TSTP Solution File: SEU618^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU618^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 03:28:36 EDT 2024
% Result : Theorem 32.14s 5.11s
% Output : CNFRefutation 32.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 344
% Syntax : Number of formulae : 391 ( 23 unt; 207 typ; 0 def)
% Number of atoms : 1521 ( 357 equ; 0 cnn)
% Maximal formula atoms : 460 ( 8 avg)
% Number of connectives : 5842 ( 506 ~; 535 |; 335 &;3523 @)
% ( 198 <=>; 745 =>; 0 <=; 0 <~>)
% Maximal formula depth : 578 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 323 ( 323 >; 0 *; 0 +; 0 <<)
% Number of symbols : 210 ( 207 usr; 141 con; 0-4 aty)
% Number of variables : 1294 ( 67 ^1121 !; 106 ?;1294 :)
% 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_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
epred1_0: $o ).
thf(decl_178,type,
esk1_2: $i > $i > $i ).
thf(decl_179,type,
esk2_2: $i > $i > $i ).
thf(decl_180,type,
esk3_2: $i > $i > $i ).
thf(decl_181,type,
esk4_1: $i > $i ).
thf(decl_182,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_183,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_184,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_185,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_186,type,
esk9_1: $i > $i ).
thf(decl_187,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_188,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_189,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_190,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_191,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_192,type,
esk15_2: $i > $i > $i ).
thf(decl_193,type,
esk16_2: $i > $i > $i ).
thf(decl_194,type,
esk17_1: $i > $i ).
thf(decl_195,type,
esk18_1: $i > $i ).
thf(decl_196,type,
esk19_1: $i > $i ).
thf(decl_197,type,
esk20_2: $i > $i > $i ).
thf(decl_198,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_199,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_200,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_201,type,
esk24_1: $i > $i ).
thf(decl_202,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_203,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_204,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_205,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_206,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_207,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_208,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_209,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_210,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_211,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_212,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_213,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_214,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_215,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_216,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_217,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_218,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_219,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_220,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_221,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_222,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_223,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_224,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_225,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_226,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_227,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_228,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_229,type,
esk52_2: $i > $i > $i ).
thf(decl_230,type,
esk53_2: $i > $i > $i ).
thf(decl_231,type,
esk54_2: $i > $i > $i ).
thf(decl_232,type,
esk55_0: $i ).
thf(decl_233,type,
esk56_0: $i ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(setukpairIR,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
=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_136,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_137,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_138,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_139,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_140,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_141,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_142,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_143,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_144,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_145,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_146,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_147,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_148,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_149,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_150,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_151,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_152,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_153,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X390: $i] :
( ( X1 @ X390 )
& ! [X391: $i] :
( ( X1 @ X391 )
=> ( X390 = X391 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_136,c_0_137]) ).
thf(c_0_154,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X392: $i] :
( ( X1 @ X392 )
& ! [X393: $i] :
( ( X1 @ X393 )
=> ( X392 = X393 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_138,c_0_137]) ).
thf(c_0_155,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X394: $i] :
( ( X1 @ X394 )
& ! [X395: $i] :
( ( X1 @ X395 )
=> ( X394 = X395 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_139,c_0_137]) ).
thf(c_0_156,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X396: $i] :
( ( X1 @ X396 )
& ! [X397: $i] :
( ( X1 @ X397 )
=> ( X396 = X397 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_140,c_0_137]) ).
thf(c_0_157,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X398: $i] :
( ( X1 @ X398 )
& ! [X399: $i] :
( ( X1 @ X399 )
=> ( X398 = X399 ) ) )
<=> ? [X400: $i] :
( ( X17 @ X400 )
& ! [X401: $i] :
( ( X17 @ X401 )
=> ( X400 = X401 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_141,c_0_137]) ).
thf(c_0_158,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X402: $i] :
( ( X1 @ X402 )
& ! [X403: $i] :
( ( X1 @ X403 )
=> ( X402 = X403 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_142,c_0_137]) ).
thf(c_0_159,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X404: $i] :
( ( X1 @ X404 )
& ! [X405: $i] :
( ( X1 @ X405 )
=> ( X404 = X405 ) ) )
=> ( ? [X406: $i] :
( ( X17 @ X406 )
& ! [X407: $i] :
( ( X17 @ X407 )
=> ( X406 = X407 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_143,c_0_137]) ).
thf(c_0_160,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_161,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_144]) ).
thf(c_0_162,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_163,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X388: $i] :
( ( X1 @ X388 )
& ! [X389: $i] :
( ( X1 @ X389 )
=> ( X388 = X389 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_145,c_0_137]) ).
thf(c_0_164,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_165,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_144]) ).
thf(c_0_166,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_146,c_0_144]) ).
thf(c_0_167,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_144]) ).
thf(c_0_168,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_169,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X386: $i] :
( ( X1 @ X386 )
& ! [X387: $i] :
( ( X1 @ X387 )
=> ( X386 = X387 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_147,c_0_137]) ).
thf(c_0_170,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X384: $i] :
( ( X1 @ X384 )
& ! [X385: $i] :
( ( X1 @ X385 )
=> ( X384 = X385 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_148,c_0_137]) ).
thf(c_0_171,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_172,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_173,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_174,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X382: $i] :
( ( X1 @ X382 )
& ! [X383: $i] :
( ( X1 @ X383 )
=> ( X382 = X383 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_149,c_0_137]) ).
thf(c_0_175,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X380: $i] :
( ( X6 @ X2 @ X380 )
& ! [X381: $i] :
( ( X6 @ X2 @ X381 )
=> ( X380 = X381 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_150,c_0_137]) ).
thf(c_0_176,plain,
( epred1_0
<=> ! [X437: $i] :
? [X438: $i] :
( ! [X439: $i] :
( ( in @ X439 @ X438 )
=> ! [X440: $i] :
( ( in @ X440 @ X439 )
=> ( in @ X440 @ X437 ) ) )
& ! [X441: $i,X442: $i] :
( ( ( in @ X441 @ X437 )
& ( in @ X442 @ X437 ) )
=> ( ! [X443: $i] :
( ( in @ X443 @ X438 )
=> ( ( in @ X441 @ X443 )
<=> ( in @ X442 @ X443 ) ) )
=> ( X441 = X442 ) ) )
& ! [X444: $i,X445: $i] :
( ( ( in @ X444 @ X438 )
& ( in @ X445 @ X438 ) )
=> ( ! [X446: $i] :
( ( in @ X446 @ X444 )
=> ( in @ X446 @ X445 ) )
| ! [X447: $i] :
( ( in @ X447 @ X445 )
=> ( in @ X447 @ X444 ) ) ) )
& ! [X448: $i] :
( ( ! [X449: $i] :
( ( in @ X449 @ X448 )
=> ( in @ X449 @ X437 ) )
& ? [X450: $i] : ( in @ X450 @ X448 ) )
=> ? [X451: $i,X452: $i] :
( ( in @ X451 @ X438 )
& ( in @ X452 @ X448 )
& ~ ? [X453: $i] :
( ( in @ X453 @ X451 )
& ( in @ X453 @ X448 ) )
& ! [X454: $i] :
( ( in @ X454 @ X438 )
=> ( ! [X455: $i] :
( ( in @ X455 @ X454 )
=> ( in @ X455 @ X451 ) )
| ( in @ X452 @ X454 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_177,negated_conjecture,
~ ( ! [X408: $i,X409: $i] :
( ! [X410: $i] :
( ( in @ X410 @ X408 )
<=> ( in @ X410 @ X409 ) )
=> ( X408 = X409 ) )
=> ( ! [X411: $i] :
~ ( in @ X411 @ emptyset )
=> ( ! [X412: $i,X413: $i,X414: $i] :
( ( in @ X414 @ ( setadjoin @ X412 @ X413 ) )
<=> ( ( X414 = X412 )
| ( in @ X414 @ X413 ) ) )
=> ( ! [X415: $i,X416: $i] :
( ( in @ X416 @ ( powerset @ X415 ) )
<=> ! [X417: $i] :
( ( in @ X417 @ X416 )
=> ( in @ X417 @ X415 ) ) )
=> ( ! [X418: $i,X419: $i] :
( ( in @ X419 @ ( setunion @ X418 ) )
<=> ? [X420: $i] :
( ( in @ X419 @ X420 )
& ( in @ X420 @ X418 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X421: $i] :
( ( in @ X421 @ omega )
=> ( in @ ( setadjoin @ X421 @ X421 ) @ omega ) )
=> ( ! [X422: $i] :
( ( ( in @ emptyset @ X422 )
& ! [X423: $i] :
( ( ( in @ X423 @ omega )
& ( in @ X423 @ X422 ) )
=> ( in @ ( setadjoin @ X423 @ X423 ) @ X422 ) ) )
=> ! [X424: $i] :
( ( in @ X424 @ omega )
=> ( in @ X424 @ X422 ) ) )
=> ( ! [X425: $i > $i > $o,X426: $i] :
( ! [X427: $i] :
( ( in @ X427 @ X426 )
=> ? [X428: $i] :
( ( X425 @ X427 @ X428 )
& ! [X429: $i] :
( ( X425 @ X427 @ X429 )
=> ( X428 = X429 ) ) ) )
=> ? [X430: $i] :
! [X431: $i] :
( ( in @ X431 @ X430 )
<=> ? [X432: $i] :
( ( in @ X432 @ X426 )
& ( X425 @ X432 @ X431 ) ) ) )
=> ( ! [X433: $i] :
( ? [X434: $i] : ( in @ X434 @ X433 )
=> ? [X435: $i] :
( ( in @ X435 @ X433 )
& ~ ? [X436: $i] :
( ( in @ X436 @ X435 )
& ( in @ X436 @ X433 ) ) ) )
=> ( epred1_0
=> ( ! [X456: $i > $o] :
( ? [X457: $i] :
( ( X456 @ X457 )
& ! [X458: $i] :
( ( X456 @ X458 )
=> ( X457 = X458 ) ) )
=> ( X456
@ ( descr
@ ^ [Z0: $i] : ( X456 @ Z0 ) ) ) )
=> ( ! [X459: $i,X460: $i > $o,X461: $i] :
( ( in @ X461 @ X459 )
=> ( ( X460 @ X461 )
=> ( in @ X461 @ ( dsetconstr @ X459 @ X460 ) ) ) )
=> ( ! [X462: $i,X463: $i > $o,X464: $i] :
( ( in @ X464 @ ( dsetconstr @ X462 @ X463 ) )
=> ( in @ X464 @ X462 ) )
=> ( ! [X465: $i,X466: $i > $o,X467: $i] :
( ( in @ X467 @ ( dsetconstr @ X465 @ X466 ) )
=> ( X466 @ X467 ) )
=> ( ! [X468: $i > $o] :
( ? [X469: $i] :
( ( X468 @ X469 )
& ! [X470: $i] :
( ( X468 @ X470 )
=> ( X469 = X470 ) ) )
=> ? [X471: $i] :
( ( X468 @ X471 )
& ! [X472: $i] :
( ( X468 @ X472 )
=> ( X471 = X472 ) ) ) )
=> ( ! [X473: $o,X474: $i] :
( ( in @ X474 @ ( prop2set @ X473 ) )
=> X473 )
=> ( ! [X475: $i] :
( ( in @ X475 @ emptyset )
=> ! [X476: $o] : X476 )
=> ( ! [X477: $i] :
( ( in @ X477 @ emptyset )
=> ~ $true )
=> ( ! [X478: $i] :
~ ( in @ X478 @ emptyset )
=> ( ! [X479: $i > $o] :
( ? [X480: $i] :
( ( X479 @ X480 )
& ! [X481: $i] :
( ( X479 @ X481 )
=> ( X480 = X481 ) ) )
=> ? [X482: $i] : ( X479 @ X482 ) )
=> ( ! [X483: $i,X484: $i] :
( ! [X485: $i] :
( ( in @ X485 @ X483 )
=> ( in @ X485 @ X484 ) )
=> ( ! [X486: $i] :
( ( in @ X486 @ X484 )
=> ( in @ X486 @ X483 ) )
=> ( X483 = X484 ) ) )
=> ( ! [X487: $i] :
( ! [X488: $i] :
~ ( in @ X488 @ X487 )
=> ( X487 = emptyset ) )
=> ( ! [X489: $i] :
( ! [X490: $i] :
~ ( in @ X490 @ X489 )
=> ( X489 = emptyset ) )
=> ( ! [X491: $i,X492: $i > $o,X493: $i] :
( ( in @ X493 @ X491 )
=> ( ( in @ X493 @ ( dsetconstr @ X491 @ X492 ) )
<=> ( X492 @ X493 ) ) )
=> ( ! [X494: $i] :
( ( X494 != emptyset )
=> ? [X495: $i] : ( in @ X495 @ X494 ) )
=> ( ! [X496: $i,X497: $i > $o,X498: $i] :
( ( in @ X498 @ X496 )
=> ( ( X497 @ X498 )
=> ( ( dsetconstr @ X496 @ X497 )
!= emptyset ) ) )
=> ( ! [X499: $i] :
( ? [X500: $i] : ( in @ X500 @ X499 )
=> ( X499 != emptyset ) )
=> ( ! [X501: $i,X502: $i] : ( in @ X501 @ ( setadjoin @ X501 @ X502 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X503: $i,X504: $i,X505: $i] :
( ( in @ X505 @ X504 )
=> ( in @ X505 @ ( setadjoin @ X503 @ X504 ) ) )
=> ( ! [X506: $i,X507: $i,X508: $i] :
( ( in @ X508 @ ( setadjoin @ X506 @ X507 ) )
=> ! [X509: $o] :
( ( ( X508 = X506 )
=> X509 )
=> ( ( ( in @ X508 @ X507 )
=> X509 )
=> X509 ) ) )
=> ( ! [X510: $i,X511: $i,X512: $i] :
( ( in @ X512 @ ( setadjoin @ X510 @ X511 ) )
=> ( ( X512 = X510 )
| ( in @ X512 @ X511 ) ) )
=> ( ! [X513: $i] :
( ( dsetconstr @ X513
@ ^ [Z0: $i] : $true )
= X513 )
=> ( ! [X514: $i,X515: $i] :
( ! [X516: $i] :
( ( in @ X516 @ X515 )
=> ( in @ X516 @ X514 ) )
=> ( in @ X515 @ ( powerset @ X514 ) ) )
=> ( ! [X517: $i] : ( in @ emptyset @ ( powerset @ X517 ) )
=> ( ! [X518: $i] : ( in @ emptyset @ ( powerset @ X518 ) )
=> ( ! [X519: $i,X520: $i,X521: $i] :
( ( in @ X520 @ ( powerset @ X519 ) )
=> ( ( in @ X521 @ X520 )
=> ( in @ X521 @ X519 ) ) )
=> ( ! [X522: $i,X523: $i,X524: $i] :
( ( in @ X523 @ X524 )
=> ( ( in @ X524 @ X522 )
=> ( in @ X523 @ ( setunion @ X522 ) ) ) )
=> ( ! [X525: $i,X526: $i] :
( ( in @ X526 @ ( setunion @ X525 ) )
=> ! [X527: $o] :
( ! [X528: $i] :
( ( in @ X526 @ X528 )
=> ( ( in @ X528 @ X525 )
=> X527 ) )
=> X527 ) )
=> ( ! [X529: $i,X530: $i] :
( ( in @ X530 @ X529 )
=> ( in @ X530 @ ( powerset @ ( setunion @ X529 ) ) ) )
=> ( ! [X531: $i > $o] :
( ? [X532: $i] :
( ( X531 @ X532 )
& ! [X533: $i] :
( ( X531 @ X533 )
=> ( X532 = X533 ) ) )
=> ? [X534: $i] :
! [X535: $i] :
( ( X531 @ X535 )
<=> ( X535 = X534 ) ) )
=> ( ! [X536: $i] :
( ( X536 != emptyset )
=> ? [X537: $i] :
( ( in @ X537 @ X536 )
& $true ) )
=> ( ! [X538: $i,X539: $i] :
( ( in @ X538 @ ( setadjoin @ X539 @ emptyset ) )
=> ( X538 = X539 ) )
=> ( ! [X540: $i,X541: $i] :
( ( X540 != X541 )
=> ~ ( in @ X541 @ ( setadjoin @ X540 @ emptyset ) ) )
=> ( ! [X542: $i,X543: $i] :
( ( X542 = X543 )
=> ( in @ X542 @ ( setadjoin @ X543 @ emptyset ) ) )
=> ( ! [X544: $i,X545: $i] :
( ( in @ X544 @ ( setadjoin @ X545 @ emptyset ) )
=> ( in @ X545 @ ( setadjoin @ X544 @ emptyset ) ) )
=> ( ! [X546: $i,X547: $i,X548: $i] :
( ( in @ X548 @ ( setadjoin @ X546 @ ( setadjoin @ X547 @ emptyset ) ) )
=> ( ( X548 = X546 )
| ( X548 = X547 ) ) )
=> ( ! [X549: $i,X550: $i] : ( in @ X549 @ ( setadjoin @ X549 @ ( setadjoin @ X550 @ emptyset ) ) )
=> ( ! [X551: $i,X552: $i] : ( in @ X552 @ ( setadjoin @ X551 @ ( setadjoin @ X552 @ emptyset ) ) )
=> ( ! [X553: $i,X554: $i > $o] :
( ? [X555: $i] :
( ( in @ X555 @ X553 )
& ( X554 @ X555 ) )
=> ( ( ( dsetconstr @ X553 @ X554 )
= emptyset )
=> ~ $true ) )
=> ( ! [X556: $i > $o,X557: $i] :
( ( in @ X557 @ emptyset )
=> ( X556 @ X557 ) )
=> ( ! [X558: $i,X559: $i > $o] :
( ~ ! [X560: $i] :
( ( in @ X560 @ X558 )
=> ( X559 @ X560 ) )
=> ? [X561: $i] :
( ( in @ X561 @ X558 )
& ~ ( X559 @ X561 ) ) )
=> ( ! [X562: $i,X563: $i > $o] :
( ! [X564: $i] :
( ( in @ X564 @ X562 )
=> ~ ( X563 @ X564 ) )
=> ~ ? [X565: $i] :
( ( in @ X565 @ X562 )
& ( X563 @ X565 ) ) )
=> ( ! [X566: $i,X567: $i > $o] :
( ~ ? [X568: $i] :
( ( in @ X568 @ X566 )
& ( X567 @ X568 ) )
=> ! [X569: $i] :
( ( in @ X569 @ X566 )
=> ~ ( X567 @ X569 ) ) )
=> ( ! [X570: $i,X571: $i > $o] :
( ? [X572: $i] :
( ( in @ X572 @ X570 )
& ~ ( X571 @ X572 ) )
=> ~ ! [X573: $i] :
( ( in @ X573 @ X570 )
=> ( X571 @ X573 ) ) )
=> ( ! [X574: $o] :
( X574
=> ( in @ emptyset @ ( prop2set @ X574 ) ) )
=> ( prop2set2propI
=> ( ! [X575: $i,X576: $i > $o] :
( ~ ? [X577: $i] :
( ( in @ X577 @ X575 )
& ( X576 @ X577 ) )
=> ! [X578: $i] :
( ( in @ X578 @ X575 )
=> ~ ( X576 @ X578 ) ) )
=> ( ! [X579: $i,X580: $i > $o] :
( ~ ! [X581: $i] :
( ( in @ X581 @ X579 )
=> ( X580 @ X581 ) )
=> ? [X582: $i] :
( ( in @ X582 @ X579 )
& ~ ( X580 @ X582 ) ) )
=> ( ! [X583: $i > $o] :
( ? [X584: $i] :
( ( X583 @ X584 )
& ! [X585: $i] :
( ( X583 @ X585 )
=> ( X584 = X585 ) ) )
=> ? [X586: $i] :
( ( X583 @ X586 )
& ! [X587: $i] :
( ( X583 @ X587 )
=> ( X586 = X587 ) ) ) )
=> ( ! [X588: $i > $o] :
( ? [X589: $i] : ( X588 @ X589 )
=> ( ! [X590: $i,X591: $i] :
( ( X588 @ X590 )
=> ( ( X588 @ X591 )
=> ( X590 = X591 ) ) )
=> ? [X592: $i] :
( ( X588 @ X592 )
& ! [X593: $i] :
( ( X588 @ X593 )
=> ( X592 = X593 ) ) ) ) )
=> ( ! [X594: $i > $o] :
( ? [X595: $i] :
! [X596: $i] :
( ( X594 @ X596 )
<=> ( X596 = X595 ) )
=> ? [X597: $i] :
( ( X594 @ X597 )
& ! [X598: $i] :
( ( X594 @ X598 )
=> ( X597 = X598 ) ) ) )
=> ( ! [X599: $i,X600: $i] :
( ( X599 = X600 )
=> ! [X601: $i,X602: $i] :
( ( X601 = X602 )
=> ( ( in @ X601 @ X599 )
=> ( in @ X602 @ X600 ) ) ) )
=> ( ! [X603: $i,X604: $i] :
( ( X603 = X604 )
=> ! [X605: $i,X606: $i] :
( ( X605 = X606 )
=> ( ( in @ X605 @ X603 )
<=> ( in @ X606 @ X604 ) ) ) )
=> ( ! [X607: $i > $o] :
( ? [X608: $i] :
( ( X607 @ X608 )
& ! [X609: $i] :
( ( X607 @ X609 )
=> ( X608 = X609 ) ) )
=> ! [X610: $i,X611: $i] :
( ( X607 @ X610 )
=> ( ( X607 @ X611 )
=> ( X610 = X611 ) ) ) )
=> ( ! [X612: $i > $o,X613: $i > $o] :
( ! [X614: $i,X615: $i] :
( ( X614 = X615 )
=> ( ( X612 @ X614 )
<=> ( X613 @ X615 ) ) )
=> ( ? [X616: $i] :
( ( X612 @ X616 )
& ! [X617: $i] :
( ( X612 @ X617 )
=> ( X616 = X617 ) ) )
<=> ? [X618: $i] :
( ( X613 @ X618 )
& ! [X619: $i] :
( ( X613 @ X619 )
=> ( X618 = X619 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X620: $i,X621: $i] :
( ( X620 = X621 )
=> ! [X622: $i,X623: $i] :
( ( X622 = X623 )
=> ( ( setadjoin @ X620 @ X622 )
= ( setadjoin @ X621 @ X623 ) ) ) )
=> ( ! [X624: $i,X625: $i] :
( ( X624 = X625 )
=> ( ( powerset @ X624 )
= ( powerset @ X625 ) ) )
=> ( ! [X626: $i,X627: $i] :
( ( X626 = X627 )
=> ( ( setunion @ X626 )
= ( setunion @ X627 ) ) )
=> ( ( omega = omega )
=> ( ! [X628: $i > $o] :
( ? [X629: $i] :
( ( X628 @ X629 )
& ! [X630: $i] :
( ( X628 @ X630 )
=> ( X629 = X630 ) ) )
=> ! [X631: $i,X632: $i] :
( ( X628 @ X631 )
=> ( ( X628 @ X632 )
=> ( X631 = X632 ) ) ) )
=> ( ! [X633: $i > $o,X634: $i > $o] :
( ! [X635: $i,X636: $i] :
( ( X635 = X636 )
=> ( ( X633 @ X635 )
<=> ( X634 @ X636 ) ) )
=> ( ? [X637: $i] :
( ( X633 @ X637 )
& ! [X638: $i] :
( ( X633 @ X638 )
=> ( X637 = X638 ) ) )
=> ( ? [X639: $i] :
( ( X634 @ X639 )
& ! [X640: $i] :
( ( X634 @ X640 )
=> ( X639 = X640 ) ) )
=> ( ( descr @ X633 )
= ( descr @ X634 ) ) ) ) )
=> ( ! [X641: $i,X642: $i] :
( ( X641 = X642 )
=> ! [X643: $i > $o,X644: $i > $o] :
( ! [X645: $i] :
( ( in @ X645 @ X641 )
=> ! [X646: $i] :
( ( in @ X646 @ X642 )
=> ( ( X645 = X646 )
=> ( ( X643 @ X645 )
<=> ( X644 @ X646 ) ) ) ) )
=> ( ( dsetconstr @ X641 @ X643 )
= ( dsetconstr @ X642 @ X644 ) ) ) )
=> ( ! [X647: $i,X648: $i] :
( ! [X649: $i] :
( ( in @ X649 @ X647 )
=> ( in @ X649 @ X648 ) )
=> ( subset @ X647 @ X648 ) )
=> ( ! [X650: $i,X651: $i] :
( ( X650 = X651 )
=> ( subset @ X651 @ X650 ) )
=> ( ! [X652: $i,X653: $i] :
( ( X652 = X653 )
=> ( subset @ X652 @ X653 ) )
=> ( ! [X654: $i,X655: $i] :
( ! [X656: $i] :
( ( in @ X656 @ X654 )
=> ( in @ X656 @ X655 ) )
=> ( subset @ X654 @ X655 ) )
=> ( ! [X657: $i] : ( subset @ emptyset @ X657 )
=> ( ! [X658: $i,X659: $i,X660: $i] :
( ( subset @ X658 @ X659 )
=> ( ( in @ X660 @ X658 )
=> ( in @ X660 @ X659 ) ) )
=> ( ! [X661: $i,X662: $i,X663: $i] :
( ( subset @ X661 @ X662 )
=> ( ~ ( in @ X663 @ X662 )
=> ~ ( in @ X663 @ X661 ) ) )
=> ( ! [X664: $i,X665: $i,X666: $i] :
( ( in @ X666 @ X664 )
=> ( ~ ( in @ X666 @ X665 )
=> ~ ( subset @ X664 @ X665 ) ) )
=> ( ! [X667: $i,X668: $i] :
( ~ ( subset @ X667 @ X668 )
=> ( X667 != X668 ) )
=> ( ! [X669: $i,X670: $i,X671: $i] :
( ( in @ X671 @ X669 )
=> ( ~ ( in @ X671 @ X670 )
=> ( X669 != X670 ) ) )
=> ( ! [X672: $i] : ( subset @ X672 @ X672 )
=> ( ! [X673: $i,X674: $i,X675: $i] :
( ( subset @ X673 @ X674 )
=> ( ( subset @ X674 @ X675 )
=> ( subset @ X673 @ X675 ) ) )
=> ( ! [X676: $i,X677: $i] : ( subset @ X677 @ ( setadjoin @ X676 @ X677 ) )
=> ( ! [X678: $i,X679: $i,X680: $i] :
( ( subset @ X678 @ X680 )
=> ( subset @ X678 @ ( setadjoin @ X679 @ X680 ) ) )
=> ( ! [X681: $i,X682: $i] :
( ( subset @ X681 @ X682 )
=> ( in @ X681 @ ( powerset @ X682 ) ) )
=> ( ! [X683: $i,X684: $i] :
( ( subset @ X683 @ X684 )
=> ( ( subset @ X684 @ X683 )
=> ( X683 = X684 ) ) )
=> ( ! [X685: $i] :
( ( subset @ X685 @ emptyset )
=> ( X685 = emptyset ) )
=> ( ! [X686: $i,X687: $i] :
( ( subset @ X687 @ X686 )
=> ( in @ X687 @ ( powerset @ X686 ) ) )
=> ( ! [X688: $i,X689: $i] :
( ( in @ X689 @ ( powerset @ X688 ) )
=> ( subset @ X689 @ X688 ) )
=> ( ! [X690: $i] : ( in @ X690 @ ( powerset @ X690 ) )
=> ( ! [X691: $i,X692: $i] :
( ( subset @ X691 @ X692 )
=> ( subset @ ( powerset @ X691 ) @ ( powerset @ X692 ) ) )
=> ( ! [X693: $i,X694: $i > $o] : ( in @ ( dsetconstr @ X693 @ X694 ) @ ( powerset @ X693 ) )
=> ( ! [X695: $i,X696: $i > $o] : ( subset @ ( dsetconstr @ X695 @ X696 ) @ X695 )
=> ( ! [X697: $i,X698: $i,X699: $i] :
( ( in @ X699 @ X697 )
=> ( in @ X699 @ ( binunion @ X697 @ X698 ) ) )
=> ( ! [X700: $i,X701: $i] : ( in @ X701 @ ( setadjoin @ X700 @ ( setadjoin @ X701 @ emptyset ) ) )
=> ( ! [X702: $i,X703: $i,X704: $i] :
( ( in @ X704 @ X703 )
=> ( in @ X704 @ ( binunion @ X702 @ X703 ) ) )
=> ( ! [X705: $i,X706: $i,X707: $i,X708: $o] :
( ( in @ X707 @ ( binunion @ X705 @ X706 ) )
=> ( ( ( in @ X707 @ X705 )
=> X708 )
=> ( ( ( in @ X707 @ X706 )
=> X708 )
=> X708 ) ) )
=> ( ! [X709: $i,X710: $i,X711: $i] :
( ( in @ X711 @ ( binunion @ X709 @ X710 ) )
=> ( ( in @ X711 @ X709 )
| ( in @ X711 @ X710 ) ) )
=> ( ! [X712: $i,X713: $i] : ( subset @ X712 @ ( binunion @ X712 @ X713 ) )
=> ( ! [X714: $i,X715: $i] : ( subset @ X715 @ ( binunion @ X714 @ X715 ) )
=> ( ! [X716: $i,X717: $i,X718: $i] :
( ( in @ X718 @ X716 )
=> ( ( in @ X718 @ X717 )
=> ( in @ X718 @ ( binintersect @ X716 @ X717 ) ) ) )
=> ( ! [X719: $i,X720: $i,X721: $i] :
( ( subset @ X721 @ X719 )
=> ( ( subset @ X721 @ X720 )
=> ( subset @ X721 @ ( binintersect @ X719 @ X720 ) ) ) )
=> ( ! [X722: $i,X723: $i,X724: $i] :
( ( in @ X724 @ ( binintersect @ X722 @ X723 ) )
=> ( in @ X724 @ X722 ) )
=> ( ! [X725: $i,X726: $i] : ( subset @ ( binintersect @ X725 @ X726 ) @ X725 )
=> ( ! [X727: $i,X728: $i] :
( ( subset @ X727 @ X728 )
=> ( ( binintersect @ X727 @ X728 )
= X727 ) )
=> ( ! [X729: $i,X730: $i] :
( ( ( binintersect @ X729 @ X730 )
= X730 )
=> ( subset @ X730 @ X729 ) )
=> ( ! [X731: $i,X732: $i,X733: $i] :
( ( in @ X733 @ ( binintersect @ X731 @ X732 ) )
=> ( in @ X733 @ X732 ) )
=> ( ! [X734: $i,X735: $i] :
( ~ ? [X736: $i] :
( ( in @ X736 @ X734 )
& ( in @ X736 @ X735 ) )
=> ( ( binintersect @ X734 @ X735 )
= emptyset ) )
=> ( ! [X737: $i,X738: $i] : ( subset @ ( binintersect @ X737 @ X738 ) @ X738 )
=> ( ! [X739: $i,X740: $i] :
( ( subset @ X740 @ X739 )
=> ( ( binintersect @ X739 @ X740 )
= X740 ) )
=> ( ! [X741: $i,X742: $i] :
( ( ( binintersect @ X741 @ X742 )
= X741 )
=> ( subset @ X741 @ X742 ) )
=> ( ! [X743: $i,X744: $i,X745: $i] :
( ( binintersect @ X743 @ ( binunion @ X744 @ X745 ) )
= ( binunion @ ( binintersect @ X743 @ X744 ) @ ( binintersect @ X743 @ X745 ) ) )
=> ( ! [X746: $i,X747: $i,X748: $i] :
( ( in @ X748 @ X746 )
=> ( ~ ( in @ X748 @ X747 )
=> ( in @ X748 @ ( setminus @ X746 @ X747 ) ) ) )
=> ( ! [X749: $i,X750: $i,X751: $i] :
( ( in @ X751 @ ( setminus @ X749 @ X750 ) )
=> ( in @ X751 @ X749 ) )
=> ( ! [X752: $i,X753: $i,X754: $i] :
( ( in @ X754 @ ( setminus @ X752 @ X753 ) )
=> ~ ( in @ X754 @ X753 ) )
=> ( ! [X755: $i,X756: $i] :
( ( subset @ X755 @ X756 )
=> ( ( setminus @ X755 @ X756 )
= emptyset ) )
=> ( ! [X757: $i,X758: $i,X759: $i] :
( ~ ( in @ X759 @ ( setminus @ X757 @ X758 ) )
=> ( ( in @ X759 @ X757 )
=> ( in @ X759 @ X758 ) ) )
=> ( ! [X760: $i,X761: $i,X762: $i] :
( ~ ( in @ X762 @ ( setminus @ X760 @ X761 ) )
=> ( ~ ( in @ X762 @ X761 )
=> ~ ( in @ X762 @ X760 ) ) )
=> ( ! [X763: $i,X764: $i,X765: $i] :
( ~ ( in @ X765 @ X763 )
=> ~ ( in @ X765 @ ( setminus @ X763 @ X764 ) ) )
=> ( ! [X766: $i,X767: $i,X768: $i] :
( ( in @ X768 @ X767 )
=> ~ ( in @ X768 @ ( setminus @ X766 @ X767 ) ) )
=> ( ! [X769: $i,X770: $i] : ( subset @ ( setminus @ X769 @ X770 ) @ X769 )
=> ( ! [X771: $i,X772: $i] :
( ( ( setminus @ X771 @ X772 )
= emptyset )
=> ( subset @ X771 @ X772 ) )
=> ( ! [X773: $i,X774: $i,X775: $i] :
( ( in @ X775 @ ( symdiff @ X773 @ X774 ) )
=> ! [X776: $o] :
( ( ( in @ X775 @ X773 )
=> ( ~ ( in @ X775 @ X774 )
=> X776 ) )
=> ( ( ~ ( in @ X775 @ X773 )
=> ( ( in @ X775 @ X774 )
=> X776 ) )
=> X776 ) ) )
=> ( ! [X777: $i,X778: $i,X779: $i] :
( ( in @ X779 @ X777 )
=> ( ~ ( in @ X779 @ X778 )
=> ( in @ X779 @ ( symdiff @ X777 @ X778 ) ) ) )
=> ( ! [X780: $i,X781: $i,X782: $i] :
( ~ ( in @ X782 @ X780 )
=> ( ( in @ X782 @ X781 )
=> ( in @ X782 @ ( symdiff @ X780 @ X781 ) ) ) )
=> ( ! [X783: $i,X784: $i,X785: $i] :
( ( in @ X785 @ X783 )
=> ( ( in @ X785 @ X784 )
=> ~ ( in @ X785 @ ( symdiff @ X783 @ X784 ) ) ) )
=> ( ! [X786: $i,X787: $i,X788: $i] :
( ~ ( in @ X788 @ X786 )
=> ( ~ ( in @ X788 @ X787 )
=> ~ ( in @ X788 @ ( symdiff @ X786 @ X787 ) ) ) )
=> ( ! [X789: $i,X790: $i] : ( in @ X790 @ ( setadjoin @ X789 @ ( setadjoin @ X790 @ emptyset ) ) )
=> ( ! [X791: $i,X792: $i] : ( in @ X791 @ ( setunion @ ( setadjoin @ ( setadjoin @ X791 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X791 @ ( setadjoin @ X792 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setukpairIR]),quantDeMorgan4]),symdiffIneg2]),setukpairIL]),binintersectER]),singletonsswitch]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),upairsetE]),binintersectSubset1]),bs114d]),upairsetIL]),setminusI]),setminusEL]),upairsetIR]),setminusER]),setminusSubset2]),c_0_151]),setminusERneg]),setminusELneg]),vacuousDall]),setminusILneg]),setminusIRneg]),quantDeMorgan1]),setminusLsub]),setminusSubset1]),quantDeMorgan2]),symdiffE]),symdiffI1]),symdiffI2]),quantDeMorgan3]),symdiffIneg1]),c_0_152]),secondinupair]),prop2setI]),notdexE]),notdallE]),c_0_153]),c_0_154]),c_0_155]),inCongP]),in__Cong]),c_0_156]),c_0_157]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_158]),c_0_159]),binintersectSubset3]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_160]),c_0_161]),c_0_162]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),uniqinunit]),binunionRsub]),notinsingleton]),binintersectI]),binintersectSubset5]),eqinunit]),binintersectEL]),binintersectLsub]),binintersectSubset2]),c_0_163]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_164]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_165]),c_0_166]),c_0_167]),c_0_168]),noeltsimpempty]),emptyI]),setext]),c_0_169]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_170]),c_0_171]),c_0_172]),c_0_173]),c_0_174]),wellorderingAx]),foundationAx]),c_0_175]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_176]) ).
thf(c_0_178,negated_conjecture,
! [X793: $i,X794: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X806: $i,X807: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i,X815: $i,X816: $i > $i > $o,X817: $i,X819: $i,X822: $i,X824: $i,X825: $i,X826: $i,X827: $i,X829: $i,X830: $i > $o,X831: $i,X833: $i,X834: $i > $o,X835: $i,X836: $i,X837: $i > $o,X838: $i,X839: $i,X840: $i > $o,X841: $i,X842: $i > $o,X843: $i,X846: $i,X847: $o,X848: $i,X849: $i,X850: $o,X851: $i,X852: $i,X853: $i > $o,X854: $i,X857: $i,X858: $i,X861: $i,X863: $i,X865: $i,X866: $i > $o,X867: $i,X868: $i,X870: $i,X871: $i > $o,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i,X878: $i,X879: $i,X880: $i,X881: $i,X882: $i,X883: $o,X884: $i,X885: $i,X886: $i,X887: $i,X888: $i,X889: $i,X891: $i,X892: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $i,X898: $i,X899: $i,X900: $i,X901: $o,X903: $i,X904: $i,X905: $i > $o,X906: $i,X909: $i,X910: $i,X911: $i,X913: $i,X914: $i,X915: $i,X916: $i,X917: $i,X918: $i,X919: $i,X920: $i,X921: $i,X922: $i,X923: $i,X924: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i > $o,X930: $i,X931: $i > $o,X932: $i,X933: $i,X934: $i > $o,X935: $i,X937: $i,X938: $i > $o,X940: $i,X941: $i,X942: $i > $o,X944: $i,X945: $i,X946: $i > $o,X947: $i,X949: $o,X950: $i,X951: $i > $o,X953: $i,X954: $i,X955: $i > $o,X956: $i,X958: $i > $o,X959: $i,X962: $i,X963: $i > $o,X964: $i,X968: $i,X969: $i > $o,X970: $i,X973: $i,X974: $i,X975: $i,X976: $i,X977: $i,X978: $i,X979: $i,X980: $i,X981: $i,X982: $i > $o,X983: $i,X985: $i,X986: $i,X987: $i > $o,X988: $i > $o,X991: $i,X994: $i,X995: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i,X1004: $i,X1005: $i,X1006: $i,X1007: $i > $o,X1008: $i,X1010: $i,X1011: $i,X1012: $i > $o,X1013: $i > $o,X1016: $i,X1018: $i,X1020: $i,X1021: $i,X1022: $i > $o,X1023: $i > $o,X1026: $i,X1027: $i,X1029: $i,X1030: $i,X1031: $i,X1032: $i,X1033: $i,X1034: $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,X1051: $i,X1052: $i,X1053: $i,X1054: $i,X1055: $i,X1056: $i,X1057: $i,X1058: $i,X1059: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i > $o,X1074: $i,X1075: $i > $o,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i,X1081: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $o,X1088: $i,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i,X1105: $i,X1106: $i,X1107: $i,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i,X1116: $i,X1117: $i,X1118: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,X1133: $i,X1134: $i,X1135: $i,X1136: $i,X1137: $i,X1138: $i,X1139: $i,X1140: $i,X1141: $i,X1142: $i,X1143: $i,X1144: $i,X1145: $i,X1146: $i,X1147: $i,X1148: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $o,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] :
( ( ~ ( in @ ( esk1_2 @ X793 @ X794 ) @ X793 )
| ~ ( in @ ( esk1_2 @ X793 @ X794 ) @ X794 )
| ( X793 = X794 ) )
& ( ( in @ ( esk1_2 @ X793 @ X794 ) @ X793 )
| ( in @ ( esk1_2 @ X793 @ X794 ) @ X794 )
| ( X793 = X794 ) )
& ~ ( in @ X796 @ emptyset )
& ( ~ ( in @ X799 @ ( setadjoin @ X797 @ X798 ) )
| ( X799 = X797 )
| ( in @ X799 @ X798 ) )
& ( ( X799 != X797 )
| ( in @ X799 @ ( setadjoin @ X797 @ X798 ) ) )
& ( ~ ( in @ X799 @ X798 )
| ( in @ X799 @ ( setadjoin @ X797 @ X798 ) ) )
& ( ~ ( in @ X801 @ ( powerset @ X800 ) )
| ~ ( in @ X802 @ X801 )
| ( in @ X802 @ X800 ) )
& ( ( in @ ( esk2_2 @ X803 @ X804 ) @ X804 )
| ( in @ X804 @ ( powerset @ X803 ) ) )
& ( ~ ( in @ ( esk2_2 @ X803 @ X804 ) @ X803 )
| ( in @ X804 @ ( powerset @ X803 ) ) )
& ( ( in @ X807 @ ( esk3_2 @ X806 @ X807 ) )
| ~ ( in @ X807 @ ( setunion @ X806 ) ) )
& ( ( in @ ( esk3_2 @ X806 @ X807 ) @ X806 )
| ~ ( in @ X807 @ ( setunion @ X806 ) ) )
& ( ~ ( in @ X810 @ X811 )
| ~ ( in @ X811 @ X809 )
| ( in @ X810 @ ( setunion @ X809 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X812 @ omega )
| ( in @ ( setadjoin @ X812 @ X812 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X813 ) @ omega )
| ~ ( in @ emptyset @ X813 )
| ~ ( in @ X815 @ omega )
| ( in @ X815 @ X813 ) )
& ( ( in @ ( esk4_1 @ X813 ) @ X813 )
| ~ ( in @ emptyset @ X813 )
| ~ ( in @ X815 @ omega )
| ( in @ X815 @ X813 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X813 ) @ ( esk4_1 @ X813 ) ) @ X813 )
| ~ ( in @ emptyset @ X813 )
| ~ ( in @ X815 @ omega )
| ( in @ X815 @ X813 ) )
& ( ( in @ ( esk8_3 @ X816 @ X817 @ X822 ) @ X817 )
| ~ ( in @ X822 @ ( esk7_2 @ X816 @ X817 ) )
| ( in @ ( esk5_2 @ X816 @ X817 ) @ X817 ) )
& ( ( X816 @ ( esk8_3 @ X816 @ X817 @ X822 ) @ X822 )
| ~ ( in @ X822 @ ( esk7_2 @ X816 @ X817 ) )
| ( in @ ( esk5_2 @ X816 @ X817 ) @ X817 ) )
& ( ~ ( in @ X825 @ X817 )
| ~ ( X816 @ X825 @ X824 )
| ( in @ X824 @ ( esk7_2 @ X816 @ X817 ) )
| ( in @ ( esk5_2 @ X816 @ X817 ) @ X817 ) )
& ( ( in @ ( esk8_3 @ X816 @ X817 @ X822 ) @ X817 )
| ~ ( in @ X822 @ ( esk7_2 @ X816 @ X817 ) )
| ( X816 @ ( esk5_2 @ X816 @ X817 ) @ ( esk6_3 @ X816 @ X817 @ X819 ) )
| ~ ( X816 @ ( esk5_2 @ X816 @ X817 ) @ X819 ) )
& ( ( X816 @ ( esk8_3 @ X816 @ X817 @ X822 ) @ X822 )
| ~ ( in @ X822 @ ( esk7_2 @ X816 @ X817 ) )
| ( X816 @ ( esk5_2 @ X816 @ X817 ) @ ( esk6_3 @ X816 @ X817 @ X819 ) )
| ~ ( X816 @ ( esk5_2 @ X816 @ X817 ) @ X819 ) )
& ( ~ ( in @ X825 @ X817 )
| ~ ( X816 @ X825 @ X824 )
| ( in @ X824 @ ( esk7_2 @ X816 @ X817 ) )
| ( X816 @ ( esk5_2 @ X816 @ X817 ) @ ( esk6_3 @ X816 @ X817 @ X819 ) )
| ~ ( X816 @ ( esk5_2 @ X816 @ X817 ) @ X819 ) )
& ( ( in @ ( esk8_3 @ X816 @ X817 @ X822 ) @ X817 )
| ~ ( in @ X822 @ ( esk7_2 @ X816 @ X817 ) )
| ( X819
!= ( esk6_3 @ X816 @ X817 @ X819 ) )
| ~ ( X816 @ ( esk5_2 @ X816 @ X817 ) @ X819 ) )
& ( ( X816 @ ( esk8_3 @ X816 @ X817 @ X822 ) @ X822 )
| ~ ( in @ X822 @ ( esk7_2 @ X816 @ X817 ) )
| ( X819
!= ( esk6_3 @ X816 @ X817 @ X819 ) )
| ~ ( X816 @ ( esk5_2 @ X816 @ X817 ) @ X819 ) )
& ( ~ ( in @ X825 @ X817 )
| ~ ( X816 @ X825 @ X824 )
| ( in @ X824 @ ( esk7_2 @ X816 @ X817 ) )
| ( X819
!= ( esk6_3 @ X816 @ X817 @ X819 ) )
| ~ ( X816 @ ( esk5_2 @ X816 @ X817 ) @ X819 ) )
& ( ( in @ ( esk9_1 @ X826 ) @ X826 )
| ~ ( in @ X827 @ X826 ) )
& ( ~ ( in @ X829 @ ( esk9_1 @ X826 ) )
| ~ ( in @ X829 @ X826 )
| ~ ( in @ X827 @ X826 ) )
& epred1_0
& ( ( X830 @ ( esk10_2 @ X830 @ X831 ) )
| ~ ( X830 @ X831 )
| ( X830 @ ( descr @ X830 ) ) )
& ( ( X831
!= ( esk10_2 @ X830 @ X831 ) )
| ~ ( X830 @ X831 )
| ( X830 @ ( descr @ X830 ) ) )
& ( ~ ( in @ X835 @ X833 )
| ~ ( X834 @ X835 )
| ( in @ X835 @ ( dsetconstr @ X833 @ X834 ) ) )
& ( ~ ( in @ X838 @ ( dsetconstr @ X836 @ X837 ) )
| ( in @ X838 @ X836 ) )
& ( ~ ( in @ X841 @ ( dsetconstr @ X839 @ X840 ) )
| ( X840 @ X841 ) )
& ( ( X842 @ ( esk12_1 @ X842 ) )
| ( X842 @ ( esk11_2 @ X842 @ X843 ) )
| ~ ( X842 @ X843 ) )
& ( ~ ( X842 @ X846 )
| ( ( esk12_1 @ X842 )
= X846 )
| ( X842 @ ( esk11_2 @ X842 @ X843 ) )
| ~ ( X842 @ X843 ) )
& ( ( X842 @ ( esk12_1 @ X842 ) )
| ( X843
!= ( esk11_2 @ X842 @ X843 ) )
| ~ ( X842 @ X843 ) )
& ( ~ ( X842 @ X846 )
| ( ( esk12_1 @ X842 )
= X846 )
| ( X843
!= ( esk11_2 @ X842 @ X843 ) )
| ~ ( X842 @ X843 ) )
& ( ~ ( in @ X848 @ ( prop2set @ X847 ) )
| X847 )
& ( ~ ( in @ X849 @ emptyset )
| X850 )
& ( ~ ( in @ X851 @ emptyset )
| ~ $true )
& ~ ( in @ X852 @ emptyset )
& ( ( X853 @ ( esk13_2 @ X853 @ X854 ) )
| ~ ( X853 @ X854 )
| ( X853 @ ( esk14_1 @ X853 ) ) )
& ( ( X854
!= ( esk13_2 @ X853 @ X854 ) )
| ~ ( X853 @ X854 )
| ( X853 @ ( esk14_1 @ X853 ) ) )
& ( ( in @ ( esk16_2 @ X857 @ X858 ) @ X858 )
| ( X857 = X858 )
| ( in @ ( esk15_2 @ X857 @ X858 ) @ X857 ) )
& ( ~ ( in @ ( esk16_2 @ X857 @ X858 ) @ X857 )
| ( X857 = X858 )
| ( in @ ( esk15_2 @ X857 @ X858 ) @ X857 ) )
& ( ( in @ ( esk16_2 @ X857 @ X858 ) @ X858 )
| ( X857 = X858 )
| ~ ( in @ ( esk15_2 @ X857 @ X858 ) @ X858 ) )
& ( ~ ( in @ ( esk16_2 @ X857 @ X858 ) @ X857 )
| ( X857 = X858 )
| ~ ( in @ ( esk15_2 @ X857 @ X858 ) @ X858 ) )
& ( ( in @ ( esk17_1 @ X861 ) @ X861 )
| ( X861 = emptyset ) )
& ( ( in @ ( esk18_1 @ X863 ) @ X863 )
| ( X863 = emptyset ) )
& ( ~ ( in @ X867 @ ( dsetconstr @ X865 @ X866 ) )
| ( X866 @ X867 )
| ~ ( in @ X867 @ X865 ) )
& ( ~ ( X866 @ X867 )
| ( in @ X867 @ ( dsetconstr @ X865 @ X866 ) )
| ~ ( in @ X867 @ X865 ) )
& ( ( X868 = emptyset )
| ( in @ ( esk19_1 @ X868 ) @ X868 ) )
& ( ~ ( in @ X872 @ X870 )
| ~ ( X871 @ X872 )
| ( ( dsetconstr @ X870 @ X871 )
!= emptyset ) )
& ( ~ ( in @ X874 @ X873 )
| ( X873 != emptyset ) )
& ( in @ X875 @ ( setadjoin @ X875 @ X876 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X879 @ X878 )
| ( in @ X879 @ ( setadjoin @ X877 @ X878 ) ) )
& ( ( in @ X882 @ X881 )
| X883
| ( X882 = X880 )
| ~ ( in @ X882 @ ( setadjoin @ X880 @ X881 ) ) )
& ( ~ X883
| X883
| ( X882 = X880 )
| ~ ( in @ X882 @ ( setadjoin @ X880 @ X881 ) ) )
& ( ( in @ X882 @ X881 )
| X883
| ~ X883
| ~ ( in @ X882 @ ( setadjoin @ X880 @ X881 ) ) )
& ( ~ X883
| X883
| ~ X883
| ~ ( in @ X882 @ ( setadjoin @ X880 @ X881 ) ) )
& ( ~ ( in @ X886 @ ( setadjoin @ X884 @ X885 ) )
| ( X886 = X884 )
| ( in @ X886 @ X885 ) )
& ( ( dsetconstr @ X887
@ ^ [Z0: $i] : $true )
= X887 )
& ( ( in @ ( esk20_2 @ X888 @ X889 ) @ X889 )
| ( in @ X889 @ ( powerset @ X888 ) ) )
& ( ~ ( in @ ( esk20_2 @ X888 @ X889 ) @ X888 )
| ( in @ X889 @ ( powerset @ X888 ) ) )
& ( in @ emptyset @ ( powerset @ X891 ) )
& ( in @ emptyset @ ( powerset @ X892 ) )
& ( ~ ( in @ X894 @ ( powerset @ X893 ) )
| ~ ( in @ X895 @ X894 )
| ( in @ X895 @ X893 ) )
& ( ~ ( in @ X897 @ X898 )
| ~ ( in @ X898 @ X896 )
| ( in @ X897 @ ( setunion @ X896 ) ) )
& ( ( in @ X900 @ ( esk21_3 @ X899 @ X900 @ X901 ) )
| X901
| ~ ( in @ X900 @ ( setunion @ X899 ) ) )
& ( ( in @ ( esk21_3 @ X899 @ X900 @ X901 ) @ X899 )
| X901
| ~ ( in @ X900 @ ( setunion @ X899 ) ) )
& ( ~ X901
| X901
| ~ ( in @ X900 @ ( setunion @ X899 ) ) )
& ( ~ ( in @ X904 @ X903 )
| ( in @ X904 @ ( powerset @ ( setunion @ X903 ) ) ) )
& ( ~ ( X905 @ X909 )
| ( X909
= ( esk23_1 @ X905 ) )
| ( X905 @ ( esk22_2 @ X905 @ X906 ) )
| ~ ( X905 @ X906 ) )
& ( ( X910
!= ( esk23_1 @ X905 ) )
| ( X905 @ X910 )
| ( X905 @ ( esk22_2 @ X905 @ X906 ) )
| ~ ( X905 @ X906 ) )
& ( ~ ( X905 @ X909 )
| ( X909
= ( esk23_1 @ X905 ) )
| ( X906
!= ( esk22_2 @ X905 @ X906 ) )
| ~ ( X905 @ X906 ) )
& ( ( X910
!= ( esk23_1 @ X905 ) )
| ( X905 @ X910 )
| ( X906
!= ( esk22_2 @ X905 @ X906 ) )
| ~ ( X905 @ X906 ) )
& ( ( in @ ( esk24_1 @ X911 ) @ X911 )
| ( X911 = emptyset ) )
& ( $true
| ( X911 = emptyset ) )
& ( ~ ( in @ X913 @ ( setadjoin @ X914 @ emptyset ) )
| ( X913 = X914 ) )
& ( ( X915 = X916 )
| ~ ( in @ X916 @ ( setadjoin @ X915 @ emptyset ) ) )
& ( ( X917 != X918 )
| ( in @ X917 @ ( setadjoin @ X918 @ emptyset ) ) )
& ( ~ ( in @ X919 @ ( setadjoin @ X920 @ emptyset ) )
| ( in @ X920 @ ( setadjoin @ X919 @ emptyset ) ) )
& ( ~ ( in @ X923 @ ( setadjoin @ X921 @ ( setadjoin @ X922 @ emptyset ) ) )
| ( X923 = X921 )
| ( X923 = X922 ) )
& ( in @ X924 @ ( setadjoin @ X924 @ ( setadjoin @ X925 @ emptyset ) ) )
& ( in @ X927 @ ( setadjoin @ X926 @ ( setadjoin @ X927 @ emptyset ) ) )
& ( ~ ( in @ X930 @ X928 )
| ~ ( X929 @ X930 )
| ( ( dsetconstr @ X928 @ X929 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X932 @ emptyset )
| ( X931 @ X932 ) )
& ( ( in @ ( esk25_2 @ X933 @ X934 ) @ X933 )
| ~ ( in @ X935 @ X933 )
| ( X934 @ X935 ) )
& ( ~ ( X934 @ ( esk25_2 @ X933 @ X934 ) )
| ~ ( in @ X935 @ X933 )
| ( X934 @ X935 ) )
& ( ( in @ ( esk26_2 @ X937 @ X938 ) @ X937 )
| ~ ( in @ X940 @ X937 )
| ~ ( X938 @ X940 ) )
& ( ( X938 @ ( esk26_2 @ X937 @ X938 ) )
| ~ ( in @ X940 @ X937 )
| ~ ( X938 @ X940 ) )
& ( ( in @ ( esk27_2 @ X941 @ X942 ) @ X941 )
| ~ ( in @ X944 @ X941 )
| ~ ( X942 @ X944 ) )
& ( ( X942 @ ( esk27_2 @ X941 @ X942 ) )
| ~ ( in @ X944 @ X941 )
| ~ ( X942 @ X944 ) )
& ( ( in @ ( esk28_2 @ X945 @ X946 ) @ X945 )
| ~ ( in @ X947 @ X945 )
| ( X946 @ X947 ) )
& ( ~ ( X946 @ ( esk28_2 @ X945 @ X946 ) )
| ~ ( in @ X947 @ X945 )
| ( X946 @ X947 ) )
& ( ~ X949
| ( in @ emptyset @ ( prop2set @ X949 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X950 @ X951 ) @ X950 )
| ~ ( in @ X953 @ X950 )
| ~ ( X951 @ X953 ) )
& ( ( X951 @ ( esk29_2 @ X950 @ X951 ) )
| ~ ( in @ X953 @ X950 )
| ~ ( X951 @ X953 ) )
& ( ( in @ ( esk30_2 @ X954 @ X955 ) @ X954 )
| ~ ( in @ X956 @ X954 )
| ( X955 @ X956 ) )
& ( ~ ( X955 @ ( esk30_2 @ X954 @ X955 ) )
| ~ ( in @ X956 @ X954 )
| ( X955 @ X956 ) )
& ( ( X958 @ ( esk32_1 @ X958 ) )
| ( X958 @ ( esk31_2 @ X958 @ X959 ) )
| ~ ( X958 @ X959 ) )
& ( ~ ( X958 @ X962 )
| ( ( esk32_1 @ X958 )
= X962 )
| ( X958 @ ( esk31_2 @ X958 @ X959 ) )
| ~ ( X958 @ X959 ) )
& ( ( X958 @ ( esk32_1 @ X958 ) )
| ( X959
!= ( esk31_2 @ X958 @ X959 ) )
| ~ ( X958 @ X959 ) )
& ( ~ ( X958 @ X962 )
| ( ( esk32_1 @ X958 )
= X962 )
| ( X959
!= ( esk31_2 @ X958 @ X959 ) )
| ~ ( X958 @ X959 ) )
& ( ( X963 @ ( esk35_1 @ X963 ) )
| ( X963 @ ( esk33_1 @ X963 ) )
| ~ ( X963 @ X964 ) )
& ( ~ ( X963 @ X968 )
| ( ( esk35_1 @ X963 )
= X968 )
| ( X963 @ ( esk33_1 @ X963 ) )
| ~ ( X963 @ X964 ) )
& ( ( X963 @ ( esk35_1 @ X963 ) )
| ( X963 @ ( esk34_1 @ X963 ) )
| ~ ( X963 @ X964 ) )
& ( ~ ( X963 @ X968 )
| ( ( esk35_1 @ X963 )
= X968 )
| ( X963 @ ( esk34_1 @ X963 ) )
| ~ ( X963 @ X964 ) )
& ( ( X963 @ ( esk35_1 @ X963 ) )
| ( ( esk33_1 @ X963 )
!= ( esk34_1 @ X963 ) )
| ~ ( X963 @ X964 ) )
& ( ~ ( X963 @ X968 )
| ( ( esk35_1 @ X963 )
= X968 )
| ( ( esk33_1 @ X963 )
!= ( esk34_1 @ X963 ) )
| ~ ( X963 @ X964 ) )
& ( ( X969 @ ( esk37_1 @ X969 ) )
| ~ ( X969 @ ( esk36_2 @ X969 @ X970 ) )
| ( ( esk36_2 @ X969 @ X970 )
!= X970 ) )
& ( ~ ( X969 @ X973 )
| ( ( esk37_1 @ X969 )
= X973 )
| ~ ( X969 @ ( esk36_2 @ X969 @ X970 ) )
| ( ( esk36_2 @ X969 @ X970 )
!= X970 ) )
& ( ( X969 @ ( esk37_1 @ X969 ) )
| ( X969 @ ( esk36_2 @ X969 @ X970 ) )
| ( ( esk36_2 @ X969 @ X970 )
= X970 ) )
& ( ~ ( X969 @ X973 )
| ( ( esk37_1 @ X969 )
= X973 )
| ( X969 @ ( esk36_2 @ X969 @ X970 ) )
| ( ( esk36_2 @ X969 @ X970 )
= X970 ) )
& ( ( X974 != X975 )
| ( X976 != X977 )
| ~ ( in @ X976 @ X974 )
| ( in @ X977 @ X975 ) )
& ( ~ ( in @ X980 @ X978 )
| ( in @ X981 @ X979 )
| ( X980 != X981 )
| ( X978 != X979 ) )
& ( ~ ( in @ X981 @ X979 )
| ( in @ X980 @ X978 )
| ( X980 != X981 )
| ( X978 != X979 ) )
& ( ( X982 @ ( esk38_2 @ X982 @ X983 ) )
| ~ ( X982 @ X983 )
| ~ ( X982 @ X985 )
| ~ ( X982 @ X986 )
| ( X985 = X986 ) )
& ( ( X983
!= ( esk38_2 @ X982 @ X983 ) )
| ~ ( X982 @ X983 )
| ~ ( X982 @ X985 )
| ~ ( X982 @ X986 )
| ( X985 = X986 ) )
& ( ( X988 @ ( esk42_2 @ X987 @ X988 ) )
| ( X987 @ ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X988 @ X994 )
| ( ( esk42_2 @ X987 @ X988 )
= X994 )
| ( X987 @ ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X988 @ ( esk42_2 @ X987 @ X988 ) )
| ( X991
!= ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X988 @ X994 )
| ( ( esk42_2 @ X987 @ X988 )
= X994 )
| ( X991
!= ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X987 @ ( esk44_2 @ X987 @ X988 ) )
| ( X988 @ ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X987 @ X998 )
| ( ( esk44_2 @ X987 @ X988 )
= X998 )
| ( X988 @ ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X987 @ ( esk44_2 @ X987 @ X988 ) )
| ( X995
!= ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X987 @ X998 )
| ( ( esk44_2 @ X987 @ X988 )
= X998 )
| ( X995
!= ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( ( esk39_2 @ X987 @ X988 )
= ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X988 @ ( esk42_2 @ X987 @ X988 ) )
| ( X987 @ ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X988 @ X994 )
| ( ( esk42_2 @ X987 @ X988 )
= X994 )
| ( X987 @ ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X988 @ ( esk42_2 @ X987 @ X988 ) )
| ( X991
!= ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X988 @ X994 )
| ( ( esk42_2 @ X987 @ X988 )
= X994 )
| ( X991
!= ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X987 @ ( esk44_2 @ X987 @ X988 ) )
| ( X988 @ ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X987 @ X998 )
| ( ( esk44_2 @ X987 @ X988 )
= X998 )
| ( X988 @ ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X987 @ ( esk44_2 @ X987 @ X988 ) )
| ( X995
!= ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X987 @ X998 )
| ( ( esk44_2 @ X987 @ X988 )
= X998 )
| ( X995
!= ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ~ ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ~ ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X988 @ ( esk42_2 @ X987 @ X988 ) )
| ( X987 @ ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X988 @ X994 )
| ( ( esk42_2 @ X987 @ X988 )
= X994 )
| ( X987 @ ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X988 @ ( esk42_2 @ X987 @ X988 ) )
| ( X991
!= ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X988 @ X994 )
| ( ( esk42_2 @ X987 @ X988 )
= X994 )
| ( X991
!= ( esk41_3 @ X987 @ X988 @ X991 ) )
| ~ ( X987 @ X991 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X987 @ ( esk44_2 @ X987 @ X988 ) )
| ( X988 @ ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X987 @ X998 )
| ( ( esk44_2 @ X987 @ X988 )
= X998 )
| ( X988 @ ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ( X987 @ ( esk44_2 @ X987 @ X988 ) )
| ( X995
!= ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( ~ ( X987 @ X998 )
| ( ( esk44_2 @ X987 @ X988 )
= X998 )
| ( X995
!= ( esk43_3 @ X987 @ X988 @ X995 ) )
| ~ ( X988 @ X995 )
| ( X987 @ ( esk39_2 @ X987 @ X988 ) )
| ( X988 @ ( esk40_2 @ X987 @ X988 ) ) )
& ( emptyset = emptyset )
& ( ( X999 != X1000 )
| ( X1001 != X1002 )
| ( ( setadjoin @ X999 @ X1001 )
= ( setadjoin @ X1000 @ X1002 ) ) )
& ( ( X1003 != X1004 )
| ( ( powerset @ X1003 )
= ( powerset @ X1004 ) ) )
& ( ( X1005 != X1006 )
| ( ( setunion @ X1005 )
= ( setunion @ X1006 ) ) )
& ( omega = omega )
& ( ( X1007 @ ( esk45_2 @ X1007 @ X1008 ) )
| ~ ( X1007 @ X1008 )
| ~ ( X1007 @ X1010 )
| ~ ( X1007 @ X1011 )
| ( X1010 = X1011 ) )
& ( ( X1008
!= ( esk45_2 @ X1007 @ X1008 ) )
| ~ ( X1007 @ X1008 )
| ~ ( X1007 @ X1010 )
| ~ ( X1007 @ X1011 )
| ( X1010 = X1011 ) )
& ( ( X1013 @ ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1012 @ ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( ( esk46_2 @ X1012 @ X1013 )
= ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1018
!= ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1012 @ ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( ( esk46_2 @ X1012 @ X1013 )
= ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1013 @ ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1016
!= ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( ( esk46_2 @ X1012 @ X1013 )
= ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1018
!= ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1016
!= ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( ( esk46_2 @ X1012 @ X1013 )
= ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1013 @ ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1012 @ ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ~ ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ~ ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1018
!= ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1012 @ ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ~ ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ~ ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1013 @ ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1016
!= ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ~ ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ~ ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1018
!= ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1016
!= ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ~ ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ~ ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1013 @ ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1012 @ ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1018
!= ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1012 @ ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1013 @ ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1016
!= ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( X1018
!= ( esk49_3 @ X1012 @ X1013 @ X1018 ) )
| ~ ( X1013 @ X1018 )
| ( ( descr @ X1012 )
= ( descr @ X1013 ) )
| ( X1016
!= ( esk48_3 @ X1012 @ X1013 @ X1016 ) )
| ~ ( X1012 @ X1016 )
| ( X1012 @ ( esk46_2 @ X1012 @ X1013 ) )
| ( X1013 @ ( esk47_2 @ X1012 @ X1013 ) ) )
& ( ( in @ ( esk50_4 @ X1020 @ X1021 @ X1022 @ X1023 ) @ X1020 )
| ( ( dsetconstr @ X1020 @ X1022 )
= ( dsetconstr @ X1021 @ X1023 ) )
| ( X1020 != X1021 ) )
& ( ( in @ ( esk51_4 @ X1020 @ X1021 @ X1022 @ X1023 ) @ X1021 )
| ( ( dsetconstr @ X1020 @ X1022 )
= ( dsetconstr @ X1021 @ X1023 ) )
| ( X1020 != X1021 ) )
& ( ( ( esk50_4 @ X1020 @ X1021 @ X1022 @ X1023 )
= ( esk51_4 @ X1020 @ X1021 @ X1022 @ X1023 ) )
| ( ( dsetconstr @ X1020 @ X1022 )
= ( dsetconstr @ X1021 @ X1023 ) )
| ( X1020 != X1021 ) )
& ( ~ ( X1022 @ ( esk50_4 @ X1020 @ X1021 @ X1022 @ X1023 ) )
| ~ ( X1023 @ ( esk51_4 @ X1020 @ X1021 @ X1022 @ X1023 ) )
| ( ( dsetconstr @ X1020 @ X1022 )
= ( dsetconstr @ X1021 @ X1023 ) )
| ( X1020 != X1021 ) )
& ( ( X1022 @ ( esk50_4 @ X1020 @ X1021 @ X1022 @ X1023 ) )
| ( X1023 @ ( esk51_4 @ X1020 @ X1021 @ X1022 @ X1023 ) )
| ( ( dsetconstr @ X1020 @ X1022 )
= ( dsetconstr @ X1021 @ X1023 ) )
| ( X1020 != X1021 ) )
& ( ( in @ ( esk52_2 @ X1026 @ X1027 ) @ X1026 )
| ( subset @ X1026 @ X1027 ) )
& ( ~ ( in @ ( esk52_2 @ X1026 @ X1027 ) @ X1027 )
| ( subset @ X1026 @ X1027 ) )
& ( ( X1029 != X1030 )
| ( subset @ X1030 @ X1029 ) )
& ( ( X1031 != X1032 )
| ( subset @ X1031 @ X1032 ) )
& ( ( in @ ( esk53_2 @ X1033 @ X1034 ) @ X1033 )
| ( subset @ X1033 @ X1034 ) )
& ( ~ ( in @ ( esk53_2 @ X1033 @ X1034 ) @ X1034 )
| ( subset @ X1033 @ X1034 ) )
& ( subset @ emptyset @ X1036 )
& ( ~ ( subset @ X1037 @ X1038 )
| ~ ( in @ X1039 @ X1037 )
| ( in @ X1039 @ X1038 ) )
& ( ~ ( subset @ X1040 @ X1041 )
| ( in @ X1042 @ X1041 )
| ~ ( in @ X1042 @ X1040 ) )
& ( ~ ( in @ X1045 @ X1043 )
| ( in @ X1045 @ X1044 )
| ~ ( subset @ X1043 @ X1044 ) )
& ( ( subset @ X1046 @ X1047 )
| ( X1046 != X1047 ) )
& ( ~ ( in @ X1050 @ X1048 )
| ( in @ X1050 @ X1049 )
| ( X1048 != X1049 ) )
& ( subset @ X1051 @ X1051 )
& ( ~ ( subset @ X1052 @ X1053 )
| ~ ( subset @ X1053 @ X1054 )
| ( subset @ X1052 @ X1054 ) )
& ( subset @ X1056 @ ( setadjoin @ X1055 @ X1056 ) )
& ( ~ ( subset @ X1057 @ X1059 )
| ( subset @ X1057 @ ( setadjoin @ X1058 @ X1059 ) ) )
& ( ~ ( subset @ X1060 @ X1061 )
| ( in @ X1060 @ ( powerset @ X1061 ) ) )
& ( ~ ( subset @ X1062 @ X1063 )
| ~ ( subset @ X1063 @ X1062 )
| ( X1062 = X1063 ) )
& ( ~ ( subset @ X1064 @ emptyset )
| ( X1064 = emptyset ) )
& ( ~ ( subset @ X1066 @ X1065 )
| ( in @ X1066 @ ( powerset @ X1065 ) ) )
& ( ~ ( in @ X1068 @ ( powerset @ X1067 ) )
| ( subset @ X1068 @ X1067 ) )
& ( in @ X1069 @ ( powerset @ X1069 ) )
& ( ~ ( subset @ X1070 @ X1071 )
| ( subset @ ( powerset @ X1070 ) @ ( powerset @ X1071 ) ) )
& ( in @ ( dsetconstr @ X1072 @ X1073 ) @ ( powerset @ X1072 ) )
& ( subset @ ( dsetconstr @ X1074 @ X1075 ) @ X1074 )
& ( ~ ( in @ X1078 @ X1076 )
| ( in @ X1078 @ ( binunion @ X1076 @ X1077 ) ) )
& ( in @ X1080 @ ( setadjoin @ X1079 @ ( setadjoin @ X1080 @ emptyset ) ) )
& ( ~ ( in @ X1083 @ X1082 )
| ( in @ X1083 @ ( binunion @ X1081 @ X1082 ) ) )
& ( ( in @ X1086 @ X1085 )
| X1087
| ( in @ X1086 @ X1084 )
| ~ ( in @ X1086 @ ( binunion @ X1084 @ X1085 ) ) )
& ( ~ X1087
| X1087
| ( in @ X1086 @ X1084 )
| ~ ( in @ X1086 @ ( binunion @ X1084 @ X1085 ) ) )
& ( ( in @ X1086 @ X1085 )
| X1087
| ~ X1087
| ~ ( in @ X1086 @ ( binunion @ X1084 @ X1085 ) ) )
& ( ~ X1087
| X1087
| ~ X1087
| ~ ( in @ X1086 @ ( binunion @ X1084 @ X1085 ) ) )
& ( ~ ( in @ X1090 @ ( binunion @ X1088 @ X1089 ) )
| ( in @ X1090 @ X1088 )
| ( in @ X1090 @ X1089 ) )
& ( subset @ X1091 @ ( binunion @ X1091 @ X1092 ) )
& ( subset @ X1094 @ ( binunion @ X1093 @ X1094 ) )
& ( ~ ( in @ X1097 @ X1095 )
| ~ ( in @ X1097 @ X1096 )
| ( in @ X1097 @ ( binintersect @ X1095 @ X1096 ) ) )
& ( ~ ( subset @ X1100 @ X1098 )
| ~ ( subset @ X1100 @ X1099 )
| ( subset @ X1100 @ ( binintersect @ X1098 @ X1099 ) ) )
& ( ~ ( in @ X1103 @ ( binintersect @ X1101 @ X1102 ) )
| ( in @ X1103 @ X1101 ) )
& ( subset @ ( binintersect @ X1104 @ X1105 ) @ X1104 )
& ( ~ ( subset @ X1106 @ X1107 )
| ( ( binintersect @ X1106 @ X1107 )
= X1106 ) )
& ( ( ( binintersect @ X1108 @ X1109 )
!= X1109 )
| ( subset @ X1109 @ X1108 ) )
& ( ~ ( in @ X1112 @ ( binintersect @ X1110 @ X1111 ) )
| ( in @ X1112 @ X1111 ) )
& ( ( in @ ( esk54_2 @ X1113 @ X1114 ) @ X1113 )
| ( ( binintersect @ X1113 @ X1114 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1113 @ X1114 ) @ X1114 )
| ( ( binintersect @ X1113 @ X1114 )
= emptyset ) )
& ( subset @ ( binintersect @ X1116 @ X1117 ) @ X1117 )
& ( ~ ( subset @ X1119 @ X1118 )
| ( ( binintersect @ X1118 @ X1119 )
= X1119 ) )
& ( ( ( binintersect @ X1120 @ X1121 )
!= X1120 )
| ( subset @ X1120 @ X1121 ) )
& ( ( binintersect @ X1122 @ ( binunion @ X1123 @ X1124 ) )
= ( binunion @ ( binintersect @ X1122 @ X1123 ) @ ( binintersect @ X1122 @ X1124 ) ) )
& ( ~ ( in @ X1127 @ X1125 )
| ( in @ X1127 @ X1126 )
| ( in @ X1127 @ ( setminus @ X1125 @ X1126 ) ) )
& ( ~ ( in @ X1130 @ ( setminus @ X1128 @ X1129 ) )
| ( in @ X1130 @ X1128 ) )
& ( ~ ( in @ X1133 @ ( setminus @ X1131 @ X1132 ) )
| ~ ( in @ X1133 @ X1132 ) )
& ( ~ ( subset @ X1134 @ X1135 )
| ( ( setminus @ X1134 @ X1135 )
= emptyset ) )
& ( ( in @ X1138 @ ( setminus @ X1136 @ X1137 ) )
| ~ ( in @ X1138 @ X1136 )
| ( in @ X1138 @ X1137 ) )
& ( ( in @ X1141 @ ( setminus @ X1139 @ X1140 ) )
| ( in @ X1141 @ X1140 )
| ~ ( in @ X1141 @ X1139 ) )
& ( ( in @ X1144 @ X1142 )
| ~ ( in @ X1144 @ ( setminus @ X1142 @ X1143 ) ) )
& ( ~ ( in @ X1147 @ X1146 )
| ~ ( in @ X1147 @ ( setminus @ X1145 @ X1146 ) ) )
& ( subset @ ( setminus @ X1148 @ X1149 ) @ X1148 )
& ( ( ( setminus @ X1150 @ X1151 )
!= emptyset )
| ( subset @ X1150 @ X1151 ) )
& ( ~ ( in @ X1154 @ X1152 )
| X1155
| ( in @ X1154 @ X1152 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ( in @ X1154 @ X1153 )
| X1155
| ( in @ X1154 @ X1152 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ~ X1155
| X1155
| ( in @ X1154 @ X1152 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ~ ( in @ X1154 @ X1152 )
| X1155
| ~ ( in @ X1154 @ X1153 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ( in @ X1154 @ X1153 )
| X1155
| ~ ( in @ X1154 @ X1153 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ~ X1155
| X1155
| ~ ( in @ X1154 @ X1153 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ~ ( in @ X1154 @ X1152 )
| X1155
| ~ X1155
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ( in @ X1154 @ X1153 )
| X1155
| ~ X1155
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ~ X1155
| X1155
| ~ X1155
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ~ ( in @ X1158 @ X1156 )
| ( in @ X1158 @ X1157 )
| ( in @ X1158 @ ( symdiff @ X1156 @ X1157 ) ) )
& ( ( in @ X1161 @ X1159 )
| ~ ( in @ X1161 @ X1160 )
| ( in @ X1161 @ ( symdiff @ X1159 @ X1160 ) ) )
& ( ~ ( in @ X1164 @ X1162 )
| ~ ( in @ X1164 @ X1163 )
| ~ ( in @ X1164 @ ( symdiff @ X1162 @ X1163 ) ) )
& ( ( in @ X1167 @ X1165 )
| ( in @ X1167 @ X1166 )
| ~ ( in @ X1167 @ ( symdiff @ X1165 @ X1166 ) ) )
& ( in @ X1169 @ ( setadjoin @ X1168 @ ( setadjoin @ X1169 @ emptyset ) ) )
& ( in @ X1170 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1170 @ ( setadjoin @ X1171 @ emptyset ) ) @ emptyset ) ) ) )
& ~ ( in @ esk56_0 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk55_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk55_0 @ ( setadjoin @ esk56_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_177])])])])])])]) ).
thf(c_0_179,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
thf(c_0_180,negated_conjecture,
! [X3: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
thf(c_0_181,negated_conjecture,
~ ( in @ esk56_0 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk55_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk55_0 @ ( setadjoin @ esk56_0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
thf(c_0_182,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) ) )
| ~ ( in @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
thf(c_0_183,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_180])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU618^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n022.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun May 19 15:32:37 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.14/5.11 # Version: 3.1.0-ho
% 32.14/5.11 # Preprocessing class: HSLMSLSSLLLCHFA.
% 32.14/5.11 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 32.14/5.11 # Starting ehoh_best5 with 300s (1) cores
% 32.14/5.11 # Starting almost_fo_3_lam with 300s (1) cores
% 32.14/5.11 # Starting new_bool_5 with 300s (1) cores
% 32.14/5.11 # Starting pre_casc_3 with 300s (1) cores
% 32.14/5.11 # Starting ho_unfolding_8 with 300s (1) cores
% 32.14/5.11 # Starting new_ho_10_cnf2 with 300s (1) cores
% 32.14/5.11 # Starting new_bool_3 with 300s (1) cores
% 32.14/5.11 # Starting new_ho_5 with 300s (1) cores
% 32.14/5.11 # new_ho_5 with pid 24779 completed with status 8
% 32.14/5.11 # new_bool_3 with pid 24778 completed with status 0
% 32.14/5.11 # Result found by new_bool_3
% 32.14/5.11 # Preprocessing class: HSLMSLSSLLLCHFA.
% 32.14/5.11 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 32.14/5.11 # Starting ehoh_best5 with 300s (1) cores
% 32.14/5.11 # Starting almost_fo_3_lam with 300s (1) cores
% 32.14/5.11 # Starting new_bool_5 with 300s (1) cores
% 32.14/5.11 # Starting pre_casc_3 with 300s (1) cores
% 32.14/5.11 # Starting ho_unfolding_8 with 300s (1) cores
% 32.14/5.11 # Starting new_ho_10_cnf2 with 300s (1) cores
% 32.14/5.11 # Starting new_bool_3 with 300s (1) cores
% 32.14/5.11 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 32.14/5.11 # Search class: HGHSM-FSLS31-MHFMMSBN
% 32.14/5.11 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 32.14/5.11 # Starting pre_casc_7 with 181s (1) cores
% 32.14/5.11 # pre_casc_7 with pid 24789 completed with status 0
% 32.14/5.11 # Result found by pre_casc_7
% 32.14/5.11 # Preprocessing class: HSLMSLSSLLLCHFA.
% 32.14/5.11 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 32.14/5.11 # Starting ehoh_best5 with 300s (1) cores
% 32.14/5.11 # Starting almost_fo_3_lam with 300s (1) cores
% 32.14/5.11 # Starting new_bool_5 with 300s (1) cores
% 32.14/5.11 # Starting pre_casc_3 with 300s (1) cores
% 32.14/5.11 # Starting ho_unfolding_8 with 300s (1) cores
% 32.14/5.11 # Starting new_ho_10_cnf2 with 300s (1) cores
% 32.14/5.11 # Starting new_bool_3 with 300s (1) cores
% 32.14/5.11 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 32.14/5.11 # Search class: HGHSM-FSLS31-MHFMMSBN
% 32.14/5.11 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 32.14/5.11 # Starting pre_casc_7 with 181s (1) cores
% 32.14/5.11 # Preprocessing time : 0.005 s
% 32.14/5.11
% 32.14/5.11 # Proof found!
% 32.14/5.11 # SZS status Theorem
% 32.14/5.11 # SZS output start CNFRefutation
% See solution above
% 32.14/5.11 # Parsed axioms : 293
% 32.14/5.11 # Removed by relevancy pruning/SinE : 157
% 32.14/5.11 # Initial clauses : 257
% 32.14/5.11 # Removed in clause preprocessing : 24
% 32.14/5.11 # Initial clauses in saturation : 233
% 32.14/5.11 # Processed clauses : 10622
% 32.14/5.11 # ...of these trivial : 319
% 32.14/5.11 # ...subsumed : 7520
% 32.14/5.11 # ...remaining for further processing : 2783
% 32.14/5.11 # Other redundant clauses eliminated : 203
% 32.14/5.11 # Clauses deleted for lack of memory : 0
% 32.14/5.11 # Backward-subsumed : 121
% 32.14/5.11 # Backward-rewritten : 113
% 32.14/5.11 # Generated clauses : 276756
% 32.14/5.11 # ...of the previous two non-redundant : 214735
% 32.14/5.11 # ...aggressively subsumed : 0
% 32.14/5.11 # Contextual simplify-reflections : 4
% 32.14/5.11 # Paramodulations : 276500
% 32.14/5.11 # Factorizations : 12
% 32.14/5.11 # NegExts : 0
% 32.14/5.11 # Equation resolutions : 203
% 32.14/5.11 # Disequality decompositions : 0
% 32.14/5.11 # Total rewrite steps : 108684
% 32.14/5.11 # ...of those cached : 102276
% 32.14/5.11 # Propositional unsat checks : 0
% 32.14/5.11 # Propositional check models : 0
% 32.14/5.11 # Propositional check unsatisfiable : 0
% 32.14/5.11 # Propositional clauses : 0
% 32.14/5.11 # Propositional clauses after purity: 0
% 32.14/5.11 # Propositional unsat core size : 0
% 32.14/5.11 # Propositional preprocessing time : 0.000
% 32.14/5.11 # Propositional encoding time : 0.000
% 32.14/5.11 # Propositional solver time : 0.000
% 32.14/5.11 # Success case prop preproc time : 0.000
% 32.14/5.11 # Success case prop encoding time : 0.000
% 32.14/5.11 # Success case prop solver time : 0.000
% 32.14/5.11 # Current number of processed clauses : 2496
% 32.14/5.11 # Positive orientable unit clauses : 435
% 32.14/5.11 # Positive unorientable unit clauses: 0
% 32.14/5.11 # Negative unit clauses : 304
% 32.14/5.11 # Non-unit-clauses : 1757
% 32.14/5.11 # Current number of unprocessed clauses: 203346
% 32.14/5.11 # ...number of literals in the above : 669389
% 32.14/5.11 # Current number of archived formulas : 0
% 32.14/5.11 # Current number of archived clauses : 274
% 32.14/5.11 # Clause-clause subsumption calls (NU) : 272099
% 32.14/5.11 # Rec. Clause-clause subsumption calls : 189344
% 32.14/5.11 # Non-unit clause-clause subsumptions : 5675
% 32.14/5.11 # Unit Clause-clause subsumption calls : 26314
% 32.14/5.11 # Rewrite failures with RHS unbound : 0
% 32.14/5.11 # BW rewrite match attempts : 2434
% 32.14/5.11 # BW rewrite match successes : 88
% 32.14/5.11 # Condensation attempts : 10622
% 32.14/5.11 # Condensation successes : 163
% 32.14/5.11 # Termbank termtop insertions : 4567593
% 32.14/5.11 # Search garbage collected termcells : 13143
% 32.14/5.11
% 32.14/5.11 # -------------------------------------------------
% 32.14/5.11 # User time : 4.399 s
% 32.14/5.11 # System time : 0.112 s
% 32.14/5.11 # Total time : 4.511 s
% 32.14/5.11 # Maximum resident set size: 5076 pages
% 32.14/5.11
% 32.14/5.11 # -------------------------------------------------
% 32.14/5.11 # User time : 4.501 s
% 32.14/5.11 # System time : 0.145 s
% 32.14/5.11 # Total time : 4.646 s
% 32.14/5.11 # Maximum resident set size: 2076 pages
% 32.14/5.11 % E---3.1 exiting
% 32.14/5.11 % E exiting
%------------------------------------------------------------------------------