%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU616^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 03:28:35 EDT 2024
% Result : Timeout 299.71s 300.03s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 340
% Syntax : Number of formulae : 385 ( 23 unt; 205 typ; 0 def)
% Number of atoms : 1506 ( 357 equ; 0 cnn)
% Maximal formula atoms : 458 ( 8 avg)
% Number of connectives : 5727 ( 503 ~; 532 |; 333 &;3422 @)
% ( 196 <=>; 741 =>; 0 <=; 0 <~>)
% Maximal formula depth : 569 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 323 ( 323 >; 0 *; 0 +; 0 <<)
% Number of symbols : 208 ( 205 usr; 139 con; 0-4 aty)
% Number of variables : 1276 ( 67 ^1103 !; 106 ?;1276 :)
% 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,
epred1_0: $o ).
thf(decl_176,type,
esk1_2: $i > $i > $i ).
thf(decl_177,type,
esk2_2: $i > $i > $i ).
thf(decl_178,type,
esk3_2: $i > $i > $i ).
thf(decl_179,type,
esk4_1: $i > $i ).
thf(decl_180,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_181,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_182,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_183,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_184,type,
esk9_1: $i > $i ).
thf(decl_185,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_186,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_187,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_188,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_189,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_190,type,
esk15_2: $i > $i > $i ).
thf(decl_191,type,
esk16_2: $i > $i > $i ).
thf(decl_192,type,
esk17_1: $i > $i ).
thf(decl_193,type,
esk18_1: $i > $i ).
thf(decl_194,type,
esk19_1: $i > $i ).
thf(decl_195,type,
esk20_2: $i > $i > $i ).
thf(decl_196,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_197,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_198,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_199,type,
esk24_1: $i > $i ).
thf(decl_200,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_201,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_202,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_203,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_204,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_205,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_206,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_207,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_208,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_209,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_210,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_211,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_212,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_213,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_214,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_215,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_216,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_217,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_218,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_219,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_220,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_221,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_222,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_223,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_224,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_225,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_226,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_227,type,
esk52_2: $i > $i > $i ).
thf(decl_228,type,
esk53_2: $i > $i > $i ).
thf(decl_229,type,
esk54_2: $i > $i > $i ).
thf(decl_230,type,
esk55_0: $i ).
thf(decl_231,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(secondinupair,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
=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
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(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(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(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
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(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(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(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(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(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(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(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(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(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_134,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_135,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_136,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_137,plain,
( 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_138,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_139,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_140,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_141,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_142,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_143,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_144,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_145,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_146,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_147,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_148,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_149,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_150,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X400: $i] :
( ( X1 @ X400 )
& ! [X401: $i] :
( ( X1 @ X401 )
=> ( X400 = X401 ) ) )
=> ( ? [X402: $i] :
( ( X17 @ X402 )
& ! [X403: $i] :
( ( X17 @ X403 )
=> ( X402 = X403 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_134,c_0_135]) ).
thf(c_0_151,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X386: $i] :
( ( X1 @ X386 )
& ! [X387: $i] :
( ( X1 @ X387 )
=> ( X386 = X387 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_136,c_0_135]) ).
thf(c_0_152,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X388: $i] :
( ( X1 @ X388 )
& ! [X389: $i] :
( ( X1 @ X389 )
=> ( X388 = X389 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_137,c_0_135]) ).
thf(c_0_153,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X390: $i] :
( ( X1 @ X390 )
& ! [X391: $i] :
( ( X1 @ X391 )
=> ( X390 = X391 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_138,c_0_135]) ).
thf(c_0_154,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X392: $i] :
( ( X1 @ X392 )
& ! [X393: $i] :
( ( X1 @ X393 )
=> ( X392 = X393 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_139,c_0_135]) ).
thf(c_0_155,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X394: $i] :
( ( X1 @ X394 )
& ! [X395: $i] :
( ( X1 @ X395 )
=> ( X394 = X395 ) ) )
<=> ? [X396: $i] :
( ( X17 @ X396 )
& ! [X397: $i] :
( ( X17 @ X397 )
=> ( X396 = X397 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_140,c_0_135]) ).
thf(c_0_156,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X398: $i] :
( ( X1 @ X398 )
& ! [X399: $i] :
( ( X1 @ X399 )
=> ( X398 = X399 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_141,c_0_135]) ).
thf(c_0_157,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_158,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_159,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_160,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_142]) ).
thf(c_0_161,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X384: $i] :
( ( X1 @ X384 )
& ! [X385: $i] :
( ( X1 @ X385 )
=> ( X384 = X385 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_143,c_0_135]) ).
thf(c_0_162,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_163,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_142]) ).
thf(c_0_164,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_144,c_0_142]) ).
thf(c_0_165,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_142]) ).
thf(c_0_166,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_167,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X382: $i] :
( ( X1 @ X382 )
& ! [X383: $i] :
( ( X1 @ X383 )
=> ( X382 = X383 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_145,c_0_135]) ).
thf(c_0_168,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X380: $i] :
( ( X1 @ X380 )
& ! [X381: $i] :
( ( X1 @ X381 )
=> ( X380 = X381 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_146,c_0_135]) ).
thf(c_0_169,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_170,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_171,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_172,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X378: $i] :
( ( X1 @ X378 )
& ! [X379: $i] :
( ( X1 @ X379 )
=> ( X378 = X379 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_147,c_0_135]) ).
thf(c_0_173,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X376: $i] :
( ( X6 @ X2 @ X376 )
& ! [X377: $i] :
( ( X6 @ X2 @ X377 )
=> ( X376 = X377 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_148,c_0_135]) ).
thf(c_0_174,plain,
( epred1_0
<=> ! [X433: $i] :
? [X434: $i] :
( ! [X435: $i] :
( ( in @ X435 @ X434 )
=> ! [X436: $i] :
( ( in @ X436 @ X435 )
=> ( in @ X436 @ X433 ) ) )
& ! [X437: $i,X438: $i] :
( ( ( in @ X437 @ X433 )
& ( in @ X438 @ X433 ) )
=> ( ! [X439: $i] :
( ( in @ X439 @ X434 )
=> ( ( in @ X437 @ X439 )
<=> ( in @ X438 @ X439 ) ) )
=> ( X437 = X438 ) ) )
& ! [X440: $i,X441: $i] :
( ( ( in @ X440 @ X434 )
& ( in @ X441 @ X434 ) )
=> ( ! [X442: $i] :
( ( in @ X442 @ X440 )
=> ( in @ X442 @ X441 ) )
| ! [X443: $i] :
( ( in @ X443 @ X441 )
=> ( in @ X443 @ X440 ) ) ) )
& ! [X444: $i] :
( ( ! [X445: $i] :
( ( in @ X445 @ X444 )
=> ( in @ X445 @ X433 ) )
& ? [X446: $i] : ( in @ X446 @ X444 ) )
=> ? [X447: $i,X448: $i] :
( ( in @ X447 @ X434 )
& ( in @ X448 @ X444 )
& ~ ? [X449: $i] :
( ( in @ X449 @ X447 )
& ( in @ X449 @ X444 ) )
& ! [X450: $i] :
( ( in @ X450 @ X434 )
=> ( ! [X451: $i] :
( ( in @ X451 @ X450 )
=> ( in @ X451 @ X447 ) )
| ( in @ X448 @ X450 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_175,negated_conjecture,
~ ( ! [X404: $i,X405: $i] :
( ! [X406: $i] :
( ( in @ X406 @ X404 )
<=> ( in @ X406 @ X405 ) )
=> ( X404 = X405 ) )
=> ( ! [X407: $i] :
~ ( in @ X407 @ emptyset )
=> ( ! [X408: $i,X409: $i,X410: $i] :
( ( in @ X410 @ ( setadjoin @ X408 @ X409 ) )
<=> ( ( X410 = X408 )
| ( in @ X410 @ X409 ) ) )
=> ( ! [X411: $i,X412: $i] :
( ( in @ X412 @ ( powerset @ X411 ) )
<=> ! [X413: $i] :
( ( in @ X413 @ X412 )
=> ( in @ X413 @ X411 ) ) )
=> ( ! [X414: $i,X415: $i] :
( ( in @ X415 @ ( setunion @ X414 ) )
<=> ? [X416: $i] :
( ( in @ X415 @ X416 )
& ( in @ X416 @ X414 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X417: $i] :
( ( in @ X417 @ omega )
=> ( in @ ( setadjoin @ X417 @ X417 ) @ omega ) )
=> ( ! [X418: $i] :
( ( ( in @ emptyset @ X418 )
& ! [X419: $i] :
( ( ( in @ X419 @ omega )
& ( in @ X419 @ X418 ) )
=> ( in @ ( setadjoin @ X419 @ X419 ) @ X418 ) ) )
=> ! [X420: $i] :
( ( in @ X420 @ omega )
=> ( in @ X420 @ X418 ) ) )
=> ( ! [X421: $i > $i > $o,X422: $i] :
( ! [X423: $i] :
( ( in @ X423 @ X422 )
=> ? [X424: $i] :
( ( X421 @ X423 @ X424 )
& ! [X425: $i] :
( ( X421 @ X423 @ X425 )
=> ( X424 = X425 ) ) ) )
=> ? [X426: $i] :
! [X427: $i] :
( ( in @ X427 @ X426 )
<=> ? [X428: $i] :
( ( in @ X428 @ X422 )
& ( X421 @ X428 @ X427 ) ) ) )
=> ( ! [X429: $i] :
( ? [X430: $i] : ( in @ X430 @ X429 )
=> ? [X431: $i] :
( ( in @ X431 @ X429 )
& ~ ? [X432: $i] :
( ( in @ X432 @ X431 )
& ( in @ X432 @ X429 ) ) ) )
=> ( epred1_0
=> ( ! [X452: $i > $o] :
( ? [X453: $i] :
( ( X452 @ X453 )
& ! [X454: $i] :
( ( X452 @ X454 )
=> ( X453 = X454 ) ) )
=> ( X452
@ ( descr
@ ^ [Z0: $i] : ( X452 @ Z0 ) ) ) )
=> ( ! [X455: $i,X456: $i > $o,X457: $i] :
( ( in @ X457 @ X455 )
=> ( ( X456 @ X457 )
=> ( in @ X457 @ ( dsetconstr @ X455 @ X456 ) ) ) )
=> ( ! [X458: $i,X459: $i > $o,X460: $i] :
( ( in @ X460 @ ( dsetconstr @ X458 @ X459 ) )
=> ( in @ X460 @ X458 ) )
=> ( ! [X461: $i,X462: $i > $o,X463: $i] :
( ( in @ X463 @ ( dsetconstr @ X461 @ X462 ) )
=> ( X462 @ X463 ) )
=> ( ! [X464: $i > $o] :
( ? [X465: $i] :
( ( X464 @ X465 )
& ! [X466: $i] :
( ( X464 @ X466 )
=> ( X465 = X466 ) ) )
=> ? [X467: $i] :
( ( X464 @ X467 )
& ! [X468: $i] :
( ( X464 @ X468 )
=> ( X467 = X468 ) ) ) )
=> ( ! [X469: $o,X470: $i] :
( ( in @ X470 @ ( prop2set @ X469 ) )
=> X469 )
=> ( ! [X471: $i] :
( ( in @ X471 @ emptyset )
=> ! [X472: $o] : X472 )
=> ( ! [X473: $i] :
( ( in @ X473 @ emptyset )
=> ~ $true )
=> ( ! [X474: $i] :
~ ( in @ X474 @ emptyset )
=> ( ! [X475: $i > $o] :
( ? [X476: $i] :
( ( X475 @ X476 )
& ! [X477: $i] :
( ( X475 @ X477 )
=> ( X476 = X477 ) ) )
=> ? [X478: $i] : ( X475 @ X478 ) )
=> ( ! [X479: $i,X480: $i] :
( ! [X481: $i] :
( ( in @ X481 @ X479 )
=> ( in @ X481 @ X480 ) )
=> ( ! [X482: $i] :
( ( in @ X482 @ X480 )
=> ( in @ X482 @ X479 ) )
=> ( X479 = X480 ) ) )
=> ( ! [X483: $i] :
( ! [X484: $i] :
~ ( in @ X484 @ X483 )
=> ( X483 = emptyset ) )
=> ( ! [X485: $i] :
( ! [X486: $i] :
~ ( in @ X486 @ X485 )
=> ( X485 = emptyset ) )
=> ( ! [X487: $i,X488: $i > $o,X489: $i] :
( ( in @ X489 @ X487 )
=> ( ( in @ X489 @ ( dsetconstr @ X487 @ X488 ) )
<=> ( X488 @ X489 ) ) )
=> ( ! [X490: $i] :
( ( X490 != emptyset )
=> ? [X491: $i] : ( in @ X491 @ X490 ) )
=> ( ! [X492: $i,X493: $i > $o,X494: $i] :
( ( in @ X494 @ X492 )
=> ( ( X493 @ X494 )
=> ( ( dsetconstr @ X492 @ X493 )
!= emptyset ) ) )
=> ( ! [X495: $i] :
( ? [X496: $i] : ( in @ X496 @ X495 )
=> ( X495 != emptyset ) )
=> ( ! [X497: $i,X498: $i] : ( in @ X497 @ ( setadjoin @ X497 @ X498 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X499: $i,X500: $i,X501: $i] :
( ( in @ X501 @ X500 )
=> ( in @ X501 @ ( setadjoin @ X499 @ X500 ) ) )
=> ( ! [X502: $i,X503: $i,X504: $i] :
( ( in @ X504 @ ( setadjoin @ X502 @ X503 ) )
=> ! [X505: $o] :
( ( ( X504 = X502 )
=> X505 )
=> ( ( ( in @ X504 @ X503 )
=> X505 )
=> X505 ) ) )
=> ( ! [X506: $i,X507: $i,X508: $i] :
( ( in @ X508 @ ( setadjoin @ X506 @ X507 ) )
=> ( ( X508 = X506 )
| ( in @ X508 @ X507 ) ) )
=> ( ! [X509: $i] :
( ( dsetconstr @ X509
@ ^ [Z0: $i] : $true )
= X509 )
=> ( ! [X510: $i,X511: $i] :
( ! [X512: $i] :
( ( in @ X512 @ X511 )
=> ( in @ X512 @ X510 ) )
=> ( in @ X511 @ ( powerset @ X510 ) ) )
=> ( ! [X513: $i] : ( in @ emptyset @ ( powerset @ X513 ) )
=> ( ! [X514: $i] : ( in @ emptyset @ ( powerset @ X514 ) )
=> ( ! [X515: $i,X516: $i,X517: $i] :
( ( in @ X516 @ ( powerset @ X515 ) )
=> ( ( in @ X517 @ X516 )
=> ( in @ X517 @ X515 ) ) )
=> ( ! [X518: $i,X519: $i,X520: $i] :
( ( in @ X519 @ X520 )
=> ( ( in @ X520 @ X518 )
=> ( in @ X519 @ ( setunion @ X518 ) ) ) )
=> ( ! [X521: $i,X522: $i] :
( ( in @ X522 @ ( setunion @ X521 ) )
=> ! [X523: $o] :
( ! [X524: $i] :
( ( in @ X522 @ X524 )
=> ( ( in @ X524 @ X521 )
=> X523 ) )
=> X523 ) )
=> ( ! [X525: $i,X526: $i] :
( ( in @ X526 @ X525 )
=> ( in @ X526 @ ( powerset @ ( setunion @ X525 ) ) ) )
=> ( ! [X527: $i > $o] :
( ? [X528: $i] :
( ( X527 @ X528 )
& ! [X529: $i] :
( ( X527 @ X529 )
=> ( X528 = X529 ) ) )
=> ? [X530: $i] :
! [X531: $i] :
( ( X527 @ X531 )
<=> ( X531 = X530 ) ) )
=> ( ! [X532: $i] :
( ( X532 != emptyset )
=> ? [X533: $i] :
( ( in @ X533 @ X532 )
& $true ) )
=> ( ! [X534: $i,X535: $i] :
( ( in @ X534 @ ( setadjoin @ X535 @ emptyset ) )
=> ( X534 = X535 ) )
=> ( ! [X536: $i,X537: $i] :
( ( X536 != X537 )
=> ~ ( in @ X537 @ ( setadjoin @ X536 @ emptyset ) ) )
=> ( ! [X538: $i,X539: $i] :
( ( X538 = X539 )
=> ( in @ X538 @ ( setadjoin @ X539 @ emptyset ) ) )
=> ( ! [X540: $i,X541: $i] :
( ( in @ X540 @ ( setadjoin @ X541 @ emptyset ) )
=> ( in @ X541 @ ( setadjoin @ X540 @ emptyset ) ) )
=> ( ! [X542: $i,X543: $i,X544: $i] :
( ( in @ X544 @ ( setadjoin @ X542 @ ( setadjoin @ X543 @ emptyset ) ) )
=> ( ( X544 = X542 )
| ( X544 = X543 ) ) )
=> ( ! [X545: $i,X546: $i] : ( in @ X545 @ ( setadjoin @ X545 @ ( setadjoin @ X546 @ emptyset ) ) )
=> ( ! [X547: $i,X548: $i] : ( in @ X548 @ ( setadjoin @ X547 @ ( setadjoin @ X548 @ emptyset ) ) )
=> ( ! [X549: $i,X550: $i > $o] :
( ? [X551: $i] :
( ( in @ X551 @ X549 )
& ( X550 @ X551 ) )
=> ( ( ( dsetconstr @ X549 @ X550 )
= emptyset )
=> ~ $true ) )
=> ( ! [X552: $i > $o,X553: $i] :
( ( in @ X553 @ emptyset )
=> ( X552 @ X553 ) )
=> ( ! [X554: $i,X555: $i > $o] :
( ~ ! [X556: $i] :
( ( in @ X556 @ X554 )
=> ( X555 @ X556 ) )
=> ? [X557: $i] :
( ( in @ X557 @ X554 )
& ~ ( X555 @ X557 ) ) )
=> ( ! [X558: $i,X559: $i > $o] :
( ! [X560: $i] :
( ( in @ X560 @ X558 )
=> ~ ( X559 @ X560 ) )
=> ~ ? [X561: $i] :
( ( in @ X561 @ X558 )
& ( X559 @ X561 ) ) )
=> ( ! [X562: $i,X563: $i > $o] :
( ~ ? [X564: $i] :
( ( in @ X564 @ X562 )
& ( X563 @ X564 ) )
=> ! [X565: $i] :
( ( in @ X565 @ X562 )
=> ~ ( X563 @ X565 ) ) )
=> ( ! [X566: $i,X567: $i > $o] :
( ? [X568: $i] :
( ( in @ X568 @ X566 )
& ~ ( X567 @ X568 ) )
=> ~ ! [X569: $i] :
( ( in @ X569 @ X566 )
=> ( X567 @ X569 ) ) )
=> ( ! [X570: $o] :
( X570
=> ( in @ emptyset @ ( prop2set @ X570 ) ) )
=> ( prop2set2propI
=> ( ! [X571: $i,X572: $i > $o] :
( ~ ? [X573: $i] :
( ( in @ X573 @ X571 )
& ( X572 @ X573 ) )
=> ! [X574: $i] :
( ( in @ X574 @ X571 )
=> ~ ( X572 @ X574 ) ) )
=> ( ! [X575: $i,X576: $i > $o] :
( ~ ! [X577: $i] :
( ( in @ X577 @ X575 )
=> ( X576 @ X577 ) )
=> ? [X578: $i] :
( ( in @ X578 @ X575 )
& ~ ( X576 @ X578 ) ) )
=> ( ! [X579: $i > $o] :
( ? [X580: $i] :
( ( X579 @ X580 )
& ! [X581: $i] :
( ( X579 @ X581 )
=> ( X580 = X581 ) ) )
=> ? [X582: $i] :
( ( X579 @ X582 )
& ! [X583: $i] :
( ( X579 @ X583 )
=> ( X582 = X583 ) ) ) )
=> ( ! [X584: $i > $o] :
( ? [X585: $i] : ( X584 @ X585 )
=> ( ! [X586: $i,X587: $i] :
( ( X584 @ X586 )
=> ( ( X584 @ X587 )
=> ( X586 = X587 ) ) )
=> ? [X588: $i] :
( ( X584 @ X588 )
& ! [X589: $i] :
( ( X584 @ X589 )
=> ( X588 = X589 ) ) ) ) )
=> ( ! [X590: $i > $o] :
( ? [X591: $i] :
! [X592: $i] :
( ( X590 @ X592 )
<=> ( X592 = X591 ) )
=> ? [X593: $i] :
( ( X590 @ X593 )
& ! [X594: $i] :
( ( X590 @ X594 )
=> ( X593 = X594 ) ) ) )
=> ( ! [X595: $i,X596: $i] :
( ( X595 = X596 )
=> ! [X597: $i,X598: $i] :
( ( X597 = X598 )
=> ( ( in @ X597 @ X595 )
=> ( in @ X598 @ X596 ) ) ) )
=> ( ! [X599: $i,X600: $i] :
( ( X599 = X600 )
=> ! [X601: $i,X602: $i] :
( ( X601 = X602 )
=> ( ( in @ X601 @ X599 )
<=> ( in @ X602 @ X600 ) ) ) )
=> ( ! [X603: $i > $o] :
( ? [X604: $i] :
( ( X603 @ X604 )
& ! [X605: $i] :
( ( X603 @ X605 )
=> ( X604 = X605 ) ) )
=> ! [X606: $i,X607: $i] :
( ( X603 @ X606 )
=> ( ( X603 @ X607 )
=> ( X606 = X607 ) ) ) )
=> ( ! [X608: $i > $o,X609: $i > $o] :
( ! [X610: $i,X611: $i] :
( ( X610 = X611 )
=> ( ( X608 @ X610 )
<=> ( X609 @ X611 ) ) )
=> ( ? [X612: $i] :
( ( X608 @ X612 )
& ! [X613: $i] :
( ( X608 @ X613 )
=> ( X612 = X613 ) ) )
<=> ? [X614: $i] :
( ( X609 @ X614 )
& ! [X615: $i] :
( ( X609 @ X615 )
=> ( X614 = X615 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X616: $i,X617: $i] :
( ( X616 = X617 )
=> ! [X618: $i,X619: $i] :
( ( X618 = X619 )
=> ( ( setadjoin @ X616 @ X618 )
= ( setadjoin @ X617 @ X619 ) ) ) )
=> ( ! [X620: $i,X621: $i] :
( ( X620 = X621 )
=> ( ( powerset @ X620 )
= ( powerset @ X621 ) ) )
=> ( ! [X622: $i,X623: $i] :
( ( X622 = X623 )
=> ( ( setunion @ X622 )
= ( setunion @ X623 ) ) )
=> ( ( omega = omega )
=> ( ! [X624: $i > $o] :
( ? [X625: $i] :
( ( X624 @ X625 )
& ! [X626: $i] :
( ( X624 @ X626 )
=> ( X625 = X626 ) ) )
=> ! [X627: $i,X628: $i] :
( ( X624 @ X627 )
=> ( ( X624 @ X628 )
=> ( X627 = X628 ) ) ) )
=> ( ! [X629: $i > $o,X630: $i > $o] :
( ! [X631: $i,X632: $i] :
( ( X631 = X632 )
=> ( ( X629 @ X631 )
<=> ( X630 @ X632 ) ) )
=> ( ? [X633: $i] :
( ( X629 @ X633 )
& ! [X634: $i] :
( ( X629 @ X634 )
=> ( X633 = X634 ) ) )
=> ( ? [X635: $i] :
( ( X630 @ X635 )
& ! [X636: $i] :
( ( X630 @ X636 )
=> ( X635 = X636 ) ) )
=> ( ( descr @ X629 )
= ( descr @ X630 ) ) ) ) )
=> ( ! [X637: $i,X638: $i] :
( ( X637 = X638 )
=> ! [X639: $i > $o,X640: $i > $o] :
( ! [X641: $i] :
( ( in @ X641 @ X637 )
=> ! [X642: $i] :
( ( in @ X642 @ X638 )
=> ( ( X641 = X642 )
=> ( ( X639 @ X641 )
<=> ( X640 @ X642 ) ) ) ) )
=> ( ( dsetconstr @ X637 @ X639 )
= ( dsetconstr @ X638 @ X640 ) ) ) )
=> ( ! [X643: $i,X644: $i] :
( ! [X645: $i] :
( ( in @ X645 @ X643 )
=> ( in @ X645 @ X644 ) )
=> ( subset @ X643 @ X644 ) )
=> ( ! [X646: $i,X647: $i] :
( ( X646 = X647 )
=> ( subset @ X647 @ X646 ) )
=> ( ! [X648: $i,X649: $i] :
( ( X648 = X649 )
=> ( subset @ X648 @ X649 ) )
=> ( ! [X650: $i,X651: $i] :
( ! [X652: $i] :
( ( in @ X652 @ X650 )
=> ( in @ X652 @ X651 ) )
=> ( subset @ X650 @ X651 ) )
=> ( ! [X653: $i] : ( subset @ emptyset @ X653 )
=> ( ! [X654: $i,X655: $i,X656: $i] :
( ( subset @ X654 @ X655 )
=> ( ( in @ X656 @ X654 )
=> ( in @ X656 @ X655 ) ) )
=> ( ! [X657: $i,X658: $i,X659: $i] :
( ( subset @ X657 @ X658 )
=> ( ~ ( in @ X659 @ X658 )
=> ~ ( in @ X659 @ X657 ) ) )
=> ( ! [X660: $i,X661: $i,X662: $i] :
( ( in @ X662 @ X660 )
=> ( ~ ( in @ X662 @ X661 )
=> ~ ( subset @ X660 @ X661 ) ) )
=> ( ! [X663: $i,X664: $i] :
( ~ ( subset @ X663 @ X664 )
=> ( X663 != X664 ) )
=> ( ! [X665: $i,X666: $i,X667: $i] :
( ( in @ X667 @ X665 )
=> ( ~ ( in @ X667 @ X666 )
=> ( X665 != X666 ) ) )
=> ( ! [X668: $i] : ( subset @ X668 @ X668 )
=> ( ! [X669: $i,X670: $i,X671: $i] :
( ( subset @ X669 @ X670 )
=> ( ( subset @ X670 @ X671 )
=> ( subset @ X669 @ X671 ) ) )
=> ( ! [X672: $i,X673: $i] : ( subset @ X673 @ ( setadjoin @ X672 @ X673 ) )
=> ( ! [X674: $i,X675: $i,X676: $i] :
( ( subset @ X674 @ X676 )
=> ( subset @ X674 @ ( setadjoin @ X675 @ X676 ) ) )
=> ( ! [X677: $i,X678: $i] :
( ( subset @ X677 @ X678 )
=> ( in @ X677 @ ( powerset @ X678 ) ) )
=> ( ! [X679: $i,X680: $i] :
( ( subset @ X679 @ X680 )
=> ( ( subset @ X680 @ X679 )
=> ( X679 = X680 ) ) )
=> ( ! [X681: $i] :
( ( subset @ X681 @ emptyset )
=> ( X681 = emptyset ) )
=> ( ! [X682: $i,X683: $i] :
( ( subset @ X683 @ X682 )
=> ( in @ X683 @ ( powerset @ X682 ) ) )
=> ( ! [X684: $i,X685: $i] :
( ( in @ X685 @ ( powerset @ X684 ) )
=> ( subset @ X685 @ X684 ) )
=> ( ! [X686: $i] : ( in @ X686 @ ( powerset @ X686 ) )
=> ( ! [X687: $i,X688: $i] :
( ( subset @ X687 @ X688 )
=> ( subset @ ( powerset @ X687 ) @ ( powerset @ X688 ) ) )
=> ( ! [X689: $i,X690: $i > $o] : ( in @ ( dsetconstr @ X689 @ X690 ) @ ( powerset @ X689 ) )
=> ( ! [X691: $i,X692: $i > $o] : ( subset @ ( dsetconstr @ X691 @ X692 ) @ X691 )
=> ( ! [X693: $i,X694: $i,X695: $i] :
( ( in @ X695 @ X693 )
=> ( in @ X695 @ ( binunion @ X693 @ X694 ) ) )
=> ( ! [X696: $i,X697: $i] : ( in @ X697 @ ( setadjoin @ X696 @ ( setadjoin @ X697 @ emptyset ) ) )
=> ( ! [X698: $i,X699: $i,X700: $i] :
( ( in @ X700 @ X699 )
=> ( in @ X700 @ ( binunion @ X698 @ X699 ) ) )
=> ( ! [X701: $i,X702: $i,X703: $i,X704: $o] :
( ( in @ X703 @ ( binunion @ X701 @ X702 ) )
=> ( ( ( in @ X703 @ X701 )
=> X704 )
=> ( ( ( in @ X703 @ X702 )
=> X704 )
=> X704 ) ) )
=> ( ! [X705: $i,X706: $i,X707: $i] :
( ( in @ X707 @ ( binunion @ X705 @ X706 ) )
=> ( ( in @ X707 @ X705 )
| ( in @ X707 @ X706 ) ) )
=> ( ! [X708: $i,X709: $i] : ( subset @ X708 @ ( binunion @ X708 @ X709 ) )
=> ( ! [X710: $i,X711: $i] : ( subset @ X711 @ ( binunion @ X710 @ X711 ) )
=> ( ! [X712: $i,X713: $i,X714: $i] :
( ( in @ X714 @ X712 )
=> ( ( in @ X714 @ X713 )
=> ( in @ X714 @ ( binintersect @ X712 @ X713 ) ) ) )
=> ( ! [X715: $i,X716: $i,X717: $i] :
( ( subset @ X717 @ X715 )
=> ( ( subset @ X717 @ X716 )
=> ( subset @ X717 @ ( binintersect @ X715 @ X716 ) ) ) )
=> ( ! [X718: $i,X719: $i,X720: $i] :
( ( in @ X720 @ ( binintersect @ X718 @ X719 ) )
=> ( in @ X720 @ X718 ) )
=> ( ! [X721: $i,X722: $i] : ( subset @ ( binintersect @ X721 @ X722 ) @ X721 )
=> ( ! [X723: $i,X724: $i] :
( ( subset @ X723 @ X724 )
=> ( ( binintersect @ X723 @ X724 )
= X723 ) )
=> ( ! [X725: $i,X726: $i] :
( ( ( binintersect @ X725 @ X726 )
= X726 )
=> ( subset @ X726 @ X725 ) )
=> ( ! [X727: $i,X728: $i,X729: $i] :
( ( in @ X729 @ ( binintersect @ X727 @ X728 ) )
=> ( in @ X729 @ X728 ) )
=> ( ! [X730: $i,X731: $i] :
( ~ ? [X732: $i] :
( ( in @ X732 @ X730 )
& ( in @ X732 @ X731 ) )
=> ( ( binintersect @ X730 @ X731 )
= emptyset ) )
=> ( ! [X733: $i,X734: $i] : ( subset @ ( binintersect @ X733 @ X734 ) @ X734 )
=> ( ! [X735: $i,X736: $i] :
( ( subset @ X736 @ X735 )
=> ( ( binintersect @ X735 @ X736 )
= X736 ) )
=> ( ! [X737: $i,X738: $i] :
( ( ( binintersect @ X737 @ X738 )
= X737 )
=> ( subset @ X737 @ X738 ) )
=> ( ! [X739: $i,X740: $i,X741: $i] :
( ( binintersect @ X739 @ ( binunion @ X740 @ X741 ) )
= ( binunion @ ( binintersect @ X739 @ X740 ) @ ( binintersect @ X739 @ X741 ) ) )
=> ( ! [X742: $i,X743: $i,X744: $i] :
( ( in @ X744 @ X742 )
=> ( ~ ( in @ X744 @ X743 )
=> ( in @ X744 @ ( setminus @ X742 @ X743 ) ) ) )
=> ( ! [X745: $i,X746: $i,X747: $i] :
( ( in @ X747 @ ( setminus @ X745 @ X746 ) )
=> ( in @ X747 @ X745 ) )
=> ( ! [X748: $i,X749: $i,X750: $i] :
( ( in @ X750 @ ( setminus @ X748 @ X749 ) )
=> ~ ( in @ X750 @ X749 ) )
=> ( ! [X751: $i,X752: $i] :
( ( subset @ X751 @ X752 )
=> ( ( setminus @ X751 @ X752 )
= emptyset ) )
=> ( ! [X753: $i,X754: $i,X755: $i] :
( ~ ( in @ X755 @ ( setminus @ X753 @ X754 ) )
=> ( ( in @ X755 @ X753 )
=> ( in @ X755 @ X754 ) ) )
=> ( ! [X756: $i,X757: $i,X758: $i] :
( ~ ( in @ X758 @ ( setminus @ X756 @ X757 ) )
=> ( ~ ( in @ X758 @ X757 )
=> ~ ( in @ X758 @ X756 ) ) )
=> ( ! [X759: $i,X760: $i,X761: $i] :
( ~ ( in @ X761 @ X759 )
=> ~ ( in @ X761 @ ( setminus @ X759 @ X760 ) ) )
=> ( ! [X762: $i,X763: $i,X764: $i] :
( ( in @ X764 @ X763 )
=> ~ ( in @ X764 @ ( setminus @ X762 @ X763 ) ) )
=> ( ! [X765: $i,X766: $i] : ( subset @ ( setminus @ X765 @ X766 ) @ X765 )
=> ( ! [X767: $i,X768: $i] :
( ( ( setminus @ X767 @ X768 )
= emptyset )
=> ( subset @ X767 @ X768 ) )
=> ( ! [X769: $i,X770: $i,X771: $i] :
( ( in @ X771 @ ( symdiff @ X769 @ X770 ) )
=> ! [X772: $o] :
( ( ( in @ X771 @ X769 )
=> ( ~ ( in @ X771 @ X770 )
=> X772 ) )
=> ( ( ~ ( in @ X771 @ X769 )
=> ( ( in @ X771 @ X770 )
=> X772 ) )
=> X772 ) ) )
=> ( ! [X773: $i,X774: $i,X775: $i] :
( ( in @ X775 @ X773 )
=> ( ~ ( in @ X775 @ X774 )
=> ( in @ X775 @ ( symdiff @ X773 @ X774 ) ) ) )
=> ( ! [X776: $i,X777: $i,X778: $i] :
( ~ ( in @ X778 @ X776 )
=> ( ( in @ X778 @ X777 )
=> ( in @ X778 @ ( symdiff @ X776 @ X777 ) ) ) )
=> ( ! [X779: $i,X780: $i,X781: $i] :
( ( in @ X781 @ X779 )
=> ( ( in @ X781 @ X780 )
=> ~ ( in @ X781 @ ( symdiff @ X779 @ X780 ) ) ) )
=> ( ! [X782: $i,X783: $i,X784: $i] :
( ~ ( in @ X784 @ X782 )
=> ( ~ ( in @ X784 @ X783 )
=> ~ ( in @ X784 @ ( symdiff @ X782 @ X783 ) ) ) )
=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ 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(assume_negation,[status(cth)],[secondinupair]),quantDeMorgan3]),symdiffI2]),symdiffIneg2]),binintersectSubset2]),eqinunit]),binintersectSubset3]),binintersectER]),disjointsetsI1]),singletonsswitch]),binintersectRsub]),binintersectSubset4]),upairsetE]),binintersectSubset1]),bs114d]),upairsetIL]),setminusI]),setminusEL]),upairsetIR]),setminusER]),setminusSubset2]),c_0_149]),setminusERneg]),setminusELneg]),vacuousDall]),setminusILneg]),setminusIRneg]),quantDeMorgan1]),setminusLsub]),setminusSubset1]),symdiffE]),quantDeMorgan2]),symdiffI1]),c_0_150]),symdiffIneg1]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_151]),c_0_152]),c_0_153]),inCongP]),in__Cong]),c_0_154]),c_0_155]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_156]),c_0_157]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_158]),c_0_159]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),c_0_160]),binunionLsub]),uniqinunit]),binunionRsub]),binintersectI]),notinsingleton]),binintersectSubset5]),binintersectEL]),binintersectLsub]),c_0_161]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_162]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_163]),c_0_164]),c_0_165]),c_0_166]),noeltsimpempty]),emptyI]),setext]),c_0_167]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_168]),c_0_169]),c_0_170]),c_0_171]),c_0_172]),wellorderingAx]),foundationAx]),c_0_173]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_174]) ).
thf(c_0_176,negated_conjecture,
! [X785: $i,X786: $i,X788: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X798: $i,X799: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X807: $i,X808: $i > $i > $o,X809: $i,X811: $i,X814: $i,X816: $i,X817: $i,X818: $i,X819: $i,X821: $i,X822: $i > $o,X823: $i,X825: $i,X826: $i > $o,X827: $i,X828: $i,X829: $i > $o,X830: $i,X831: $i,X832: $i > $o,X833: $i,X834: $i > $o,X835: $i,X838: $i,X839: $o,X840: $i,X841: $i,X842: $o,X843: $i,X844: $i,X845: $i > $o,X846: $i,X849: $i,X850: $i,X853: $i,X855: $i,X857: $i,X858: $i > $o,X859: $i,X860: $i,X862: $i,X863: $i > $o,X864: $i,X865: $i,X866: $i,X867: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $o,X876: $i,X877: $i,X878: $i,X879: $i,X880: $i,X881: $i,X883: $i,X884: $i,X885: $i,X886: $i,X887: $i,X888: $i,X889: $i,X890: $i,X891: $i,X892: $i,X893: $o,X895: $i,X896: $i,X897: $i > $o,X898: $i,X901: $i,X902: $i,X903: $i,X905: $i,X906: $i,X907: $i,X908: $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 > $o,X922: $i,X923: $i > $o,X924: $i,X925: $i,X926: $i > $o,X927: $i,X929: $i,X930: $i > $o,X932: $i,X933: $i,X934: $i > $o,X936: $i,X937: $i,X938: $i > $o,X939: $i,X941: $o,X942: $i,X943: $i > $o,X945: $i,X946: $i,X947: $i > $o,X948: $i,X950: $i > $o,X951: $i,X954: $i,X955: $i > $o,X956: $i,X960: $i,X961: $i > $o,X962: $i,X965: $i,X966: $i,X967: $i,X968: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i > $o,X975: $i,X977: $i,X978: $i,X979: $i > $o,X980: $i > $o,X983: $i,X986: $i,X987: $i,X990: $i,X991: $i,X992: $i,X993: $i,X994: $i,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i > $o,X1000: $i,X1002: $i,X1003: $i,X1004: $i > $o,X1005: $i > $o,X1008: $i,X1010: $i,X1012: $i,X1013: $i,X1014: $i > $o,X1015: $i > $o,X1018: $i,X1019: $i,X1021: $i,X1022: $i,X1023: $i,X1024: $i,X1025: $i,X1026: $i,X1028: $i,X1029: $i,X1030: $i,X1031: $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 > $o,X1066: $i,X1067: $i > $o,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $o,X1080: $i,X1081: $i,X1082: $i,X1083: $i,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,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i,X1115: $i,X1116: $i,X1117: $i,X1118: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,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: $o,X1148: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i] :
( ( ~ ( in @ ( esk1_2 @ X785 @ X786 ) @ X785 )
| ~ ( in @ ( esk1_2 @ X785 @ X786 ) @ X786 )
| ( X785 = X786 ) )
& ( ( in @ ( esk1_2 @ X785 @ X786 ) @ X785 )
| ( in @ ( esk1_2 @ X785 @ X786 ) @ X786 )
| ( X785 = X786 ) )
& ~ ( in @ X788 @ emptyset )
& ( ~ ( in @ X791 @ ( setadjoin @ X789 @ X790 ) )
| ( X791 = X789 )
| ( in @ X791 @ X790 ) )
& ( ( X791 != X789 )
| ( in @ X791 @ ( setadjoin @ X789 @ X790 ) ) )
& ( ~ ( in @ X791 @ X790 )
| ( in @ X791 @ ( setadjoin @ X789 @ X790 ) ) )
& ( ~ ( in @ X793 @ ( powerset @ X792 ) )
| ~ ( in @ X794 @ X793 )
| ( in @ X794 @ X792 ) )
& ( ( in @ ( esk2_2 @ X795 @ X796 ) @ X796 )
| ( in @ X796 @ ( powerset @ X795 ) ) )
& ( ~ ( in @ ( esk2_2 @ X795 @ X796 ) @ X795 )
| ( in @ X796 @ ( powerset @ X795 ) ) )
& ( ( in @ X799 @ ( esk3_2 @ X798 @ X799 ) )
| ~ ( in @ X799 @ ( setunion @ X798 ) ) )
& ( ( in @ ( esk3_2 @ X798 @ X799 ) @ X798 )
| ~ ( in @ X799 @ ( setunion @ X798 ) ) )
& ( ~ ( in @ X802 @ X803 )
| ~ ( in @ X803 @ X801 )
| ( in @ X802 @ ( setunion @ X801 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X804 @ omega )
| ( in @ ( setadjoin @ X804 @ X804 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X805 ) @ omega )
| ~ ( in @ emptyset @ X805 )
| ~ ( in @ X807 @ omega )
| ( in @ X807 @ X805 ) )
& ( ( in @ ( esk4_1 @ X805 ) @ X805 )
| ~ ( in @ emptyset @ X805 )
| ~ ( in @ X807 @ omega )
| ( in @ X807 @ X805 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X805 ) @ ( esk4_1 @ X805 ) ) @ X805 )
| ~ ( in @ emptyset @ X805 )
| ~ ( in @ X807 @ omega )
| ( in @ X807 @ X805 ) )
& ( ( in @ ( esk8_3 @ X808 @ X809 @ X814 ) @ X809 )
| ~ ( in @ X814 @ ( esk7_2 @ X808 @ X809 ) )
| ( in @ ( esk5_2 @ X808 @ X809 ) @ X809 ) )
& ( ( X808 @ ( esk8_3 @ X808 @ X809 @ X814 ) @ X814 )
| ~ ( in @ X814 @ ( esk7_2 @ X808 @ X809 ) )
| ( in @ ( esk5_2 @ X808 @ X809 ) @ X809 ) )
& ( ~ ( in @ X817 @ X809 )
| ~ ( X808 @ X817 @ X816 )
| ( in @ X816 @ ( esk7_2 @ X808 @ X809 ) )
| ( in @ ( esk5_2 @ X808 @ X809 ) @ X809 ) )
& ( ( in @ ( esk8_3 @ X808 @ X809 @ X814 ) @ X809 )
| ~ ( in @ X814 @ ( esk7_2 @ X808 @ X809 ) )
| ( X808 @ ( esk5_2 @ X808 @ X809 ) @ ( esk6_3 @ X808 @ X809 @ X811 ) )
| ~ ( X808 @ ( esk5_2 @ X808 @ X809 ) @ X811 ) )
& ( ( X808 @ ( esk8_3 @ X808 @ X809 @ X814 ) @ X814 )
| ~ ( in @ X814 @ ( esk7_2 @ X808 @ X809 ) )
| ( X808 @ ( esk5_2 @ X808 @ X809 ) @ ( esk6_3 @ X808 @ X809 @ X811 ) )
| ~ ( X808 @ ( esk5_2 @ X808 @ X809 ) @ X811 ) )
& ( ~ ( in @ X817 @ X809 )
| ~ ( X808 @ X817 @ X816 )
| ( in @ X816 @ ( esk7_2 @ X808 @ X809 ) )
| ( X808 @ ( esk5_2 @ X808 @ X809 ) @ ( esk6_3 @ X808 @ X809 @ X811 ) )
| ~ ( X808 @ ( esk5_2 @ X808 @ X809 ) @ X811 ) )
& ( ( in @ ( esk8_3 @ X808 @ X809 @ X814 ) @ X809 )
| ~ ( in @ X814 @ ( esk7_2 @ X808 @ X809 ) )
| ( X811
!= ( esk6_3 @ X808 @ X809 @ X811 ) )
| ~ ( X808 @ ( esk5_2 @ X808 @ X809 ) @ X811 ) )
& ( ( X808 @ ( esk8_3 @ X808 @ X809 @ X814 ) @ X814 )
| ~ ( in @ X814 @ ( esk7_2 @ X808 @ X809 ) )
| ( X811
!= ( esk6_3 @ X808 @ X809 @ X811 ) )
| ~ ( X808 @ ( esk5_2 @ X808 @ X809 ) @ X811 ) )
& ( ~ ( in @ X817 @ X809 )
| ~ ( X808 @ X817 @ X816 )
| ( in @ X816 @ ( esk7_2 @ X808 @ X809 ) )
| ( X811
!= ( esk6_3 @ X808 @ X809 @ X811 ) )
| ~ ( X808 @ ( esk5_2 @ X808 @ X809 ) @ X811 ) )
& ( ( in @ ( esk9_1 @ X818 ) @ X818 )
| ~ ( in @ X819 @ X818 ) )
& ( ~ ( in @ X821 @ ( esk9_1 @ X818 ) )
| ~ ( in @ X821 @ X818 )
| ~ ( in @ X819 @ X818 ) )
& epred1_0
& ( ( X822 @ ( esk10_2 @ X822 @ X823 ) )
| ~ ( X822 @ X823 )
| ( X822 @ ( descr @ X822 ) ) )
& ( ( X823
!= ( esk10_2 @ X822 @ X823 ) )
| ~ ( X822 @ X823 )
| ( X822 @ ( descr @ X822 ) ) )
& ( ~ ( in @ X827 @ X825 )
| ~ ( X826 @ X827 )
| ( in @ X827 @ ( dsetconstr @ X825 @ X826 ) ) )
& ( ~ ( in @ X830 @ ( dsetconstr @ X828 @ X829 ) )
| ( in @ X830 @ X828 ) )
& ( ~ ( in @ X833 @ ( dsetconstr @ X831 @ X832 ) )
| ( X832 @ X833 ) )
& ( ( X834 @ ( esk12_1 @ X834 ) )
| ( X834 @ ( esk11_2 @ X834 @ X835 ) )
| ~ ( X834 @ X835 ) )
& ( ~ ( X834 @ X838 )
| ( ( esk12_1 @ X834 )
= X838 )
| ( X834 @ ( esk11_2 @ X834 @ X835 ) )
| ~ ( X834 @ X835 ) )
& ( ( X834 @ ( esk12_1 @ X834 ) )
| ( X835
!= ( esk11_2 @ X834 @ X835 ) )
| ~ ( X834 @ X835 ) )
& ( ~ ( X834 @ X838 )
| ( ( esk12_1 @ X834 )
= X838 )
| ( X835
!= ( esk11_2 @ X834 @ X835 ) )
| ~ ( X834 @ X835 ) )
& ( ~ ( in @ X840 @ ( prop2set @ X839 ) )
| X839 )
& ( ~ ( in @ X841 @ emptyset )
| X842 )
& ( ~ ( in @ X843 @ emptyset )
| ~ $true )
& ~ ( in @ X844 @ emptyset )
& ( ( X845 @ ( esk13_2 @ X845 @ X846 ) )
| ~ ( X845 @ X846 )
| ( X845 @ ( esk14_1 @ X845 ) ) )
& ( ( X846
!= ( esk13_2 @ X845 @ X846 ) )
| ~ ( X845 @ X846 )
| ( X845 @ ( esk14_1 @ X845 ) ) )
& ( ( in @ ( esk16_2 @ X849 @ X850 ) @ X850 )
| ( X849 = X850 )
| ( in @ ( esk15_2 @ X849 @ X850 ) @ X849 ) )
& ( ~ ( in @ ( esk16_2 @ X849 @ X850 ) @ X849 )
| ( X849 = X850 )
| ( in @ ( esk15_2 @ X849 @ X850 ) @ X849 ) )
& ( ( in @ ( esk16_2 @ X849 @ X850 ) @ X850 )
| ( X849 = X850 )
| ~ ( in @ ( esk15_2 @ X849 @ X850 ) @ X850 ) )
& ( ~ ( in @ ( esk16_2 @ X849 @ X850 ) @ X849 )
| ( X849 = X850 )
| ~ ( in @ ( esk15_2 @ X849 @ X850 ) @ X850 ) )
& ( ( in @ ( esk17_1 @ X853 ) @ X853 )
| ( X853 = emptyset ) )
& ( ( in @ ( esk18_1 @ X855 ) @ X855 )
| ( X855 = emptyset ) )
& ( ~ ( in @ X859 @ ( dsetconstr @ X857 @ X858 ) )
| ( X858 @ X859 )
| ~ ( in @ X859 @ X857 ) )
& ( ~ ( X858 @ X859 )
| ( in @ X859 @ ( dsetconstr @ X857 @ X858 ) )
| ~ ( in @ X859 @ X857 ) )
& ( ( X860 = emptyset )
| ( in @ ( esk19_1 @ X860 ) @ X860 ) )
& ( ~ ( in @ X864 @ X862 )
| ~ ( X863 @ X864 )
| ( ( dsetconstr @ X862 @ X863 )
!= emptyset ) )
& ( ~ ( in @ X866 @ X865 )
| ( X865 != emptyset ) )
& ( in @ X867 @ ( setadjoin @ X867 @ X868 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X871 @ X870 )
| ( in @ X871 @ ( setadjoin @ X869 @ X870 ) ) )
& ( ( in @ X874 @ X873 )
| X875
| ( X874 = X872 )
| ~ ( in @ X874 @ ( setadjoin @ X872 @ X873 ) ) )
& ( ~ X875
| X875
| ( X874 = X872 )
| ~ ( in @ X874 @ ( setadjoin @ X872 @ X873 ) ) )
& ( ( in @ X874 @ X873 )
| X875
| ~ X875
| ~ ( in @ X874 @ ( setadjoin @ X872 @ X873 ) ) )
& ( ~ X875
| X875
| ~ X875
| ~ ( in @ X874 @ ( setadjoin @ X872 @ X873 ) ) )
& ( ~ ( in @ X878 @ ( setadjoin @ X876 @ X877 ) )
| ( X878 = X876 )
| ( in @ X878 @ X877 ) )
& ( ( dsetconstr @ X879
@ ^ [Z0: $i] : $true )
= X879 )
& ( ( in @ ( esk20_2 @ X880 @ X881 ) @ X881 )
| ( in @ X881 @ ( powerset @ X880 ) ) )
& ( ~ ( in @ ( esk20_2 @ X880 @ X881 ) @ X880 )
| ( in @ X881 @ ( powerset @ X880 ) ) )
& ( in @ emptyset @ ( powerset @ X883 ) )
& ( in @ emptyset @ ( powerset @ X884 ) )
& ( ~ ( in @ X886 @ ( powerset @ X885 ) )
| ~ ( in @ X887 @ X886 )
| ( in @ X887 @ X885 ) )
& ( ~ ( in @ X889 @ X890 )
| ~ ( in @ X890 @ X888 )
| ( in @ X889 @ ( setunion @ X888 ) ) )
& ( ( in @ X892 @ ( esk21_3 @ X891 @ X892 @ X893 ) )
| X893
| ~ ( in @ X892 @ ( setunion @ X891 ) ) )
& ( ( in @ ( esk21_3 @ X891 @ X892 @ X893 ) @ X891 )
| X893
| ~ ( in @ X892 @ ( setunion @ X891 ) ) )
& ( ~ X893
| X893
| ~ ( in @ X892 @ ( setunion @ X891 ) ) )
& ( ~ ( in @ X896 @ X895 )
| ( in @ X896 @ ( powerset @ ( setunion @ X895 ) ) ) )
& ( ~ ( X897 @ X901 )
| ( X901
= ( esk23_1 @ X897 ) )
| ( X897 @ ( esk22_2 @ X897 @ X898 ) )
| ~ ( X897 @ X898 ) )
& ( ( X902
!= ( esk23_1 @ X897 ) )
| ( X897 @ X902 )
| ( X897 @ ( esk22_2 @ X897 @ X898 ) )
| ~ ( X897 @ X898 ) )
& ( ~ ( X897 @ X901 )
| ( X901
= ( esk23_1 @ X897 ) )
| ( X898
!= ( esk22_2 @ X897 @ X898 ) )
| ~ ( X897 @ X898 ) )
& ( ( X902
!= ( esk23_1 @ X897 ) )
| ( X897 @ X902 )
| ( X898
!= ( esk22_2 @ X897 @ X898 ) )
| ~ ( X897 @ X898 ) )
& ( ( in @ ( esk24_1 @ X903 ) @ X903 )
| ( X903 = emptyset ) )
& ( $true
| ( X903 = emptyset ) )
& ( ~ ( in @ X905 @ ( setadjoin @ X906 @ emptyset ) )
| ( X905 = X906 ) )
& ( ( X907 = X908 )
| ~ ( in @ X908 @ ( setadjoin @ X907 @ emptyset ) ) )
& ( ( X909 != X910 )
| ( in @ X909 @ ( setadjoin @ X910 @ emptyset ) ) )
& ( ~ ( in @ X911 @ ( setadjoin @ X912 @ emptyset ) )
| ( in @ X912 @ ( setadjoin @ X911 @ emptyset ) ) )
& ( ~ ( in @ X915 @ ( setadjoin @ X913 @ ( setadjoin @ X914 @ emptyset ) ) )
| ( X915 = X913 )
| ( X915 = X914 ) )
& ( in @ X916 @ ( setadjoin @ X916 @ ( setadjoin @ X917 @ emptyset ) ) )
& ( in @ X919 @ ( setadjoin @ X918 @ ( setadjoin @ X919 @ emptyset ) ) )
& ( ~ ( in @ X922 @ X920 )
| ~ ( X921 @ X922 )
| ( ( dsetconstr @ X920 @ X921 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X924 @ emptyset )
| ( X923 @ X924 ) )
& ( ( in @ ( esk25_2 @ X925 @ X926 ) @ X925 )
| ~ ( in @ X927 @ X925 )
| ( X926 @ X927 ) )
& ( ~ ( X926 @ ( esk25_2 @ X925 @ X926 ) )
| ~ ( in @ X927 @ X925 )
| ( X926 @ X927 ) )
& ( ( in @ ( esk26_2 @ X929 @ X930 ) @ X929 )
| ~ ( in @ X932 @ X929 )
| ~ ( X930 @ X932 ) )
& ( ( X930 @ ( esk26_2 @ X929 @ X930 ) )
| ~ ( in @ X932 @ X929 )
| ~ ( X930 @ X932 ) )
& ( ( in @ ( esk27_2 @ X933 @ X934 ) @ X933 )
| ~ ( in @ X936 @ X933 )
| ~ ( X934 @ X936 ) )
& ( ( X934 @ ( esk27_2 @ X933 @ X934 ) )
| ~ ( in @ X936 @ X933 )
| ~ ( X934 @ X936 ) )
& ( ( in @ ( esk28_2 @ X937 @ X938 ) @ X937 )
| ~ ( in @ X939 @ X937 )
| ( X938 @ X939 ) )
& ( ~ ( X938 @ ( esk28_2 @ X937 @ X938 ) )
| ~ ( in @ X939 @ X937 )
| ( X938 @ X939 ) )
& ( ~ X941
| ( in @ emptyset @ ( prop2set @ X941 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X942 @ X943 ) @ X942 )
| ~ ( in @ X945 @ X942 )
| ~ ( X943 @ X945 ) )
& ( ( X943 @ ( esk29_2 @ X942 @ X943 ) )
| ~ ( in @ X945 @ X942 )
| ~ ( X943 @ X945 ) )
& ( ( in @ ( esk30_2 @ X946 @ X947 ) @ X946 )
| ~ ( in @ X948 @ X946 )
| ( X947 @ X948 ) )
& ( ~ ( X947 @ ( esk30_2 @ X946 @ X947 ) )
| ~ ( in @ X948 @ X946 )
| ( X947 @ X948 ) )
& ( ( X950 @ ( esk32_1 @ X950 ) )
| ( X950 @ ( esk31_2 @ X950 @ X951 ) )
| ~ ( X950 @ X951 ) )
& ( ~ ( X950 @ X954 )
| ( ( esk32_1 @ X950 )
= X954 )
| ( X950 @ ( esk31_2 @ X950 @ X951 ) )
| ~ ( X950 @ X951 ) )
& ( ( X950 @ ( esk32_1 @ X950 ) )
| ( X951
!= ( esk31_2 @ X950 @ X951 ) )
| ~ ( X950 @ X951 ) )
& ( ~ ( X950 @ X954 )
| ( ( esk32_1 @ X950 )
= X954 )
| ( X951
!= ( esk31_2 @ X950 @ X951 ) )
| ~ ( X950 @ X951 ) )
& ( ( X955 @ ( esk35_1 @ X955 ) )
| ( X955 @ ( esk33_1 @ X955 ) )
| ~ ( X955 @ X956 ) )
& ( ~ ( X955 @ X960 )
| ( ( esk35_1 @ X955 )
= X960 )
| ( X955 @ ( esk33_1 @ X955 ) )
| ~ ( X955 @ X956 ) )
& ( ( X955 @ ( esk35_1 @ X955 ) )
| ( X955 @ ( esk34_1 @ X955 ) )
| ~ ( X955 @ X956 ) )
& ( ~ ( X955 @ X960 )
| ( ( esk35_1 @ X955 )
= X960 )
| ( X955 @ ( esk34_1 @ X955 ) )
| ~ ( X955 @ X956 ) )
& ( ( X955 @ ( esk35_1 @ X955 ) )
| ( ( esk33_1 @ X955 )
!= ( esk34_1 @ X955 ) )
| ~ ( X955 @ X956 ) )
& ( ~ ( X955 @ X960 )
| ( ( esk35_1 @ X955 )
= X960 )
| ( ( esk33_1 @ X955 )
!= ( esk34_1 @ X955 ) )
| ~ ( X955 @ X956 ) )
& ( ( X961 @ ( esk37_1 @ X961 ) )
| ~ ( X961 @ ( esk36_2 @ X961 @ X962 ) )
| ( ( esk36_2 @ X961 @ X962 )
!= X962 ) )
& ( ~ ( X961 @ X965 )
| ( ( esk37_1 @ X961 )
= X965 )
| ~ ( X961 @ ( esk36_2 @ X961 @ X962 ) )
| ( ( esk36_2 @ X961 @ X962 )
!= X962 ) )
& ( ( X961 @ ( esk37_1 @ X961 ) )
| ( X961 @ ( esk36_2 @ X961 @ X962 ) )
| ( ( esk36_2 @ X961 @ X962 )
= X962 ) )
& ( ~ ( X961 @ X965 )
| ( ( esk37_1 @ X961 )
= X965 )
| ( X961 @ ( esk36_2 @ X961 @ X962 ) )
| ( ( esk36_2 @ X961 @ X962 )
= X962 ) )
& ( ( X966 != X967 )
| ( X968 != X969 )
| ~ ( in @ X968 @ X966 )
| ( in @ X969 @ X967 ) )
& ( ~ ( in @ X972 @ X970 )
| ( in @ X973 @ X971 )
| ( X972 != X973 )
| ( X970 != X971 ) )
& ( ~ ( in @ X973 @ X971 )
| ( in @ X972 @ X970 )
| ( X972 != X973 )
| ( X970 != X971 ) )
& ( ( X974 @ ( esk38_2 @ X974 @ X975 ) )
| ~ ( X974 @ X975 )
| ~ ( X974 @ X977 )
| ~ ( X974 @ X978 )
| ( X977 = X978 ) )
& ( ( X975
!= ( esk38_2 @ X974 @ X975 ) )
| ~ ( X974 @ X975 )
| ~ ( X974 @ X977 )
| ~ ( X974 @ X978 )
| ( X977 = X978 ) )
& ( ( X980 @ ( esk42_2 @ X979 @ X980 ) )
| ( X979 @ ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X980 @ X986 )
| ( ( esk42_2 @ X979 @ X980 )
= X986 )
| ( X979 @ ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X980 @ ( esk42_2 @ X979 @ X980 ) )
| ( X983
!= ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X980 @ X986 )
| ( ( esk42_2 @ X979 @ X980 )
= X986 )
| ( X983
!= ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X979 @ ( esk44_2 @ X979 @ X980 ) )
| ( X980 @ ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X979 @ X990 )
| ( ( esk44_2 @ X979 @ X980 )
= X990 )
| ( X980 @ ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X979 @ ( esk44_2 @ X979 @ X980 ) )
| ( X987
!= ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X979 @ X990 )
| ( ( esk44_2 @ X979 @ X980 )
= X990 )
| ( X987
!= ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( ( esk39_2 @ X979 @ X980 )
= ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X980 @ ( esk42_2 @ X979 @ X980 ) )
| ( X979 @ ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X980 @ X986 )
| ( ( esk42_2 @ X979 @ X980 )
= X986 )
| ( X979 @ ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X980 @ ( esk42_2 @ X979 @ X980 ) )
| ( X983
!= ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X980 @ X986 )
| ( ( esk42_2 @ X979 @ X980 )
= X986 )
| ( X983
!= ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X979 @ ( esk44_2 @ X979 @ X980 ) )
| ( X980 @ ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X979 @ X990 )
| ( ( esk44_2 @ X979 @ X980 )
= X990 )
| ( X980 @ ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X979 @ ( esk44_2 @ X979 @ X980 ) )
| ( X987
!= ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X979 @ X990 )
| ( ( esk44_2 @ X979 @ X980 )
= X990 )
| ( X987
!= ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ~ ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ~ ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X980 @ ( esk42_2 @ X979 @ X980 ) )
| ( X979 @ ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X980 @ X986 )
| ( ( esk42_2 @ X979 @ X980 )
= X986 )
| ( X979 @ ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X980 @ ( esk42_2 @ X979 @ X980 ) )
| ( X983
!= ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X980 @ X986 )
| ( ( esk42_2 @ X979 @ X980 )
= X986 )
| ( X983
!= ( esk41_3 @ X979 @ X980 @ X983 ) )
| ~ ( X979 @ X983 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X979 @ ( esk44_2 @ X979 @ X980 ) )
| ( X980 @ ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X979 @ X990 )
| ( ( esk44_2 @ X979 @ X980 )
= X990 )
| ( X980 @ ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ( X979 @ ( esk44_2 @ X979 @ X980 ) )
| ( X987
!= ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( ~ ( X979 @ X990 )
| ( ( esk44_2 @ X979 @ X980 )
= X990 )
| ( X987
!= ( esk43_3 @ X979 @ X980 @ X987 ) )
| ~ ( X980 @ X987 )
| ( X979 @ ( esk39_2 @ X979 @ X980 ) )
| ( X980 @ ( esk40_2 @ X979 @ X980 ) ) )
& ( emptyset = emptyset )
& ( ( X991 != X992 )
| ( X993 != X994 )
| ( ( setadjoin @ X991 @ X993 )
= ( setadjoin @ X992 @ X994 ) ) )
& ( ( X995 != X996 )
| ( ( powerset @ X995 )
= ( powerset @ X996 ) ) )
& ( ( X997 != X998 )
| ( ( setunion @ X997 )
= ( setunion @ X998 ) ) )
& ( omega = omega )
& ( ( X999 @ ( esk45_2 @ X999 @ X1000 ) )
| ~ ( X999 @ X1000 )
| ~ ( X999 @ X1002 )
| ~ ( X999 @ X1003 )
| ( X1002 = X1003 ) )
& ( ( X1000
!= ( esk45_2 @ X999 @ X1000 ) )
| ~ ( X999 @ X1000 )
| ~ ( X999 @ X1002 )
| ~ ( X999 @ X1003 )
| ( X1002 = X1003 ) )
& ( ( X1005 @ ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1004 @ ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( ( esk46_2 @ X1004 @ X1005 )
= ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1010
!= ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1004 @ ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( ( esk46_2 @ X1004 @ X1005 )
= ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1005 @ ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1008
!= ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( ( esk46_2 @ X1004 @ X1005 )
= ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1010
!= ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1008
!= ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( ( esk46_2 @ X1004 @ X1005 )
= ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1005 @ ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1004 @ ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ~ ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ~ ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1010
!= ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1004 @ ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ~ ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ~ ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1005 @ ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1008
!= ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ~ ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ~ ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1010
!= ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1008
!= ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ~ ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ~ ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1005 @ ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1004 @ ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1010
!= ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1004 @ ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1005 @ ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1008
!= ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( X1010
!= ( esk49_3 @ X1004 @ X1005 @ X1010 ) )
| ~ ( X1005 @ X1010 )
| ( ( descr @ X1004 )
= ( descr @ X1005 ) )
| ( X1008
!= ( esk48_3 @ X1004 @ X1005 @ X1008 ) )
| ~ ( X1004 @ X1008 )
| ( X1004 @ ( esk46_2 @ X1004 @ X1005 ) )
| ( X1005 @ ( esk47_2 @ X1004 @ X1005 ) ) )
& ( ( in @ ( esk50_4 @ X1012 @ X1013 @ X1014 @ X1015 ) @ X1012 )
| ( ( dsetconstr @ X1012 @ X1014 )
= ( dsetconstr @ X1013 @ X1015 ) )
| ( X1012 != X1013 ) )
& ( ( in @ ( esk51_4 @ X1012 @ X1013 @ X1014 @ X1015 ) @ X1013 )
| ( ( dsetconstr @ X1012 @ X1014 )
= ( dsetconstr @ X1013 @ X1015 ) )
| ( X1012 != X1013 ) )
& ( ( ( esk50_4 @ X1012 @ X1013 @ X1014 @ X1015 )
= ( esk51_4 @ X1012 @ X1013 @ X1014 @ X1015 ) )
| ( ( dsetconstr @ X1012 @ X1014 )
= ( dsetconstr @ X1013 @ X1015 ) )
| ( X1012 != X1013 ) )
& ( ~ ( X1014 @ ( esk50_4 @ X1012 @ X1013 @ X1014 @ X1015 ) )
| ~ ( X1015 @ ( esk51_4 @ X1012 @ X1013 @ X1014 @ X1015 ) )
| ( ( dsetconstr @ X1012 @ X1014 )
= ( dsetconstr @ X1013 @ X1015 ) )
| ( X1012 != X1013 ) )
& ( ( X1014 @ ( esk50_4 @ X1012 @ X1013 @ X1014 @ X1015 ) )
| ( X1015 @ ( esk51_4 @ X1012 @ X1013 @ X1014 @ X1015 ) )
| ( ( dsetconstr @ X1012 @ X1014 )
= ( dsetconstr @ X1013 @ X1015 ) )
| ( X1012 != X1013 ) )
& ( ( in @ ( esk52_2 @ X1018 @ X1019 ) @ X1018 )
| ( subset @ X1018 @ X1019 ) )
& ( ~ ( in @ ( esk52_2 @ X1018 @ X1019 ) @ X1019 )
| ( subset @ X1018 @ X1019 ) )
& ( ( X1021 != X1022 )
| ( subset @ X1022 @ X1021 ) )
& ( ( X1023 != X1024 )
| ( subset @ X1023 @ X1024 ) )
& ( ( in @ ( esk53_2 @ X1025 @ X1026 ) @ X1025 )
| ( subset @ X1025 @ X1026 ) )
& ( ~ ( in @ ( esk53_2 @ X1025 @ X1026 ) @ X1026 )
| ( subset @ X1025 @ X1026 ) )
& ( subset @ emptyset @ X1028 )
& ( ~ ( subset @ X1029 @ X1030 )
| ~ ( in @ X1031 @ X1029 )
| ( in @ X1031 @ X1030 ) )
& ( ~ ( subset @ X1032 @ X1033 )
| ( in @ X1034 @ X1033 )
| ~ ( in @ X1034 @ X1032 ) )
& ( ~ ( in @ X1037 @ X1035 )
| ( in @ X1037 @ X1036 )
| ~ ( subset @ X1035 @ X1036 ) )
& ( ( subset @ X1038 @ X1039 )
| ( X1038 != X1039 ) )
& ( ~ ( in @ X1042 @ X1040 )
| ( in @ X1042 @ X1041 )
| ( X1040 != X1041 ) )
& ( subset @ X1043 @ X1043 )
& ( ~ ( subset @ X1044 @ X1045 )
| ~ ( subset @ X1045 @ X1046 )
| ( subset @ X1044 @ X1046 ) )
& ( subset @ X1048 @ ( setadjoin @ X1047 @ X1048 ) )
& ( ~ ( subset @ X1049 @ X1051 )
| ( subset @ X1049 @ ( setadjoin @ X1050 @ X1051 ) ) )
& ( ~ ( subset @ X1052 @ X1053 )
| ( in @ X1052 @ ( powerset @ X1053 ) ) )
& ( ~ ( subset @ X1054 @ X1055 )
| ~ ( subset @ X1055 @ X1054 )
| ( X1054 = X1055 ) )
& ( ~ ( subset @ X1056 @ emptyset )
| ( X1056 = emptyset ) )
& ( ~ ( subset @ X1058 @ X1057 )
| ( in @ X1058 @ ( powerset @ X1057 ) ) )
& ( ~ ( in @ X1060 @ ( powerset @ X1059 ) )
| ( subset @ X1060 @ X1059 ) )
& ( in @ X1061 @ ( powerset @ X1061 ) )
& ( ~ ( subset @ X1062 @ X1063 )
| ( subset @ ( powerset @ X1062 ) @ ( powerset @ X1063 ) ) )
& ( in @ ( dsetconstr @ X1064 @ X1065 ) @ ( powerset @ X1064 ) )
& ( subset @ ( dsetconstr @ X1066 @ X1067 ) @ X1066 )
& ( ~ ( in @ X1070 @ X1068 )
| ( in @ X1070 @ ( binunion @ X1068 @ X1069 ) ) )
& ( in @ X1072 @ ( setadjoin @ X1071 @ ( setadjoin @ X1072 @ emptyset ) ) )
& ( ~ ( in @ X1075 @ X1074 )
| ( in @ X1075 @ ( binunion @ X1073 @ X1074 ) ) )
& ( ( in @ X1078 @ X1077 )
| X1079
| ( in @ X1078 @ X1076 )
| ~ ( in @ X1078 @ ( binunion @ X1076 @ X1077 ) ) )
& ( ~ X1079
| X1079
| ( in @ X1078 @ X1076 )
| ~ ( in @ X1078 @ ( binunion @ X1076 @ X1077 ) ) )
& ( ( in @ X1078 @ X1077 )
| X1079
| ~ X1079
| ~ ( in @ X1078 @ ( binunion @ X1076 @ X1077 ) ) )
& ( ~ X1079
| X1079
| ~ X1079
| ~ ( in @ X1078 @ ( binunion @ X1076 @ X1077 ) ) )
& ( ~ ( in @ X1082 @ ( binunion @ X1080 @ X1081 ) )
| ( in @ X1082 @ X1080 )
| ( in @ X1082 @ X1081 ) )
& ( subset @ X1083 @ ( binunion @ X1083 @ X1084 ) )
& ( subset @ X1086 @ ( binunion @ X1085 @ X1086 ) )
& ( ~ ( in @ X1089 @ X1087 )
| ~ ( in @ X1089 @ X1088 )
| ( in @ X1089 @ ( binintersect @ X1087 @ X1088 ) ) )
& ( ~ ( subset @ X1092 @ X1090 )
| ~ ( subset @ X1092 @ X1091 )
| ( subset @ X1092 @ ( binintersect @ X1090 @ X1091 ) ) )
& ( ~ ( in @ X1095 @ ( binintersect @ X1093 @ X1094 ) )
| ( in @ X1095 @ X1093 ) )
& ( subset @ ( binintersect @ X1096 @ X1097 ) @ X1096 )
& ( ~ ( subset @ X1098 @ X1099 )
| ( ( binintersect @ X1098 @ X1099 )
= X1098 ) )
& ( ( ( binintersect @ X1100 @ X1101 )
!= X1101 )
| ( subset @ X1101 @ X1100 ) )
& ( ~ ( in @ X1104 @ ( binintersect @ X1102 @ X1103 ) )
| ( in @ X1104 @ X1103 ) )
& ( ( in @ ( esk54_2 @ X1105 @ X1106 ) @ X1105 )
| ( ( binintersect @ X1105 @ X1106 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1105 @ X1106 ) @ X1106 )
| ( ( binintersect @ X1105 @ X1106 )
= emptyset ) )
& ( subset @ ( binintersect @ X1108 @ X1109 ) @ X1109 )
& ( ~ ( subset @ X1111 @ X1110 )
| ( ( binintersect @ X1110 @ X1111 )
= X1111 ) )
& ( ( ( binintersect @ X1112 @ X1113 )
!= X1112 )
| ( subset @ X1112 @ X1113 ) )
& ( ( binintersect @ X1114 @ ( binunion @ X1115 @ X1116 ) )
= ( binunion @ ( binintersect @ X1114 @ X1115 ) @ ( binintersect @ X1114 @ X1116 ) ) )
& ( ~ ( in @ X1119 @ X1117 )
| ( in @ X1119 @ X1118 )
| ( in @ X1119 @ ( setminus @ X1117 @ X1118 ) ) )
& ( ~ ( in @ X1122 @ ( setminus @ X1120 @ X1121 ) )
| ( in @ X1122 @ X1120 ) )
& ( ~ ( in @ X1125 @ ( setminus @ X1123 @ X1124 ) )
| ~ ( in @ X1125 @ X1124 ) )
& ( ~ ( subset @ X1126 @ X1127 )
| ( ( setminus @ X1126 @ X1127 )
= emptyset ) )
& ( ( in @ X1130 @ ( setminus @ X1128 @ X1129 ) )
| ~ ( in @ X1130 @ X1128 )
| ( in @ X1130 @ X1129 ) )
& ( ( in @ X1133 @ ( setminus @ X1131 @ X1132 ) )
| ( in @ X1133 @ X1132 )
| ~ ( in @ X1133 @ X1131 ) )
& ( ( in @ X1136 @ X1134 )
| ~ ( in @ X1136 @ ( setminus @ X1134 @ X1135 ) ) )
& ( ~ ( in @ X1139 @ X1138 )
| ~ ( in @ X1139 @ ( setminus @ X1137 @ X1138 ) ) )
& ( subset @ ( setminus @ X1140 @ X1141 ) @ X1140 )
& ( ( ( setminus @ X1142 @ X1143 )
!= emptyset )
| ( subset @ X1142 @ X1143 ) )
& ( ~ ( in @ X1146 @ X1144 )
| X1147
| ( in @ X1146 @ X1144 )
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ( in @ X1146 @ X1145 )
| X1147
| ( in @ X1146 @ X1144 )
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ~ X1147
| X1147
| ( in @ X1146 @ X1144 )
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ~ ( in @ X1146 @ X1144 )
| X1147
| ~ ( in @ X1146 @ X1145 )
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ( in @ X1146 @ X1145 )
| X1147
| ~ ( in @ X1146 @ X1145 )
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ~ X1147
| X1147
| ~ ( in @ X1146 @ X1145 )
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ~ ( in @ X1146 @ X1144 )
| X1147
| ~ X1147
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ( in @ X1146 @ X1145 )
| X1147
| ~ X1147
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ~ X1147
| X1147
| ~ X1147
| ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) )
& ( ~ ( in @ X1150 @ X1148 )
| ( in @ X1150 @ X1149 )
| ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) ) )
& ( ( in @ X1153 @ X1151 )
| ~ ( in @ X1153 @ X1152 )
| ( in @ X1153 @ ( symdiff @ X1151 @ X1152 ) ) )
& ( ~ ( in @ X1156 @ X1154 )
| ~ ( in @ X1156 @ X1155 )
| ~ ( in @ X1156 @ ( symdiff @ X1154 @ X1155 ) ) )
& ( ( in @ X1159 @ X1157 )
| ( in @ X1159 @ X1158 )
| ~ ( in @ X1159 @ ( symdiff @ X1157 @ X1158 ) ) )
& ~ ( in @ esk56_0 @ ( setadjoin @ esk55_0 @ ( setadjoin @ esk56_0 @ 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_175])])])])])])]) ).
thf(c_0_177,negated_conjecture,
~ ( in @ esk56_0 @ ( setadjoin @ esk55_0 @ ( setadjoin @ esk56_0 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_178,negated_conjecture,
! [X3: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
thf(c_0_179,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_178])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU616^1 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.09 % Command : run_E %s %d THM
% 0.08/0.28 % Computer : n014.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sun May 19 16:10:07 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.13/0.38 Running higher-order theorem proving
% 0.13/0.38 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
% 299.71/300.03 # Version: 3.1.0-ho
% 299.71/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 299.71/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 299.71/300.03 # Starting ehoh_best5 with 300s (1) cores
% 299.71/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 299.71/300.03 # Starting new_bool_5 with 300s (1) cores
% 299.71/300.03 # Starting pre_casc_3 with 300s (1) cores
% 299.71/300.03 # Starting ho_unfolding_8 with 300s (1) cores
% 299.71/300.03 # Starting new_ho_10_cnf2 with 300s (1) cores
% 299.71/300.03 # Starting new_bool_3 with 300s (1) cores
% 299.71/300.03 # Starting new_ho_5 with 300s (1) cores
% 299.71/300.03 # new_bool_3 with pid 6643 completed with status 0
% 299.71/300.03 # Result found by new_bool_3
% 299.71/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 299.71/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 299.71/300.03 # Starting ehoh_best5 with 300s (1) cores
% 299.71/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 299.71/300.03 # Starting new_bool_5 with 300s (1) cores
% 299.71/300.03 # Starting pre_casc_3 with 300s (1) cores
% 299.71/300.03 # Starting ho_unfolding_8 with 300s (1) cores
% 299.71/300.03 # Starting new_ho_10_cnf2 with 300s (1) cores
% 299.71/300.03 # Starting new_bool_3 with 300s (1) cores
% 299.71/300.03 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 299.71/300.03 # Search class: HGHSM-FSLS31-SHFMMSBN
% 299.71/300.03 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 299.71/300.03 # Starting sh3 with 181s (1) cores
% 299.71/300.03 # sh3 with pid 6649 completed with status 0
% 299.71/300.03 # Result found by sh3
% 299.71/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 299.71/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 299.71/300.03 # Starting ehoh_best5 with 300s (1) cores
% 299.71/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 299.71/300.03 # Starting new_bool_5 with 300s (1) cores
% 299.71/300.03 # Starting pre_casc_3 with 300s (1) cores
% 299.71/300.03 # Starting ho_unfolding_8 with 300s (1) cores
% 299.71/300.03 # Starting new_ho_10_cnf2 with 300s (1) cores
% 299.71/300.03 # Starting new_bool_3 with 300s (1) cores
% 299.71/300.03 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 299.71/300.03 # Search class: HGHSM-FSLS31-SHFMMSBN
% 299.71/300.03 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 299.71/300.03 # Starting sh3 with 181s (1) cores
% 299.71/300.03 # Preprocessing time : 0.004 s
% 299.71/300.03 # Presaturation interreduction done
% 299.71/300.03
% 299.71/300.03 # Proof found!
% 299.71/300.03 # SZS status Theorem
% 299.71/300.03 # SZS output start CNFRefutation
% See solution above
% 299.71/300.03 # Parsed axioms : 289
% 299.71/300.03 # Removed by relevancy pruning/SinE : 155
% 299.71/300.03 # Initial clauses : 255
% 299.71/300.03 # Removed in clause preprocessing : 24
% 299.71/300.03 # Initial clauses in saturation : 231
% 299.71/300.03 # Processed clauses : 67
% 299.71/300.03 # ...of these trivial : 1
% 299.71/300.03 # ...subsumed : 11
% 299.71/300.03 # ...remaining for further processing : 55
% 299.71/300.03 # Other redundant clauses eliminated : 5
% 299.71/300.03 # Clauses deleted for lack of memory : 0
% 299.71/300.03 # Backward-subsumed : 0
% 299.71/300.03 # Backward-rewritten : 2
% 299.71/300.03 # Generated clauses : 5
% 299.71/300.03 # ...of the previous two non-redundant : 1
% 299.71/300.03 # ...aggressively subsumed : 0
% 299.71/300.03 # Contextual simplify-reflections : 0
% 299.71/300.03 # Paramodulations : 0
% 299.71/300.03 # Factorizations : 0
% 299.71/300.03 # NegExts : 0
% 299.71/300.03 # Equation resolutions : 5
% 299.71/300.03 # Disequality decompositions : 0
% 299.71/300.03 # Total rewrite steps : 7
% 299.71/300.03 # ...of those cached : 2
% 299.71/300.03 # Propositional unsat checks : 0
% 299.71/300.03 # Propositional check models : 0
% 299.71/300.03 # Propositional check unsatisfiable : 0
% 299.71/300.03 # Propositional clauses : 0
% 299.71/300.03 # Propositional clauses after purity: 0
% 299.71/300.03 # Propositional unsat core size : 0
% 299.71/300.03 # Propositional preprocessing time : 0.000
% 299.71/300.03 # Propositional encoding time : 0.000
% 299.71/300.03 # Propositional solver time : 0.000
% 299.71/300.03 # Success case prop preproc time : 0.000
% 299.71/300.03 # Success case prop encoding time : 0.000
% 299.71/300.03 # Success case prop solver time : 0.000
% 299.71/300.03 # Current number of processed clauses : 48
% 299.71/300.03 # Positive orientable unit clauses : 19
% 299.71/300.03 # Positive unorientable unit clauses: 0
% 299.71/300.03 # Negative unit clauses : 2
% 299.71/300.03 # Non-unit-clauses : 27
% 299.71/300.03 # Current number of unprocessed clauses: 165
% 299.71/300.03 # ...number of literals in the above : 628
% 299.71/300.03 # Current number of archived formulas : 0
% 299.71/300.03 # Current number of archived clauses : 2
% 299.71/300.03 # Clause-clause subsumption calls (NU) : 48
% 299.71/300.03 # Rec. Clause-clause subsumption calls : 43
% 299.71/300.03 # Non-unit clause-clause subsumptions : 6
% 299.71/300.03 # Unit Clause-clause subsumption calls : 11
% 299.71/300.03 # Rewrite failures with RHS unbound : 0
% 299.71/300.03 # BW rewrite match attempts : 8
% 299.71/300.03 # BW rewrite match successes : 2
% 299.71/300.03 # Condensation attempts : 0
% 299.71/300.03 # Condensation successes : 0
% 299.71/300.03 # Termbank termtop insertions : 31035
% 299.71/300.03 # Search garbage collected termcells : 13059
% 299.71/300.03
% 299.71/300.03 # -------------------------------------------------
% 299.71/300.03 # User time : 0.036 s
% 299.71/300.03 # System time : 0.007 s
% 299.71/300.03 # Total time : 0.043 s
% 299.71/300.03 # Maximum resident set size: 5076 pages
% 299.71/300.03
% 299.71/300.03 # -------------------------------------------------
% 299.71/300.03 # User time : 0.043 s
% 299.71/300.03 # System time : 0.011 s
% 299.71/300.03 # Total time : 0.053 s
% 299.71/300.03 # Maximum resident set size: 2324 pages
% 299.71/300.03 % E---3.1 exiting
% 299.71/300.03 % E exiting
%------------------------------------------------------------------------------