%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU617^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.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 0.19s 0.57s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 342
% Syntax : Number of formulae : 389 ( 23 unt; 206 typ; 0 def)
% Number of atoms : 1516 ( 357 equ; 0 cnn)
% Maximal formula atoms : 459 ( 8 avg)
% Number of connectives : 5795 ( 506 ~; 535 |; 334 &;3480 @)
% ( 197 <=>; 743 =>; 0 <=; 0 <~>)
% Maximal formula depth : 575 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 323 ( 323 >; 0 *; 0 +; 0 <<)
% Number of symbols : 209 ( 206 usr; 140 con; 0-4 aty)
% Number of variables : 1288 ( 67 ^1115 !; 106 ?;1288 :)
% 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,
epred1_0: $o ).
thf(decl_177,type,
esk1_2: $i > $i > $i ).
thf(decl_178,type,
esk2_2: $i > $i > $i ).
thf(decl_179,type,
esk3_2: $i > $i > $i ).
thf(decl_180,type,
esk4_1: $i > $i ).
thf(decl_181,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_182,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_183,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_184,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_185,type,
esk9_1: $i > $i ).
thf(decl_186,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_187,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_188,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_189,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_190,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_191,type,
esk15_2: $i > $i > $i ).
thf(decl_192,type,
esk16_2: $i > $i > $i ).
thf(decl_193,type,
esk17_1: $i > $i ).
thf(decl_194,type,
esk18_1: $i > $i ).
thf(decl_195,type,
esk19_1: $i > $i ).
thf(decl_196,type,
esk20_2: $i > $i > $i ).
thf(decl_197,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_198,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_199,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_200,type,
esk24_1: $i > $i ).
thf(decl_201,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_202,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_203,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_204,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_205,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_206,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_207,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_208,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_209,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_210,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_211,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_212,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_213,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_214,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_215,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_216,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_217,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_218,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_219,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_220,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_221,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_222,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_223,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_224,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_225,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_226,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_227,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_228,type,
esk52_2: $i > $i > $i ).
thf(decl_229,type,
esk53_2: $i > $i > $i ).
thf(decl_230,type,
esk54_2: $i > $i > $i ).
thf(decl_231,type,
esk55_0: $i ).
thf(decl_232,type,
esk56_0: $i ).
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(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(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(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(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(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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
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(setukpairIL,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
=> ! [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(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(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
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(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(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(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(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(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(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(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(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
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(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
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(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
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(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(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_135,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_136,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_137,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_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,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_144,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_145,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_146,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_147,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_148,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_149,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_150,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_151,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X402: $i] :
( ( X1 @ X402 )
& ! [X403: $i] :
( ( X1 @ X403 )
=> ( X402 = X403 ) ) )
=> ( ? [X404: $i] :
( ( X17 @ X404 )
& ! [X405: $i] :
( ( X17 @ X405 )
=> ( X404 = X405 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_135,c_0_136]) ).
thf(c_0_152,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X388: $i] :
( ( X1 @ X388 )
& ! [X389: $i] :
( ( X1 @ X389 )
=> ( X388 = X389 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_137,c_0_136]) ).
thf(c_0_153,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X390: $i] :
( ( X1 @ X390 )
& ! [X391: $i] :
( ( X1 @ X391 )
=> ( X390 = X391 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_138,c_0_136]) ).
thf(c_0_154,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X392: $i] :
( ( X1 @ X392 )
& ! [X393: $i] :
( ( X1 @ X393 )
=> ( X392 = X393 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_139,c_0_136]) ).
thf(c_0_155,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X394: $i] :
( ( X1 @ X394 )
& ! [X395: $i] :
( ( X1 @ X395 )
=> ( X394 = X395 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_140,c_0_136]) ).
thf(c_0_156,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X396: $i] :
( ( X1 @ X396 )
& ! [X397: $i] :
( ( X1 @ X397 )
=> ( X396 = X397 ) ) )
<=> ? [X398: $i] :
( ( X17 @ X398 )
& ! [X399: $i] :
( ( X17 @ X399 )
=> ( X398 = X399 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_141,c_0_136]) ).
thf(c_0_157,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X400: $i] :
( ( X1 @ X400 )
& ! [X401: $i] :
( ( X1 @ X401 )
=> ( X400 = X401 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_142,c_0_136]) ).
thf(c_0_158,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_159,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_160,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_161,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_143]) ).
thf(c_0_162,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X386: $i] :
( ( X1 @ X386 )
& ! [X387: $i] :
( ( X1 @ X387 )
=> ( X386 = X387 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_144,c_0_136]) ).
thf(c_0_163,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_164,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_143]) ).
thf(c_0_165,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_145,c_0_143]) ).
thf(c_0_166,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_143]) ).
thf(c_0_167,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_168,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X384: $i] :
( ( X1 @ X384 )
& ! [X385: $i] :
( ( X1 @ X385 )
=> ( X384 = X385 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_146,c_0_136]) ).
thf(c_0_169,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X382: $i] :
( ( X1 @ X382 )
& ! [X383: $i] :
( ( X1 @ X383 )
=> ( X382 = X383 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_147,c_0_136]) ).
thf(c_0_170,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_171,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_172,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_173,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X380: $i] :
( ( X1 @ X380 )
& ! [X381: $i] :
( ( X1 @ X381 )
=> ( X380 = X381 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_148,c_0_136]) ).
thf(c_0_174,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X378: $i] :
( ( X6 @ X2 @ X378 )
& ! [X379: $i] :
( ( X6 @ X2 @ X379 )
=> ( X378 = X379 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_149,c_0_136]) ).
thf(c_0_175,plain,
( epred1_0
<=> ! [X435: $i] :
? [X436: $i] :
( ! [X437: $i] :
( ( in @ X437 @ X436 )
=> ! [X438: $i] :
( ( in @ X438 @ X437 )
=> ( in @ X438 @ X435 ) ) )
& ! [X439: $i,X440: $i] :
( ( ( in @ X439 @ X435 )
& ( in @ X440 @ X435 ) )
=> ( ! [X441: $i] :
( ( in @ X441 @ X436 )
=> ( ( in @ X439 @ X441 )
<=> ( in @ X440 @ X441 ) ) )
=> ( X439 = X440 ) ) )
& ! [X442: $i,X443: $i] :
( ( ( in @ X442 @ X436 )
& ( in @ X443 @ X436 ) )
=> ( ! [X444: $i] :
( ( in @ X444 @ X442 )
=> ( in @ X444 @ X443 ) )
| ! [X445: $i] :
( ( in @ X445 @ X443 )
=> ( in @ X445 @ X442 ) ) ) )
& ! [X446: $i] :
( ( ! [X447: $i] :
( ( in @ X447 @ X446 )
=> ( in @ X447 @ X435 ) )
& ? [X448: $i] : ( in @ X448 @ X446 ) )
=> ? [X449: $i,X450: $i] :
( ( in @ X449 @ X436 )
& ( in @ X450 @ X446 )
& ~ ? [X451: $i] :
( ( in @ X451 @ X449 )
& ( in @ X451 @ X446 ) )
& ! [X452: $i] :
( ( in @ X452 @ X436 )
=> ( ! [X453: $i] :
( ( in @ X453 @ X452 )
=> ( in @ X453 @ X449 ) )
| ( in @ X450 @ X452 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_176,negated_conjecture,
~ ( ! [X406: $i,X407: $i] :
( ! [X408: $i] :
( ( in @ X408 @ X406 )
<=> ( in @ X408 @ X407 ) )
=> ( X406 = X407 ) )
=> ( ! [X409: $i] :
~ ( in @ X409 @ emptyset )
=> ( ! [X410: $i,X411: $i,X412: $i] :
( ( in @ X412 @ ( setadjoin @ X410 @ X411 ) )
<=> ( ( X412 = X410 )
| ( in @ X412 @ X411 ) ) )
=> ( ! [X413: $i,X414: $i] :
( ( in @ X414 @ ( powerset @ X413 ) )
<=> ! [X415: $i] :
( ( in @ X415 @ X414 )
=> ( in @ X415 @ X413 ) ) )
=> ( ! [X416: $i,X417: $i] :
( ( in @ X417 @ ( setunion @ X416 ) )
<=> ? [X418: $i] :
( ( in @ X417 @ X418 )
& ( in @ X418 @ X416 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X419: $i] :
( ( in @ X419 @ omega )
=> ( in @ ( setadjoin @ X419 @ X419 ) @ omega ) )
=> ( ! [X420: $i] :
( ( ( in @ emptyset @ X420 )
& ! [X421: $i] :
( ( ( in @ X421 @ omega )
& ( in @ X421 @ X420 ) )
=> ( in @ ( setadjoin @ X421 @ X421 ) @ X420 ) ) )
=> ! [X422: $i] :
( ( in @ X422 @ omega )
=> ( in @ X422 @ X420 ) ) )
=> ( ! [X423: $i > $i > $o,X424: $i] :
( ! [X425: $i] :
( ( in @ X425 @ X424 )
=> ? [X426: $i] :
( ( X423 @ X425 @ X426 )
& ! [X427: $i] :
( ( X423 @ X425 @ X427 )
=> ( X426 = X427 ) ) ) )
=> ? [X428: $i] :
! [X429: $i] :
( ( in @ X429 @ X428 )
<=> ? [X430: $i] :
( ( in @ X430 @ X424 )
& ( X423 @ X430 @ X429 ) ) ) )
=> ( ! [X431: $i] :
( ? [X432: $i] : ( in @ X432 @ X431 )
=> ? [X433: $i] :
( ( in @ X433 @ X431 )
& ~ ? [X434: $i] :
( ( in @ X434 @ X433 )
& ( in @ X434 @ X431 ) ) ) )
=> ( epred1_0
=> ( ! [X454: $i > $o] :
( ? [X455: $i] :
( ( X454 @ X455 )
& ! [X456: $i] :
( ( X454 @ X456 )
=> ( X455 = X456 ) ) )
=> ( X454
@ ( descr
@ ^ [Z0: $i] : ( X454 @ Z0 ) ) ) )
=> ( ! [X457: $i,X458: $i > $o,X459: $i] :
( ( in @ X459 @ X457 )
=> ( ( X458 @ X459 )
=> ( in @ X459 @ ( dsetconstr @ X457 @ X458 ) ) ) )
=> ( ! [X460: $i,X461: $i > $o,X462: $i] :
( ( in @ X462 @ ( dsetconstr @ X460 @ X461 ) )
=> ( in @ X462 @ X460 ) )
=> ( ! [X463: $i,X464: $i > $o,X465: $i] :
( ( in @ X465 @ ( dsetconstr @ X463 @ X464 ) )
=> ( X464 @ X465 ) )
=> ( ! [X466: $i > $o] :
( ? [X467: $i] :
( ( X466 @ X467 )
& ! [X468: $i] :
( ( X466 @ X468 )
=> ( X467 = X468 ) ) )
=> ? [X469: $i] :
( ( X466 @ X469 )
& ! [X470: $i] :
( ( X466 @ X470 )
=> ( X469 = X470 ) ) ) )
=> ( ! [X471: $o,X472: $i] :
( ( in @ X472 @ ( prop2set @ X471 ) )
=> X471 )
=> ( ! [X473: $i] :
( ( in @ X473 @ emptyset )
=> ! [X474: $o] : X474 )
=> ( ! [X475: $i] :
( ( in @ X475 @ emptyset )
=> ~ $true )
=> ( ! [X476: $i] :
~ ( in @ X476 @ emptyset )
=> ( ! [X477: $i > $o] :
( ? [X478: $i] :
( ( X477 @ X478 )
& ! [X479: $i] :
( ( X477 @ X479 )
=> ( X478 = X479 ) ) )
=> ? [X480: $i] : ( X477 @ X480 ) )
=> ( ! [X481: $i,X482: $i] :
( ! [X483: $i] :
( ( in @ X483 @ X481 )
=> ( in @ X483 @ X482 ) )
=> ( ! [X484: $i] :
( ( in @ X484 @ X482 )
=> ( in @ X484 @ X481 ) )
=> ( X481 = X482 ) ) )
=> ( ! [X485: $i] :
( ! [X486: $i] :
~ ( in @ X486 @ X485 )
=> ( X485 = emptyset ) )
=> ( ! [X487: $i] :
( ! [X488: $i] :
~ ( in @ X488 @ X487 )
=> ( X487 = emptyset ) )
=> ( ! [X489: $i,X490: $i > $o,X491: $i] :
( ( in @ X491 @ X489 )
=> ( ( in @ X491 @ ( dsetconstr @ X489 @ X490 ) )
<=> ( X490 @ X491 ) ) )
=> ( ! [X492: $i] :
( ( X492 != emptyset )
=> ? [X493: $i] : ( in @ X493 @ X492 ) )
=> ( ! [X494: $i,X495: $i > $o,X496: $i] :
( ( in @ X496 @ X494 )
=> ( ( X495 @ X496 )
=> ( ( dsetconstr @ X494 @ X495 )
!= emptyset ) ) )
=> ( ! [X497: $i] :
( ? [X498: $i] : ( in @ X498 @ X497 )
=> ( X497 != emptyset ) )
=> ( ! [X499: $i,X500: $i] : ( in @ X499 @ ( setadjoin @ X499 @ X500 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X501: $i,X502: $i,X503: $i] :
( ( in @ X503 @ X502 )
=> ( in @ X503 @ ( setadjoin @ X501 @ X502 ) ) )
=> ( ! [X504: $i,X505: $i,X506: $i] :
( ( in @ X506 @ ( setadjoin @ X504 @ X505 ) )
=> ! [X507: $o] :
( ( ( X506 = X504 )
=> X507 )
=> ( ( ( in @ X506 @ X505 )
=> X507 )
=> X507 ) ) )
=> ( ! [X508: $i,X509: $i,X510: $i] :
( ( in @ X510 @ ( setadjoin @ X508 @ X509 ) )
=> ( ( X510 = X508 )
| ( in @ X510 @ X509 ) ) )
=> ( ! [X511: $i] :
( ( dsetconstr @ X511
@ ^ [Z0: $i] : $true )
= X511 )
=> ( ! [X512: $i,X513: $i] :
( ! [X514: $i] :
( ( in @ X514 @ X513 )
=> ( in @ X514 @ X512 ) )
=> ( in @ X513 @ ( powerset @ X512 ) ) )
=> ( ! [X515: $i] : ( in @ emptyset @ ( powerset @ X515 ) )
=> ( ! [X516: $i] : ( in @ emptyset @ ( powerset @ X516 ) )
=> ( ! [X517: $i,X518: $i,X519: $i] :
( ( in @ X518 @ ( powerset @ X517 ) )
=> ( ( in @ X519 @ X518 )
=> ( in @ X519 @ X517 ) ) )
=> ( ! [X520: $i,X521: $i,X522: $i] :
( ( in @ X521 @ X522 )
=> ( ( in @ X522 @ X520 )
=> ( in @ X521 @ ( setunion @ X520 ) ) ) )
=> ( ! [X523: $i,X524: $i] :
( ( in @ X524 @ ( setunion @ X523 ) )
=> ! [X525: $o] :
( ! [X526: $i] :
( ( in @ X524 @ X526 )
=> ( ( in @ X526 @ X523 )
=> X525 ) )
=> X525 ) )
=> ( ! [X527: $i,X528: $i] :
( ( in @ X528 @ X527 )
=> ( in @ X528 @ ( powerset @ ( setunion @ X527 ) ) ) )
=> ( ! [X529: $i > $o] :
( ? [X530: $i] :
( ( X529 @ X530 )
& ! [X531: $i] :
( ( X529 @ X531 )
=> ( X530 = X531 ) ) )
=> ? [X532: $i] :
! [X533: $i] :
( ( X529 @ X533 )
<=> ( X533 = X532 ) ) )
=> ( ! [X534: $i] :
( ( X534 != emptyset )
=> ? [X535: $i] :
( ( in @ X535 @ X534 )
& $true ) )
=> ( ! [X536: $i,X537: $i] :
( ( in @ X536 @ ( setadjoin @ X537 @ emptyset ) )
=> ( X536 = X537 ) )
=> ( ! [X538: $i,X539: $i] :
( ( X538 != X539 )
=> ~ ( in @ X539 @ ( setadjoin @ X538 @ emptyset ) ) )
=> ( ! [X540: $i,X541: $i] :
( ( X540 = X541 )
=> ( in @ X540 @ ( setadjoin @ X541 @ emptyset ) ) )
=> ( ! [X542: $i,X543: $i] :
( ( in @ X542 @ ( setadjoin @ X543 @ emptyset ) )
=> ( in @ X543 @ ( setadjoin @ X542 @ emptyset ) ) )
=> ( ! [X544: $i,X545: $i,X546: $i] :
( ( in @ X546 @ ( setadjoin @ X544 @ ( setadjoin @ X545 @ emptyset ) ) )
=> ( ( X546 = X544 )
| ( X546 = X545 ) ) )
=> ( ! [X547: $i,X548: $i] : ( in @ X547 @ ( setadjoin @ X547 @ ( setadjoin @ X548 @ emptyset ) ) )
=> ( ! [X549: $i,X550: $i] : ( in @ X550 @ ( setadjoin @ X549 @ ( setadjoin @ X550 @ emptyset ) ) )
=> ( ! [X551: $i,X552: $i > $o] :
( ? [X553: $i] :
( ( in @ X553 @ X551 )
& ( X552 @ X553 ) )
=> ( ( ( dsetconstr @ X551 @ X552 )
= emptyset )
=> ~ $true ) )
=> ( ! [X554: $i > $o,X555: $i] :
( ( in @ X555 @ emptyset )
=> ( X554 @ X555 ) )
=> ( ! [X556: $i,X557: $i > $o] :
( ~ ! [X558: $i] :
( ( in @ X558 @ X556 )
=> ( X557 @ X558 ) )
=> ? [X559: $i] :
( ( in @ X559 @ X556 )
& ~ ( X557 @ X559 ) ) )
=> ( ! [X560: $i,X561: $i > $o] :
( ! [X562: $i] :
( ( in @ X562 @ X560 )
=> ~ ( X561 @ X562 ) )
=> ~ ? [X563: $i] :
( ( in @ X563 @ X560 )
& ( X561 @ X563 ) ) )
=> ( ! [X564: $i,X565: $i > $o] :
( ~ ? [X566: $i] :
( ( in @ X566 @ X564 )
& ( X565 @ X566 ) )
=> ! [X567: $i] :
( ( in @ X567 @ X564 )
=> ~ ( X565 @ X567 ) ) )
=> ( ! [X568: $i,X569: $i > $o] :
( ? [X570: $i] :
( ( in @ X570 @ X568 )
& ~ ( X569 @ X570 ) )
=> ~ ! [X571: $i] :
( ( in @ X571 @ X568 )
=> ( X569 @ X571 ) ) )
=> ( ! [X572: $o] :
( X572
=> ( in @ emptyset @ ( prop2set @ X572 ) ) )
=> ( prop2set2propI
=> ( ! [X573: $i,X574: $i > $o] :
( ~ ? [X575: $i] :
( ( in @ X575 @ X573 )
& ( X574 @ X575 ) )
=> ! [X576: $i] :
( ( in @ X576 @ X573 )
=> ~ ( X574 @ X576 ) ) )
=> ( ! [X577: $i,X578: $i > $o] :
( ~ ! [X579: $i] :
( ( in @ X579 @ X577 )
=> ( X578 @ X579 ) )
=> ? [X580: $i] :
( ( in @ X580 @ X577 )
& ~ ( X578 @ X580 ) ) )
=> ( ! [X581: $i > $o] :
( ? [X582: $i] :
( ( X581 @ X582 )
& ! [X583: $i] :
( ( X581 @ X583 )
=> ( X582 = X583 ) ) )
=> ? [X584: $i] :
( ( X581 @ X584 )
& ! [X585: $i] :
( ( X581 @ X585 )
=> ( X584 = X585 ) ) ) )
=> ( ! [X586: $i > $o] :
( ? [X587: $i] : ( X586 @ X587 )
=> ( ! [X588: $i,X589: $i] :
( ( X586 @ X588 )
=> ( ( X586 @ X589 )
=> ( X588 = X589 ) ) )
=> ? [X590: $i] :
( ( X586 @ X590 )
& ! [X591: $i] :
( ( X586 @ X591 )
=> ( X590 = X591 ) ) ) ) )
=> ( ! [X592: $i > $o] :
( ? [X593: $i] :
! [X594: $i] :
( ( X592 @ X594 )
<=> ( X594 = X593 ) )
=> ? [X595: $i] :
( ( X592 @ X595 )
& ! [X596: $i] :
( ( X592 @ X596 )
=> ( X595 = X596 ) ) ) )
=> ( ! [X597: $i,X598: $i] :
( ( X597 = X598 )
=> ! [X599: $i,X600: $i] :
( ( X599 = X600 )
=> ( ( in @ X599 @ X597 )
=> ( in @ X600 @ X598 ) ) ) )
=> ( ! [X601: $i,X602: $i] :
( ( X601 = X602 )
=> ! [X603: $i,X604: $i] :
( ( X603 = X604 )
=> ( ( in @ X603 @ X601 )
<=> ( in @ X604 @ X602 ) ) ) )
=> ( ! [X605: $i > $o] :
( ? [X606: $i] :
( ( X605 @ X606 )
& ! [X607: $i] :
( ( X605 @ X607 )
=> ( X606 = X607 ) ) )
=> ! [X608: $i,X609: $i] :
( ( X605 @ X608 )
=> ( ( X605 @ X609 )
=> ( X608 = X609 ) ) ) )
=> ( ! [X610: $i > $o,X611: $i > $o] :
( ! [X612: $i,X613: $i] :
( ( X612 = X613 )
=> ( ( X610 @ X612 )
<=> ( X611 @ X613 ) ) )
=> ( ? [X614: $i] :
( ( X610 @ X614 )
& ! [X615: $i] :
( ( X610 @ X615 )
=> ( X614 = X615 ) ) )
<=> ? [X616: $i] :
( ( X611 @ X616 )
& ! [X617: $i] :
( ( X611 @ X617 )
=> ( X616 = X617 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X618: $i,X619: $i] :
( ( X618 = X619 )
=> ! [X620: $i,X621: $i] :
( ( X620 = X621 )
=> ( ( setadjoin @ X618 @ X620 )
= ( setadjoin @ X619 @ X621 ) ) ) )
=> ( ! [X622: $i,X623: $i] :
( ( X622 = X623 )
=> ( ( powerset @ X622 )
= ( powerset @ X623 ) ) )
=> ( ! [X624: $i,X625: $i] :
( ( X624 = X625 )
=> ( ( setunion @ X624 )
= ( setunion @ X625 ) ) )
=> ( ( omega = omega )
=> ( ! [X626: $i > $o] :
( ? [X627: $i] :
( ( X626 @ X627 )
& ! [X628: $i] :
( ( X626 @ X628 )
=> ( X627 = X628 ) ) )
=> ! [X629: $i,X630: $i] :
( ( X626 @ X629 )
=> ( ( X626 @ X630 )
=> ( X629 = X630 ) ) ) )
=> ( ! [X631: $i > $o,X632: $i > $o] :
( ! [X633: $i,X634: $i] :
( ( X633 = X634 )
=> ( ( X631 @ X633 )
<=> ( X632 @ X634 ) ) )
=> ( ? [X635: $i] :
( ( X631 @ X635 )
& ! [X636: $i] :
( ( X631 @ X636 )
=> ( X635 = X636 ) ) )
=> ( ? [X637: $i] :
( ( X632 @ X637 )
& ! [X638: $i] :
( ( X632 @ X638 )
=> ( X637 = X638 ) ) )
=> ( ( descr @ X631 )
= ( descr @ X632 ) ) ) ) )
=> ( ! [X639: $i,X640: $i] :
( ( X639 = X640 )
=> ! [X641: $i > $o,X642: $i > $o] :
( ! [X643: $i] :
( ( in @ X643 @ X639 )
=> ! [X644: $i] :
( ( in @ X644 @ X640 )
=> ( ( X643 = X644 )
=> ( ( X641 @ X643 )
<=> ( X642 @ X644 ) ) ) ) )
=> ( ( dsetconstr @ X639 @ X641 )
= ( dsetconstr @ X640 @ X642 ) ) ) )
=> ( ! [X645: $i,X646: $i] :
( ! [X647: $i] :
( ( in @ X647 @ X645 )
=> ( in @ X647 @ X646 ) )
=> ( subset @ X645 @ X646 ) )
=> ( ! [X648: $i,X649: $i] :
( ( X648 = X649 )
=> ( subset @ X649 @ X648 ) )
=> ( ! [X650: $i,X651: $i] :
( ( X650 = X651 )
=> ( subset @ X650 @ X651 ) )
=> ( ! [X652: $i,X653: $i] :
( ! [X654: $i] :
( ( in @ X654 @ X652 )
=> ( in @ X654 @ X653 ) )
=> ( subset @ X652 @ X653 ) )
=> ( ! [X655: $i] : ( subset @ emptyset @ X655 )
=> ( ! [X656: $i,X657: $i,X658: $i] :
( ( subset @ X656 @ X657 )
=> ( ( in @ X658 @ X656 )
=> ( in @ X658 @ X657 ) ) )
=> ( ! [X659: $i,X660: $i,X661: $i] :
( ( subset @ X659 @ X660 )
=> ( ~ ( in @ X661 @ X660 )
=> ~ ( in @ X661 @ X659 ) ) )
=> ( ! [X662: $i,X663: $i,X664: $i] :
( ( in @ X664 @ X662 )
=> ( ~ ( in @ X664 @ X663 )
=> ~ ( subset @ X662 @ X663 ) ) )
=> ( ! [X665: $i,X666: $i] :
( ~ ( subset @ X665 @ X666 )
=> ( X665 != X666 ) )
=> ( ! [X667: $i,X668: $i,X669: $i] :
( ( in @ X669 @ X667 )
=> ( ~ ( in @ X669 @ X668 )
=> ( X667 != X668 ) ) )
=> ( ! [X670: $i] : ( subset @ X670 @ X670 )
=> ( ! [X671: $i,X672: $i,X673: $i] :
( ( subset @ X671 @ X672 )
=> ( ( subset @ X672 @ X673 )
=> ( subset @ X671 @ X673 ) ) )
=> ( ! [X674: $i,X675: $i] : ( subset @ X675 @ ( setadjoin @ X674 @ X675 ) )
=> ( ! [X676: $i,X677: $i,X678: $i] :
( ( subset @ X676 @ X678 )
=> ( subset @ X676 @ ( setadjoin @ X677 @ X678 ) ) )
=> ( ! [X679: $i,X680: $i] :
( ( subset @ X679 @ X680 )
=> ( in @ X679 @ ( powerset @ X680 ) ) )
=> ( ! [X681: $i,X682: $i] :
( ( subset @ X681 @ X682 )
=> ( ( subset @ X682 @ X681 )
=> ( X681 = X682 ) ) )
=> ( ! [X683: $i] :
( ( subset @ X683 @ emptyset )
=> ( X683 = emptyset ) )
=> ( ! [X684: $i,X685: $i] :
( ( subset @ X685 @ X684 )
=> ( in @ X685 @ ( powerset @ X684 ) ) )
=> ( ! [X686: $i,X687: $i] :
( ( in @ X687 @ ( powerset @ X686 ) )
=> ( subset @ X687 @ X686 ) )
=> ( ! [X688: $i] : ( in @ X688 @ ( powerset @ X688 ) )
=> ( ! [X689: $i,X690: $i] :
( ( subset @ X689 @ X690 )
=> ( subset @ ( powerset @ X689 ) @ ( powerset @ X690 ) ) )
=> ( ! [X691: $i,X692: $i > $o] : ( in @ ( dsetconstr @ X691 @ X692 ) @ ( powerset @ X691 ) )
=> ( ! [X693: $i,X694: $i > $o] : ( subset @ ( dsetconstr @ X693 @ X694 ) @ X693 )
=> ( ! [X695: $i,X696: $i,X697: $i] :
( ( in @ X697 @ X695 )
=> ( in @ X697 @ ( binunion @ X695 @ X696 ) ) )
=> ( ! [X698: $i,X699: $i] : ( in @ X699 @ ( setadjoin @ X698 @ ( setadjoin @ X699 @ emptyset ) ) )
=> ( ! [X700: $i,X701: $i,X702: $i] :
( ( in @ X702 @ X701 )
=> ( in @ X702 @ ( binunion @ X700 @ X701 ) ) )
=> ( ! [X703: $i,X704: $i,X705: $i,X706: $o] :
( ( in @ X705 @ ( binunion @ X703 @ X704 ) )
=> ( ( ( in @ X705 @ X703 )
=> X706 )
=> ( ( ( in @ X705 @ X704 )
=> X706 )
=> X706 ) ) )
=> ( ! [X707: $i,X708: $i,X709: $i] :
( ( in @ X709 @ ( binunion @ X707 @ X708 ) )
=> ( ( in @ X709 @ X707 )
| ( in @ X709 @ X708 ) ) )
=> ( ! [X710: $i,X711: $i] : ( subset @ X710 @ ( binunion @ X710 @ X711 ) )
=> ( ! [X712: $i,X713: $i] : ( subset @ X713 @ ( binunion @ X712 @ X713 ) )
=> ( ! [X714: $i,X715: $i,X716: $i] :
( ( in @ X716 @ X714 )
=> ( ( in @ X716 @ X715 )
=> ( in @ X716 @ ( binintersect @ X714 @ X715 ) ) ) )
=> ( ! [X717: $i,X718: $i,X719: $i] :
( ( subset @ X719 @ X717 )
=> ( ( subset @ X719 @ X718 )
=> ( subset @ X719 @ ( binintersect @ X717 @ X718 ) ) ) )
=> ( ! [X720: $i,X721: $i,X722: $i] :
( ( in @ X722 @ ( binintersect @ X720 @ X721 ) )
=> ( in @ X722 @ X720 ) )
=> ( ! [X723: $i,X724: $i] : ( subset @ ( binintersect @ X723 @ X724 ) @ X723 )
=> ( ! [X725: $i,X726: $i] :
( ( subset @ X725 @ X726 )
=> ( ( binintersect @ X725 @ X726 )
= X725 ) )
=> ( ! [X727: $i,X728: $i] :
( ( ( binintersect @ X727 @ X728 )
= X728 )
=> ( subset @ X728 @ X727 ) )
=> ( ! [X729: $i,X730: $i,X731: $i] :
( ( in @ X731 @ ( binintersect @ X729 @ X730 ) )
=> ( in @ X731 @ X730 ) )
=> ( ! [X732: $i,X733: $i] :
( ~ ? [X734: $i] :
( ( in @ X734 @ X732 )
& ( in @ X734 @ X733 ) )
=> ( ( binintersect @ X732 @ X733 )
= emptyset ) )
=> ( ! [X735: $i,X736: $i] : ( subset @ ( binintersect @ X735 @ X736 ) @ X736 )
=> ( ! [X737: $i,X738: $i] :
( ( subset @ X738 @ X737 )
=> ( ( binintersect @ X737 @ X738 )
= X738 ) )
=> ( ! [X739: $i,X740: $i] :
( ( ( binintersect @ X739 @ X740 )
= X739 )
=> ( subset @ X739 @ X740 ) )
=> ( ! [X741: $i,X742: $i,X743: $i] :
( ( binintersect @ X741 @ ( binunion @ X742 @ X743 ) )
= ( binunion @ ( binintersect @ X741 @ X742 ) @ ( binintersect @ X741 @ X743 ) ) )
=> ( ! [X744: $i,X745: $i,X746: $i] :
( ( in @ X746 @ X744 )
=> ( ~ ( in @ X746 @ X745 )
=> ( in @ X746 @ ( setminus @ X744 @ X745 ) ) ) )
=> ( ! [X747: $i,X748: $i,X749: $i] :
( ( in @ X749 @ ( setminus @ X747 @ X748 ) )
=> ( in @ X749 @ X747 ) )
=> ( ! [X750: $i,X751: $i,X752: $i] :
( ( in @ X752 @ ( setminus @ X750 @ X751 ) )
=> ~ ( in @ X752 @ X751 ) )
=> ( ! [X753: $i,X754: $i] :
( ( subset @ X753 @ X754 )
=> ( ( setminus @ X753 @ X754 )
= emptyset ) )
=> ( ! [X755: $i,X756: $i,X757: $i] :
( ~ ( in @ X757 @ ( setminus @ X755 @ X756 ) )
=> ( ( in @ X757 @ X755 )
=> ( in @ X757 @ X756 ) ) )
=> ( ! [X758: $i,X759: $i,X760: $i] :
( ~ ( in @ X760 @ ( setminus @ X758 @ X759 ) )
=> ( ~ ( in @ X760 @ X759 )
=> ~ ( in @ X760 @ X758 ) ) )
=> ( ! [X761: $i,X762: $i,X763: $i] :
( ~ ( in @ X763 @ X761 )
=> ~ ( in @ X763 @ ( setminus @ X761 @ X762 ) ) )
=> ( ! [X764: $i,X765: $i,X766: $i] :
( ( in @ X766 @ X765 )
=> ~ ( in @ X766 @ ( setminus @ X764 @ X765 ) ) )
=> ( ! [X767: $i,X768: $i] : ( subset @ ( setminus @ X767 @ X768 ) @ X767 )
=> ( ! [X769: $i,X770: $i] :
( ( ( setminus @ X769 @ X770 )
= emptyset )
=> ( subset @ X769 @ X770 ) )
=> ( ! [X771: $i,X772: $i,X773: $i] :
( ( in @ X773 @ ( symdiff @ X771 @ X772 ) )
=> ! [X774: $o] :
( ( ( in @ X773 @ X771 )
=> ( ~ ( in @ X773 @ X772 )
=> X774 ) )
=> ( ( ~ ( in @ X773 @ X771 )
=> ( ( in @ X773 @ X772 )
=> X774 ) )
=> X774 ) ) )
=> ( ! [X775: $i,X776: $i,X777: $i] :
( ( in @ X777 @ X775 )
=> ( ~ ( in @ X777 @ X776 )
=> ( in @ X777 @ ( symdiff @ X775 @ X776 ) ) ) )
=> ( ! [X778: $i,X779: $i,X780: $i] :
( ~ ( in @ X780 @ X778 )
=> ( ( in @ X780 @ X779 )
=> ( in @ X780 @ ( symdiff @ X778 @ X779 ) ) ) )
=> ( ! [X781: $i,X782: $i,X783: $i] :
( ( in @ X783 @ X781 )
=> ( ( in @ X783 @ X782 )
=> ~ ( in @ X783 @ ( symdiff @ X781 @ X782 ) ) ) )
=> ( ! [X784: $i,X785: $i,X786: $i] :
( ~ ( in @ X786 @ X784 )
=> ( ~ ( in @ X786 @ X785 )
=> ~ ( in @ X786 @ ( symdiff @ X784 @ X785 ) ) ) )
=> ( ! [X787: $i,X788: $i] : ( in @ X788 @ ( setadjoin @ X787 @ ( setadjoin @ X788 @ emptyset ) ) )
=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( 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(assume_negation,[status(cth)],[setukpairIL]),symdiffIneg1]),secondinupair]),binintersectSubset3]),binintersectER]),disjointsetsI1]),singletonsswitch]),binintersectRsub]),binintersectSubset4]),upairsetE]),binintersectSubset1]),bs114d]),upairsetIL]),setminusI]),setminusEL]),upairsetIR]),setminusER]),setminusSubset2]),c_0_150]),setminusERneg]),setminusELneg]),vacuousDall]),setminusILneg]),quantDeMorgan1]),setminusIRneg]),setminusLsub]),setminusSubset1]),quantDeMorgan2]),symdiffE]),symdiffI1]),symdiffI2]),quantDeMorgan3]),c_0_151]),symdiffIneg2]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_152]),c_0_153]),c_0_154]),inCongP]),in__Cong]),c_0_155]),c_0_156]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_157]),binintersectSubset2]),c_0_158]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_159]),c_0_160]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),c_0_161]),binunionRsub]),uniqinunit]),binintersectI]),notinsingleton]),eqinunit]),binintersectSubset5]),binintersectEL]),binintersectLsub]),c_0_162]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_163]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_164]),c_0_165]),c_0_166]),c_0_167]),noeltsimpempty]),emptyI]),setext]),c_0_168]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_169]),c_0_170]),c_0_171]),c_0_172]),c_0_173]),wellorderingAx]),foundationAx]),c_0_174]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_175]) ).
thf(c_0_177,negated_conjecture,
! [X789: $i,X790: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X802: $i,X803: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i,X811: $i,X812: $i > $i > $o,X813: $i,X815: $i,X818: $i,X820: $i,X821: $i,X822: $i,X823: $i,X825: $i,X826: $i > $o,X827: $i,X829: $i,X830: $i > $o,X831: $i,X832: $i,X833: $i > $o,X834: $i,X835: $i,X836: $i > $o,X837: $i,X838: $i > $o,X839: $i,X842: $i,X843: $o,X844: $i,X845: $i,X846: $o,X847: $i,X848: $i,X849: $i > $o,X850: $i,X853: $i,X854: $i,X857: $i,X859: $i,X861: $i,X862: $i > $o,X863: $i,X864: $i,X866: $i,X867: $i > $o,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i,X878: $i,X879: $o,X880: $i,X881: $i,X882: $i,X883: $i,X884: $i,X885: $i,X887: $i,X888: $i,X889: $i,X890: $i,X891: $i,X892: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $o,X899: $i,X900: $i,X901: $i > $o,X902: $i,X905: $i,X906: $i,X907: $i,X909: $i,X910: $i,X911: $i,X912: $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 > $o,X926: $i,X927: $i > $o,X928: $i,X929: $i,X930: $i > $o,X931: $i,X933: $i,X934: $i > $o,X936: $i,X937: $i,X938: $i > $o,X940: $i,X941: $i,X942: $i > $o,X943: $i,X945: $o,X946: $i,X947: $i > $o,X949: $i,X950: $i,X951: $i > $o,X952: $i,X954: $i > $o,X955: $i,X958: $i,X959: $i > $o,X960: $i,X964: $i,X965: $i > $o,X966: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i,X975: $i,X976: $i,X977: $i,X978: $i > $o,X979: $i,X981: $i,X982: $i,X983: $i > $o,X984: $i > $o,X987: $i,X990: $i,X991: $i,X994: $i,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i > $o,X1004: $i,X1006: $i,X1007: $i,X1008: $i > $o,X1009: $i > $o,X1012: $i,X1014: $i,X1016: $i,X1017: $i,X1018: $i > $o,X1019: $i > $o,X1022: $i,X1023: $i,X1025: $i,X1026: $i,X1027: $i,X1028: $i,X1029: $i,X1030: $i,X1032: $i,X1033: $i,X1034: $i,X1035: $i,X1036: $i,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1041: $i,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i,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 > $o,X1070: $i,X1071: $i > $o,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i,X1081: $i,X1082: $i,X1083: $o,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $i,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i,X1105: $i,X1106: $i,X1107: $i,X1108: $i,X1109: $i,X1110: $i,X1112: $i,X1113: $i,X1114: $i,X1115: $i,X1116: $i,X1117: $i,X1118: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,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: $o,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1164: $i,X1165: $i] :
( ( ~ ( in @ ( esk1_2 @ X789 @ X790 ) @ X789 )
| ~ ( in @ ( esk1_2 @ X789 @ X790 ) @ X790 )
| ( X789 = X790 ) )
& ( ( in @ ( esk1_2 @ X789 @ X790 ) @ X789 )
| ( in @ ( esk1_2 @ X789 @ X790 ) @ X790 )
| ( X789 = X790 ) )
& ~ ( in @ X792 @ emptyset )
& ( ~ ( in @ X795 @ ( setadjoin @ X793 @ X794 ) )
| ( X795 = X793 )
| ( in @ X795 @ X794 ) )
& ( ( X795 != X793 )
| ( in @ X795 @ ( setadjoin @ X793 @ X794 ) ) )
& ( ~ ( in @ X795 @ X794 )
| ( in @ X795 @ ( setadjoin @ X793 @ X794 ) ) )
& ( ~ ( in @ X797 @ ( powerset @ X796 ) )
| ~ ( in @ X798 @ X797 )
| ( in @ X798 @ X796 ) )
& ( ( in @ ( esk2_2 @ X799 @ X800 ) @ X800 )
| ( in @ X800 @ ( powerset @ X799 ) ) )
& ( ~ ( in @ ( esk2_2 @ X799 @ X800 ) @ X799 )
| ( in @ X800 @ ( powerset @ X799 ) ) )
& ( ( in @ X803 @ ( esk3_2 @ X802 @ X803 ) )
| ~ ( in @ X803 @ ( setunion @ X802 ) ) )
& ( ( in @ ( esk3_2 @ X802 @ X803 ) @ X802 )
| ~ ( in @ X803 @ ( setunion @ X802 ) ) )
& ( ~ ( in @ X806 @ X807 )
| ~ ( in @ X807 @ X805 )
| ( in @ X806 @ ( setunion @ X805 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X808 @ omega )
| ( in @ ( setadjoin @ X808 @ X808 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X809 ) @ omega )
| ~ ( in @ emptyset @ X809 )
| ~ ( in @ X811 @ omega )
| ( in @ X811 @ X809 ) )
& ( ( in @ ( esk4_1 @ X809 ) @ X809 )
| ~ ( in @ emptyset @ X809 )
| ~ ( in @ X811 @ omega )
| ( in @ X811 @ X809 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X809 ) @ ( esk4_1 @ X809 ) ) @ X809 )
| ~ ( in @ emptyset @ X809 )
| ~ ( in @ X811 @ omega )
| ( in @ X811 @ X809 ) )
& ( ( in @ ( esk8_3 @ X812 @ X813 @ X818 ) @ X813 )
| ~ ( in @ X818 @ ( esk7_2 @ X812 @ X813 ) )
| ( in @ ( esk5_2 @ X812 @ X813 ) @ X813 ) )
& ( ( X812 @ ( esk8_3 @ X812 @ X813 @ X818 ) @ X818 )
| ~ ( in @ X818 @ ( esk7_2 @ X812 @ X813 ) )
| ( in @ ( esk5_2 @ X812 @ X813 ) @ X813 ) )
& ( ~ ( in @ X821 @ X813 )
| ~ ( X812 @ X821 @ X820 )
| ( in @ X820 @ ( esk7_2 @ X812 @ X813 ) )
| ( in @ ( esk5_2 @ X812 @ X813 ) @ X813 ) )
& ( ( in @ ( esk8_3 @ X812 @ X813 @ X818 ) @ X813 )
| ~ ( in @ X818 @ ( esk7_2 @ X812 @ X813 ) )
| ( X812 @ ( esk5_2 @ X812 @ X813 ) @ ( esk6_3 @ X812 @ X813 @ X815 ) )
| ~ ( X812 @ ( esk5_2 @ X812 @ X813 ) @ X815 ) )
& ( ( X812 @ ( esk8_3 @ X812 @ X813 @ X818 ) @ X818 )
| ~ ( in @ X818 @ ( esk7_2 @ X812 @ X813 ) )
| ( X812 @ ( esk5_2 @ X812 @ X813 ) @ ( esk6_3 @ X812 @ X813 @ X815 ) )
| ~ ( X812 @ ( esk5_2 @ X812 @ X813 ) @ X815 ) )
& ( ~ ( in @ X821 @ X813 )
| ~ ( X812 @ X821 @ X820 )
| ( in @ X820 @ ( esk7_2 @ X812 @ X813 ) )
| ( X812 @ ( esk5_2 @ X812 @ X813 ) @ ( esk6_3 @ X812 @ X813 @ X815 ) )
| ~ ( X812 @ ( esk5_2 @ X812 @ X813 ) @ X815 ) )
& ( ( in @ ( esk8_3 @ X812 @ X813 @ X818 ) @ X813 )
| ~ ( in @ X818 @ ( esk7_2 @ X812 @ X813 ) )
| ( X815
!= ( esk6_3 @ X812 @ X813 @ X815 ) )
| ~ ( X812 @ ( esk5_2 @ X812 @ X813 ) @ X815 ) )
& ( ( X812 @ ( esk8_3 @ X812 @ X813 @ X818 ) @ X818 )
| ~ ( in @ X818 @ ( esk7_2 @ X812 @ X813 ) )
| ( X815
!= ( esk6_3 @ X812 @ X813 @ X815 ) )
| ~ ( X812 @ ( esk5_2 @ X812 @ X813 ) @ X815 ) )
& ( ~ ( in @ X821 @ X813 )
| ~ ( X812 @ X821 @ X820 )
| ( in @ X820 @ ( esk7_2 @ X812 @ X813 ) )
| ( X815
!= ( esk6_3 @ X812 @ X813 @ X815 ) )
| ~ ( X812 @ ( esk5_2 @ X812 @ X813 ) @ X815 ) )
& ( ( in @ ( esk9_1 @ X822 ) @ X822 )
| ~ ( in @ X823 @ X822 ) )
& ( ~ ( in @ X825 @ ( esk9_1 @ X822 ) )
| ~ ( in @ X825 @ X822 )
| ~ ( in @ X823 @ X822 ) )
& epred1_0
& ( ( X826 @ ( esk10_2 @ X826 @ X827 ) )
| ~ ( X826 @ X827 )
| ( X826 @ ( descr @ X826 ) ) )
& ( ( X827
!= ( esk10_2 @ X826 @ X827 ) )
| ~ ( X826 @ X827 )
| ( X826 @ ( descr @ X826 ) ) )
& ( ~ ( in @ X831 @ X829 )
| ~ ( X830 @ X831 )
| ( in @ X831 @ ( dsetconstr @ X829 @ X830 ) ) )
& ( ~ ( in @ X834 @ ( dsetconstr @ X832 @ X833 ) )
| ( in @ X834 @ X832 ) )
& ( ~ ( in @ X837 @ ( dsetconstr @ X835 @ X836 ) )
| ( X836 @ X837 ) )
& ( ( X838 @ ( esk12_1 @ X838 ) )
| ( X838 @ ( esk11_2 @ X838 @ X839 ) )
| ~ ( X838 @ X839 ) )
& ( ~ ( X838 @ X842 )
| ( ( esk12_1 @ X838 )
= X842 )
| ( X838 @ ( esk11_2 @ X838 @ X839 ) )
| ~ ( X838 @ X839 ) )
& ( ( X838 @ ( esk12_1 @ X838 ) )
| ( X839
!= ( esk11_2 @ X838 @ X839 ) )
| ~ ( X838 @ X839 ) )
& ( ~ ( X838 @ X842 )
| ( ( esk12_1 @ X838 )
= X842 )
| ( X839
!= ( esk11_2 @ X838 @ X839 ) )
| ~ ( X838 @ X839 ) )
& ( ~ ( in @ X844 @ ( prop2set @ X843 ) )
| X843 )
& ( ~ ( in @ X845 @ emptyset )
| X846 )
& ( ~ ( in @ X847 @ emptyset )
| ~ $true )
& ~ ( in @ X848 @ emptyset )
& ( ( X849 @ ( esk13_2 @ X849 @ X850 ) )
| ~ ( X849 @ X850 )
| ( X849 @ ( esk14_1 @ X849 ) ) )
& ( ( X850
!= ( esk13_2 @ X849 @ X850 ) )
| ~ ( X849 @ X850 )
| ( X849 @ ( esk14_1 @ X849 ) ) )
& ( ( in @ ( esk16_2 @ X853 @ X854 ) @ X854 )
| ( X853 = X854 )
| ( in @ ( esk15_2 @ X853 @ X854 ) @ X853 ) )
& ( ~ ( in @ ( esk16_2 @ X853 @ X854 ) @ X853 )
| ( X853 = X854 )
| ( in @ ( esk15_2 @ X853 @ X854 ) @ X853 ) )
& ( ( in @ ( esk16_2 @ X853 @ X854 ) @ X854 )
| ( X853 = X854 )
| ~ ( in @ ( esk15_2 @ X853 @ X854 ) @ X854 ) )
& ( ~ ( in @ ( esk16_2 @ X853 @ X854 ) @ X853 )
| ( X853 = X854 )
| ~ ( in @ ( esk15_2 @ X853 @ X854 ) @ X854 ) )
& ( ( in @ ( esk17_1 @ X857 ) @ X857 )
| ( X857 = emptyset ) )
& ( ( in @ ( esk18_1 @ X859 ) @ X859 )
| ( X859 = emptyset ) )
& ( ~ ( in @ X863 @ ( dsetconstr @ X861 @ X862 ) )
| ( X862 @ X863 )
| ~ ( in @ X863 @ X861 ) )
& ( ~ ( X862 @ X863 )
| ( in @ X863 @ ( dsetconstr @ X861 @ X862 ) )
| ~ ( in @ X863 @ X861 ) )
& ( ( X864 = emptyset )
| ( in @ ( esk19_1 @ X864 ) @ X864 ) )
& ( ~ ( in @ X868 @ X866 )
| ~ ( X867 @ X868 )
| ( ( dsetconstr @ X866 @ X867 )
!= emptyset ) )
& ( ~ ( in @ X870 @ X869 )
| ( X869 != emptyset ) )
& ( in @ X871 @ ( setadjoin @ X871 @ X872 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X875 @ X874 )
| ( in @ X875 @ ( setadjoin @ X873 @ X874 ) ) )
& ( ( in @ X878 @ X877 )
| X879
| ( X878 = X876 )
| ~ ( in @ X878 @ ( setadjoin @ X876 @ X877 ) ) )
& ( ~ X879
| X879
| ( X878 = X876 )
| ~ ( in @ X878 @ ( setadjoin @ X876 @ X877 ) ) )
& ( ( in @ X878 @ X877 )
| X879
| ~ X879
| ~ ( in @ X878 @ ( setadjoin @ X876 @ X877 ) ) )
& ( ~ X879
| X879
| ~ X879
| ~ ( in @ X878 @ ( setadjoin @ X876 @ X877 ) ) )
& ( ~ ( in @ X882 @ ( setadjoin @ X880 @ X881 ) )
| ( X882 = X880 )
| ( in @ X882 @ X881 ) )
& ( ( dsetconstr @ X883
@ ^ [Z0: $i] : $true )
= X883 )
& ( ( in @ ( esk20_2 @ X884 @ X885 ) @ X885 )
| ( in @ X885 @ ( powerset @ X884 ) ) )
& ( ~ ( in @ ( esk20_2 @ X884 @ X885 ) @ X884 )
| ( in @ X885 @ ( powerset @ X884 ) ) )
& ( in @ emptyset @ ( powerset @ X887 ) )
& ( in @ emptyset @ ( powerset @ X888 ) )
& ( ~ ( in @ X890 @ ( powerset @ X889 ) )
| ~ ( in @ X891 @ X890 )
| ( in @ X891 @ X889 ) )
& ( ~ ( in @ X893 @ X894 )
| ~ ( in @ X894 @ X892 )
| ( in @ X893 @ ( setunion @ X892 ) ) )
& ( ( in @ X896 @ ( esk21_3 @ X895 @ X896 @ X897 ) )
| X897
| ~ ( in @ X896 @ ( setunion @ X895 ) ) )
& ( ( in @ ( esk21_3 @ X895 @ X896 @ X897 ) @ X895 )
| X897
| ~ ( in @ X896 @ ( setunion @ X895 ) ) )
& ( ~ X897
| X897
| ~ ( in @ X896 @ ( setunion @ X895 ) ) )
& ( ~ ( in @ X900 @ X899 )
| ( in @ X900 @ ( powerset @ ( setunion @ X899 ) ) ) )
& ( ~ ( X901 @ X905 )
| ( X905
= ( esk23_1 @ X901 ) )
| ( X901 @ ( esk22_2 @ X901 @ X902 ) )
| ~ ( X901 @ X902 ) )
& ( ( X906
!= ( esk23_1 @ X901 ) )
| ( X901 @ X906 )
| ( X901 @ ( esk22_2 @ X901 @ X902 ) )
| ~ ( X901 @ X902 ) )
& ( ~ ( X901 @ X905 )
| ( X905
= ( esk23_1 @ X901 ) )
| ( X902
!= ( esk22_2 @ X901 @ X902 ) )
| ~ ( X901 @ X902 ) )
& ( ( X906
!= ( esk23_1 @ X901 ) )
| ( X901 @ X906 )
| ( X902
!= ( esk22_2 @ X901 @ X902 ) )
| ~ ( X901 @ X902 ) )
& ( ( in @ ( esk24_1 @ X907 ) @ X907 )
| ( X907 = emptyset ) )
& ( $true
| ( X907 = emptyset ) )
& ( ~ ( in @ X909 @ ( setadjoin @ X910 @ emptyset ) )
| ( X909 = X910 ) )
& ( ( X911 = X912 )
| ~ ( in @ X912 @ ( setadjoin @ X911 @ emptyset ) ) )
& ( ( X913 != X914 )
| ( in @ X913 @ ( setadjoin @ X914 @ emptyset ) ) )
& ( ~ ( in @ X915 @ ( setadjoin @ X916 @ emptyset ) )
| ( in @ X916 @ ( setadjoin @ X915 @ emptyset ) ) )
& ( ~ ( in @ X919 @ ( setadjoin @ X917 @ ( setadjoin @ X918 @ emptyset ) ) )
| ( X919 = X917 )
| ( X919 = X918 ) )
& ( in @ X920 @ ( setadjoin @ X920 @ ( setadjoin @ X921 @ emptyset ) ) )
& ( in @ X923 @ ( setadjoin @ X922 @ ( setadjoin @ X923 @ emptyset ) ) )
& ( ~ ( in @ X926 @ X924 )
| ~ ( X925 @ X926 )
| ( ( dsetconstr @ X924 @ X925 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X928 @ emptyset )
| ( X927 @ X928 ) )
& ( ( in @ ( esk25_2 @ X929 @ X930 ) @ X929 )
| ~ ( in @ X931 @ X929 )
| ( X930 @ X931 ) )
& ( ~ ( X930 @ ( esk25_2 @ X929 @ X930 ) )
| ~ ( in @ X931 @ X929 )
| ( X930 @ X931 ) )
& ( ( in @ ( esk26_2 @ X933 @ X934 ) @ X933 )
| ~ ( in @ X936 @ X933 )
| ~ ( X934 @ X936 ) )
& ( ( X934 @ ( esk26_2 @ X933 @ X934 ) )
| ~ ( in @ X936 @ X933 )
| ~ ( X934 @ X936 ) )
& ( ( in @ ( esk27_2 @ X937 @ X938 ) @ X937 )
| ~ ( in @ X940 @ X937 )
| ~ ( X938 @ X940 ) )
& ( ( X938 @ ( esk27_2 @ X937 @ X938 ) )
| ~ ( in @ X940 @ X937 )
| ~ ( X938 @ X940 ) )
& ( ( in @ ( esk28_2 @ X941 @ X942 ) @ X941 )
| ~ ( in @ X943 @ X941 )
| ( X942 @ X943 ) )
& ( ~ ( X942 @ ( esk28_2 @ X941 @ X942 ) )
| ~ ( in @ X943 @ X941 )
| ( X942 @ X943 ) )
& ( ~ X945
| ( in @ emptyset @ ( prop2set @ X945 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X946 @ X947 ) @ X946 )
| ~ ( in @ X949 @ X946 )
| ~ ( X947 @ X949 ) )
& ( ( X947 @ ( esk29_2 @ X946 @ X947 ) )
| ~ ( in @ X949 @ X946 )
| ~ ( X947 @ X949 ) )
& ( ( in @ ( esk30_2 @ X950 @ X951 ) @ X950 )
| ~ ( in @ X952 @ X950 )
| ( X951 @ X952 ) )
& ( ~ ( X951 @ ( esk30_2 @ X950 @ X951 ) )
| ~ ( in @ X952 @ X950 )
| ( X951 @ X952 ) )
& ( ( X954 @ ( esk32_1 @ X954 ) )
| ( X954 @ ( esk31_2 @ X954 @ X955 ) )
| ~ ( X954 @ X955 ) )
& ( ~ ( X954 @ X958 )
| ( ( esk32_1 @ X954 )
= X958 )
| ( X954 @ ( esk31_2 @ X954 @ X955 ) )
| ~ ( X954 @ X955 ) )
& ( ( X954 @ ( esk32_1 @ X954 ) )
| ( X955
!= ( esk31_2 @ X954 @ X955 ) )
| ~ ( X954 @ X955 ) )
& ( ~ ( X954 @ X958 )
| ( ( esk32_1 @ X954 )
= X958 )
| ( X955
!= ( esk31_2 @ X954 @ X955 ) )
| ~ ( X954 @ X955 ) )
& ( ( X959 @ ( esk35_1 @ X959 ) )
| ( X959 @ ( esk33_1 @ X959 ) )
| ~ ( X959 @ X960 ) )
& ( ~ ( X959 @ X964 )
| ( ( esk35_1 @ X959 )
= X964 )
| ( X959 @ ( esk33_1 @ X959 ) )
| ~ ( X959 @ X960 ) )
& ( ( X959 @ ( esk35_1 @ X959 ) )
| ( X959 @ ( esk34_1 @ X959 ) )
| ~ ( X959 @ X960 ) )
& ( ~ ( X959 @ X964 )
| ( ( esk35_1 @ X959 )
= X964 )
| ( X959 @ ( esk34_1 @ X959 ) )
| ~ ( X959 @ X960 ) )
& ( ( X959 @ ( esk35_1 @ X959 ) )
| ( ( esk33_1 @ X959 )
!= ( esk34_1 @ X959 ) )
| ~ ( X959 @ X960 ) )
& ( ~ ( X959 @ X964 )
| ( ( esk35_1 @ X959 )
= X964 )
| ( ( esk33_1 @ X959 )
!= ( esk34_1 @ X959 ) )
| ~ ( X959 @ X960 ) )
& ( ( X965 @ ( esk37_1 @ X965 ) )
| ~ ( X965 @ ( esk36_2 @ X965 @ X966 ) )
| ( ( esk36_2 @ X965 @ X966 )
!= X966 ) )
& ( ~ ( X965 @ X969 )
| ( ( esk37_1 @ X965 )
= X969 )
| ~ ( X965 @ ( esk36_2 @ X965 @ X966 ) )
| ( ( esk36_2 @ X965 @ X966 )
!= X966 ) )
& ( ( X965 @ ( esk37_1 @ X965 ) )
| ( X965 @ ( esk36_2 @ X965 @ X966 ) )
| ( ( esk36_2 @ X965 @ X966 )
= X966 ) )
& ( ~ ( X965 @ X969 )
| ( ( esk37_1 @ X965 )
= X969 )
| ( X965 @ ( esk36_2 @ X965 @ X966 ) )
| ( ( esk36_2 @ X965 @ X966 )
= X966 ) )
& ( ( X970 != X971 )
| ( X972 != X973 )
| ~ ( in @ X972 @ X970 )
| ( in @ X973 @ X971 ) )
& ( ~ ( in @ X976 @ X974 )
| ( in @ X977 @ X975 )
| ( X976 != X977 )
| ( X974 != X975 ) )
& ( ~ ( in @ X977 @ X975 )
| ( in @ X976 @ X974 )
| ( X976 != X977 )
| ( X974 != X975 ) )
& ( ( X978 @ ( esk38_2 @ X978 @ X979 ) )
| ~ ( X978 @ X979 )
| ~ ( X978 @ X981 )
| ~ ( X978 @ X982 )
| ( X981 = X982 ) )
& ( ( X979
!= ( esk38_2 @ X978 @ X979 ) )
| ~ ( X978 @ X979 )
| ~ ( X978 @ X981 )
| ~ ( X978 @ X982 )
| ( X981 = X982 ) )
& ( ( X984 @ ( esk42_2 @ X983 @ X984 ) )
| ( X983 @ ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X984 @ X990 )
| ( ( esk42_2 @ X983 @ X984 )
= X990 )
| ( X983 @ ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X984 @ ( esk42_2 @ X983 @ X984 ) )
| ( X987
!= ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X984 @ X990 )
| ( ( esk42_2 @ X983 @ X984 )
= X990 )
| ( X987
!= ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X983 @ ( esk44_2 @ X983 @ X984 ) )
| ( X984 @ ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X983 @ X994 )
| ( ( esk44_2 @ X983 @ X984 )
= X994 )
| ( X984 @ ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X983 @ ( esk44_2 @ X983 @ X984 ) )
| ( X991
!= ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X983 @ X994 )
| ( ( esk44_2 @ X983 @ X984 )
= X994 )
| ( X991
!= ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( ( esk39_2 @ X983 @ X984 )
= ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X984 @ ( esk42_2 @ X983 @ X984 ) )
| ( X983 @ ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X984 @ X990 )
| ( ( esk42_2 @ X983 @ X984 )
= X990 )
| ( X983 @ ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X984 @ ( esk42_2 @ X983 @ X984 ) )
| ( X987
!= ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X984 @ X990 )
| ( ( esk42_2 @ X983 @ X984 )
= X990 )
| ( X987
!= ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X983 @ ( esk44_2 @ X983 @ X984 ) )
| ( X984 @ ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X983 @ X994 )
| ( ( esk44_2 @ X983 @ X984 )
= X994 )
| ( X984 @ ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X983 @ ( esk44_2 @ X983 @ X984 ) )
| ( X991
!= ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X983 @ X994 )
| ( ( esk44_2 @ X983 @ X984 )
= X994 )
| ( X991
!= ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ~ ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ~ ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X984 @ ( esk42_2 @ X983 @ X984 ) )
| ( X983 @ ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X984 @ X990 )
| ( ( esk42_2 @ X983 @ X984 )
= X990 )
| ( X983 @ ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X984 @ ( esk42_2 @ X983 @ X984 ) )
| ( X987
!= ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X984 @ X990 )
| ( ( esk42_2 @ X983 @ X984 )
= X990 )
| ( X987
!= ( esk41_3 @ X983 @ X984 @ X987 ) )
| ~ ( X983 @ X987 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X983 @ ( esk44_2 @ X983 @ X984 ) )
| ( X984 @ ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X983 @ X994 )
| ( ( esk44_2 @ X983 @ X984 )
= X994 )
| ( X984 @ ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ( X983 @ ( esk44_2 @ X983 @ X984 ) )
| ( X991
!= ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( ~ ( X983 @ X994 )
| ( ( esk44_2 @ X983 @ X984 )
= X994 )
| ( X991
!= ( esk43_3 @ X983 @ X984 @ X991 ) )
| ~ ( X984 @ X991 )
| ( X983 @ ( esk39_2 @ X983 @ X984 ) )
| ( X984 @ ( esk40_2 @ X983 @ X984 ) ) )
& ( emptyset = emptyset )
& ( ( X995 != X996 )
| ( X997 != X998 )
| ( ( setadjoin @ X995 @ X997 )
= ( setadjoin @ X996 @ X998 ) ) )
& ( ( X999 != X1000 )
| ( ( powerset @ X999 )
= ( powerset @ X1000 ) ) )
& ( ( X1001 != X1002 )
| ( ( setunion @ X1001 )
= ( setunion @ X1002 ) ) )
& ( omega = omega )
& ( ( X1003 @ ( esk45_2 @ X1003 @ X1004 ) )
| ~ ( X1003 @ X1004 )
| ~ ( X1003 @ X1006 )
| ~ ( X1003 @ X1007 )
| ( X1006 = X1007 ) )
& ( ( X1004
!= ( esk45_2 @ X1003 @ X1004 ) )
| ~ ( X1003 @ X1004 )
| ~ ( X1003 @ X1006 )
| ~ ( X1003 @ X1007 )
| ( X1006 = X1007 ) )
& ( ( X1009 @ ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1008 @ ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( ( esk46_2 @ X1008 @ X1009 )
= ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1014
!= ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1008 @ ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( ( esk46_2 @ X1008 @ X1009 )
= ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1009 @ ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1012
!= ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( ( esk46_2 @ X1008 @ X1009 )
= ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1014
!= ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1012
!= ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( ( esk46_2 @ X1008 @ X1009 )
= ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1009 @ ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1008 @ ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ~ ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ~ ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1014
!= ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1008 @ ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ~ ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ~ ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1009 @ ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1012
!= ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ~ ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ~ ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1014
!= ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1012
!= ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ~ ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ~ ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1009 @ ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1008 @ ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1014
!= ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1008 @ ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1009 @ ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1012
!= ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( X1014
!= ( esk49_3 @ X1008 @ X1009 @ X1014 ) )
| ~ ( X1009 @ X1014 )
| ( ( descr @ X1008 )
= ( descr @ X1009 ) )
| ( X1012
!= ( esk48_3 @ X1008 @ X1009 @ X1012 ) )
| ~ ( X1008 @ X1012 )
| ( X1008 @ ( esk46_2 @ X1008 @ X1009 ) )
| ( X1009 @ ( esk47_2 @ X1008 @ X1009 ) ) )
& ( ( in @ ( esk50_4 @ X1016 @ X1017 @ X1018 @ X1019 ) @ X1016 )
| ( ( dsetconstr @ X1016 @ X1018 )
= ( dsetconstr @ X1017 @ X1019 ) )
| ( X1016 != X1017 ) )
& ( ( in @ ( esk51_4 @ X1016 @ X1017 @ X1018 @ X1019 ) @ X1017 )
| ( ( dsetconstr @ X1016 @ X1018 )
= ( dsetconstr @ X1017 @ X1019 ) )
| ( X1016 != X1017 ) )
& ( ( ( esk50_4 @ X1016 @ X1017 @ X1018 @ X1019 )
= ( esk51_4 @ X1016 @ X1017 @ X1018 @ X1019 ) )
| ( ( dsetconstr @ X1016 @ X1018 )
= ( dsetconstr @ X1017 @ X1019 ) )
| ( X1016 != X1017 ) )
& ( ~ ( X1018 @ ( esk50_4 @ X1016 @ X1017 @ X1018 @ X1019 ) )
| ~ ( X1019 @ ( esk51_4 @ X1016 @ X1017 @ X1018 @ X1019 ) )
| ( ( dsetconstr @ X1016 @ X1018 )
= ( dsetconstr @ X1017 @ X1019 ) )
| ( X1016 != X1017 ) )
& ( ( X1018 @ ( esk50_4 @ X1016 @ X1017 @ X1018 @ X1019 ) )
| ( X1019 @ ( esk51_4 @ X1016 @ X1017 @ X1018 @ X1019 ) )
| ( ( dsetconstr @ X1016 @ X1018 )
= ( dsetconstr @ X1017 @ X1019 ) )
| ( X1016 != X1017 ) )
& ( ( in @ ( esk52_2 @ X1022 @ X1023 ) @ X1022 )
| ( subset @ X1022 @ X1023 ) )
& ( ~ ( in @ ( esk52_2 @ X1022 @ X1023 ) @ X1023 )
| ( subset @ X1022 @ X1023 ) )
& ( ( X1025 != X1026 )
| ( subset @ X1026 @ X1025 ) )
& ( ( X1027 != X1028 )
| ( subset @ X1027 @ X1028 ) )
& ( ( in @ ( esk53_2 @ X1029 @ X1030 ) @ X1029 )
| ( subset @ X1029 @ X1030 ) )
& ( ~ ( in @ ( esk53_2 @ X1029 @ X1030 ) @ X1030 )
| ( subset @ X1029 @ X1030 ) )
& ( subset @ emptyset @ X1032 )
& ( ~ ( subset @ X1033 @ X1034 )
| ~ ( in @ X1035 @ X1033 )
| ( in @ X1035 @ X1034 ) )
& ( ~ ( subset @ X1036 @ X1037 )
| ( in @ X1038 @ X1037 )
| ~ ( in @ X1038 @ X1036 ) )
& ( ~ ( in @ X1041 @ X1039 )
| ( in @ X1041 @ X1040 )
| ~ ( subset @ X1039 @ X1040 ) )
& ( ( subset @ X1042 @ X1043 )
| ( X1042 != X1043 ) )
& ( ~ ( in @ X1046 @ X1044 )
| ( in @ X1046 @ X1045 )
| ( X1044 != X1045 ) )
& ( subset @ X1047 @ X1047 )
& ( ~ ( subset @ X1048 @ X1049 )
| ~ ( subset @ X1049 @ X1050 )
| ( subset @ X1048 @ X1050 ) )
& ( subset @ X1052 @ ( setadjoin @ X1051 @ X1052 ) )
& ( ~ ( subset @ X1053 @ X1055 )
| ( subset @ X1053 @ ( setadjoin @ X1054 @ X1055 ) ) )
& ( ~ ( subset @ X1056 @ X1057 )
| ( in @ X1056 @ ( powerset @ X1057 ) ) )
& ( ~ ( subset @ X1058 @ X1059 )
| ~ ( subset @ X1059 @ X1058 )
| ( X1058 = X1059 ) )
& ( ~ ( subset @ X1060 @ emptyset )
| ( X1060 = emptyset ) )
& ( ~ ( subset @ X1062 @ X1061 )
| ( in @ X1062 @ ( powerset @ X1061 ) ) )
& ( ~ ( in @ X1064 @ ( powerset @ X1063 ) )
| ( subset @ X1064 @ X1063 ) )
& ( in @ X1065 @ ( powerset @ X1065 ) )
& ( ~ ( subset @ X1066 @ X1067 )
| ( subset @ ( powerset @ X1066 ) @ ( powerset @ X1067 ) ) )
& ( in @ ( dsetconstr @ X1068 @ X1069 ) @ ( powerset @ X1068 ) )
& ( subset @ ( dsetconstr @ X1070 @ X1071 ) @ X1070 )
& ( ~ ( in @ X1074 @ X1072 )
| ( in @ X1074 @ ( binunion @ X1072 @ X1073 ) ) )
& ( in @ X1076 @ ( setadjoin @ X1075 @ ( setadjoin @ X1076 @ emptyset ) ) )
& ( ~ ( in @ X1079 @ X1078 )
| ( in @ X1079 @ ( binunion @ X1077 @ X1078 ) ) )
& ( ( in @ X1082 @ X1081 )
| X1083
| ( in @ X1082 @ X1080 )
| ~ ( in @ X1082 @ ( binunion @ X1080 @ X1081 ) ) )
& ( ~ X1083
| X1083
| ( in @ X1082 @ X1080 )
| ~ ( in @ X1082 @ ( binunion @ X1080 @ X1081 ) ) )
& ( ( in @ X1082 @ X1081 )
| X1083
| ~ X1083
| ~ ( in @ X1082 @ ( binunion @ X1080 @ X1081 ) ) )
& ( ~ X1083
| X1083
| ~ X1083
| ~ ( in @ X1082 @ ( binunion @ X1080 @ X1081 ) ) )
& ( ~ ( in @ X1086 @ ( binunion @ X1084 @ X1085 ) )
| ( in @ X1086 @ X1084 )
| ( in @ X1086 @ X1085 ) )
& ( subset @ X1087 @ ( binunion @ X1087 @ X1088 ) )
& ( subset @ X1090 @ ( binunion @ X1089 @ X1090 ) )
& ( ~ ( in @ X1093 @ X1091 )
| ~ ( in @ X1093 @ X1092 )
| ( in @ X1093 @ ( binintersect @ X1091 @ X1092 ) ) )
& ( ~ ( subset @ X1096 @ X1094 )
| ~ ( subset @ X1096 @ X1095 )
| ( subset @ X1096 @ ( binintersect @ X1094 @ X1095 ) ) )
& ( ~ ( in @ X1099 @ ( binintersect @ X1097 @ X1098 ) )
| ( in @ X1099 @ X1097 ) )
& ( subset @ ( binintersect @ X1100 @ X1101 ) @ X1100 )
& ( ~ ( subset @ X1102 @ X1103 )
| ( ( binintersect @ X1102 @ X1103 )
= X1102 ) )
& ( ( ( binintersect @ X1104 @ X1105 )
!= X1105 )
| ( subset @ X1105 @ X1104 ) )
& ( ~ ( in @ X1108 @ ( binintersect @ X1106 @ X1107 ) )
| ( in @ X1108 @ X1107 ) )
& ( ( in @ ( esk54_2 @ X1109 @ X1110 ) @ X1109 )
| ( ( binintersect @ X1109 @ X1110 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1109 @ X1110 ) @ X1110 )
| ( ( binintersect @ X1109 @ X1110 )
= emptyset ) )
& ( subset @ ( binintersect @ X1112 @ X1113 ) @ X1113 )
& ( ~ ( subset @ X1115 @ X1114 )
| ( ( binintersect @ X1114 @ X1115 )
= X1115 ) )
& ( ( ( binintersect @ X1116 @ X1117 )
!= X1116 )
| ( subset @ X1116 @ X1117 ) )
& ( ( binintersect @ X1118 @ ( binunion @ X1119 @ X1120 ) )
= ( binunion @ ( binintersect @ X1118 @ X1119 ) @ ( binintersect @ X1118 @ X1120 ) ) )
& ( ~ ( in @ X1123 @ X1121 )
| ( in @ X1123 @ X1122 )
| ( in @ X1123 @ ( setminus @ X1121 @ X1122 ) ) )
& ( ~ ( in @ X1126 @ ( setminus @ X1124 @ X1125 ) )
| ( in @ X1126 @ X1124 ) )
& ( ~ ( in @ X1129 @ ( setminus @ X1127 @ X1128 ) )
| ~ ( in @ X1129 @ X1128 ) )
& ( ~ ( subset @ X1130 @ X1131 )
| ( ( setminus @ X1130 @ X1131 )
= emptyset ) )
& ( ( in @ X1134 @ ( setminus @ X1132 @ X1133 ) )
| ~ ( in @ X1134 @ X1132 )
| ( in @ X1134 @ X1133 ) )
& ( ( in @ X1137 @ ( setminus @ X1135 @ X1136 ) )
| ( in @ X1137 @ X1136 )
| ~ ( in @ X1137 @ X1135 ) )
& ( ( in @ X1140 @ X1138 )
| ~ ( in @ X1140 @ ( setminus @ X1138 @ X1139 ) ) )
& ( ~ ( in @ X1143 @ X1142 )
| ~ ( in @ X1143 @ ( setminus @ X1141 @ X1142 ) ) )
& ( subset @ ( setminus @ X1144 @ X1145 ) @ X1144 )
& ( ( ( setminus @ X1146 @ X1147 )
!= emptyset )
| ( subset @ X1146 @ X1147 ) )
& ( ~ ( in @ X1150 @ X1148 )
| X1151
| ( in @ X1150 @ X1148 )
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ( in @ X1150 @ X1149 )
| X1151
| ( in @ X1150 @ X1148 )
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ~ X1151
| X1151
| ( in @ X1150 @ X1148 )
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ~ ( in @ X1150 @ X1148 )
| X1151
| ~ ( in @ X1150 @ X1149 )
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ( in @ X1150 @ X1149 )
| X1151
| ~ ( in @ X1150 @ X1149 )
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ~ X1151
| X1151
| ~ ( in @ X1150 @ X1149 )
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ~ ( in @ X1150 @ X1148 )
| X1151
| ~ X1151
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ( in @ X1150 @ X1149 )
| X1151
| ~ X1151
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ~ X1151
| X1151
| ~ X1151
| ~ ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ~ ( in @ X1154 @ X1152 )
| ( in @ X1154 @ X1153 )
| ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ( in @ X1157 @ X1155 )
| ~ ( in @ X1157 @ X1156 )
| ( in @ X1157 @ ( symdiff @ X1155 @ X1156 ) ) )
& ( ~ ( in @ X1160 @ X1158 )
| ~ ( in @ X1160 @ X1159 )
| ~ ( in @ X1160 @ ( symdiff @ X1158 @ X1159 ) ) )
& ( ( in @ X1163 @ X1161 )
| ( in @ X1163 @ X1162 )
| ~ ( in @ X1163 @ ( symdiff @ X1161 @ X1162 ) ) )
& ( in @ X1165 @ ( setadjoin @ X1164 @ ( setadjoin @ X1165 @ emptyset ) ) )
& ~ ( in @ esk55_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_176])])])])])])]) ).
thf(c_0_178,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_177]) ).
thf(c_0_179,negated_conjecture,
! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
thf(c_0_180,negated_conjecture,
~ ( in @ esk55_0 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk55_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk55_0 @ ( setadjoin @ esk56_0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
thf(c_0_181,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ X3 @ X4 ) ) )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
thf(c_0_182,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_179])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU617^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 17:57:22 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.45 Running higher-order theorem proving
% 0.19/0.45 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
% 0.19/0.57 # Version: 3.1.0-ho
% 0.19/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.19/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.19/0.57 # Starting pre_casc_3 with 300s (1) cores
% 0.19/0.57 # Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.19/0.57 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 # Starting new_ho_5 with 300s (1) cores
% 0.19/0.57 # new_bool_3 with pid 26518 completed with status 0
% 0.19/0.57 # Result found by new_bool_3
% 0.19/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.19/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.19/0.57 # Starting pre_casc_3 with 300s (1) cores
% 0.19/0.57 # Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.19/0.57 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.57 # Search class: HGHSM-FSLS31-MHFMMSBN
% 0.19/0.57 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.57 # Starting pre_casc_7 with 181s (1) cores
% 0.19/0.57 # pre_casc_7 with pid 26524 completed with status 0
% 0.19/0.57 # Result found by pre_casc_7
% 0.19/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.19/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.19/0.57 # Starting pre_casc_3 with 300s (1) cores
% 0.19/0.57 # Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.19/0.57 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.57 # Search class: HGHSM-FSLS31-MHFMMSBN
% 0.19/0.57 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.57 # Starting pre_casc_7 with 181s (1) cores
% 0.19/0.57 # Preprocessing time : 0.005 s
% 0.19/0.57
% 0.19/0.57 # Proof found!
% 0.19/0.57 # SZS status Theorem
% 0.19/0.57 # SZS output start CNFRefutation
% See solution above
% 1.10/0.57 # Parsed axioms : 291
% 1.10/0.57 # Removed by relevancy pruning/SinE : 156
% 1.10/0.57 # Initial clauses : 256
% 1.10/0.57 # Removed in clause preprocessing : 24
% 1.10/0.57 # Initial clauses in saturation : 232
% 1.10/0.57 # Processed clauses : 411
% 1.10/0.57 # ...of these trivial : 11
% 1.10/0.57 # ...subsumed : 166
% 1.10/0.57 # ...remaining for further processing : 234
% 1.10/0.57 # Other redundant clauses eliminated : 19
% 1.10/0.57 # Clauses deleted for lack of memory : 0
% 1.10/0.57 # Backward-subsumed : 2
% 1.10/0.57 # Backward-rewritten : 2
% 1.10/0.57 # Generated clauses : 1445
% 1.10/0.57 # ...of the previous two non-redundant : 1139
% 1.10/0.57 # ...aggressively subsumed : 0
% 1.10/0.57 # Contextual simplify-reflections : 0
% 1.10/0.57 # Paramodulations : 1425
% 1.10/0.57 # Factorizations : 0
% 1.10/0.57 # NegExts : 0
% 1.10/0.57 # Equation resolutions : 19
% 1.10/0.57 # Disequality decompositions : 0
% 1.10/0.57 # Total rewrite steps : 280
% 1.10/0.57 # ...of those cached : 233
% 1.10/0.57 # Propositional unsat checks : 0
% 1.10/0.57 # Propositional check models : 0
% 1.10/0.57 # Propositional check unsatisfiable : 0
% 1.10/0.57 # Propositional clauses : 0
% 1.10/0.57 # Propositional clauses after purity: 0
% 1.10/0.57 # Propositional unsat core size : 0
% 1.10/0.57 # Propositional preprocessing time : 0.000
% 1.10/0.57 # Propositional encoding time : 0.000
% 1.10/0.57 # Propositional solver time : 0.000
% 1.10/0.57 # Success case prop preproc time : 0.000
% 1.10/0.57 # Success case prop encoding time : 0.000
% 1.10/0.57 # Success case prop solver time : 0.000
% 1.10/0.57 # Current number of processed clauses : 224
% 1.10/0.57 # Positive orientable unit clauses : 33
% 1.10/0.57 # Positive unorientable unit clauses: 0
% 1.10/0.57 # Negative unit clauses : 48
% 1.10/0.57 # Non-unit-clauses : 143
% 1.10/0.57 # Current number of unprocessed clauses: 955
% 1.10/0.57 # ...number of literals in the above : 2541
% 1.10/0.57 # Current number of archived formulas : 0
% 1.10/0.57 # Current number of archived clauses : 4
% 1.10/0.57 # Clause-clause subsumption calls (NU) : 1756
% 1.10/0.57 # Rec. Clause-clause subsumption calls : 1326
% 1.10/0.57 # Non-unit clause-clause subsumptions : 129
% 1.10/0.57 # Unit Clause-clause subsumption calls : 415
% 1.10/0.57 # Rewrite failures with RHS unbound : 0
% 1.10/0.57 # BW rewrite match attempts : 6
% 1.10/0.57 # BW rewrite match successes : 2
% 1.10/0.57 # Condensation attempts : 411
% 1.10/0.57 # Condensation successes : 4
% 1.10/0.57 # Termbank termtop insertions : 50426
% 1.10/0.57 # Search garbage collected termcells : 13102
% 1.10/0.57
% 1.10/0.57 # -------------------------------------------------
% 1.10/0.57 # User time : 0.075 s
% 1.10/0.57 # System time : 0.013 s
% 1.10/0.57 # Total time : 0.089 s
% 1.10/0.57 # Maximum resident set size: 5080 pages
% 1.10/0.57
% 1.10/0.57 # -------------------------------------------------
% 1.10/0.57 # User time : 0.081 s
% 1.10/0.57 # System time : 0.018 s
% 1.10/0.57 # Total time : 0.099 s
% 1.10/0.57 # Maximum resident set size: 2072 pages
% 1.10/0.57 % E---3.1 exiting
% 1.10/0.57 % E exiting
%------------------------------------------------------------------------------