk42_2 @ X1084 @ X1085 ) )
| ( X1088
!= ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1085 @ X1091 )
| ( ( esk42_2 @ X1084 @ X1085 )
= X1091 )
| ( X1088
!= ( esk41_3 @ X1084 @ X1085 @ X1088 ) )
| ~ ( X1084 @ X1088 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1084 @ ( esk44_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1084 @ X1095 )
| ( ( esk44_2 @ X1084 @ X1085 )
= X1095 )
| ( X1085 @ ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ( X1084 @ ( esk44_2 @ X1084 @ X1085 ) )
| ( X1092
!= ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( ~ ( X1084 @ X1095 )
| ( ( esk44_2 @ X1084 @ X1085 )
= X1095 )
| ( X1092
!= ( esk43_3 @ X1084 @ X1085 @ X1092 ) )
| ~ ( X1085 @ X1092 )
| ( X1084 @ ( esk39_2 @ X1084 @ X1085 ) )
| ( X1085 @ ( esk40_2 @ X1084 @ X1085 ) ) )
& ( emptyset = emptyset )
& ( ( X1096 != X1097 )
| ( X1098 != X1099 )
| ( ( setadjoin @ X1096 @ X1098 )
= ( setadjoin @ X1097 @ X1099 ) ) )
& ( ( X1100 != X1101 )
| ( ( powerset @ X1100 )
= ( powerset @ X1101 ) ) )
& ( ( X1102 != X1103 )
| ( ( setunion @ X1102 )
= ( setunion @ X1103 ) ) )
& ( omega = omega )
& ( ( X1104 @ ( esk45_2 @ X1104 @ X1105 ) )
| ~ ( X1104 @ X1105 )
| ~ ( X1104 @ X1107 )
| ~ ( X1104 @ X1108 )
| ( X1107 = X1108 ) )
& ( ( X1105
!= ( esk45_2 @ X1104 @ X1105 ) )
| ~ ( X1104 @ X1105 )
| ~ ( X1104 @ X1107 )
| ~ ( X1104 @ X1108 )
| ( X1107 = X1108 ) )
& ( ( X1110 @ ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1109 @ ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( ( esk46_2 @ X1109 @ X1110 )
= ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1115
!= ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1109 @ ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( ( esk46_2 @ X1109 @ X1110 )
= ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1110 @ ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1113
!= ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( ( esk46_2 @ X1109 @ X1110 )
= ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1115
!= ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1113
!= ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( ( esk46_2 @ X1109 @ X1110 )
= ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1110 @ ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1109 @ ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ~ ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ~ ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1115
!= ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1109 @ ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ~ ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ~ ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1110 @ ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1113
!= ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ~ ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ~ ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1115
!= ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1113
!= ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ~ ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ~ ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1110 @ ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1109 @ ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1115
!= ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1109 @ ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1110 @ ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1113
!= ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( X1115
!= ( esk49_3 @ X1109 @ X1110 @ X1115 ) )
| ~ ( X1110 @ X1115 )
| ( ( descr @ X1109 )
= ( descr @ X1110 ) )
| ( X1113
!= ( esk48_3 @ X1109 @ X1110 @ X1113 ) )
| ~ ( X1109 @ X1113 )
| ( X1109 @ ( esk46_2 @ X1109 @ X1110 ) )
| ( X1110 @ ( esk47_2 @ X1109 @ X1110 ) ) )
& ( ( in @ ( esk50_4 @ X1117 @ X1118 @ X1119 @ X1120 ) @ X1117 )
| ( ( dsetconstr @ X1117 @ X1119 )
= ( dsetconstr @ X1118 @ X1120 ) )
| ( X1117 != X1118 ) )
& ( ( in @ ( esk51_4 @ X1117 @ X1118 @ X1119 @ X1120 ) @ X1118 )
| ( ( dsetconstr @ X1117 @ X1119 )
= ( dsetconstr @ X1118 @ X1120 ) )
| ( X1117 != X1118 ) )
& ( ( ( esk50_4 @ X1117 @ X1118 @ X1119 @ X1120 )
= ( esk51_4 @ X1117 @ X1118 @ X1119 @ X1120 ) )
| ( ( dsetconstr @ X1117 @ X1119 )
= ( dsetconstr @ X1118 @ X1120 ) )
| ( X1117 != X1118 ) )
& ( ~ ( X1119 @ ( esk50_4 @ X1117 @ X1118 @ X1119 @ X1120 ) )
| ~ ( X1120 @ ( esk51_4 @ X1117 @ X1118 @ X1119 @ X1120 ) )
| ( ( dsetconstr @ X1117 @ X1119 )
= ( dsetconstr @ X1118 @ X1120 ) )
| ( X1117 != X1118 ) )
& ( ( X1119 @ ( esk50_4 @ X1117 @ X1118 @ X1119 @ X1120 ) )
| ( X1120 @ ( esk51_4 @ X1117 @ X1118 @ X1119 @ X1120 ) )
| ( ( dsetconstr @ X1117 @ X1119 )
= ( dsetconstr @ X1118 @ X1120 ) )
| ( X1117 != X1118 ) )
& ( ( in @ ( esk52_2 @ X1123 @ X1124 ) @ X1123 )
| ( subset @ X1123 @ X1124 ) )
& ( ~ ( in @ ( esk52_2 @ X1123 @ X1124 ) @ X1124 )
| ( subset @ X1123 @ X1124 ) )
& ( ( X1126 != X1127 )
| ( subset @ X1127 @ X1126 ) )
& ( ( X1128 != X1129 )
| ( subset @ X1128 @ X1129 ) )
& ( ( in @ ( esk53_2 @ X1130 @ X1131 ) @ X1130 )
| ( subset @ X1130 @ X1131 ) )
& ( ~ ( in @ ( esk53_2 @ X1130 @ X1131 ) @ X1131 )
| ( subset @ X1130 @ X1131 ) )
& ( subset @ emptyset @ X1133 )
& ( ~ ( subset @ X1134 @ X1135 )
| ~ ( in @ X1136 @ X1134 )
| ( in @ X1136 @ X1135 ) )
& ( ~ ( subset @ X1137 @ X1138 )
| ( in @ X1139 @ X1138 )
| ~ ( in @ X1139 @ X1137 ) )
& ( ~ ( in @ X1142 @ X1140 )
| ( in @ X1142 @ X1141 )
| ~ ( subset @ X1140 @ X1141 ) )
& ( ( subset @ X1143 @ X1144 )
| ( X1143 != X1144 ) )
& ( ~ ( in @ X1147 @ X1145 )
| ( in @ X1147 @ X1146 )
| ( X1145 != X1146 ) )
& ( subset @ X1148 @ X1148 )
& ( ~ ( subset @ X1149 @ X1150 )
| ~ ( subset @ X1150 @ X1151 )
| ( subset @ X1149 @ X1151 ) )
& ( subset @ X1153 @ ( setadjoin @ X1152 @ X1153 ) )
& ( ~ ( subset @ X1154 @ X1156 )
| ( subset @ X1154 @ ( setadjoin @ X1155 @ X1156 ) ) )
& ( ~ ( subset @ X1157 @ X1158 )
| ( in @ X1157 @ ( powerset @ X1158 ) ) )
& ( ~ ( subset @ X1159 @ X1160 )
| ~ ( subset @ X1160 @ X1159 )
| ( X1159 = X1160 ) )
& ( ~ ( subset @ X1161 @ emptyset )
| ( X1161 = emptyset ) )
& ( ~ ( subset @ X1163 @ X1162 )
| ( in @ X1163 @ ( powerset @ X1162 ) ) )
& ( ~ ( in @ X1165 @ ( powerset @ X1164 ) )
| ( subset @ X1165 @ X1164 ) )
& ( in @ X1166 @ ( powerset @ X1166 ) )
& ( ~ ( subset @ X1167 @ X1168 )
| ( subset @ ( powerset @ X1167 ) @ ( powerset @ X1168 ) ) )
& ( in @ ( dsetconstr @ X1169 @ X1170 ) @ ( powerset @ X1169 ) )
& ( subset @ ( dsetconstr @ X1171 @ X1172 ) @ X1171 )
& ( ~ ( in @ X1175 @ X1173 )
| ( in @ X1175 @ ( binunion @ X1173 @ X1174 ) ) )
& ( in @ X1177 @ ( setadjoin @ X1176 @ ( setadjoin @ X1177 @ emptyset ) ) )
& ( ~ ( in @ X1180 @ X1179 )
| ( in @ X1180 @ ( binunion @ X1178 @ X1179 ) ) )
& ( ( in @ X1183 @ X1182 )
| X1184
| ( in @ X1183 @ X1181 )
| ~ ( in @ X1183 @ ( binunion @ X1181 @ X1182 ) ) )
& ( ~ X1184
| X1184
| ( in @ X1183 @ X1181 )
| ~ ( in @ X1183 @ ( binunion @ X1181 @ X1182 ) ) )
& ( ( in @ X1183 @ X1182 )
| X1184
| ~ X1184
| ~ ( in @ X1183 @ ( binunion @ X1181 @ X1182 ) ) )
& ( ~ X1184
| X1184
| ~ X1184
| ~ ( in @ X1183 @ ( binunion @ X1181 @ X1182 ) ) )
& ( ~ ( in @ X1187 @ ( binunion @ X1185 @ X1186 ) )
| ( in @ X1187 @ X1185 )
| ( in @ X1187 @ X1186 ) )
& ( subset @ X1188 @ ( binunion @ X1188 @ X1189 ) )
& ( subset @ X1191 @ ( binunion @ X1190 @ X1191 ) )
& ( ~ ( in @ X1194 @ X1192 )
| ~ ( in @ X1194 @ X1193 )
| ( in @ X1194 @ ( binintersect @ X1192 @ X1193 ) ) )
& ( ~ ( subset @ X1197 @ X1195 )
| ~ ( subset @ X1197 @ X1196 )
| ( subset @ X1197 @ ( binintersect @ X1195 @ X1196 ) ) )
& ( ~ ( in @ X1200 @ ( binintersect @ X1198 @ X1199 ) )
| ( in @ X1200 @ X1198 ) )
& ( subset @ ( binintersect @ X1201 @ X1202 ) @ X1201 )
& ( ~ ( subset @ X1203 @ X1204 )
| ( ( binintersect @ X1203 @ X1204 )
= X1203 ) )
& ( ( ( binintersect @ X1205 @ X1206 )
!= X1206 )
| ( subset @ X1206 @ X1205 ) )
& ( ~ ( in @ X1209 @ ( binintersect @ X1207 @ X1208 ) )
| ( in @ X1209 @ X1208 ) )
& ( ( in @ ( esk54_2 @ X1210 @ X1211 ) @ X1210 )
| ( ( binintersect @ X1210 @ X1211 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1210 @ X1211 ) @ X1211 )
| ( ( binintersect @ X1210 @ X1211 )
= emptyset ) )
& ( subset @ ( binintersect @ X1213 @ X1214 ) @ X1214 )
& ( ~ ( subset @ X1216 @ X1215 )
| ( ( binintersect @ X1215 @ X1216 )
= X1216 ) )
& ( ( ( binintersect @ X1217 @ X1218 )
!= X1217 )
| ( subset @ X1217 @ X1218 ) )
& ( ( binintersect @ X1219 @ ( binunion @ X1220 @ X1221 ) )
= ( binunion @ ( binintersect @ X1219 @ X1220 ) @ ( binintersect @ X1219 @ X1221 ) ) )
& ( ~ ( in @ X1224 @ X1222 )
| ( in @ X1224 @ X1223 )
| ( in @ X1224 @ ( setminus @ X1222 @ X1223 ) ) )
& ( ~ ( in @ X1227 @ ( setminus @ X1225 @ X1226 ) )
| ( in @ X1227 @ X1225 ) )
& ( ~ ( in @ X1230 @ ( setminus @ X1228 @ X1229 ) )
| ~ ( in @ X1230 @ X1229 ) )
& ( ~ ( subset @ X1231 @ X1232 )
| ( ( setminus @ X1231 @ X1232 )
= emptyset ) )
& ( ( in @ X1235 @ ( setminus @ X1233 @ X1234 ) )
| ~ ( in @ X1235 @ X1233 )
| ( in @ X1235 @ X1234 ) )
& ( ( in @ X1238 @ ( setminus @ X1236 @ X1237 ) )
| ( in @ X1238 @ X1237 )
| ~ ( in @ X1238 @ X1236 ) )
& ( ( in @ X1241 @ X1239 )
| ~ ( in @ X1241 @ ( setminus @ X1239 @ X1240 ) ) )
& ( ~ ( in @ X1244 @ X1243 )
| ~ ( in @ X1244 @ ( setminus @ X1242 @ X1243 ) ) )
& ( subset @ ( setminus @ X1245 @ X1246 ) @ X1245 )
& ( ( ( setminus @ X1247 @ X1248 )
!= emptyset )
| ( subset @ X1247 @ X1248 ) )
& ( ~ ( in @ X1251 @ X1249 )
| X1252
| ( in @ X1251 @ X1249 )
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ( in @ X1251 @ X1250 )
| X1252
| ( in @ X1251 @ X1249 )
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ~ X1252
| X1252
| ( in @ X1251 @ X1249 )
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ~ ( in @ X1251 @ X1249 )
| X1252
| ~ ( in @ X1251 @ X1250 )
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ( in @ X1251 @ X1250 )
| X1252
| ~ ( in @ X1251 @ X1250 )
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ~ X1252
| X1252
| ~ ( in @ X1251 @ X1250 )
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ~ ( in @ X1251 @ X1249 )
| X1252
| ~ X1252
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ( in @ X1251 @ X1250 )
| X1252
| ~ X1252
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ~ X1252
| X1252
| ~ X1252
| ~ ( in @ X1251 @ ( symdiff @ X1249 @ X1250 ) ) )
& ( ~ ( in @ X1255 @ X1253 )
| ( in @ X1255 @ X1254 )
| ( in @ X1255 @ ( symdiff @ X1253 @ X1254 ) ) )
& ( ( in @ X1258 @ X1256 )
| ~ ( in @ X1258 @ X1257 )
| ( in @ X1258 @ ( symdiff @ X1256 @ X1257 ) ) )
& ( ~ ( in @ X1261 @ X1259 )
| ~ ( in @ X1261 @ X1260 )
| ~ ( in @ X1261 @ ( symdiff @ X1259 @ X1260 ) ) )
& ( ( in @ X1264 @ X1262 )
| ( in @ X1264 @ X1263 )
| ~ ( in @ X1264 @ ( symdiff @ X1262 @ X1263 ) ) )
& ( in @ X1266 @ ( setadjoin @ X1265 @ ( setadjoin @ X1266 @ emptyset ) ) )
& ( in @ X1267 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1267 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1267 @ ( setadjoin @ X1268 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1269 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1269 @ ( setadjoin @ X1270 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk55_2 @ X1271 @ X1272 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1271 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1271 @ ( setadjoin @ X1272 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk56_2 @ X1271 @ X1272 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1271 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1271 @ ( setadjoin @ X1272 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1271 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1271 @ ( setadjoin @ X1272 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk55_2 @ X1271 @ X1272 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk55_2 @ X1271 @ X1272 ) @ ( setadjoin @ ( esk56_2 @ X1271 @ X1272 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( esk57_2 @ X1275 @ X1276 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1275 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1275 @ ( setadjoin @ X1276 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk58_2 @ X1275 @ X1276 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1275 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1275 @ ( setadjoin @ X1276 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1275 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1275 @ ( setadjoin @ X1276 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk57_2 @ X1275 @ X1276 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk57_2 @ X1275 @ X1276 ) @ ( setadjoin @ ( esk58_2 @ X1275 @ X1276 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ X1280 @ X1279 )
| ( subset @ ( setadjoin @ X1280 @ emptyset ) @ X1279 ) )
& ( ~ ( in @ X1282 @ X1281 )
| ( in @ ( setadjoin @ X1282 @ emptyset ) @ ( powerset @ X1281 ) ) )
& ( ~ ( in @ X1285 @ X1283 )
| ( in @ ( setadjoin @ X1285 @ emptyset ) @ ( powerset @ ( binunion @ X1283 @ X1284 ) ) ) )
& ( ~ ( in @ X1288 @ ( setadjoin @ X1286 @ ( setadjoin @ X1287 @ emptyset ) ) )
| ( X1288 = X1286 )
| ( X1288 = X1287 ) )
& ( ~ ( in @ X1291 @ X1289 )
| ~ ( in @ X1292 @ X1290 )
| ( subset @ ( setadjoin @ X1291 @ ( setadjoin @ X1292 @ emptyset ) ) @ ( binunion @ X1289 @ X1290 ) ) )
& ( ~ ( in @ X1295 @ X1293 )
| ~ ( in @ X1296 @ X1294 )
| ( in @ ( setadjoin @ X1295 @ ( setadjoin @ X1296 @ emptyset ) ) @ ( powerset @ ( binunion @ X1293 @ X1294 ) ) ) )
& ( ~ ( in @ X1299 @ X1297 )
| ~ ( in @ X1300 @ X1298 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1299 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1299 @ ( setadjoin @ X1300 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1297 @ X1298 ) ) ) )
& ( ~ ( in @ X1303 @ X1301 )
| ~ ( in @ X1304 @ X1302 )
| ( in @ ( setadjoin @ ( setadjoin @ X1303 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1303 @ ( setadjoin @ X1304 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1301 @ X1302 ) ) ) ) )
& ( ~ ( in @ X1307 @ X1305 )
| ~ ( in @ X1308 @ X1306 )
| ( in @ ( setadjoin @ ( setadjoin @ X1307 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1307 @ ( setadjoin @ X1308 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1305 @ X1306 ) ) ) ) )
& ( ~ ( in @ X1311 @ X1309 )
| ~ ( in @ X1312 @ X1310 )
| ( in @ ( setadjoin @ ( setadjoin @ X1311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1311 @ ( setadjoin @ X1312 @ emptyset ) ) @ emptyset ) )
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1309 @ X1310 ) ) )
@ ^ [Z0: $i] :
? [X886: $i] :
( ( in @ X886 @ X1309 )
& ? [X887: $i] :
( ( in @ X887 @ X1310 )
& ( Z0
= ( setadjoin @ ( setadjoin @ X886 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X886 @ ( setadjoin @ X887 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) )
& ( in @ esk61_0
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ esk59_0 @ esk60_0 ) ) )
@ ^ [Z0: $i] :
? [X888: $i] :
( ( in @ X888 @ esk59_0 )
& ? [X889: $i] :
( ( in @ X889 @ esk60_0 )
& ( Z0
= ( setadjoin @ ( setadjoin @ X888 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X888 @ ( setadjoin @ X889 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
& ( ~ ( in @ X1316 @ esk59_0 )
| ~ ( in @ X1317 @ esk60_0 )
| ( esk61_0
!= ( setadjoin @ ( setadjoin @ X1316 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1316 @ ( setadjoin @ X1317 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])])])])]) ).
thf(c_0_203,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( X1 @ X2 )
| ~ ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
thf(c_0_204,negated_conjecture,
( in @ esk61_0
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ esk59_0 @ esk60_0 ) ) )
@ ^ [Z0: $i] :
? [X1341: $i] :
( ( in @ X1341 @ esk59_0 )
& ? [X1342: $i] :
( ( in @ X1342 @ esk60_0 )
& ( Z0
= ( setadjoin @ ( setadjoin @ X1341 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1341 @ ( setadjoin @ X1342 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
thf(c_0_205,negated_conjecture,
? [X1343: $i] :
( ( in @ X1343 @ esk59_0 )
& ? [X1344: $i] :
( ( in @ X1344 @ esk60_0 )
& ( esk61_0
= ( setadjoin @ ( setadjoin @ X1343 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1343 @ ( setadjoin @ X1344 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
thf(c_0_206,negated_conjecture,
! [X2: $i,X3: $i] :
( ~ ( in @ X2 @ esk59_0 )
| ~ ( in @ X3 @ esk60_0 )
| ( esk61_0
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
thf(c_0_207,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk67_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk67_0 @ ( setadjoin @ esk68_0 @ emptyset ) ) @ emptyset ) )
= esk61_0 ),
inference(dynamic_cnf,[status(thm)],[c_0_205]) ).
thf(c_0_208,negated_conjecture,
in @ esk68_0 @ esk60_0,
inference(dynamic_cnf,[status(thm)],[c_0_205]) ).
thf(c_0_209,negated_conjecture,
in @ esk67_0 @ esk59_0,
inference(dynamic_cnf,[status(thm)],[c_0_205]) ).
thf(c_0_210,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_208]),c_0_209])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU631^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 15:34:08 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.23/0.49 Running higher-order theorem proving
% 0.23/0.49 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
% 3.14/0.89 # Version: 3.1.0-ho
% 3.14/0.89 # Preprocessing class: HSLMSLSSLLLCHFA.
% 3.14/0.89 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.14/0.89 # Starting ehoh_best5 with 300s (1) cores
% 3.14/0.89 # Starting almost_fo_3_lam with 300s (1) cores
% 3.14/0.89 # Starting new_bool_5 with 300s (1) cores
% 3.14/0.89 # Starting pre_casc_3 with 300s (1) cores
% 3.14/0.89 # Starting ho_unfolding_8 with 300s (1) cores
% 3.14/0.89 # Starting new_ho_10_cnf2 with 300s (1) cores
% 3.14/0.89 # Starting new_bool_3 with 300s (1) cores
% 3.14/0.89 # Starting new_ho_5 with 300s (1) cores
% 3.14/0.89 # new_bool_3 with pid 12006 completed with status 0
% 3.14/0.89 # Result found by new_bool_3
% 3.14/0.89 # Preprocessing class: HSLMSLSSLLLCHFA.
% 3.14/0.89 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.14/0.89 # Starting ehoh_best5 with 300s (1) cores
% 3.14/0.89 # Starting almost_fo_3_lam with 300s (1) cores
% 3.14/0.89 # Starting new_bool_5 with 300s (1) cores
% 3.14/0.89 # Starting pre_casc_3 with 300s (1) cores
% 3.14/0.89 # Starting ho_unfolding_8 with 300s (1) cores
% 3.14/0.89 # Starting new_ho_10_cnf2 with 300s (1) cores
% 3.14/0.89 # Starting new_bool_3 with 300s (1) cores
% 3.14/0.89 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.14/0.89 # Search class: HGHSM-FSLM31-DHFMMSBN
% 3.14/0.89 # partial match(1): HGHSM-FSLM31-MHFMMSBN
% 3.14/0.89 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 3.14/0.89 # Starting new_ho_10_cnf2 with 163s (1) cores
% 3.14/0.89 # new_ho_10_cnf2 with pid 12011 completed with status 0
% 3.14/0.89 # Result found by new_ho_10_cnf2
% 3.14/0.89 # Preprocessing class: HSLMSLSSLLLCHFA.
% 3.14/0.89 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.14/0.89 # Starting ehoh_best5 with 300s (1) cores
% 3.14/0.89 # Starting almost_fo_3_lam with 300s (1) cores
% 3.14/0.89 # Starting new_bool_5 with 300s (1) cores
% 3.14/0.89 # Starting pre_casc_3 with 300s (1) cores
% 3.14/0.89 # Starting ho_unfolding_8 with 300s (1) cores
% 3.14/0.89 # Starting new_ho_10_cnf2 with 300s (1) cores
% 3.14/0.89 # Starting new_bool_3 with 300s (1) cores
% 3.14/0.89 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.14/0.89 # Search class: HGHSM-FSLM31-DHFMMSBN
% 3.14/0.89 # partial match(1): HGHSM-FSLM31-MHFMMSBN
% 3.14/0.89 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 3.14/0.89 # Starting new_ho_10_cnf2 with 163s (1) cores
% 3.14/0.89 # Preprocessing time : 0.005 s
% 3.14/0.89 # Presaturation interreduction done
% 3.14/0.89
% 3.14/0.89 # Proof found!
% 3.14/0.89 # SZS status Theorem
% 3.14/0.89 # SZS output start CNFRefutation
% See solution above
% 3.14/0.89 # Parsed axioms : 323
% 3.14/0.89 # Removed by relevancy pruning/SinE : 171
% 3.14/0.89 # Initial clauses : 275
% 3.14/0.89 # Removed in clause preprocessing : 24
% 3.14/0.89 # Initial clauses in saturation : 251
% 3.14/0.89 # Processed clauses : 884
% 3.14/0.89 # ...of these trivial : 17
% 3.14/0.89 # ...subsumed : 201
% 3.14/0.89 # ...remaining for further processing : 666
% 3.14/0.89 # Other redundant clauses eliminated : 20
% 3.14/0.89 # Clauses deleted for lack of memory : 0
% 3.14/0.89 # Backward-subsumed : 3
% 3.14/0.89 # Backward-rewritten : 4
% 3.14/0.89 # Generated clauses : 10188
% 3.14/0.89 # ...of the previous two non-redundant : 9946
% 3.14/0.89 # ...aggressively subsumed : 0
% 3.14/0.89 # Contextual simplify-reflections : 0
% 3.14/0.89 # Paramodulations : 10163
% 3.14/0.89 # Factorizations : 2
% 3.14/0.89 # NegExts : 0
% 3.14/0.89 # Equation resolutions : 20
% 3.14/0.89 # Disequality decompositions : 0
% 3.14/0.89 # Total rewrite steps : 343
% 3.14/0.89 # ...of those cached : 274
% 3.14/0.89 # Propositional unsat checks : 0
% 3.14/0.89 # Propositional check models : 0
% 3.14/0.89 # Propositional check unsatisfiable : 0
% 3.14/0.89 # Propositional clauses : 0
% 3.14/0.89 # Propositional clauses after purity: 0
% 3.14/0.89 # Propositional unsat core size : 0
% 3.14/0.89 # Propositional preprocessing time : 0.000
% 3.14/0.89 # Propositional encoding time : 0.000
% 3.14/0.89 # Propositional solver time : 0.000
% 3.14/0.89 # Success case prop preproc time : 0.000
% 3.14/0.89 # Success case prop encoding time : 0.000
% 3.14/0.89 # Success case prop solver time : 0.000
% 3.14/0.89 # Current number of processed clauses : 430
% 3.14/0.89 # Positive orientable unit clauses : 52
% 3.14/0.89 # Positive unorientable unit clauses: 0
% 3.14/0.89 # Negative unit clauses : 2
% 3.14/0.89 # Non-unit-clauses : 376
% 3.14/0.89 # Current number of unprocessed clauses: 9486
% 3.14/0.89 # ...number of literals in the above : 36534
% 3.14/0.89 # Current number of archived formulas : 0
% 3.14/0.89 # Current number of archived clauses : 223
% 3.14/0.89 # Clause-clause subsumption calls (NU) : 21278
% 3.14/0.89 # Rec. Clause-clause subsumption calls : 10588
% 3.14/0.89 # Non-unit clause-clause subsumptions : 128
% 3.14/0.89 # Unit Clause-clause subsumption calls : 183
% 3.14/0.89 # Rewrite failures with RHS unbound : 0
% 3.14/0.89 # BW rewrite match attempts : 18
% 3.14/0.89 # BW rewrite match successes : 4
% 3.14/0.89 # Condensation attempts : 884
% 3.14/0.89 # Condensation successes : 4
% 3.14/0.89 # Termbank termtop insertions : 234531
% 3.14/0.89 # Search garbage collected termcells : 14331
% 3.14/0.89
% 3.14/0.89 # -------------------------------------------------
% 3.14/0.89 # User time : 0.325 s
% 3.14/0.89 # System time : 0.018 s
% 3.14/0.89 # Total time : 0.344 s
% 3.14/0.89 # Maximum resident set size: 5460 pages
% 3.14/0.89
% 3.14/0.89 # -------------------------------------------------
% 3.14/0.89 # User time : 0.332 s
% 3.14/0.89 # System time : 0.023 s
% 3.14/0.89 # Total time : 0.355 s
% 3.14/0.89 # Maximum resident set size: 2152 pages
% 3.14/0.89 % E---3.1 exiting
% 3.14/0.90 % E exiting
%------------------------------------------------------------------------------