%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU650^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 03:28:50 EDT 2024
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 405
% Syntax : Number of formulae : 440 ( 5 unt; 238 typ; 0 def)
% Number of atoms : 1733 ( 267 equ; 0 cnn)
% Maximal formula atoms : 511 ( 8 avg)
% Number of connectives : 6082 ( 418 ~; 401 |; 318 &;3857 @)
% ( 229 <=>; 859 =>; 0 <=; 0 <~>)
% Maximal formula depth : 640 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 301 ( 301 >; 0 *; 0 +; 0 <<)
% Number of symbols : 241 ( 238 usr; 173 con; 0-4 aty)
% Number of variables : 1457 ( 71 ^1306 !; 80 ?;1457 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
epred1_0: $o ).
thf(decl_219,type,
esk1_2: $i > $i > $i ).
thf(decl_220,type,
esk2_2: $i > $i > $i ).
thf(decl_221,type,
esk3_2: $i > $i > $i ).
thf(decl_222,type,
esk4_1: $i > $i ).
thf(decl_223,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_224,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_225,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_226,type,
esk8_1: $i > $i ).
thf(decl_227,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_228,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_229,type,
esk11_2: $i > $i > $i ).
thf(decl_230,type,
esk12_2: $i > $i > $i ).
thf(decl_231,type,
esk13_1: $i > $i ).
thf(decl_232,type,
esk14_1: $i > $i ).
thf(decl_233,type,
esk15_1: $i > $i ).
thf(decl_234,type,
esk16_2: $i > $i > $i ).
thf(decl_235,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_236,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_237,type,
esk19_1: $i > $i ).
thf(decl_238,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_239,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_240,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_241,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_242,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_243,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_244,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_245,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_246,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_247,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_248,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_249,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_250,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_251,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_252,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_253,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_254,type,
esk36_2: $i > $i > $i ).
thf(decl_255,type,
esk37_2: $i > $i > $i ).
thf(decl_256,type,
esk38_2: $i > $i > $i ).
thf(decl_257,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_258,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_259,type,
esk41_2: $i > $i > $i ).
thf(decl_260,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_261,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_262,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_263,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_264,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_265,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_266,type,
esk48_0: $i ).
thf(decl_267,type,
esk49_0: $i ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(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(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(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(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(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(setukpairinjR12,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
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(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
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(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(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(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(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(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
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(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
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(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(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(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(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(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(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(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(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
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(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
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(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
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(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_166,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_167,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_168,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_169,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_170,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_171,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_172,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_173,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_174,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_175,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_176,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_177,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_178,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_179,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_180,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_181,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_182,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_183,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_184,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_185,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_186,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_187,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_188,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_189,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_190,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_191,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_192,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_193,plain,
( epred1_0
<=> ! [X501: $i] :
? [X502: $i] :
( ! [X503: $i] :
( ( in @ X503 @ X502 )
=> ! [X504: $i] :
( ( in @ X504 @ X503 )
=> ( in @ X504 @ X501 ) ) )
& ! [X505: $i,X506: $i] :
( ( ( in @ X505 @ X501 )
& ( in @ X506 @ X501 ) )
=> ( ! [X507: $i] :
( ( in @ X507 @ X502 )
=> ( ( in @ X505 @ X507 )
<=> ( in @ X506 @ X507 ) ) )
=> ( X505 = X506 ) ) )
& ! [X508: $i,X509: $i] :
( ( ( in @ X508 @ X502 )
& ( in @ X509 @ X502 ) )
=> ( ! [X510: $i] :
( ( in @ X510 @ X508 )
=> ( in @ X510 @ X509 ) )
| ! [X511: $i] :
( ( in @ X511 @ X509 )
=> ( in @ X511 @ X508 ) ) ) )
& ! [X512: $i] :
( ( ! [X513: $i] :
( ( in @ X513 @ X512 )
=> ( in @ X513 @ X501 ) )
& ? [X514: $i] : ( in @ X514 @ X512 ) )
=> ? [X515: $i,X516: $i] :
( ( in @ X515 @ X502 )
& ( in @ X516 @ X512 )
& ~ ? [X517: $i] :
( ( in @ X517 @ X515 )
& ( in @ X517 @ X512 ) )
& ! [X518: $i] :
( ( in @ X518 @ X502 )
=> ( ! [X519: $i] :
( ( in @ X519 @ X518 )
=> ( in @ X519 @ X515 ) )
| ( in @ X516 @ X518 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_194,negated_conjecture,
~ ( ! [X474: $i,X475: $i] :
( ! [X476: $i] :
( ( in @ X476 @ X474 )
<=> ( in @ X476 @ X475 ) )
=> ( X474 = X475 ) )
=> ( ! [X477: $i] :
~ ( in @ X477 @ emptyset )
=> ( ! [X478: $i,X479: $i,X480: $i] :
( ( in @ X480 @ ( setadjoin @ X478 @ X479 ) )
<=> ( ( X480 = X478 )
| ( in @ X480 @ X479 ) ) )
=> ( ! [X481: $i,X482: $i] :
( ( in @ X482 @ ( powerset @ X481 ) )
<=> ! [X483: $i] :
( ( in @ X483 @ X482 )
=> ( in @ X483 @ X481 ) ) )
=> ( ! [X484: $i,X485: $i] :
( ( in @ X485 @ ( setunion @ X484 ) )
<=> ? [X486: $i] :
( ( in @ X485 @ X486 )
& ( in @ X486 @ X484 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X487: $i] :
( ( in @ X487 @ omega )
=> ( in @ ( setadjoin @ X487 @ X487 ) @ omega ) )
=> ( ! [X488: $i] :
( ( ( in @ emptyset @ X488 )
& ! [X489: $i] :
( ( ( in @ X489 @ omega )
& ( in @ X489 @ X488 ) )
=> ( in @ ( setadjoin @ X489 @ X489 ) @ X488 ) ) )
=> ! [X490: $i] :
( ( in @ X490 @ omega )
=> ( in @ X490 @ X488 ) ) )
=> ( ! [X491: $i > $i > $o,X492: $i] :
( ! [X493: $i] :
( ( in @ X493 @ X492 )
=> ( exu @ ( X491 @ X493 ) ) )
=> ? [X494: $i] :
! [X495: $i] :
( ( in @ X495 @ X494 )
<=> ? [X496: $i] :
( ( in @ X496 @ X492 )
& ( X491 @ X496 @ X495 ) ) ) )
=> ( ! [X497: $i] :
( ? [X498: $i] : ( in @ X498 @ X497 )
=> ? [X499: $i] :
( ( in @ X499 @ X497 )
& ~ ? [X500: $i] :
( ( in @ X500 @ X499 )
& ( in @ X500 @ X497 ) ) ) )
=> ( epred1_0
=> ( ! [X520: $i > $o] :
( ( exu @ X520 )
=> ( X520
@ ( descr
@ ^ [Z0: $i] : ( X520 @ Z0 ) ) ) )
=> ( ! [X521: $i,X522: $i > $o,X523: $i] :
( ( in @ X523 @ X521 )
=> ( ( X522 @ X523 )
=> ( in @ X523 @ ( dsetconstr @ X521 @ X522 ) ) ) )
=> ( ! [X524: $i,X525: $i > $o,X526: $i] :
( ( in @ X526 @ ( dsetconstr @ X524 @ X525 ) )
=> ( in @ X526 @ X524 ) )
=> ( ! [X527: $i,X528: $i > $o,X529: $i] :
( ( in @ X529 @ ( dsetconstr @ X527 @ X528 ) )
=> ( X528 @ X529 ) )
=> ( ! [X530: $i > $o] :
( ( exu @ X530 )
=> ? [X531: $i] :
( ( X530 @ X531 )
& ! [X532: $i] :
( ( X530 @ X532 )
=> ( X531 = X532 ) ) ) )
=> ( ! [X533: $o,X534: $i] :
( ( in @ X534 @ ( prop2set @ X533 ) )
=> X533 )
=> ( ! [X535: $i] :
( ( in @ X535 @ emptyset )
=> ! [X536: $o] : X536 )
=> ( ! [X537: $i] :
( ( in @ X537 @ emptyset )
=> ~ $true )
=> ( ! [X538: $i] :
~ ( in @ X538 @ emptyset )
=> ( ! [X539: $i > $o] :
( ( exu @ X539 )
=> ? [X540: $i] : ( X539 @ X540 ) )
=> ( ! [X541: $i,X542: $i] :
( ! [X543: $i] :
( ( in @ X543 @ X541 )
=> ( in @ X543 @ X542 ) )
=> ( ! [X544: $i] :
( ( in @ X544 @ X542 )
=> ( in @ X544 @ X541 ) )
=> ( X541 = X542 ) ) )
=> ( ! [X545: $i] :
( ! [X546: $i] :
~ ( in @ X546 @ X545 )
=> ( X545 = emptyset ) )
=> ( ! [X547: $i] :
( ! [X548: $i] :
~ ( in @ X548 @ X547 )
=> ( X547 = emptyset ) )
=> ( ! [X549: $i,X550: $i > $o,X551: $i] :
( ( in @ X551 @ X549 )
=> ( ( in @ X551 @ ( dsetconstr @ X549 @ X550 ) )
<=> ( X550 @ X551 ) ) )
=> ( ! [X552: $i] :
( ( nonempty @ X552 )
=> ? [X553: $i] : ( in @ X553 @ X552 ) )
=> ( ! [X554: $i,X555: $i > $o,X556: $i] :
( ( in @ X556 @ X554 )
=> ( ( X555 @ X556 )
=> ( nonempty @ ( dsetconstr @ X554 @ X555 ) ) ) )
=> ( ! [X557: $i] :
( ? [X558: $i] : ( in @ X558 @ X557 )
=> ( nonempty @ X557 ) )
=> ( ! [X559: $i,X560: $i] : ( in @ X559 @ ( setadjoin @ X559 @ X560 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X561: $i,X562: $i,X563: $i] :
( ( in @ X563 @ X562 )
=> ( in @ X563 @ ( setadjoin @ X561 @ X562 ) ) )
=> ( ! [X564: $i,X565: $i,X566: $i] :
( ( in @ X566 @ ( setadjoin @ X564 @ X565 ) )
=> ! [X567: $o] :
( ( ( X566 = X564 )
=> X567 )
=> ( ( ( in @ X566 @ X565 )
=> X567 )
=> X567 ) ) )
=> ( ! [X568: $i,X569: $i,X570: $i] :
( ( in @ X570 @ ( setadjoin @ X568 @ X569 ) )
=> ( ( X570 = X568 )
| ( in @ X570 @ X569 ) ) )
=> ( ! [X571: $i] :
( ( dsetconstr @ X571
@ ^ [Z0: $i] : $true )
= X571 )
=> ( ! [X572: $i,X573: $i] :
( ! [X574: $i] :
( ( in @ X574 @ X573 )
=> ( in @ X574 @ X572 ) )
=> ( in @ X573 @ ( powerset @ X572 ) ) )
=> ( ! [X575: $i] : ( in @ emptyset @ ( powerset @ X575 ) )
=> ( ! [X576: $i] : ( in @ emptyset @ ( powerset @ X576 ) )
=> ( ! [X577: $i,X578: $i,X579: $i] :
( ( in @ X578 @ ( powerset @ X577 ) )
=> ( ( in @ X579 @ X578 )
=> ( in @ X579 @ X577 ) ) )
=> ( ! [X580: $i,X581: $i,X582: $i] :
( ( in @ X581 @ X582 )
=> ( ( in @ X582 @ X580 )
=> ( in @ X581 @ ( setunion @ X580 ) ) ) )
=> ( ! [X583: $i,X584: $i] :
( ( in @ X584 @ ( setunion @ X583 ) )
=> ! [X585: $o] :
( ! [X586: $i] :
( ( in @ X584 @ X586 )
=> ( ( in @ X586 @ X583 )
=> X585 ) )
=> X585 ) )
=> ( ! [X587: $i,X588: $i] :
( ( in @ X588 @ X587 )
=> ( in @ X588 @ ( powerset @ ( setunion @ X587 ) ) ) )
=> ( ! [X589: $i > $o] :
( ( exu @ X589 )
=> ? [X590: $i] :
! [X591: $i] :
( ( X589 @ X591 )
<=> ( X591 = X590 ) ) )
=> ( ! [X592: $i] :
( ( nonempty @ X592 )
=> ? [X593: $i] :
( ( in @ X593 @ X592 )
& $true ) )
=> ( ! [X594: $i,X595: $i] :
( ( in @ X594 @ ( setadjoin @ X595 @ emptyset ) )
=> ( X594 = X595 ) )
=> ( ! [X596: $i,X597: $i] :
( ( X596 != X597 )
=> ~ ( in @ X597 @ ( setadjoin @ X596 @ emptyset ) ) )
=> ( ! [X598: $i,X599: $i] :
( ( X598 = X599 )
=> ( in @ X598 @ ( setadjoin @ X599 @ emptyset ) ) )
=> ( ! [X600: $i,X601: $i] :
( ( in @ X600 @ ( setadjoin @ X601 @ emptyset ) )
=> ( in @ X601 @ ( setadjoin @ X600 @ emptyset ) ) )
=> ( ! [X602: $i,X603: $i,X604: $i] :
( ( in @ X604 @ ( setadjoin @ X602 @ ( setadjoin @ X603 @ emptyset ) ) )
=> ( ( X604 = X602 )
| ( X604 = X603 ) ) )
=> ( ! [X605: $i,X606: $i] : ( in @ X605 @ ( setadjoin @ X605 @ ( setadjoin @ X606 @ emptyset ) ) )
=> ( ! [X607: $i,X608: $i] : ( in @ X608 @ ( setadjoin @ X607 @ ( setadjoin @ X608 @ emptyset ) ) )
=> ( ! [X609: $i,X610: $i > $o] :
( ? [X611: $i] :
( ( in @ X611 @ X609 )
& ( X610 @ X611 ) )
=> ( ( ( dsetconstr @ X609 @ X610 )
= emptyset )
=> ~ $true ) )
=> ( ! [X612: $i > $o,X613: $i] :
( ( in @ X613 @ emptyset )
=> ( X612 @ X613 ) )
=> ( ! [X614: $i,X615: $i > $o] :
( ~ ! [X616: $i] :
( ( in @ X616 @ X614 )
=> ( X615 @ X616 ) )
=> ? [X617: $i] :
( ( in @ X617 @ X614 )
& ~ ( X615 @ X617 ) ) )
=> ( ! [X618: $i,X619: $i > $o] :
( ! [X620: $i] :
( ( in @ X620 @ X618 )
=> ~ ( X619 @ X620 ) )
=> ~ ? [X621: $i] :
( ( in @ X621 @ X618 )
& ( X619 @ X621 ) ) )
=> ( ! [X622: $i,X623: $i > $o] :
( ~ ? [X624: $i] :
( ( in @ X624 @ X622 )
& ( X623 @ X624 ) )
=> ! [X625: $i] :
( ( in @ X625 @ X622 )
=> ~ ( X623 @ X625 ) ) )
=> ( ! [X626: $i,X627: $i > $o] :
( ? [X628: $i] :
( ( in @ X628 @ X626 )
& ~ ( X627 @ X628 ) )
=> ~ ! [X629: $i] :
( ( in @ X629 @ X626 )
=> ( X627 @ X629 ) ) )
=> ( ! [X630: $o] :
( X630
=> ( in @ emptyset @ ( prop2set @ X630 ) ) )
=> ( prop2set2propI
=> ( ! [X631: $i,X632: $i > $o] :
( ~ ? [X633: $i] :
( ( in @ X633 @ X631 )
& ( X632 @ X633 ) )
=> ! [X634: $i] :
( ( in @ X634 @ X631 )
=> ~ ( X632 @ X634 ) ) )
=> ( ! [X635: $i,X636: $i > $o] :
( ~ ! [X637: $i] :
( ( in @ X637 @ X635 )
=> ( X636 @ X637 ) )
=> ? [X638: $i] :
( ( in @ X638 @ X635 )
& ~ ( X636 @ X638 ) ) )
=> ( ! [X639: $i > $o] :
( ? [X640: $i] :
( ( X639 @ X640 )
& ! [X641: $i] :
( ( X639 @ X641 )
=> ( X640 = X641 ) ) )
=> ( exu @ X639 ) )
=> ( ! [X642: $i > $o] :
( ? [X643: $i] : ( X642 @ X643 )
=> ( ! [X644: $i,X645: $i] :
( ( X642 @ X644 )
=> ( ( X642 @ X645 )
=> ( X644 = X645 ) ) )
=> ( exu @ X642 ) ) )
=> ( ! [X646: $i > $o] :
( ? [X647: $i] :
! [X648: $i] :
( ( X646 @ X648 )
<=> ( X648 = X647 ) )
=> ( exu @ X646 ) )
=> ( ! [X649: $i,X650: $i] :
( ( X649 = X650 )
=> ! [X651: $i,X652: $i] :
( ( X651 = X652 )
=> ( ( in @ X651 @ X649 )
=> ( in @ X652 @ X650 ) ) ) )
=> ( ! [X653: $i,X654: $i] :
( ( X653 = X654 )
=> ! [X655: $i,X656: $i] :
( ( X655 = X656 )
=> ( ( in @ X655 @ X653 )
<=> ( in @ X656 @ X654 ) ) ) )
=> ( ! [X657: $i > $o] :
( ( exu @ X657 )
=> ! [X658: $i,X659: $i] :
( ( X657 @ X658 )
=> ( ( X657 @ X659 )
=> ( X658 = X659 ) ) ) )
=> ( ! [X660: $i > $o,X661: $i > $o] :
( ! [X662: $i,X663: $i] :
( ( X662 = X663 )
=> ( ( X660 @ X662 )
<=> ( X661 @ X663 ) ) )
=> ( ( exu @ X660 )
<=> ( exu @ X661 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X664: $i,X665: $i] :
( ( X664 = X665 )
=> ! [X666: $i,X667: $i] :
( ( X666 = X667 )
=> ( ( setadjoin @ X664 @ X666 )
= ( setadjoin @ X665 @ X667 ) ) ) )
=> ( ! [X668: $i,X669: $i] :
( ( X668 = X669 )
=> ( ( powerset @ X668 )
= ( powerset @ X669 ) ) )
=> ( ! [X670: $i,X671: $i] :
( ( X670 = X671 )
=> ( ( setunion @ X670 )
= ( setunion @ X671 ) ) )
=> ( ( omega = omega )
=> ( ! [X672: $i > $o] :
( ( exu @ X672 )
=> ! [X673: $i,X674: $i] :
( ( X672 @ X673 )
=> ( ( X672 @ X674 )
=> ( X673 = X674 ) ) ) )
=> ( ! [X675: $i > $o,X676: $i > $o] :
( ! [X677: $i,X678: $i] :
( ( X677 = X678 )
=> ( ( X675 @ X677 )
<=> ( X676 @ X678 ) ) )
=> ( ( exu @ X675 )
=> ( ( exu @ X676 )
=> ( ( descr @ X675 )
= ( descr @ X676 ) ) ) ) )
=> ( ! [X679: $i,X680: $i] :
( ( X679 = X680 )
=> ! [X681: $i > $o,X682: $i > $o] :
( ! [X683: $i] :
( ( in @ X683 @ X679 )
=> ! [X684: $i] :
( ( in @ X684 @ X680 )
=> ( ( X683 = X684 )
=> ( ( X681 @ X683 )
<=> ( X682 @ X684 ) ) ) ) )
=> ( ( dsetconstr @ X679 @ X681 )
= ( dsetconstr @ X680 @ X682 ) ) ) )
=> ( ! [X685: $i,X686: $i] :
( ! [X687: $i] :
( ( in @ X687 @ X685 )
=> ( in @ X687 @ X686 ) )
=> ( subset @ X685 @ X686 ) )
=> ( ! [X688: $i,X689: $i] :
( ( X688 = X689 )
=> ( subset @ X689 @ X688 ) )
=> ( ! [X690: $i,X691: $i] :
( ( X690 = X691 )
=> ( subset @ X690 @ X691 ) )
=> ( ! [X692: $i,X693: $i] :
( ! [X694: $i] :
( ( in @ X694 @ X692 )
=> ( in @ X694 @ X693 ) )
=> ( subset @ X692 @ X693 ) )
=> ( ! [X695: $i] : ( subset @ emptyset @ X695 )
=> ( ! [X696: $i,X697: $i,X698: $i] :
( ( subset @ X696 @ X697 )
=> ( ( in @ X698 @ X696 )
=> ( in @ X698 @ X697 ) ) )
=> ( ! [X699: $i,X700: $i,X701: $i] :
( ( subset @ X699 @ X700 )
=> ( ~ ( in @ X701 @ X700 )
=> ~ ( in @ X701 @ X699 ) ) )
=> ( ! [X702: $i,X703: $i,X704: $i] :
( ( in @ X704 @ X702 )
=> ( ~ ( in @ X704 @ X703 )
=> ~ ( subset @ X702 @ X703 ) ) )
=> ( ! [X705: $i,X706: $i] :
( ~ ( subset @ X705 @ X706 )
=> ( X705 != X706 ) )
=> ( ! [X707: $i,X708: $i,X709: $i] :
( ( in @ X709 @ X707 )
=> ( ~ ( in @ X709 @ X708 )
=> ( X707 != X708 ) ) )
=> ( ! [X710: $i] : ( subset @ X710 @ X710 )
=> ( ! [X711: $i,X712: $i,X713: $i] :
( ( subset @ X711 @ X712 )
=> ( ( subset @ X712 @ X713 )
=> ( subset @ X711 @ X713 ) ) )
=> ( ! [X714: $i,X715: $i] : ( subset @ X715 @ ( setadjoin @ X714 @ X715 ) )
=> ( ! [X716: $i,X717: $i,X718: $i] :
( ( subset @ X716 @ X718 )
=> ( subset @ X716 @ ( setadjoin @ X717 @ X718 ) ) )
=> ( ! [X719: $i,X720: $i] :
( ( subset @ X719 @ X720 )
=> ( in @ X719 @ ( powerset @ X720 ) ) )
=> ( ! [X721: $i,X722: $i] :
( ( subset @ X721 @ X722 )
=> ( ( subset @ X722 @ X721 )
=> ( X721 = X722 ) ) )
=> ( ! [X723: $i] :
( ( subset @ X723 @ emptyset )
=> ( X723 = emptyset ) )
=> ( ! [X724: $i,X725: $i] :
( ( subset @ X725 @ X724 )
=> ( in @ X725 @ ( powerset @ X724 ) ) )
=> ( ! [X726: $i,X727: $i] :
( ( in @ X727 @ ( powerset @ X726 ) )
=> ( subset @ X727 @ X726 ) )
=> ( ! [X728: $i] : ( in @ X728 @ ( powerset @ X728 ) )
=> ( ! [X729: $i,X730: $i] :
( ( subset @ X729 @ X730 )
=> ( subset @ ( powerset @ X729 ) @ ( powerset @ X730 ) ) )
=> ( ! [X731: $i,X732: $i > $o] : ( in @ ( dsetconstr @ X731 @ X732 ) @ ( powerset @ X731 ) )
=> ( ! [X733: $i,X734: $i > $o] : ( subset @ ( dsetconstr @ X733 @ X734 ) @ X733 )
=> ( ! [X735: $i,X736: $i,X737: $i] :
( ( in @ X737 @ X735 )
=> ( in @ X737 @ ( binunion @ X735 @ X736 ) ) )
=> ( ! [X738: $i,X739: $i] : ( in @ X739 @ ( setadjoin @ X738 @ ( setadjoin @ X739 @ emptyset ) ) )
=> ( ! [X740: $i,X741: $i,X742: $i] :
( ( in @ X742 @ X741 )
=> ( in @ X742 @ ( binunion @ X740 @ X741 ) ) )
=> ( ! [X743: $i,X744: $i,X745: $i,X746: $o] :
( ( in @ X745 @ ( binunion @ X743 @ X744 ) )
=> ( ( ( in @ X745 @ X743 )
=> X746 )
=> ( ( ( in @ X745 @ X744 )
=> X746 )
=> X746 ) ) )
=> ( ! [X747: $i,X748: $i,X749: $i] :
( ( in @ X749 @ ( binunion @ X747 @ X748 ) )
=> ( ( in @ X749 @ X747 )
| ( in @ X749 @ X748 ) ) )
=> ( ! [X750: $i,X751: $i] : ( subset @ X750 @ ( binunion @ X750 @ X751 ) )
=> ( ! [X752: $i,X753: $i] : ( subset @ X753 @ ( binunion @ X752 @ X753 ) )
=> ( ! [X754: $i,X755: $i,X756: $i] :
( ( in @ X756 @ X754 )
=> ( ( in @ X756 @ X755 )
=> ( in @ X756 @ ( binintersect @ X754 @ X755 ) ) ) )
=> ( ! [X757: $i,X758: $i,X759: $i] :
( ( subset @ X759 @ X757 )
=> ( ( subset @ X759 @ X758 )
=> ( subset @ X759 @ ( binintersect @ X757 @ X758 ) ) ) )
=> ( ! [X760: $i,X761: $i,X762: $i] :
( ( in @ X762 @ ( binintersect @ X760 @ X761 ) )
=> ( in @ X762 @ X760 ) )
=> ( ! [X763: $i,X764: $i] : ( subset @ ( binintersect @ X763 @ X764 ) @ X763 )
=> ( ! [X765: $i,X766: $i] :
( ( subset @ X765 @ X766 )
=> ( ( binintersect @ X765 @ X766 )
= X765 ) )
=> ( ! [X767: $i,X768: $i] :
( ( ( binintersect @ X767 @ X768 )
= X768 )
=> ( subset @ X768 @ X767 ) )
=> ( ! [X769: $i,X770: $i,X771: $i] :
( ( in @ X771 @ ( binintersect @ X769 @ X770 ) )
=> ( in @ X771 @ X770 ) )
=> ( ! [X772: $i,X773: $i] :
( ~ ? [X774: $i] :
( ( in @ X774 @ X772 )
& ( in @ X774 @ X773 ) )
=> ( ( binintersect @ X772 @ X773 )
= emptyset ) )
=> ( ! [X775: $i,X776: $i] : ( subset @ ( binintersect @ X775 @ X776 ) @ X776 )
=> ( ! [X777: $i,X778: $i] :
( ( subset @ X778 @ X777 )
=> ( ( binintersect @ X777 @ X778 )
= X778 ) )
=> ( ! [X779: $i,X780: $i] :
( ( ( binintersect @ X779 @ X780 )
= X779 )
=> ( subset @ X779 @ X780 ) )
=> ( ! [X781: $i,X782: $i,X783: $i] :
( ( binintersect @ X781 @ ( binunion @ X782 @ X783 ) )
= ( binunion @ ( binintersect @ X781 @ X782 ) @ ( binintersect @ X781 @ X783 ) ) )
=> ( ! [X784: $i,X785: $i,X786: $i] :
( ( in @ X786 @ X784 )
=> ( ~ ( in @ X786 @ X785 )
=> ( in @ X786 @ ( setminus @ X784 @ X785 ) ) ) )
=> ( ! [X787: $i,X788: $i,X789: $i] :
( ( in @ X789 @ ( setminus @ X787 @ X788 ) )
=> ( in @ X789 @ X787 ) )
=> ( ! [X790: $i,X791: $i,X792: $i] :
( ( in @ X792 @ ( setminus @ X790 @ X791 ) )
=> ~ ( in @ X792 @ X791 ) )
=> ( ! [X793: $i,X794: $i] :
( ( subset @ X793 @ X794 )
=> ( ( setminus @ X793 @ X794 )
= emptyset ) )
=> ( ! [X795: $i,X796: $i,X797: $i] :
( ~ ( in @ X797 @ ( setminus @ X795 @ X796 ) )
=> ( ( in @ X797 @ X795 )
=> ( in @ X797 @ X796 ) ) )
=> ( ! [X798: $i,X799: $i,X800: $i] :
( ~ ( in @ X800 @ ( setminus @ X798 @ X799 ) )
=> ( ~ ( in @ X800 @ X799 )
=> ~ ( in @ X800 @ X798 ) ) )
=> ( ! [X801: $i,X802: $i,X803: $i] :
( ~ ( in @ X803 @ X801 )
=> ~ ( in @ X803 @ ( setminus @ X801 @ X802 ) ) )
=> ( ! [X804: $i,X805: $i,X806: $i] :
( ( in @ X806 @ X805 )
=> ~ ( in @ X806 @ ( setminus @ X804 @ X805 ) ) )
=> ( ! [X807: $i,X808: $i] : ( subset @ ( setminus @ X807 @ X808 ) @ X807 )
=> ( ! [X809: $i,X810: $i] :
( ( ( setminus @ X809 @ X810 )
= emptyset )
=> ( subset @ X809 @ X810 ) )
=> ( ! [X811: $i,X812: $i,X813: $i] :
( ( in @ X813 @ ( symdiff @ X811 @ X812 ) )
=> ! [X814: $o] :
( ( ( in @ X813 @ X811 )
=> ( ~ ( in @ X813 @ X812 )
=> X814 ) )
=> ( ( ~ ( in @ X813 @ X811 )
=> ( ( in @ X813 @ X812 )
=> X814 ) )
=> X814 ) ) )
=> ( ! [X815: $i,X816: $i,X817: $i] :
( ( in @ X817 @ X815 )
=> ( ~ ( in @ X817 @ X816 )
=> ( in @ X817 @ ( symdiff @ X815 @ X816 ) ) ) )
=> ( ! [X818: $i,X819: $i,X820: $i] :
( ~ ( in @ X820 @ X818 )
=> ( ( in @ X820 @ X819 )
=> ( in @ X820 @ ( symdiff @ X818 @ X819 ) ) ) )
=> ( ! [X821: $i,X822: $i,X823: $i] :
( ( in @ X823 @ X821 )
=> ( ( in @ X823 @ X822 )
=> ~ ( in @ X823 @ ( symdiff @ X821 @ X822 ) ) ) )
=> ( ! [X824: $i,X825: $i,X826: $i] :
( ~ ( in @ X826 @ X824 )
=> ( ~ ( in @ X826 @ X825 )
=> ~ ( in @ X826 @ ( symdiff @ X824 @ X825 ) ) ) )
=> ( ! [X827: $i,X828: $i] : ( in @ X828 @ ( setadjoin @ X827 @ ( setadjoin @ X828 @ emptyset ) ) )
=> ( ! [X829: $i,X830: $i] : ( in @ X829 @ ( setunion @ ( setadjoin @ ( setadjoin @ X829 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X829 @ ( setadjoin @ X830 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X831: $i,X832: $i] : ( in @ X832 @ ( setunion @ ( setadjoin @ ( setadjoin @ X831 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X831 @ ( setadjoin @ X832 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X833: $i,X834: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X833 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X833 @ ( setadjoin @ X834 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X835: $i,X836: $i] : ( iskpair @ ( kpair @ X835 @ X836 ) )
=> ( ! [X837: $i,X838: $i] :
( ( in @ X838 @ X837 )
=> ( subset @ ( setadjoin @ X838 @ emptyset ) @ X837 ) )
=> ( ! [X839: $i,X840: $i] :
( ( in @ X840 @ X839 )
=> ( in @ ( setadjoin @ X840 @ emptyset ) @ ( powerset @ X839 ) ) )
=> ( ! [X841: $i,X842: $i,X843: $i] :
( ( in @ X843 @ X841 )
=> ( in @ ( setadjoin @ X843 @ emptyset ) @ ( powerset @ ( binunion @ X841 @ X842 ) ) ) )
=> ( ! [X844: $i,X845: $i,X846: $i] :
( ( in @ X846 @ ( setadjoin @ X844 @ ( setadjoin @ X845 @ emptyset ) ) )
=> ( ( X846 = X844 )
| ( X846 = X845 ) ) )
=> ( ! [X847: $i,X848: $i,X849: $i] :
( ( in @ X849 @ X847 )
=> ! [X850: $i] :
( ( in @ X850 @ X848 )
=> ( subset @ ( setadjoin @ X849 @ ( setadjoin @ X850 @ emptyset ) ) @ ( binunion @ X847 @ X848 ) ) ) )
=> ( ! [X851: $i,X852: $i,X853: $i] :
( ( in @ X853 @ X851 )
=> ! [X854: $i] :
( ( in @ X854 @ X852 )
=> ( in @ ( setadjoin @ X853 @ ( setadjoin @ X854 @ emptyset ) ) @ ( powerset @ ( binunion @ X851 @ X852 ) ) ) ) )
=> ( ! [X855: $i,X856: $i,X857: $i] :
( ( in @ X857 @ X855 )
=> ! [X858: $i] :
( ( in @ X858 @ X856 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X857 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X857 @ ( setadjoin @ X858 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X855 @ X856 ) ) ) ) )
=> ( ! [X859: $i,X860: $i,X861: $i] :
( ( in @ X861 @ X859 )
=> ! [X862: $i] :
( ( in @ X862 @ X860 )
=> ( in @ ( setadjoin @ ( setadjoin @ X861 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X861 @ ( setadjoin @ X862 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X859 @ X860 ) ) ) ) ) )
=> ( ! [X863: $i,X864: $i,X865: $i] :
( ( in @ X865 @ X863 )
=> ! [X866: $i] :
( ( in @ X866 @ X864 )
=> ( in @ ( kpair @ X865 @ X866 ) @ ( powerset @ ( powerset @ ( binunion @ X863 @ X864 ) ) ) ) ) )
=> ( ! [X867: $i,X868: $i,X869: $i] :
( ( in @ X869 @ X867 )
=> ! [X870: $i] :
( ( in @ X870 @ X868 )
=> ( in @ ( kpair @ X869 @ X870 ) @ ( cartprod @ X867 @ X868 ) ) ) )
=> ( ! [X871: $i,X872: $i,X873: $i] :
( ( in @ X873 @ ( cartprod @ X871 @ X872 ) )
=> ? [X874: $i] :
( ( in @ X874 @ X871 )
& ? [X875: $i] :
( ( in @ X875 @ X872 )
& ( X873
= ( kpair @ X874 @ X875 ) ) ) ) )
=> ( ! [X876: $i,X877: $i,X878: $i] :
( ( in @ X878 @ ( cartprod @ X876 @ X877 ) )
=> ( iskpair @ X878 ) )
=> ( ! [X879: $i,X880: $i] :
( ( in @ X880 @ ( setunion @ X879 ) )
=> ? [X881: $i] :
( ( in @ X881 @ X879 )
& ( in @ X880 @ X881 ) ) )
=> ( ! [X882: $i] : ( subset @ ( setunion @ ( setadjoin @ X882 @ emptyset ) ) @ X882 )
=> ( ! [X883: $i] : ( subset @ X883 @ ( setunion @ ( setadjoin @ X883 @ emptyset ) ) )
=> ( ! [X884: $i] :
( ( setunion @ ( setadjoin @ X884 @ emptyset ) )
= X884 )
=> ( ! [X885: $i,X886: $i > $o] :
( ! [X887: $i] :
( ( in @ X887 @ X885 )
=> ! [X888: $i] :
( ( in @ X888 @ X885 )
=> ( ( X886 @ X887 )
=> ( ( X886 @ X888 )
=> ( X887 = X888 ) ) ) ) )
=> ( ? [X889: $i] :
( ( in @ X889 @ X885 )
& ( X886 @ X889 ) )
=> ( singleton @ ( dsetconstr @ X885 @ X886 ) ) ) )
=> ( ! [X890: $i,X891: $i > $o] :
( ( ex1 @ X890 @ X891 )
=> ? [X892: $i] :
( ( in @ X892 @ X890 )
& ( X891 @ X892 ) ) )
=> ( ! [X893: $i,X894: $i > $o,X895: $i] :
( ( in @ X895 @ X893 )
=> ( ( X894 @ X895 )
=> ( ! [X896: $i] :
( ( in @ X896 @ X893 )
=> ( ( X894 @ X896 )
=> ( X896 = X895 ) ) )
=> ( ex1 @ X893 @ X894 ) ) ) )
=> ( ! [X897: $i,X898: $i > $o] :
( ! [X899: $i] :
( ( in @ X899 @ X897 )
=> ! [X900: $i] :
( ( in @ X900 @ X897 )
=> ( ( X898 @ X899 )
=> ( ( X898 @ X900 )
=> ( X899 = X900 ) ) ) ) )
=> ( ? [X901: $i] :
( ( in @ X901 @ X897 )
& ( X898 @ X901 ) )
=> ( ex1 @ X897 @ X898 ) ) )
=> ( ! [X902: $i,X903: $i] :
( ( ( setadjoin @ X902 @ emptyset )
= ( setadjoin @ X903 @ emptyset ) )
=> ( X902 = X903 ) )
=> ( ! [X904: $i,X905: $i,X906: $i] :
( ( in @ ( setadjoin @ X906 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X904 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X904 @ ( setadjoin @ X905 @ emptyset ) ) @ emptyset ) ) )
=> ( X904 = X906 ) )
=> ( ! [X907: $i] :
( ( iskpair @ X907 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X907 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X907 ) ) ) )
=> ( ! [X908: $i] :
( ( singleton @ X908 )
=> ( in @ ( setunion @ X908 ) @ X908 ) )
=> ( ! [X909: $i,X910: $i] :
( ( kfst @ ( kpair @ X909 @ X910 ) )
= X909 )
=> ( ! [X911: $i,X912: $i,X913: $i] :
( ( in @ X913 @ ( cartprod @ X911 @ X912 ) )
=> ( in @ ( kfst @ X913 ) @ X911 ) )
=> ( ! [X914: $i,X915: $i,X916: $i,X917: $i] :
( ( ( setadjoin @ ( setadjoin @ X914 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X914 @ ( setadjoin @ X915 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X916 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X916 @ ( setadjoin @ X917 @ emptyset ) ) @ emptyset ) ) )
=> ( X914 = X916 ) )
=> ( ! [X918: $i,X919: $i,X920: $i,X921: $i] :
( ( ( kpair @ X918 @ X919 )
= ( kpair @ X920 @ X921 ) )
=> ( X918 = X920 ) )
=> ( ! [X922: $i,X923: $i] :
( ( X922 = X923 )
=> ( ( setadjoin @ X922 @ ( setadjoin @ X923 @ emptyset ) )
= ( setadjoin @ X922 @ emptyset ) ) )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[setukpairinjR12]),quantDeMorgan4]),cartprodmempair]),setukpairinjR11]),symdiffE]),symdiffI1]),symdiffI2]),singletonsswitch]),symdiffIneg1]),symdiffIneg2]),upairsetE]),secondinupair]),setukpairIL]),upairsetIL]),setukpairIR]),kpairiskpair]),upairsetIR]),kpairp]),singletonsubset]),c_0_166]),singletoninpowerset]),singletoninpowunion]),vacuousDall]),upairset2E]),upairsubunion]),quantDeMorgan1]),upairinpowunion]),ubforcartprodlem1]),quantDeMorgan2]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),quantDeMorgan3]),cartprodmempair1]),c_0_167]),setunionE2]),setunionsingleton1]),setunionsingleton2]),prop2setI]),setunionsingleton]),c_0_168]),notdexE]),c_0_169]),c_0_170]),notdallE]),c_0_171]),singletonsuniq]),setukpairinjL1]),c_0_172]),c_0_173]),theprop]),kfstpairEq]),c_0_174]),cartprodfstin]),setukpairinjL2]),c_0_175]),setukpairinjL]),inCongP]),in__Cong]),c_0_176]),c_0_177]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_178]),c_0_179]),binintersectSubset3]),binintersectER]),disjointsetsI1]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_180]),c_0_181]),c_0_182]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),nonemptyImpWitness]),binintersectI]),uniqinunit]),binintersectSubset5]),notinsingleton]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),eqinunit]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_183]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_184]),nonemptyE1]),c_0_185]),noeltsimpempty]),emptyI]),setext]),c_0_186]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_187]),c_0_188]),c_0_189]),c_0_190]),c_0_191]),wellorderingAx]),foundationAx]),c_0_192]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_193]) ).
thf(c_0_195,negated_conjecture,
! [X924: $i,X925: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i,X932: $i,X933: $i,X934: $i,X935: $i,X937: $i,X938: $i,X940: $i,X941: $i,X942: $i,X943: $i,X944: $i,X946: $i,X947: $i > $i > $o,X948: $i,X951: $i,X953: $i,X954: $i,X955: $i,X956: $i,X958: $i,X959: $i > $o,X960: $i,X961: $i > $o,X962: $i,X963: $i,X964: $i > $o,X965: $i,X966: $i,X967: $i > $o,X968: $i,X969: $i > $o,X971: $i,X972: $o,X973: $i,X974: $i,X975: $o,X976: $i,X977: $i,X978: $i > $o,X980: $i,X981: $i,X984: $i,X986: $i,X988: $i,X989: $i > $o,X990: $i,X991: $i,X993: $i,X994: $i > $o,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i,X1004: $i,X1005: $i,X1006: $o,X1007: $i,X1008: $i,X1009: $i,X1010: $i,X1011: $i,X1012: $i,X1014: $i,X1015: $i,X1016: $i,X1017: $i,X1018: $i,X1019: $i,X1020: $i,X1021: $i,X1022: $i,X1023: $i,X1024: $o,X1026: $i,X1027: $i,X1028: $i > $o,X1030: $i,X1031: $i,X1032: $i,X1034: $i,X1035: $i,X1036: $i,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1041: $i,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i > $o,X1051: $i,X1052: $i > $o,X1053: $i,X1054: $i,X1055: $i > $o,X1056: $i,X1058: $i,X1059: $i > $o,X1061: $i,X1062: $i,X1063: $i > $o,X1065: $i,X1066: $i,X1067: $i > $o,X1068: $i,X1070: $o,X1071: $i,X1072: $i > $o,X1074: $i,X1075: $i,X1076: $i > $o,X1077: $i,X1079: $i > $o,X1080: $i,X1082: $i > $o,X1083: $i,X1086: $i > $o,X1087: $i,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i > $o,X1098: $i,X1099: $i,X1100: $i > $o,X1101: $i > $o,X1104: $i,X1105: $i,X1106: $i,X1107: $i,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i > $o,X1113: $i,X1114: $i,X1115: $i > $o,X1116: $i > $o,X1119: $i,X1120: $i,X1121: $i > $o,X1122: $i > $o,X1125: $i,X1126: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,X1133: $i,X1135: $i,X1136: $i,X1137: $i,X1138: $i,X1139: $i,X1140: $i,X1141: $i,X1142: $i,X1143: $i,X1144: $i,X1145: $i,X1146: $i,X1147: $i,X1148: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1164: $i,X1165: $i,X1166: $i,X1167: $i,X1168: $i,X1169: $i,X1170: $i,X1171: $i,X1172: $i > $o,X1173: $i,X1174: $i > $o,X1175: $i,X1176: $i,X1177: $i,X1178: $i,X1179: $i,X1180: $i,X1181: $i,X1182: $i,X1183: $i,X1184: $i,X1185: $i,X1186: $o,X1187: $i,X1188: $i,X1189: $i,X1190: $i,X1191: $i,X1192: $i,X1193: $i,X1194: $i,X1195: $i,X1196: $i,X1197: $i,X1198: $i,X1199: $i,X1200: $i,X1201: $i,X1202: $i,X1203: $i,X1204: $i,X1205: $i,X1206: $i,X1207: $i,X1208: $i,X1209: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,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: $i,X1253: $i,X1254: $o,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,X1273: $i,X1274: $i,X1275: $i,X1276: $i,X1277: $i,X1278: $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,X1313: $i,X1316: $i,X1317: $i,X1318: $i,X1319: $i,X1320: $i,X1322: $i,X1323: $i,X1324: $i,X1325: $i,X1326: $i > $o,X1329: $i,X1330: $i,X1331: $i > $o,X1333: $i,X1334: $i > $o,X1335: $i,X1337: $i,X1338: $i > $o,X1341: $i,X1342: $i,X1343: $i,X1344: $i,X1345: $i,X1346: $i,X1347: $i,X1348: $i,X1349: $i,X1350: $i,X1351: $i,X1352: $i,X1353: $i,X1354: $i,X1355: $i,X1356: $i,X1357: $i,X1358: $i,X1359: $i,X1360: $i,X1361: $i,X1362: $i,X1363: $i] :
( ( ~ ( in @ ( esk1_2 @ X924 @ X925 ) @ X924 )
| ~ ( in @ ( esk1_2 @ X924 @ X925 ) @ X925 )
| ( X924 = X925 ) )
& ( ( in @ ( esk1_2 @ X924 @ X925 ) @ X924 )
| ( in @ ( esk1_2 @ X924 @ X925 ) @ X925 )
| ( X924 = X925 ) )
& ~ ( in @ X927 @ emptyset )
& ( ~ ( in @ X930 @ ( setadjoin @ X928 @ X929 ) )
| ( X930 = X928 )
| ( in @ X930 @ X929 ) )
& ( ( X930 != X928 )
| ( in @ X930 @ ( setadjoin @ X928 @ X929 ) ) )
& ( ~ ( in @ X930 @ X929 )
| ( in @ X930 @ ( setadjoin @ X928 @ X929 ) ) )
& ( ~ ( in @ X932 @ ( powerset @ X931 ) )
| ~ ( in @ X933 @ X932 )
| ( in @ X933 @ X931 ) )
& ( ( in @ ( esk2_2 @ X934 @ X935 ) @ X935 )
| ( in @ X935 @ ( powerset @ X934 ) ) )
& ( ~ ( in @ ( esk2_2 @ X934 @ X935 ) @ X934 )
| ( in @ X935 @ ( powerset @ X934 ) ) )
& ( ( in @ X938 @ ( esk3_2 @ X937 @ X938 ) )
| ~ ( in @ X938 @ ( setunion @ X937 ) ) )
& ( ( in @ ( esk3_2 @ X937 @ X938 ) @ X937 )
| ~ ( in @ X938 @ ( setunion @ X937 ) ) )
& ( ~ ( in @ X941 @ X942 )
| ~ ( in @ X942 @ X940 )
| ( in @ X941 @ ( setunion @ X940 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X943 @ omega )
| ( in @ ( setadjoin @ X943 @ X943 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X944 ) @ omega )
| ~ ( in @ emptyset @ X944 )
| ~ ( in @ X946 @ omega )
| ( in @ X946 @ X944 ) )
& ( ( in @ ( esk4_1 @ X944 ) @ X944 )
| ~ ( in @ emptyset @ X944 )
| ~ ( in @ X946 @ omega )
| ( in @ X946 @ X944 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X944 ) @ ( esk4_1 @ X944 ) ) @ X944 )
| ~ ( in @ emptyset @ X944 )
| ~ ( in @ X946 @ omega )
| ( in @ X946 @ X944 ) )
& ( ( in @ ( esk7_3 @ X947 @ X948 @ X951 ) @ X948 )
| ~ ( in @ X951 @ ( esk6_2 @ X947 @ X948 ) )
| ( in @ ( esk5_2 @ X947 @ X948 ) @ X948 ) )
& ( ( X947 @ ( esk7_3 @ X947 @ X948 @ X951 ) @ X951 )
| ~ ( in @ X951 @ ( esk6_2 @ X947 @ X948 ) )
| ( in @ ( esk5_2 @ X947 @ X948 ) @ X948 ) )
& ( ~ ( in @ X954 @ X948 )
| ~ ( X947 @ X954 @ X953 )
| ( in @ X953 @ ( esk6_2 @ X947 @ X948 ) )
| ( in @ ( esk5_2 @ X947 @ X948 ) @ X948 ) )
& ( ( in @ ( esk7_3 @ X947 @ X948 @ X951 ) @ X948 )
| ~ ( in @ X951 @ ( esk6_2 @ X947 @ X948 ) )
| ~ ( exu @ ( X947 @ ( esk5_2 @ X947 @ X948 ) ) ) )
& ( ( X947 @ ( esk7_3 @ X947 @ X948 @ X951 ) @ X951 )
| ~ ( in @ X951 @ ( esk6_2 @ X947 @ X948 ) )
| ~ ( exu @ ( X947 @ ( esk5_2 @ X947 @ X948 ) ) ) )
& ( ~ ( in @ X954 @ X948 )
| ~ ( X947 @ X954 @ X953 )
| ( in @ X953 @ ( esk6_2 @ X947 @ X948 ) )
| ~ ( exu @ ( X947 @ ( esk5_2 @ X947 @ X948 ) ) ) )
& ( ( in @ ( esk8_1 @ X955 ) @ X955 )
| ~ ( in @ X956 @ X955 ) )
& ( ~ ( in @ X958 @ ( esk8_1 @ X955 ) )
| ~ ( in @ X958 @ X955 )
| ~ ( in @ X956 @ X955 ) )
& epred1_0
& ( ~ ( exu @ X959 )
| ( X959 @ ( descr @ X959 ) ) )
& ( ~ ( in @ X962 @ X960 )
| ~ ( X961 @ X962 )
| ( in @ X962 @ ( dsetconstr @ X960 @ X961 ) ) )
& ( ~ ( in @ X965 @ ( dsetconstr @ X963 @ X964 ) )
| ( in @ X965 @ X963 ) )
& ( ~ ( in @ X968 @ ( dsetconstr @ X966 @ X967 ) )
| ( X967 @ X968 ) )
& ( ( X969 @ ( esk9_1 @ X969 ) )
| ~ ( exu @ X969 ) )
& ( ~ ( X969 @ X971 )
| ( ( esk9_1 @ X969 )
= X971 )
| ~ ( exu @ X969 ) )
& ( ~ ( in @ X973 @ ( prop2set @ X972 ) )
| X972 )
& ( ~ ( in @ X974 @ emptyset )
| X975 )
& ( ~ ( in @ X976 @ emptyset )
| ~ $true )
& ~ ( in @ X977 @ emptyset )
& ( ~ ( exu @ X978 )
| ( X978 @ ( esk10_1 @ X978 ) ) )
& ( ( in @ ( esk12_2 @ X980 @ X981 ) @ X981 )
| ( X980 = X981 )
| ( in @ ( esk11_2 @ X980 @ X981 ) @ X980 ) )
& ( ~ ( in @ ( esk12_2 @ X980 @ X981 ) @ X980 )
| ( X980 = X981 )
| ( in @ ( esk11_2 @ X980 @ X981 ) @ X980 ) )
& ( ( in @ ( esk12_2 @ X980 @ X981 ) @ X981 )
| ( X980 = X981 )
| ~ ( in @ ( esk11_2 @ X980 @ X981 ) @ X981 ) )
& ( ~ ( in @ ( esk12_2 @ X980 @ X981 ) @ X980 )
| ( X980 = X981 )
| ~ ( in @ ( esk11_2 @ X980 @ X981 ) @ X981 ) )
& ( ( in @ ( esk13_1 @ X984 ) @ X984 )
| ( X984 = emptyset ) )
& ( ( in @ ( esk14_1 @ X986 ) @ X986 )
| ( X986 = emptyset ) )
& ( ~ ( in @ X990 @ ( dsetconstr @ X988 @ X989 ) )
| ( X989 @ X990 )
| ~ ( in @ X990 @ X988 ) )
& ( ~ ( X989 @ X990 )
| ( in @ X990 @ ( dsetconstr @ X988 @ X989 ) )
| ~ ( in @ X990 @ X988 ) )
& ( ~ ( nonempty @ X991 )
| ( in @ ( esk15_1 @ X991 ) @ X991 ) )
& ( ~ ( in @ X995 @ X993 )
| ~ ( X994 @ X995 )
| ( nonempty @ ( dsetconstr @ X993 @ X994 ) ) )
& ( ~ ( in @ X997 @ X996 )
| ( nonempty @ X996 ) )
& ( in @ X998 @ ( setadjoin @ X998 @ X999 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1002 @ X1001 )
| ( in @ X1002 @ ( setadjoin @ X1000 @ X1001 ) ) )
& ( ( in @ X1005 @ X1004 )
| X1006
| ( X1005 = X1003 )
| ~ ( in @ X1005 @ ( setadjoin @ X1003 @ X1004 ) ) )
& ( ~ X1006
| X1006
| ( X1005 = X1003 )
| ~ ( in @ X1005 @ ( setadjoin @ X1003 @ X1004 ) ) )
& ( ( in @ X1005 @ X1004 )
| X1006
| ~ X1006
| ~ ( in @ X1005 @ ( setadjoin @ X1003 @ X1004 ) ) )
& ( ~ X1006
| X1006
| ~ X1006
| ~ ( in @ X1005 @ ( setadjoin @ X1003 @ X1004 ) ) )
& ( ~ ( in @ X1009 @ ( setadjoin @ X1007 @ X1008 ) )
| ( X1009 = X1007 )
| ( in @ X1009 @ X1008 ) )
& ( ( dsetconstr @ X1010
@ ^ [Z0: $i] : $true )
= X1010 )
& ( ( in @ ( esk16_2 @ X1011 @ X1012 ) @ X1012 )
| ( in @ X1012 @ ( powerset @ X1011 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1011 @ X1012 ) @ X1011 )
| ( in @ X1012 @ ( powerset @ X1011 ) ) )
& ( in @ emptyset @ ( powerset @ X1014 ) )
& ( in @ emptyset @ ( powerset @ X1015 ) )
& ( ~ ( in @ X1017 @ ( powerset @ X1016 ) )
| ~ ( in @ X1018 @ X1017 )
| ( in @ X1018 @ X1016 ) )
& ( ~ ( in @ X1020 @ X1021 )
| ~ ( in @ X1021 @ X1019 )
| ( in @ X1020 @ ( setunion @ X1019 ) ) )
& ( ( in @ X1023 @ ( esk17_3 @ X1022 @ X1023 @ X1024 ) )
| X1024
| ~ ( in @ X1023 @ ( setunion @ X1022 ) ) )
& ( ( in @ ( esk17_3 @ X1022 @ X1023 @ X1024 ) @ X1022 )
| X1024
| ~ ( in @ X1023 @ ( setunion @ X1022 ) ) )
& ( ~ X1024
| X1024
| ~ ( in @ X1023 @ ( setunion @ X1022 ) ) )
& ( ~ ( in @ X1027 @ X1026 )
| ( in @ X1027 @ ( powerset @ ( setunion @ X1026 ) ) ) )
& ( ~ ( X1028 @ X1030 )
| ( X1030
= ( esk18_1 @ X1028 ) )
| ~ ( exu @ X1028 ) )
& ( ( X1031
!= ( esk18_1 @ X1028 ) )
| ( X1028 @ X1031 )
| ~ ( exu @ X1028 ) )
& ( ( in @ ( esk19_1 @ X1032 ) @ X1032 )
| ~ ( nonempty @ X1032 ) )
& ( $true
| ~ ( nonempty @ X1032 ) )
& ( ~ ( in @ X1034 @ ( setadjoin @ X1035 @ emptyset ) )
| ( X1034 = X1035 ) )
& ( ( X1036 = X1037 )
| ~ ( in @ X1037 @ ( setadjoin @ X1036 @ emptyset ) ) )
& ( ( X1038 != X1039 )
| ( in @ X1038 @ ( setadjoin @ X1039 @ emptyset ) ) )
& ( ~ ( in @ X1040 @ ( setadjoin @ X1041 @ emptyset ) )
| ( in @ X1041 @ ( setadjoin @ X1040 @ emptyset ) ) )
& ( ~ ( in @ X1044 @ ( setadjoin @ X1042 @ ( setadjoin @ X1043 @ emptyset ) ) )
| ( X1044 = X1042 )
| ( X1044 = X1043 ) )
& ( in @ X1045 @ ( setadjoin @ X1045 @ ( setadjoin @ X1046 @ emptyset ) ) )
& ( in @ X1048 @ ( setadjoin @ X1047 @ ( setadjoin @ X1048 @ emptyset ) ) )
& ( ~ ( in @ X1051 @ X1049 )
| ~ ( X1050 @ X1051 )
| ( ( dsetconstr @ X1049 @ X1050 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1053 @ emptyset )
| ( X1052 @ X1053 ) )
& ( ( in @ ( esk20_2 @ X1054 @ X1055 ) @ X1054 )
| ~ ( in @ X1056 @ X1054 )
| ( X1055 @ X1056 ) )
& ( ~ ( X1055 @ ( esk20_2 @ X1054 @ X1055 ) )
| ~ ( in @ X1056 @ X1054 )
| ( X1055 @ X1056 ) )
& ( ( in @ ( esk21_2 @ X1058 @ X1059 ) @ X1058 )
| ~ ( in @ X1061 @ X1058 )
| ~ ( X1059 @ X1061 ) )
& ( ( X1059 @ ( esk21_2 @ X1058 @ X1059 ) )
| ~ ( in @ X1061 @ X1058 )
| ~ ( X1059 @ X1061 ) )
& ( ( in @ ( esk22_2 @ X1062 @ X1063 ) @ X1062 )
| ~ ( in @ X1065 @ X1062 )
| ~ ( X1063 @ X1065 ) )
& ( ( X1063 @ ( esk22_2 @ X1062 @ X1063 ) )
| ~ ( in @ X1065 @ X1062 )
| ~ ( X1063 @ X1065 ) )
& ( ( in @ ( esk23_2 @ X1066 @ X1067 ) @ X1066 )
| ~ ( in @ X1068 @ X1066 )
| ( X1067 @ X1068 ) )
& ( ~ ( X1067 @ ( esk23_2 @ X1066 @ X1067 ) )
| ~ ( in @ X1068 @ X1066 )
| ( X1067 @ X1068 ) )
& ( ~ X1070
| ( in @ emptyset @ ( prop2set @ X1070 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1071 @ X1072 ) @ X1071 )
| ~ ( in @ X1074 @ X1071 )
| ~ ( X1072 @ X1074 ) )
& ( ( X1072 @ ( esk24_2 @ X1071 @ X1072 ) )
| ~ ( in @ X1074 @ X1071 )
| ~ ( X1072 @ X1074 ) )
& ( ( in @ ( esk25_2 @ X1075 @ X1076 ) @ X1075 )
| ~ ( in @ X1077 @ X1075 )
| ( X1076 @ X1077 ) )
& ( ~ ( X1076 @ ( esk25_2 @ X1075 @ X1076 ) )
| ~ ( in @ X1077 @ X1075 )
| ( X1076 @ X1077 ) )
& ( ( X1079 @ ( esk26_2 @ X1079 @ X1080 ) )
| ~ ( X1079 @ X1080 )
| ( exu @ X1079 ) )
& ( ( X1080
!= ( esk26_2 @ X1079 @ X1080 ) )
| ~ ( X1079 @ X1080 )
| ( exu @ X1079 ) )
& ( ( X1082 @ ( esk27_1 @ X1082 ) )
| ( exu @ X1082 )
| ~ ( X1082 @ X1083 ) )
& ( ( X1082 @ ( esk28_1 @ X1082 ) )
| ( exu @ X1082 )
| ~ ( X1082 @ X1083 ) )
& ( ( ( esk27_1 @ X1082 )
!= ( esk28_1 @ X1082 ) )
| ( exu @ X1082 )
| ~ ( X1082 @ X1083 ) )
& ( ~ ( X1086 @ ( esk29_2 @ X1086 @ X1087 ) )
| ( ( esk29_2 @ X1086 @ X1087 )
!= X1087 )
| ( exu @ X1086 ) )
& ( ( X1086 @ ( esk29_2 @ X1086 @ X1087 ) )
| ( ( esk29_2 @ X1086 @ X1087 )
= X1087 )
| ( exu @ X1086 ) )
& ( ( X1089 != X1090 )
| ( X1091 != X1092 )
| ~ ( in @ X1091 @ X1089 )
| ( in @ X1092 @ X1090 ) )
& ( ~ ( in @ X1095 @ X1093 )
| ( in @ X1096 @ X1094 )
| ( X1095 != X1096 )
| ( X1093 != X1094 ) )
& ( ~ ( in @ X1096 @ X1094 )
| ( in @ X1095 @ X1093 )
| ( X1095 != X1096 )
| ( X1093 != X1094 ) )
& ( ~ ( exu @ X1097 )
| ~ ( X1097 @ X1098 )
| ~ ( X1097 @ X1099 )
| ( X1098 = X1099 ) )
& ( ~ ( exu @ X1100 )
| ( exu @ X1101 )
| ( ( esk30_2 @ X1100 @ X1101 )
= ( esk31_2 @ X1100 @ X1101 ) ) )
& ( ~ ( exu @ X1101 )
| ( exu @ X1100 )
| ( ( esk30_2 @ X1100 @ X1101 )
= ( esk31_2 @ X1100 @ X1101 ) ) )
& ( ~ ( exu @ X1100 )
| ( exu @ X1101 )
| ~ ( X1100 @ ( esk30_2 @ X1100 @ X1101 ) )
| ~ ( X1101 @ ( esk31_2 @ X1100 @ X1101 ) ) )
& ( ~ ( exu @ X1101 )
| ( exu @ X1100 )
| ~ ( X1100 @ ( esk30_2 @ X1100 @ X1101 ) )
| ~ ( X1101 @ ( esk31_2 @ X1100 @ X1101 ) ) )
& ( ~ ( exu @ X1100 )
| ( exu @ X1101 )
| ( X1100 @ ( esk30_2 @ X1100 @ X1101 ) )
| ( X1101 @ ( esk31_2 @ X1100 @ X1101 ) ) )
& ( ~ ( exu @ X1101 )
| ( exu @ X1100 )
| ( X1100 @ ( esk30_2 @ X1100 @ X1101 ) )
| ( X1101 @ ( esk31_2 @ X1100 @ X1101 ) ) )
& ( emptyset = emptyset )
& ( ( X1104 != X1105 )
| ( X1106 != X1107 )
| ( ( setadjoin @ X1104 @ X1106 )
= ( setadjoin @ X1105 @ X1107 ) ) )
& ( ( X1108 != X1109 )
| ( ( powerset @ X1108 )
= ( powerset @ X1109 ) ) )
& ( ( X1110 != X1111 )
| ( ( setunion @ X1110 )
= ( setunion @ X1111 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1112 )
| ~ ( X1112 @ X1113 )
| ~ ( X1112 @ X1114 )
| ( X1113 = X1114 ) )
& ( ( ( esk32_2 @ X1115 @ X1116 )
= ( esk33_2 @ X1115 @ X1116 ) )
| ~ ( exu @ X1115 )
| ~ ( exu @ X1116 )
| ( ( descr @ X1115 )
= ( descr @ X1116 ) ) )
& ( ~ ( X1115 @ ( esk32_2 @ X1115 @ X1116 ) )
| ~ ( X1116 @ ( esk33_2 @ X1115 @ X1116 ) )
| ~ ( exu @ X1115 )
| ~ ( exu @ X1116 )
| ( ( descr @ X1115 )
= ( descr @ X1116 ) ) )
& ( ( X1115 @ ( esk32_2 @ X1115 @ X1116 ) )
| ( X1116 @ ( esk33_2 @ X1115 @ X1116 ) )
| ~ ( exu @ X1115 )
| ~ ( exu @ X1116 )
| ( ( descr @ X1115 )
= ( descr @ X1116 ) ) )
& ( ( in @ ( esk34_4 @ X1119 @ X1120 @ X1121 @ X1122 ) @ X1119 )
| ( ( dsetconstr @ X1119 @ X1121 )
= ( dsetconstr @ X1120 @ X1122 ) )
| ( X1119 != X1120 ) )
& ( ( in @ ( esk35_4 @ X1119 @ X1120 @ X1121 @ X1122 ) @ X1120 )
| ( ( dsetconstr @ X1119 @ X1121 )
= ( dsetconstr @ X1120 @ X1122 ) )
| ( X1119 != X1120 ) )
& ( ( ( esk34_4 @ X1119 @ X1120 @ X1121 @ X1122 )
= ( esk35_4 @ X1119 @ X1120 @ X1121 @ X1122 ) )
| ( ( dsetconstr @ X1119 @ X1121 )
= ( dsetconstr @ X1120 @ X1122 ) )
| ( X1119 != X1120 ) )
& ( ~ ( X1121 @ ( esk34_4 @ X1119 @ X1120 @ X1121 @ X1122 ) )
| ~ ( X1122 @ ( esk35_4 @ X1119 @ X1120 @ X1121 @ X1122 ) )
| ( ( dsetconstr @ X1119 @ X1121 )
= ( dsetconstr @ X1120 @ X1122 ) )
| ( X1119 != X1120 ) )
& ( ( X1121 @ ( esk34_4 @ X1119 @ X1120 @ X1121 @ X1122 ) )
| ( X1122 @ ( esk35_4 @ X1119 @ X1120 @ X1121 @ X1122 ) )
| ( ( dsetconstr @ X1119 @ X1121 )
= ( dsetconstr @ X1120 @ X1122 ) )
| ( X1119 != X1120 ) )
& ( ( in @ ( esk36_2 @ X1125 @ X1126 ) @ X1125 )
| ( subset @ X1125 @ X1126 ) )
& ( ~ ( in @ ( esk36_2 @ X1125 @ X1126 ) @ X1126 )
| ( subset @ X1125 @ X1126 ) )
& ( ( X1128 != X1129 )
| ( subset @ X1129 @ X1128 ) )
& ( ( X1130 != X1131 )
| ( subset @ X1130 @ X1131 ) )
& ( ( in @ ( esk37_2 @ X1132 @ X1133 ) @ X1132 )
| ( subset @ X1132 @ X1133 ) )
& ( ~ ( in @ ( esk37_2 @ X1132 @ X1133 ) @ X1133 )
| ( subset @ X1132 @ X1133 ) )
& ( subset @ emptyset @ X1135 )
& ( ~ ( subset @ X1136 @ X1137 )
| ~ ( in @ X1138 @ X1136 )
| ( in @ X1138 @ X1137 ) )
& ( ~ ( subset @ X1139 @ X1140 )
| ( in @ X1141 @ X1140 )
| ~ ( in @ X1141 @ X1139 ) )
& ( ~ ( in @ X1144 @ X1142 )
| ( in @ X1144 @ X1143 )
| ~ ( subset @ X1142 @ X1143 ) )
& ( ( subset @ X1145 @ X1146 )
| ( X1145 != X1146 ) )
& ( ~ ( in @ X1149 @ X1147 )
| ( in @ X1149 @ X1148 )
| ( X1147 != X1148 ) )
& ( subset @ X1150 @ X1150 )
& ( ~ ( subset @ X1151 @ X1152 )
| ~ ( subset @ X1152 @ X1153 )
| ( subset @ X1151 @ X1153 ) )
& ( subset @ X1155 @ ( setadjoin @ X1154 @ X1155 ) )
& ( ~ ( subset @ X1156 @ X1158 )
| ( subset @ X1156 @ ( setadjoin @ X1157 @ X1158 ) ) )
& ( ~ ( subset @ X1159 @ X1160 )
| ( in @ X1159 @ ( powerset @ X1160 ) ) )
& ( ~ ( subset @ X1161 @ X1162 )
| ~ ( subset @ X1162 @ X1161 )
| ( X1161 = X1162 ) )
& ( ~ ( subset @ X1163 @ emptyset )
| ( X1163 = emptyset ) )
& ( ~ ( subset @ X1165 @ X1164 )
| ( in @ X1165 @ ( powerset @ X1164 ) ) )
& ( ~ ( in @ X1167 @ ( powerset @ X1166 ) )
| ( subset @ X1167 @ X1166 ) )
& ( in @ X1168 @ ( powerset @ X1168 ) )
& ( ~ ( subset @ X1169 @ X1170 )
| ( subset @ ( powerset @ X1169 ) @ ( powerset @ X1170 ) ) )
& ( in @ ( dsetconstr @ X1171 @ X1172 ) @ ( powerset @ X1171 ) )
& ( subset @ ( dsetconstr @ X1173 @ X1174 ) @ X1173 )
& ( ~ ( in @ X1177 @ X1175 )
| ( in @ X1177 @ ( binunion @ X1175 @ X1176 ) ) )
& ( in @ X1179 @ ( setadjoin @ X1178 @ ( setadjoin @ X1179 @ emptyset ) ) )
& ( ~ ( in @ X1182 @ X1181 )
| ( in @ X1182 @ ( binunion @ X1180 @ X1181 ) ) )
& ( ( in @ X1185 @ X1184 )
| X1186
| ( in @ X1185 @ X1183 )
| ~ ( in @ X1185 @ ( binunion @ X1183 @ X1184 ) ) )
& ( ~ X1186
| X1186
| ( in @ X1185 @ X1183 )
| ~ ( in @ X1185 @ ( binunion @ X1183 @ X1184 ) ) )
& ( ( in @ X1185 @ X1184 )
| X1186
| ~ X1186
| ~ ( in @ X1185 @ ( binunion @ X1183 @ X1184 ) ) )
& ( ~ X1186
| X1186
| ~ X1186
| ~ ( in @ X1185 @ ( binunion @ X1183 @ X1184 ) ) )
& ( ~ ( in @ X1189 @ ( binunion @ X1187 @ X1188 ) )
| ( in @ X1189 @ X1187 )
| ( in @ X1189 @ X1188 ) )
& ( subset @ X1190 @ ( binunion @ X1190 @ X1191 ) )
& ( subset @ X1193 @ ( binunion @ X1192 @ X1193 ) )
& ( ~ ( in @ X1196 @ X1194 )
| ~ ( in @ X1196 @ X1195 )
| ( in @ X1196 @ ( binintersect @ X1194 @ X1195 ) ) )
& ( ~ ( subset @ X1199 @ X1197 )
| ~ ( subset @ X1199 @ X1198 )
| ( subset @ X1199 @ ( binintersect @ X1197 @ X1198 ) ) )
& ( ~ ( in @ X1202 @ ( binintersect @ X1200 @ X1201 ) )
| ( in @ X1202 @ X1200 ) )
& ( subset @ ( binintersect @ X1203 @ X1204 ) @ X1203 )
& ( ~ ( subset @ X1205 @ X1206 )
| ( ( binintersect @ X1205 @ X1206 )
= X1205 ) )
& ( ( ( binintersect @ X1207 @ X1208 )
!= X1208 )
| ( subset @ X1208 @ X1207 ) )
& ( ~ ( in @ X1211 @ ( binintersect @ X1209 @ X1210 ) )
| ( in @ X1211 @ X1210 ) )
& ( ( in @ ( esk38_2 @ X1212 @ X1213 ) @ X1212 )
| ( ( binintersect @ X1212 @ X1213 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1212 @ X1213 ) @ X1213 )
| ( ( binintersect @ X1212 @ X1213 )
= emptyset ) )
& ( subset @ ( binintersect @ X1215 @ X1216 ) @ X1216 )
& ( ~ ( subset @ X1218 @ X1217 )
| ( ( binintersect @ X1217 @ X1218 )
= X1218 ) )
& ( ( ( binintersect @ X1219 @ X1220 )
!= X1219 )
| ( subset @ X1219 @ X1220 ) )
& ( ( binintersect @ X1221 @ ( binunion @ X1222 @ X1223 ) )
= ( binunion @ ( binintersect @ X1221 @ X1222 ) @ ( binintersect @ X1221 @ X1223 ) ) )
& ( ~ ( in @ X1226 @ X1224 )
| ( in @ X1226 @ X1225 )
| ( in @ X1226 @ ( setminus @ X1224 @ X1225 ) ) )
& ( ~ ( in @ X1229 @ ( setminus @ X1227 @ X1228 ) )
| ( in @ X1229 @ X1227 ) )
& ( ~ ( in @ X1232 @ ( setminus @ X1230 @ X1231 ) )
| ~ ( in @ X1232 @ X1231 ) )
& ( ~ ( subset @ X1233 @ X1234 )
| ( ( setminus @ X1233 @ X1234 )
= emptyset ) )
& ( ( in @ X1237 @ ( setminus @ X1235 @ X1236 ) )
| ~ ( in @ X1237 @ X1235 )
| ( in @ X1237 @ X1236 ) )
& ( ( in @ X1240 @ ( setminus @ X1238 @ X1239 ) )
| ( in @ X1240 @ X1239 )
| ~ ( in @ X1240 @ X1238 ) )
& ( ( in @ X1243 @ X1241 )
| ~ ( in @ X1243 @ ( setminus @ X1241 @ X1242 ) ) )
& ( ~ ( in @ X1246 @ X1245 )
| ~ ( in @ X1246 @ ( setminus @ X1244 @ X1245 ) ) )
& ( subset @ ( setminus @ X1247 @ X1248 ) @ X1247 )
& ( ( ( setminus @ X1249 @ X1250 )
!= emptyset )
| ( subset @ X1249 @ X1250 ) )
& ( ~ ( in @ X1253 @ X1251 )
| X1254
| ( in @ X1253 @ X1251 )
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ( in @ X1253 @ X1252 )
| X1254
| ( in @ X1253 @ X1251 )
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ~ X1254
| X1254
| ( in @ X1253 @ X1251 )
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ~ ( in @ X1253 @ X1251 )
| X1254
| ~ ( in @ X1253 @ X1252 )
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ( in @ X1253 @ X1252 )
| X1254
| ~ ( in @ X1253 @ X1252 )
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ~ X1254
| X1254
| ~ ( in @ X1253 @ X1252 )
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ~ ( in @ X1253 @ X1251 )
| X1254
| ~ X1254
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ( in @ X1253 @ X1252 )
| X1254
| ~ X1254
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ~ X1254
| X1254
| ~ X1254
| ~ ( in @ X1253 @ ( symdiff @ X1251 @ X1252 ) ) )
& ( ~ ( in @ X1257 @ X1255 )
| ( in @ X1257 @ X1256 )
| ( in @ X1257 @ ( symdiff @ X1255 @ X1256 ) ) )
& ( ( in @ X1260 @ X1258 )
| ~ ( in @ X1260 @ X1259 )
| ( in @ X1260 @ ( symdiff @ X1258 @ X1259 ) ) )
& ( ~ ( in @ X1263 @ X1261 )
| ~ ( in @ X1263 @ X1262 )
| ~ ( in @ X1263 @ ( symdiff @ X1261 @ X1262 ) ) )
& ( ( in @ X1266 @ X1264 )
| ( in @ X1266 @ X1265 )
| ~ ( in @ X1266 @ ( symdiff @ X1264 @ X1265 ) ) )
& ( in @ X1268 @ ( setadjoin @ X1267 @ ( setadjoin @ X1268 @ emptyset ) ) )
& ( in @ X1269 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1269 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1269 @ ( setadjoin @ X1270 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1272 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1271 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1271 @ ( setadjoin @ X1272 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1273 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1273 @ ( setadjoin @ X1274 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1275 @ X1276 ) )
& ( ~ ( in @ X1278 @ X1277 )
| ( subset @ ( setadjoin @ X1278 @ emptyset ) @ X1277 ) )
& ( ~ ( in @ X1280 @ X1279 )
| ( in @ ( setadjoin @ X1280 @ emptyset ) @ ( powerset @ X1279 ) ) )
& ( ~ ( in @ X1283 @ X1281 )
| ( in @ ( setadjoin @ X1283 @ emptyset ) @ ( powerset @ ( binunion @ X1281 @ X1282 ) ) ) )
& ( ~ ( in @ X1286 @ ( setadjoin @ X1284 @ ( setadjoin @ X1285 @ emptyset ) ) )
| ( X1286 = X1284 )
| ( X1286 = X1285 ) )
& ( ~ ( in @ X1289 @ X1287 )
| ~ ( in @ X1290 @ X1288 )
| ( subset @ ( setadjoin @ X1289 @ ( setadjoin @ X1290 @ emptyset ) ) @ ( binunion @ X1287 @ X1288 ) ) )
& ( ~ ( in @ X1293 @ X1291 )
| ~ ( in @ X1294 @ X1292 )
| ( in @ ( setadjoin @ X1293 @ ( setadjoin @ X1294 @ emptyset ) ) @ ( powerset @ ( binunion @ X1291 @ X1292 ) ) ) )
& ( ~ ( in @ X1297 @ X1295 )
| ~ ( in @ X1298 @ X1296 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1297 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1297 @ ( setadjoin @ X1298 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1295 @ X1296 ) ) ) )
& ( ~ ( in @ X1301 @ X1299 )
| ~ ( in @ X1302 @ X1300 )
| ( in @ ( setadjoin @ ( setadjoin @ X1301 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1301 @ ( setadjoin @ X1302 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1299 @ X1300 ) ) ) ) )
& ( ~ ( in @ X1305 @ X1303 )
| ~ ( in @ X1306 @ X1304 )
| ( in @ ( kpair @ X1305 @ X1306 ) @ ( powerset @ ( powerset @ ( binunion @ X1303 @ X1304 ) ) ) ) )
& ( ~ ( in @ X1309 @ X1307 )
| ~ ( in @ X1310 @ X1308 )
| ( in @ ( kpair @ X1309 @ X1310 ) @ ( cartprod @ X1307 @ X1308 ) ) )
& ( ( in @ ( esk39_3 @ X1311 @ X1312 @ X1313 ) @ X1311 )
| ~ ( in @ X1313 @ ( cartprod @ X1311 @ X1312 ) ) )
& ( ( in @ ( esk40_3 @ X1311 @ X1312 @ X1313 ) @ X1312 )
| ~ ( in @ X1313 @ ( cartprod @ X1311 @ X1312 ) ) )
& ( ( X1313
= ( kpair @ ( esk39_3 @ X1311 @ X1312 @ X1313 ) @ ( esk40_3 @ X1311 @ X1312 @ X1313 ) ) )
| ~ ( in @ X1313 @ ( cartprod @ X1311 @ X1312 ) ) )
& ( ~ ( in @ X1318 @ ( cartprod @ X1316 @ X1317 ) )
| ( iskpair @ X1318 ) )
& ( ( in @ ( esk41_2 @ X1319 @ X1320 ) @ X1319 )
| ~ ( in @ X1320 @ ( setunion @ X1319 ) ) )
& ( ( in @ X1320 @ ( esk41_2 @ X1319 @ X1320 ) )
| ~ ( in @ X1320 @ ( setunion @ X1319 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1322 @ emptyset ) ) @ X1322 )
& ( subset @ X1323 @ ( setunion @ ( setadjoin @ X1323 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1324 @ emptyset ) )
= X1324 )
& ( ( in @ ( esk42_2 @ X1325 @ X1326 ) @ X1325 )
| ~ ( in @ X1329 @ X1325 )
| ~ ( X1326 @ X1329 )
| ( singleton @ ( dsetconstr @ X1325 @ X1326 ) ) )
& ( ( in @ ( esk43_2 @ X1325 @ X1326 ) @ X1325 )
| ~ ( in @ X1329 @ X1325 )
| ~ ( X1326 @ X1329 )
| ( singleton @ ( dsetconstr @ X1325 @ X1326 ) ) )
& ( ( X1326 @ ( esk42_2 @ X1325 @ X1326 ) )
| ~ ( in @ X1329 @ X1325 )
| ~ ( X1326 @ X1329 )
| ( singleton @ ( dsetconstr @ X1325 @ X1326 ) ) )
& ( ( X1326 @ ( esk43_2 @ X1325 @ X1326 ) )
| ~ ( in @ X1329 @ X1325 )
| ~ ( X1326 @ X1329 )
| ( singleton @ ( dsetconstr @ X1325 @ X1326 ) ) )
& ( ( ( esk42_2 @ X1325 @ X1326 )
!= ( esk43_2 @ X1325 @ X1326 ) )
| ~ ( in @ X1329 @ X1325 )
| ~ ( X1326 @ X1329 )
| ( singleton @ ( dsetconstr @ X1325 @ X1326 ) ) )
& ( ( in @ ( esk44_2 @ X1330 @ X1331 ) @ X1330 )
| ~ ( ex1 @ X1330 @ X1331 ) )
& ( ( X1331 @ ( esk44_2 @ X1330 @ X1331 ) )
| ~ ( ex1 @ X1330 @ X1331 ) )
& ( ( in @ ( esk45_3 @ X1333 @ X1334 @ X1335 ) @ X1333 )
| ( ex1 @ X1333 @ X1334 )
| ~ ( X1334 @ X1335 )
| ~ ( in @ X1335 @ X1333 ) )
& ( ( X1334 @ ( esk45_3 @ X1333 @ X1334 @ X1335 ) )
| ( ex1 @ X1333 @ X1334 )
| ~ ( X1334 @ X1335 )
| ~ ( in @ X1335 @ X1333 ) )
& ( ( ( esk45_3 @ X1333 @ X1334 @ X1335 )
!= X1335 )
| ( ex1 @ X1333 @ X1334 )
| ~ ( X1334 @ X1335 )
| ~ ( in @ X1335 @ X1333 ) )
& ( ( in @ ( esk46_2 @ X1337 @ X1338 ) @ X1337 )
| ~ ( in @ X1341 @ X1337 )
| ~ ( X1338 @ X1341 )
| ( ex1 @ X1337 @ X1338 ) )
& ( ( in @ ( esk47_2 @ X1337 @ X1338 ) @ X1337 )
| ~ ( in @ X1341 @ X1337 )
| ~ ( X1338 @ X1341 )
| ( ex1 @ X1337 @ X1338 ) )
& ( ( X1338 @ ( esk46_2 @ X1337 @ X1338 ) )
| ~ ( in @ X1341 @ X1337 )
| ~ ( X1338 @ X1341 )
| ( ex1 @ X1337 @ X1338 ) )
& ( ( X1338 @ ( esk47_2 @ X1337 @ X1338 ) )
| ~ ( in @ X1341 @ X1337 )
| ~ ( X1338 @ X1341 )
| ( ex1 @ X1337 @ X1338 ) )
& ( ( ( esk46_2 @ X1337 @ X1338 )
!= ( esk47_2 @ X1337 @ X1338 ) )
| ~ ( in @ X1341 @ X1337 )
| ~ ( X1338 @ X1341 )
| ( ex1 @ X1337 @ X1338 ) )
& ( ( ( setadjoin @ X1342 @ emptyset )
!= ( setadjoin @ X1343 @ emptyset ) )
| ( X1342 = X1343 ) )
& ( ~ ( in @ ( setadjoin @ X1346 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1344 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1344 @ ( setadjoin @ X1345 @ emptyset ) ) @ emptyset ) ) )
| ( X1344 = X1346 ) )
& ( ~ ( iskpair @ X1347 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1347 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1347 ) ) ) )
& ( ~ ( singleton @ X1348 )
| ( in @ ( setunion @ X1348 ) @ X1348 ) )
& ( ( kfst @ ( kpair @ X1349 @ X1350 ) )
= X1349 )
& ( ~ ( in @ X1353 @ ( cartprod @ X1351 @ X1352 ) )
| ( in @ ( kfst @ X1353 ) @ X1351 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1354 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1354 @ ( setadjoin @ X1355 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1356 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1356 @ ( setadjoin @ X1357 @ emptyset ) ) @ emptyset ) ) )
| ( X1354 = X1356 ) )
& ( ( ( kpair @ X1358 @ X1359 )
!= ( kpair @ X1360 @ X1361 ) )
| ( X1358 = X1360 ) )
& ( ( X1362 != X1363 )
| ( ( setadjoin @ X1362 @ ( setadjoin @ X1363 @ emptyset ) )
= ( setadjoin @ X1362 @ emptyset ) ) )
& ( esk48_0 = esk49_0 )
& ( ( setadjoin @ ( setadjoin @ esk48_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk48_0 @ ( setadjoin @ esk49_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ esk48_0 @ 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_194])])])])])])]) ).
thf(c_0_196,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk48_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk48_0 @ ( setadjoin @ esk49_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ esk48_0 @ emptyset ) @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
thf(c_0_197,negated_conjecture,
esk48_0 = esk49_0,
inference(split_conjunct,[status(thm)],[c_0_195]) ).
thf(c_0_198,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
thf(c_0_199,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk48_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk48_0 @ ( setadjoin @ esk48_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ esk48_0 @ emptyset ) @ emptyset ) ),
inference(rw,[status(thm)],[c_0_196,c_0_197]) ).
thf(c_0_200,negated_conjecture,
! [X2: $i] :
( ( setadjoin @ X2 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ),
inference(er,[status(thm)],[c_0_198]) ).
thf(c_0_201,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_200])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU650^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 17:01:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 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
% 0.19/0.57 # Version: 3.1.0-ho
% 0.19/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.19/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.19/0.57 # Starting pre_casc_3 with 300s (1) cores
% 0.19/0.57 # Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.19/0.57 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 # Starting new_ho_5 with 300s (1) cores
% 0.19/0.57 # new_bool_5 with pid 22918 completed with status 0
% 0.19/0.57 # Result found by new_bool_5
% 0.19/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.19/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.19/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.19/0.57 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.19/0.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.57 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.19/0.57 # new_ho_10_cnf2 with pid 22940 completed with status 0
% 0.19/0.57 # Result found by new_ho_10_cnf2
% 0.19/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.19/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.19/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.19/0.57 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.19/0.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.57 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.19/0.57 # Preprocessing time : 0.005 s
% 0.19/0.57 # Presaturation interreduction done
% 0.19/0.57
% 0.19/0.57 # Proof found!
% 0.19/0.57 # SZS status Theorem
% 0.19/0.57 # SZS output start CNFRefutation
% See solution above
% 0.19/0.57 # Parsed axioms : 369
% 0.19/0.57 # Removed by relevancy pruning/SinE : 203
% 0.19/0.57 # Initial clauses : 263
% 0.19/0.57 # Removed in clause preprocessing : 25
% 0.19/0.57 # Initial clauses in saturation : 238
% 0.19/0.57 # Processed clauses : 345
% 0.19/0.57 # ...of these trivial : 7
% 0.19/0.57 # ...subsumed : 34
% 0.19/0.57 # ...remaining for further processing : 304
% 0.19/0.57 # Other redundant clauses eliminated : 14
% 0.19/0.57 # Clauses deleted for lack of memory : 0
% 0.19/0.57 # Backward-subsumed : 0
% 0.19/0.57 # Backward-rewritten : 4
% 0.19/0.57 # Generated clauses : 198
% 0.19/0.57 # ...of the previous two non-redundant : 152
% 0.19/0.57 # ...aggressively subsumed : 0
% 0.19/0.57 # Contextual simplify-reflections : 0
% 0.19/0.57 # Paramodulations : 183
% 0.19/0.57 # Factorizations : 0
% 0.19/0.57 # NegExts : 0
% 0.19/0.57 # Equation resolutions : 15
% 0.19/0.57 # Disequality decompositions : 0
% 0.19/0.57 # Total rewrite steps : 60
% 0.19/0.57 # ...of those cached : 38
% 0.19/0.57 # Propositional unsat checks : 0
% 0.19/0.57 # Propositional check models : 0
% 0.19/0.57 # Propositional check unsatisfiable : 0
% 0.19/0.57 # Propositional clauses : 0
% 0.19/0.57 # Propositional clauses after purity: 0
% 0.19/0.57 # Propositional unsat core size : 0
% 0.19/0.57 # Propositional preprocessing time : 0.000
% 0.19/0.57 # Propositional encoding time : 0.000
% 0.19/0.57 # Propositional solver time : 0.000
% 0.19/0.57 # Success case prop preproc time : 0.000
% 0.19/0.57 # Success case prop encoding time : 0.000
% 0.19/0.57 # Success case prop solver time : 0.000
% 0.19/0.57 # Current number of processed clauses : 86
% 0.19/0.57 # Positive orientable unit clauses : 35
% 0.19/0.57 # Positive unorientable unit clauses: 0
% 0.19/0.57 # Negative unit clauses : 6
% 0.19/0.57 # Non-unit-clauses : 45
% 0.19/0.57 # Current number of unprocessed clauses: 246
% 0.19/0.57 # ...number of literals in the above : 615
% 0.19/0.57 # Current number of archived formulas : 0
% 0.19/0.57 # Current number of archived clauses : 206
% 0.19/0.57 # Clause-clause subsumption calls (NU) : 5255
% 0.19/0.57 # Rec. Clause-clause subsumption calls : 3038
% 0.19/0.57 # Non-unit clause-clause subsumptions : 24
% 0.19/0.57 # Unit Clause-clause subsumption calls : 29
% 0.19/0.57 # Rewrite failures with RHS unbound : 0
% 0.19/0.57 # BW rewrite match attempts : 20
% 0.19/0.57 # BW rewrite match successes : 2
% 0.19/0.57 # Condensation attempts : 345
% 0.19/0.57 # Condensation successes : 4
% 0.19/0.57 # Termbank termtop insertions : 40454
% 0.19/0.57 # Search garbage collected termcells : 14622
% 0.19/0.57
% 0.19/0.57 # -------------------------------------------------
% 0.19/0.57 # User time : 0.068 s
% 0.19/0.57 # System time : 0.014 s
% 0.19/0.57 # Total time : 0.082 s
% 0.19/0.57 # Maximum resident set size: 5488 pages
% 0.19/0.57
% 0.19/0.57 # -------------------------------------------------
% 0.19/0.57 # User time : 0.075 s
% 0.19/0.57 # System time : 0.020 s
% 0.19/0.57 # Total time : 0.094 s
% 0.19/0.57 # Maximum resident set size: 2208 pages
% 0.19/0.57 % E---3.1 exiting
% 0.19/0.58 % E exiting
%------------------------------------------------------------------------------