%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU630^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 03:28:41 EDT 2024
% Result : Theorem 68.68s 9.18s
% Output : CNFRefutation 68.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 361
% Syntax : Number of formulae : 399 ( 9 unt; 211 typ; 0 def)
% Number of atoms : 1544 ( 218 equ; 0 cnn)
% Maximal formula atoms : 439 ( 8 avg)
% Number of connectives : 5325 ( 389 ~; 361 |; 281 &;3349 @)
% ( 205 <=>; 740 =>; 0 <=; 0 <~>)
% Maximal formula depth : 565 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 263 ( 263 >; 0 *; 0 +; 0 <<)
% Number of symbols : 214 ( 211 usr; 155 con; 0-4 aty)
% Number of variables : 1315 ( 64 ^1178 !; 73 ?;1315 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
epred1_0: $o ).
thf(decl_192,type,
esk1_2: $i > $i > $i ).
thf(decl_193,type,
esk2_2: $i > $i > $i ).
thf(decl_194,type,
esk3_2: $i > $i > $i ).
thf(decl_195,type,
esk4_1: $i > $i ).
thf(decl_196,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_197,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_198,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_199,type,
esk8_1: $i > $i ).
thf(decl_200,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_201,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_202,type,
esk11_2: $i > $i > $i ).
thf(decl_203,type,
esk12_2: $i > $i > $i ).
thf(decl_204,type,
esk13_1: $i > $i ).
thf(decl_205,type,
esk14_1: $i > $i ).
thf(decl_206,type,
esk15_1: $i > $i ).
thf(decl_207,type,
esk16_2: $i > $i > $i ).
thf(decl_208,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_209,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_210,type,
esk19_1: $i > $i ).
thf(decl_211,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_212,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_213,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_214,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_215,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_216,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_217,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_218,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_219,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_220,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_221,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_222,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_223,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_224,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_225,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_226,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_227,type,
esk36_2: $i > $i > $i ).
thf(decl_228,type,
esk37_2: $i > $i > $i ).
thf(decl_229,type,
esk38_2: $i > $i > $i ).
thf(decl_230,type,
esk39_0: $i ).
thf(decl_231,type,
esk40_0: $i ).
thf(decl_232,type,
esk41_0: $i ).
thf(decl_233,type,
esk42_0: $i ).
thf(decl_240,type,
epred3_2: $i > $i > $i > $o ).
thf(decl_241,type,
esk48_3: $i > $i > $i > $i ).
thf(decl_242,type,
esk49_3: $i > $i > $i > $i ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
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(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(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(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(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
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(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(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(cartprodpairin,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
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(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
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(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
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(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(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(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(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(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(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(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(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(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
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(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
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(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
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(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
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(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(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(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(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(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(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(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(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(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(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(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
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(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(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(cartprod,axiom,
( cartprod
= ( ^ [X4: $i,X5: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ( in @ X3 @ X4 )
& ? [X14: $i] :
( ( in @ X14 @ X5 )
& ( X2
= ( kpair @ X3 @ X14 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprod) ).
thf(c_0_147,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_148,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_149,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_150,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_151,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_152,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_153,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_154,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_155,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_156,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_157,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_158,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_159,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_160,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_161,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_162,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_163,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_164,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_165,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_166,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_167,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_168,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_169,plain,
( epred1_0
<=> ! [X445: $i] :
? [X446: $i] :
( ! [X447: $i] :
( ( in @ X447 @ X446 )
=> ! [X448: $i] :
( ( in @ X448 @ X447 )
=> ( in @ X448 @ X445 ) ) )
& ! [X449: $i,X450: $i] :
( ( ( in @ X449 @ X445 )
& ( in @ X450 @ X445 ) )
=> ( ! [X451: $i] :
( ( in @ X451 @ X446 )
=> ( ( in @ X449 @ X451 )
<=> ( in @ X450 @ X451 ) ) )
=> ( X449 = X450 ) ) )
& ! [X452: $i,X453: $i] :
( ( ( in @ X452 @ X446 )
& ( in @ X453 @ X446 ) )
=> ( ! [X454: $i] :
( ( in @ X454 @ X452 )
=> ( in @ X454 @ X453 ) )
| ! [X455: $i] :
( ( in @ X455 @ X453 )
=> ( in @ X455 @ X452 ) ) ) )
& ! [X456: $i] :
( ( ! [X457: $i] :
( ( in @ X457 @ X456 )
=> ( in @ X457 @ X445 ) )
& ? [X458: $i] : ( in @ X458 @ X456 ) )
=> ? [X459: $i,X460: $i] :
( ( in @ X459 @ X446 )
& ( in @ X460 @ X456 )
& ~ ? [X461: $i] :
( ( in @ X461 @ X459 )
& ( in @ X461 @ X456 ) )
& ! [X462: $i] :
( ( in @ X462 @ X446 )
=> ( ! [X463: $i] :
( ( in @ X463 @ X462 )
=> ( in @ X463 @ X459 ) )
| ( in @ X460 @ X462 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_170,negated_conjecture,
~ ( ! [X418: $i,X419: $i] :
( ! [X420: $i] :
( ( in @ X420 @ X418 )
<=> ( in @ X420 @ X419 ) )
=> ( X418 = X419 ) )
=> ( ! [X421: $i] :
~ ( in @ X421 @ emptyset )
=> ( ! [X422: $i,X423: $i,X424: $i] :
( ( in @ X424 @ ( setadjoin @ X422 @ X423 ) )
<=> ( ( X424 = X422 )
| ( in @ X424 @ X423 ) ) )
=> ( ! [X425: $i,X426: $i] :
( ( in @ X426 @ ( powerset @ X425 ) )
<=> ! [X427: $i] :
( ( in @ X427 @ X426 )
=> ( in @ X427 @ X425 ) ) )
=> ( ! [X428: $i,X429: $i] :
( ( in @ X429 @ ( setunion @ X428 ) )
<=> ? [X430: $i] :
( ( in @ X429 @ X430 )
& ( in @ X430 @ X428 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X431: $i] :
( ( in @ X431 @ omega )
=> ( in @ ( setadjoin @ X431 @ X431 ) @ omega ) )
=> ( ! [X432: $i] :
( ( ( in @ emptyset @ X432 )
& ! [X433: $i] :
( ( ( in @ X433 @ omega )
& ( in @ X433 @ X432 ) )
=> ( in @ ( setadjoin @ X433 @ X433 ) @ X432 ) ) )
=> ! [X434: $i] :
( ( in @ X434 @ omega )
=> ( in @ X434 @ X432 ) ) )
=> ( ! [X435: $i > $i > $o,X436: $i] :
( ! [X437: $i] :
( ( in @ X437 @ X436 )
=> ( exu @ ( X435 @ X437 ) ) )
=> ? [X438: $i] :
! [X439: $i] :
( ( in @ X439 @ X438 )
<=> ? [X440: $i] :
( ( in @ X440 @ X436 )
& ( X435 @ X440 @ X439 ) ) ) )
=> ( ! [X441: $i] :
( ? [X442: $i] : ( in @ X442 @ X441 )
=> ? [X443: $i] :
( ( in @ X443 @ X441 )
& ~ ? [X444: $i] :
( ( in @ X444 @ X443 )
& ( in @ X444 @ X441 ) ) ) )
=> ( epred1_0
=> ( ! [X464: $i > $o] :
( ( exu @ X464 )
=> ( X464
@ ( descr
@ ^ [Z0: $i] : ( X464 @ Z0 ) ) ) )
=> ( ! [X465: $i,X466: $i > $o,X467: $i] :
( ( in @ X467 @ X465 )
=> ( ( X466 @ X467 )
=> ( in @ X467 @ ( dsetconstr @ X465 @ X466 ) ) ) )
=> ( ! [X468: $i,X469: $i > $o,X470: $i] :
( ( in @ X470 @ ( dsetconstr @ X468 @ X469 ) )
=> ( in @ X470 @ X468 ) )
=> ( ! [X471: $i,X472: $i > $o,X473: $i] :
( ( in @ X473 @ ( dsetconstr @ X471 @ X472 ) )
=> ( X472 @ X473 ) )
=> ( ! [X474: $i > $o] :
( ( exu @ X474 )
=> ? [X475: $i] :
( ( X474 @ X475 )
& ! [X476: $i] :
( ( X474 @ X476 )
=> ( X475 = X476 ) ) ) )
=> ( ! [X477: $o,X478: $i] :
( ( in @ X478 @ ( prop2set @ X477 ) )
=> X477 )
=> ( ! [X479: $i] :
( ( in @ X479 @ emptyset )
=> ! [X480: $o] : X480 )
=> ( ! [X481: $i] :
( ( in @ X481 @ emptyset )
=> ~ $true )
=> ( ! [X482: $i] :
~ ( in @ X482 @ emptyset )
=> ( ! [X483: $i > $o] :
( ( exu @ X483 )
=> ? [X484: $i] : ( X483 @ X484 ) )
=> ( ! [X485: $i,X486: $i] :
( ! [X487: $i] :
( ( in @ X487 @ X485 )
=> ( in @ X487 @ X486 ) )
=> ( ! [X488: $i] :
( ( in @ X488 @ X486 )
=> ( in @ X488 @ X485 ) )
=> ( X485 = X486 ) ) )
=> ( ! [X489: $i] :
( ! [X490: $i] :
~ ( in @ X490 @ X489 )
=> ( X489 = emptyset ) )
=> ( ! [X491: $i] :
( ! [X492: $i] :
~ ( in @ X492 @ X491 )
=> ( X491 = emptyset ) )
=> ( ! [X493: $i,X494: $i > $o,X495: $i] :
( ( in @ X495 @ X493 )
=> ( ( in @ X495 @ ( dsetconstr @ X493 @ X494 ) )
<=> ( X494 @ X495 ) ) )
=> ( ! [X496: $i] :
( ( nonempty @ X496 )
=> ? [X497: $i] : ( in @ X497 @ X496 ) )
=> ( ! [X498: $i,X499: $i > $o,X500: $i] :
( ( in @ X500 @ X498 )
=> ( ( X499 @ X500 )
=> ( nonempty @ ( dsetconstr @ X498 @ X499 ) ) ) )
=> ( ! [X501: $i] :
( ? [X502: $i] : ( in @ X502 @ X501 )
=> ( nonempty @ X501 ) )
=> ( ! [X503: $i,X504: $i] : ( in @ X503 @ ( setadjoin @ X503 @ X504 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X505: $i,X506: $i,X507: $i] :
( ( in @ X507 @ X506 )
=> ( in @ X507 @ ( setadjoin @ X505 @ X506 ) ) )
=> ( ! [X508: $i,X509: $i,X510: $i] :
( ( in @ X510 @ ( setadjoin @ X508 @ X509 ) )
=> ! [X511: $o] :
( ( ( X510 = X508 )
=> X511 )
=> ( ( ( in @ X510 @ X509 )
=> X511 )
=> X511 ) ) )
=> ( ! [X512: $i,X513: $i,X514: $i] :
( ( in @ X514 @ ( setadjoin @ X512 @ X513 ) )
=> ( ( X514 = X512 )
| ( in @ X514 @ X513 ) ) )
=> ( ! [X515: $i] :
( ( dsetconstr @ X515
@ ^ [Z0: $i] : $true )
= X515 )
=> ( ! [X516: $i,X517: $i] :
( ! [X518: $i] :
( ( in @ X518 @ X517 )
=> ( in @ X518 @ X516 ) )
=> ( in @ X517 @ ( powerset @ X516 ) ) )
=> ( ! [X519: $i] : ( in @ emptyset @ ( powerset @ X519 ) )
=> ( ! [X520: $i] : ( in @ emptyset @ ( powerset @ X520 ) )
=> ( ! [X521: $i,X522: $i,X523: $i] :
( ( in @ X522 @ ( powerset @ X521 ) )
=> ( ( in @ X523 @ X522 )
=> ( in @ X523 @ X521 ) ) )
=> ( ! [X524: $i,X525: $i,X526: $i] :
( ( in @ X525 @ X526 )
=> ( ( in @ X526 @ X524 )
=> ( in @ X525 @ ( setunion @ X524 ) ) ) )
=> ( ! [X527: $i,X528: $i] :
( ( in @ X528 @ ( setunion @ X527 ) )
=> ! [X529: $o] :
( ! [X530: $i] :
( ( in @ X528 @ X530 )
=> ( ( in @ X530 @ X527 )
=> X529 ) )
=> X529 ) )
=> ( ! [X531: $i,X532: $i] :
( ( in @ X532 @ X531 )
=> ( in @ X532 @ ( powerset @ ( setunion @ X531 ) ) ) )
=> ( ! [X533: $i > $o] :
( ( exu @ X533 )
=> ? [X534: $i] :
! [X535: $i] :
( ( X533 @ X535 )
<=> ( X535 = X534 ) ) )
=> ( ! [X536: $i] :
( ( nonempty @ X536 )
=> ? [X537: $i] :
( ( in @ X537 @ X536 )
& $true ) )
=> ( ! [X538: $i,X539: $i] :
( ( in @ X538 @ ( setadjoin @ X539 @ emptyset ) )
=> ( X538 = X539 ) )
=> ( ! [X540: $i,X541: $i] :
( ( X540 != X541 )
=> ~ ( in @ X541 @ ( setadjoin @ X540 @ emptyset ) ) )
=> ( ! [X542: $i,X543: $i] :
( ( X542 = X543 )
=> ( in @ X542 @ ( setadjoin @ X543 @ emptyset ) ) )
=> ( ! [X544: $i,X545: $i] :
( ( in @ X544 @ ( setadjoin @ X545 @ emptyset ) )
=> ( in @ X545 @ ( setadjoin @ X544 @ emptyset ) ) )
=> ( ! [X546: $i,X547: $i,X548: $i] :
( ( in @ X548 @ ( setadjoin @ X546 @ ( setadjoin @ X547 @ emptyset ) ) )
=> ( ( X548 = X546 )
| ( X548 = X547 ) ) )
=> ( ! [X549: $i,X550: $i] : ( in @ X549 @ ( setadjoin @ X549 @ ( setadjoin @ X550 @ emptyset ) ) )
=> ( ! [X551: $i,X552: $i] : ( in @ X552 @ ( setadjoin @ X551 @ ( setadjoin @ X552 @ emptyset ) ) )
=> ( ! [X553: $i,X554: $i > $o] :
( ? [X555: $i] :
( ( in @ X555 @ X553 )
& ( X554 @ X555 ) )
=> ( ( ( dsetconstr @ X553 @ X554 )
= emptyset )
=> ~ $true ) )
=> ( ! [X556: $i > $o,X557: $i] :
( ( in @ X557 @ emptyset )
=> ( X556 @ X557 ) )
=> ( ! [X558: $i,X559: $i > $o] :
( ~ ! [X560: $i] :
( ( in @ X560 @ X558 )
=> ( X559 @ X560 ) )
=> ? [X561: $i] :
( ( in @ X561 @ X558 )
& ~ ( X559 @ X561 ) ) )
=> ( ! [X562: $i,X563: $i > $o] :
( ! [X564: $i] :
( ( in @ X564 @ X562 )
=> ~ ( X563 @ X564 ) )
=> ~ ? [X565: $i] :
( ( in @ X565 @ X562 )
& ( X563 @ X565 ) ) )
=> ( ! [X566: $i,X567: $i > $o] :
( ~ ? [X568: $i] :
( ( in @ X568 @ X566 )
& ( X567 @ X568 ) )
=> ! [X569: $i] :
( ( in @ X569 @ X566 )
=> ~ ( X567 @ X569 ) ) )
=> ( ! [X570: $i,X571: $i > $o] :
( ? [X572: $i] :
( ( in @ X572 @ X570 )
& ~ ( X571 @ X572 ) )
=> ~ ! [X573: $i] :
( ( in @ X573 @ X570 )
=> ( X571 @ X573 ) ) )
=> ( ! [X574: $o] :
( X574
=> ( in @ emptyset @ ( prop2set @ X574 ) ) )
=> ( prop2set2propI
=> ( ! [X575: $i,X576: $i > $o] :
( ~ ? [X577: $i] :
( ( in @ X577 @ X575 )
& ( X576 @ X577 ) )
=> ! [X578: $i] :
( ( in @ X578 @ X575 )
=> ~ ( X576 @ X578 ) ) )
=> ( ! [X579: $i,X580: $i > $o] :
( ~ ! [X581: $i] :
( ( in @ X581 @ X579 )
=> ( X580 @ X581 ) )
=> ? [X582: $i] :
( ( in @ X582 @ X579 )
& ~ ( X580 @ X582 ) ) )
=> ( ! [X583: $i > $o] :
( ? [X584: $i] :
( ( X583 @ X584 )
& ! [X585: $i] :
( ( X583 @ X585 )
=> ( X584 = X585 ) ) )
=> ( exu @ X583 ) )
=> ( ! [X586: $i > $o] :
( ? [X587: $i] : ( X586 @ X587 )
=> ( ! [X588: $i,X589: $i] :
( ( X586 @ X588 )
=> ( ( X586 @ X589 )
=> ( X588 = X589 ) ) )
=> ( exu @ X586 ) ) )
=> ( ! [X590: $i > $o] :
( ? [X591: $i] :
! [X592: $i] :
( ( X590 @ X592 )
<=> ( X592 = X591 ) )
=> ( exu @ X590 ) )
=> ( ! [X593: $i,X594: $i] :
( ( X593 = X594 )
=> ! [X595: $i,X596: $i] :
( ( X595 = X596 )
=> ( ( in @ X595 @ X593 )
=> ( in @ X596 @ X594 ) ) ) )
=> ( ! [X597: $i,X598: $i] :
( ( X597 = X598 )
=> ! [X599: $i,X600: $i] :
( ( X599 = X600 )
=> ( ( in @ X599 @ X597 )
<=> ( in @ X600 @ X598 ) ) ) )
=> ( ! [X601: $i > $o] :
( ( exu @ X601 )
=> ! [X602: $i,X603: $i] :
( ( X601 @ X602 )
=> ( ( X601 @ X603 )
=> ( X602 = X603 ) ) ) )
=> ( ! [X604: $i > $o,X605: $i > $o] :
( ! [X606: $i,X607: $i] :
( ( X606 = X607 )
=> ( ( X604 @ X606 )
<=> ( X605 @ X607 ) ) )
=> ( ( exu @ X604 )
<=> ( exu @ X605 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X608: $i,X609: $i] :
( ( X608 = X609 )
=> ! [X610: $i,X611: $i] :
( ( X610 = X611 )
=> ( ( setadjoin @ X608 @ X610 )
= ( setadjoin @ X609 @ X611 ) ) ) )
=> ( ! [X612: $i,X613: $i] :
( ( X612 = X613 )
=> ( ( powerset @ X612 )
= ( powerset @ X613 ) ) )
=> ( ! [X614: $i,X615: $i] :
( ( X614 = X615 )
=> ( ( setunion @ X614 )
= ( setunion @ X615 ) ) )
=> ( ( omega = omega )
=> ( ! [X616: $i > $o] :
( ( exu @ X616 )
=> ! [X617: $i,X618: $i] :
( ( X616 @ X617 )
=> ( ( X616 @ X618 )
=> ( X617 = X618 ) ) ) )
=> ( ! [X619: $i > $o,X620: $i > $o] :
( ! [X621: $i,X622: $i] :
( ( X621 = X622 )
=> ( ( X619 @ X621 )
<=> ( X620 @ X622 ) ) )
=> ( ( exu @ X619 )
=> ( ( exu @ X620 )
=> ( ( descr @ X619 )
= ( descr @ X620 ) ) ) ) )
=> ( ! [X623: $i,X624: $i] :
( ( X623 = X624 )
=> ! [X625: $i > $o,X626: $i > $o] :
( ! [X627: $i] :
( ( in @ X627 @ X623 )
=> ! [X628: $i] :
( ( in @ X628 @ X624 )
=> ( ( X627 = X628 )
=> ( ( X625 @ X627 )
<=> ( X626 @ X628 ) ) ) ) )
=> ( ( dsetconstr @ X623 @ X625 )
= ( dsetconstr @ X624 @ X626 ) ) ) )
=> ( ! [X629: $i,X630: $i] :
( ! [X631: $i] :
( ( in @ X631 @ X629 )
=> ( in @ X631 @ X630 ) )
=> ( subset @ X629 @ X630 ) )
=> ( ! [X632: $i,X633: $i] :
( ( X632 = X633 )
=> ( subset @ X633 @ X632 ) )
=> ( ! [X634: $i,X635: $i] :
( ( X634 = X635 )
=> ( subset @ X634 @ X635 ) )
=> ( ! [X636: $i,X637: $i] :
( ! [X638: $i] :
( ( in @ X638 @ X636 )
=> ( in @ X638 @ X637 ) )
=> ( subset @ X636 @ X637 ) )
=> ( ! [X639: $i] : ( subset @ emptyset @ X639 )
=> ( ! [X640: $i,X641: $i,X642: $i] :
( ( subset @ X640 @ X641 )
=> ( ( in @ X642 @ X640 )
=> ( in @ X642 @ X641 ) ) )
=> ( ! [X643: $i,X644: $i,X645: $i] :
( ( subset @ X643 @ X644 )
=> ( ~ ( in @ X645 @ X644 )
=> ~ ( in @ X645 @ X643 ) ) )
=> ( ! [X646: $i,X647: $i,X648: $i] :
( ( in @ X648 @ X646 )
=> ( ~ ( in @ X648 @ X647 )
=> ~ ( subset @ X646 @ X647 ) ) )
=> ( ! [X649: $i,X650: $i] :
( ~ ( subset @ X649 @ X650 )
=> ( X649 != X650 ) )
=> ( ! [X651: $i,X652: $i,X653: $i] :
( ( in @ X653 @ X651 )
=> ( ~ ( in @ X653 @ X652 )
=> ( X651 != X652 ) ) )
=> ( ! [X654: $i] : ( subset @ X654 @ X654 )
=> ( ! [X655: $i,X656: $i,X657: $i] :
( ( subset @ X655 @ X656 )
=> ( ( subset @ X656 @ X657 )
=> ( subset @ X655 @ X657 ) ) )
=> ( ! [X658: $i,X659: $i] : ( subset @ X659 @ ( setadjoin @ X658 @ X659 ) )
=> ( ! [X660: $i,X661: $i,X662: $i] :
( ( subset @ X660 @ X662 )
=> ( subset @ X660 @ ( setadjoin @ X661 @ X662 ) ) )
=> ( ! [X663: $i,X664: $i] :
( ( subset @ X663 @ X664 )
=> ( in @ X663 @ ( powerset @ X664 ) ) )
=> ( ! [X665: $i,X666: $i] :
( ( subset @ X665 @ X666 )
=> ( ( subset @ X666 @ X665 )
=> ( X665 = X666 ) ) )
=> ( ! [X667: $i] :
( ( subset @ X667 @ emptyset )
=> ( X667 = emptyset ) )
=> ( ! [X668: $i,X669: $i] :
( ( subset @ X669 @ X668 )
=> ( in @ X669 @ ( powerset @ X668 ) ) )
=> ( ! [X670: $i,X671: $i] :
( ( in @ X671 @ ( powerset @ X670 ) )
=> ( subset @ X671 @ X670 ) )
=> ( ! [X672: $i] : ( in @ X672 @ ( powerset @ X672 ) )
=> ( ! [X673: $i,X674: $i] :
( ( subset @ X673 @ X674 )
=> ( subset @ ( powerset @ X673 ) @ ( powerset @ X674 ) ) )
=> ( ! [X675: $i,X676: $i > $o] : ( in @ ( dsetconstr @ X675 @ X676 ) @ ( powerset @ X675 ) )
=> ( ! [X677: $i,X678: $i > $o] : ( subset @ ( dsetconstr @ X677 @ X678 ) @ X677 )
=> ( ! [X679: $i,X680: $i,X681: $i] :
( ( in @ X681 @ X679 )
=> ( in @ X681 @ ( binunion @ X679 @ X680 ) ) )
=> ( ! [X682: $i,X683: $i] : ( in @ X683 @ ( setadjoin @ X682 @ ( setadjoin @ X683 @ emptyset ) ) )
=> ( ! [X684: $i,X685: $i,X686: $i] :
( ( in @ X686 @ X685 )
=> ( in @ X686 @ ( binunion @ X684 @ X685 ) ) )
=> ( ! [X687: $i,X688: $i,X689: $i,X690: $o] :
( ( in @ X689 @ ( binunion @ X687 @ X688 ) )
=> ( ( ( in @ X689 @ X687 )
=> X690 )
=> ( ( ( in @ X689 @ X688 )
=> X690 )
=> X690 ) ) )
=> ( ! [X691: $i,X692: $i,X693: $i] :
( ( in @ X693 @ ( binunion @ X691 @ X692 ) )
=> ( ( in @ X693 @ X691 )
| ( in @ X693 @ X692 ) ) )
=> ( ! [X694: $i,X695: $i] : ( subset @ X694 @ ( binunion @ X694 @ X695 ) )
=> ( ! [X696: $i,X697: $i] : ( subset @ X697 @ ( binunion @ X696 @ X697 ) )
=> ( ! [X698: $i,X699: $i,X700: $i] :
( ( in @ X700 @ X698 )
=> ( ( in @ X700 @ X699 )
=> ( in @ X700 @ ( binintersect @ X698 @ X699 ) ) ) )
=> ( ! [X701: $i,X702: $i,X703: $i] :
( ( subset @ X703 @ X701 )
=> ( ( subset @ X703 @ X702 )
=> ( subset @ X703 @ ( binintersect @ X701 @ X702 ) ) ) )
=> ( ! [X704: $i,X705: $i,X706: $i] :
( ( in @ X706 @ ( binintersect @ X704 @ X705 ) )
=> ( in @ X706 @ X704 ) )
=> ( ! [X707: $i,X708: $i] : ( subset @ ( binintersect @ X707 @ X708 ) @ X707 )
=> ( ! [X709: $i,X710: $i] :
( ( subset @ X709 @ X710 )
=> ( ( binintersect @ X709 @ X710 )
= X709 ) )
=> ( ! [X711: $i,X712: $i] :
( ( ( binintersect @ X711 @ X712 )
= X712 )
=> ( subset @ X712 @ X711 ) )
=> ( ! [X713: $i,X714: $i,X715: $i] :
( ( in @ X715 @ ( binintersect @ X713 @ X714 ) )
=> ( in @ X715 @ X714 ) )
=> ( ! [X716: $i,X717: $i] :
( ~ ? [X718: $i] :
( ( in @ X718 @ X716 )
& ( in @ X718 @ X717 ) )
=> ( ( binintersect @ X716 @ X717 )
= emptyset ) )
=> ( ! [X719: $i,X720: $i] : ( subset @ ( binintersect @ X719 @ X720 ) @ X720 )
=> ( ! [X721: $i,X722: $i] :
( ( subset @ X722 @ X721 )
=> ( ( binintersect @ X721 @ X722 )
= X722 ) )
=> ( ! [X723: $i,X724: $i] :
( ( ( binintersect @ X723 @ X724 )
= X723 )
=> ( subset @ X723 @ X724 ) )
=> ( ! [X725: $i,X726: $i,X727: $i] :
( ( binintersect @ X725 @ ( binunion @ X726 @ X727 ) )
= ( binunion @ ( binintersect @ X725 @ X726 ) @ ( binintersect @ X725 @ X727 ) ) )
=> ( ! [X728: $i,X729: $i,X730: $i] :
( ( in @ X730 @ X728 )
=> ( ~ ( in @ X730 @ X729 )
=> ( in @ X730 @ ( setminus @ X728 @ X729 ) ) ) )
=> ( ! [X731: $i,X732: $i,X733: $i] :
( ( in @ X733 @ ( setminus @ X731 @ X732 ) )
=> ( in @ X733 @ X731 ) )
=> ( ! [X734: $i,X735: $i,X736: $i] :
( ( in @ X736 @ ( setminus @ X734 @ X735 ) )
=> ~ ( in @ X736 @ X735 ) )
=> ( ! [X737: $i,X738: $i] :
( ( subset @ X737 @ X738 )
=> ( ( setminus @ X737 @ X738 )
= emptyset ) )
=> ( ! [X739: $i,X740: $i,X741: $i] :
( ~ ( in @ X741 @ ( setminus @ X739 @ X740 ) )
=> ( ( in @ X741 @ X739 )
=> ( in @ X741 @ X740 ) ) )
=> ( ! [X742: $i,X743: $i,X744: $i] :
( ~ ( in @ X744 @ ( setminus @ X742 @ X743 ) )
=> ( ~ ( in @ X744 @ X743 )
=> ~ ( in @ X744 @ X742 ) ) )
=> ( ! [X745: $i,X746: $i,X747: $i] :
( ~ ( in @ X747 @ X745 )
=> ~ ( in @ X747 @ ( setminus @ X745 @ X746 ) ) )
=> ( ! [X748: $i,X749: $i,X750: $i] :
( ( in @ X750 @ X749 )
=> ~ ( in @ X750 @ ( setminus @ X748 @ X749 ) ) )
=> ( ! [X751: $i,X752: $i] : ( subset @ ( setminus @ X751 @ X752 ) @ X751 )
=> ( ! [X753: $i,X754: $i] :
( ( ( setminus @ X753 @ X754 )
= emptyset )
=> ( subset @ X753 @ X754 ) )
=> ( ! [X755: $i,X756: $i,X757: $i] :
( ( in @ X757 @ ( symdiff @ X755 @ X756 ) )
=> ! [X758: $o] :
( ( ( in @ X757 @ X755 )
=> ( ~ ( in @ X757 @ X756 )
=> X758 ) )
=> ( ( ~ ( in @ X757 @ X755 )
=> ( ( in @ X757 @ X756 )
=> X758 ) )
=> X758 ) ) )
=> ( ! [X759: $i,X760: $i,X761: $i] :
( ( in @ X761 @ X759 )
=> ( ~ ( in @ X761 @ X760 )
=> ( in @ X761 @ ( symdiff @ X759 @ X760 ) ) ) )
=> ( ! [X762: $i,X763: $i,X764: $i] :
( ~ ( in @ X764 @ X762 )
=> ( ( in @ X764 @ X763 )
=> ( in @ X764 @ ( symdiff @ X762 @ X763 ) ) ) )
=> ( ! [X765: $i,X766: $i,X767: $i] :
( ( in @ X767 @ X765 )
=> ( ( in @ X767 @ X766 )
=> ~ ( in @ X767 @ ( symdiff @ X765 @ X766 ) ) ) )
=> ( ! [X768: $i,X769: $i,X770: $i] :
( ~ ( in @ X770 @ X768 )
=> ( ~ ( in @ X770 @ X769 )
=> ~ ( in @ X770 @ ( symdiff @ X768 @ X769 ) ) ) )
=> ( ! [X771: $i,X772: $i] : ( in @ X772 @ ( setadjoin @ X771 @ ( setadjoin @ X772 @ emptyset ) ) )
=> ( ! [X773: $i,X774: $i] : ( in @ X773 @ ( setunion @ ( setadjoin @ ( setadjoin @ X773 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X773 @ ( setadjoin @ X774 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X775: $i,X776: $i] : ( in @ X776 @ ( setunion @ ( setadjoin @ ( setadjoin @ X775 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X775 @ ( setadjoin @ X776 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X777: $i,X778: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X777 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X777 @ ( setadjoin @ X778 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X779: $i,X780: $i] : ( iskpair @ ( kpair @ X779 @ X780 ) )
=> ( ! [X781: $i,X782: $i] :
( ( in @ X782 @ X781 )
=> ( subset @ ( setadjoin @ X782 @ emptyset ) @ X781 ) )
=> ( ! [X783: $i,X784: $i] :
( ( in @ X784 @ X783 )
=> ( in @ ( setadjoin @ X784 @ emptyset ) @ ( powerset @ X783 ) ) )
=> ( ! [X785: $i,X786: $i,X787: $i] :
( ( in @ X787 @ X785 )
=> ( in @ ( setadjoin @ X787 @ emptyset ) @ ( powerset @ ( binunion @ X785 @ X786 ) ) ) )
=> ( ! [X788: $i,X789: $i,X790: $i] :
( ( in @ X790 @ ( setadjoin @ X788 @ ( setadjoin @ X789 @ emptyset ) ) )
=> ( ( X790 = X788 )
| ( X790 = X789 ) ) )
=> ( ! [X791: $i,X792: $i,X793: $i] :
( ( in @ X793 @ X791 )
=> ! [X794: $i] :
( ( in @ X794 @ X792 )
=> ( subset @ ( setadjoin @ X793 @ ( setadjoin @ X794 @ emptyset ) ) @ ( binunion @ X791 @ X792 ) ) ) )
=> ( ! [X795: $i,X796: $i,X797: $i] :
( ( in @ X797 @ X795 )
=> ! [X798: $i] :
( ( in @ X798 @ X796 )
=> ( in @ ( setadjoin @ X797 @ ( setadjoin @ X798 @ emptyset ) ) @ ( powerset @ ( binunion @ X795 @ X796 ) ) ) ) )
=> ( ! [X799: $i,X800: $i,X801: $i] :
( ( in @ X801 @ X799 )
=> ! [X802: $i] :
( ( in @ X802 @ X800 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X801 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X801 @ ( setadjoin @ X802 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X799 @ X800 ) ) ) ) )
=> ( ! [X803: $i,X804: $i,X805: $i] :
( ( in @ X805 @ X803 )
=> ! [X806: $i] :
( ( in @ X806 @ X804 )
=> ( in @ ( setadjoin @ ( setadjoin @ X805 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X805 @ ( setadjoin @ X806 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X803 @ X804 ) ) ) ) ) )
=> ( ! [X807: $i,X808: $i,X809: $i] :
( ( in @ X809 @ X807 )
=> ! [X810: $i] :
( ( in @ X810 @ X808 )
=> ( in @ ( kpair @ X809 @ X810 ) @ ( powerset @ ( powerset @ ( binunion @ X807 @ X808 ) ) ) ) ) )
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cartprodpairin]),notdexE]),upairset2E]),ubforcartprodlem3]),setminusER]),setminusSubset2]),setminusERneg]),upairsetIL]),setminusELneg]),setminusILneg]),upairsetIR]),setminusIRneg]),setminusLsub]),c_0_147]),setminusSubset1]),symdiffE]),vacuousDall]),symdiffI1]),symdiffI2]),quantDeMorgan1]),symdiffIneg1]),symdiffIneg2]),quantDeMorgan2]),secondinupair]),setukpairIL]),quantDeMorgan3]),setukpairIR]),kpairiskpair]),quantDeMorgan4]),kpairp]),singletonsubset]),singletoninpowerset]),prop2setI]),singletoninpowunion]),eqimpsubset2]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),notdallE]),ubforcartprodlem2]),c_0_148]),c_0_149]),c_0_150]),inCongP]),in__Cong]),c_0_151]),c_0_152]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_153]),c_0_154]),c_0_155]),subsetI1]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_156]),c_0_157]),binunionIL]),eqinunit]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),singletonsswitch]),upairsetE]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_158]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_159]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_160]),nonemptyE1]),c_0_161]),noeltsimpempty]),emptyI]),setext]),c_0_162]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_163]),c_0_164]),c_0_165]),c_0_166]),c_0_167]),wellorderingAx]),foundationAx]),c_0_168]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_169]) ).
thf(c_0_171,plain,
! [X811: $i,X812: $i] :
( ( cartprod @ X811 @ X812 )
= ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X811 @ X812 ) ) )
@ ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ X811 )
& ? [X14: $i] :
( ( in @ X14 @ X812 )
& ( Z0
= ( kpair @ X3 @ X14 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[cartprod])]) ).
thf(c_0_172,negated_conjecture,
! [X815: $i,X816: $i,X818: $i,X819: $i,X820: $i,X821: $i,X822: $i,X823: $i,X824: $i,X825: $i,X826: $i,X828: $i,X829: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X837: $i,X838: $i > $i > $o,X839: $i,X842: $i,X844: $i,X845: $i,X846: $i,X847: $i,X849: $i,X850: $i > $o,X851: $i,X852: $i > $o,X853: $i,X854: $i,X855: $i > $o,X856: $i,X857: $i,X858: $i > $o,X859: $i,X860: $i > $o,X862: $i,X863: $o,X864: $i,X865: $i,X866: $o,X867: $i,X868: $i,X869: $i > $o,X871: $i,X872: $i,X875: $i,X877: $i,X879: $i,X880: $i > $o,X881: $i,X882: $i,X884: $i,X885: $i > $o,X886: $i,X887: $i,X888: $i,X889: $i,X890: $i,X891: $i,X892: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $o,X898: $i,X899: $i,X900: $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: $o,X917: $i,X918: $i,X919: $i > $o,X921: $i,X922: $i,X923: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i,X932: $i,X933: $i,X934: $i,X935: $i,X936: $i,X937: $i,X938: $i,X939: $i,X940: $i,X941: $i > $o,X942: $i,X943: $i > $o,X944: $i,X945: $i,X946: $i > $o,X947: $i,X949: $i,X950: $i > $o,X952: $i,X953: $i,X954: $i > $o,X956: $i,X957: $i,X958: $i > $o,X959: $i,X961: $o,X962: $i,X963: $i > $o,X965: $i,X966: $i,X967: $i > $o,X968: $i,X970: $i > $o,X971: $i,X973: $i > $o,X974: $i,X977: $i > $o,X978: $i,X980: $i,X981: $i,X982: $i,X983: $i,X984: $i,X985: $i,X986: $i,X987: $i,X988: $i > $o,X989: $i,X990: $i,X991: $i > $o,X992: $i > $o,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i > $o,X1004: $i,X1005: $i,X1006: $i > $o,X1007: $i > $o,X1010: $i,X1011: $i,X1012: $i > $o,X1013: $i > $o,X1016: $i,X1017: $i,X1019: $i,X1020: $i,X1021: $i,X1022: $i,X1023: $i,X1024: $i,X1026: $i,X1027: $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 > $o,X1064: $i,X1065: $i > $o,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $o,X1078: $i,X1079: $i,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,X1106: $i,X1107: $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: $o,X1146: $i,X1147: $i,X1148: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1164: $i,X1165: $i,X1166: $i,X1167: $i,X1168: $i,X1169: $i,X1170: $i,X1171: $i,X1172: $i,X1173: $i,X1174: $i,X1175: $i,X1176: $i,X1177: $i,X1178: $i,X1179: $i,X1180: $i,X1181: $i,X1182: $i,X1183: $i,X1184: $i,X1185: $i,X1186: $i,X1187: $i,X1188: $i,X1189: $i,X1190: $i,X1191: $i,X1192: $i,X1193: $i,X1194: $i,X1195: $i,X1196: $i,X1197: $i] :
( ( ~ ( in @ ( esk1_2 @ X815 @ X816 ) @ X815 )
| ~ ( in @ ( esk1_2 @ X815 @ X816 ) @ X816 )
| ( X815 = X816 ) )
& ( ( in @ ( esk1_2 @ X815 @ X816 ) @ X815 )
| ( in @ ( esk1_2 @ X815 @ X816 ) @ X816 )
| ( X815 = X816 ) )
& ~ ( in @ X818 @ emptyset )
& ( ~ ( in @ X821 @ ( setadjoin @ X819 @ X820 ) )
| ( X821 = X819 )
| ( in @ X821 @ X820 ) )
& ( ( X821 != X819 )
| ( in @ X821 @ ( setadjoin @ X819 @ X820 ) ) )
& ( ~ ( in @ X821 @ X820 )
| ( in @ X821 @ ( setadjoin @ X819 @ X820 ) ) )
& ( ~ ( in @ X823 @ ( powerset @ X822 ) )
| ~ ( in @ X824 @ X823 )
| ( in @ X824 @ X822 ) )
& ( ( in @ ( esk2_2 @ X825 @ X826 ) @ X826 )
| ( in @ X826 @ ( powerset @ X825 ) ) )
& ( ~ ( in @ ( esk2_2 @ X825 @ X826 ) @ X825 )
| ( in @ X826 @ ( powerset @ X825 ) ) )
& ( ( in @ X829 @ ( esk3_2 @ X828 @ X829 ) )
| ~ ( in @ X829 @ ( setunion @ X828 ) ) )
& ( ( in @ ( esk3_2 @ X828 @ X829 ) @ X828 )
| ~ ( in @ X829 @ ( setunion @ X828 ) ) )
& ( ~ ( in @ X832 @ X833 )
| ~ ( in @ X833 @ X831 )
| ( in @ X832 @ ( setunion @ X831 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X834 @ omega )
| ( in @ ( setadjoin @ X834 @ X834 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X835 ) @ omega )
| ~ ( in @ emptyset @ X835 )
| ~ ( in @ X837 @ omega )
| ( in @ X837 @ X835 ) )
& ( ( in @ ( esk4_1 @ X835 ) @ X835 )
| ~ ( in @ emptyset @ X835 )
| ~ ( in @ X837 @ omega )
| ( in @ X837 @ X835 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X835 ) @ ( esk4_1 @ X835 ) ) @ X835 )
| ~ ( in @ emptyset @ X835 )
| ~ ( in @ X837 @ omega )
| ( in @ X837 @ X835 ) )
& ( ( in @ ( esk7_3 @ X838 @ X839 @ X842 ) @ X839 )
| ~ ( in @ X842 @ ( esk6_2 @ X838 @ X839 ) )
| ( in @ ( esk5_2 @ X838 @ X839 ) @ X839 ) )
& ( ( X838 @ ( esk7_3 @ X838 @ X839 @ X842 ) @ X842 )
| ~ ( in @ X842 @ ( esk6_2 @ X838 @ X839 ) )
| ( in @ ( esk5_2 @ X838 @ X839 ) @ X839 ) )
& ( ~ ( in @ X845 @ X839 )
| ~ ( X838 @ X845 @ X844 )
| ( in @ X844 @ ( esk6_2 @ X838 @ X839 ) )
| ( in @ ( esk5_2 @ X838 @ X839 ) @ X839 ) )
& ( ( in @ ( esk7_3 @ X838 @ X839 @ X842 ) @ X839 )
| ~ ( in @ X842 @ ( esk6_2 @ X838 @ X839 ) )
| ~ ( exu @ ( X838 @ ( esk5_2 @ X838 @ X839 ) ) ) )
& ( ( X838 @ ( esk7_3 @ X838 @ X839 @ X842 ) @ X842 )
| ~ ( in @ X842 @ ( esk6_2 @ X838 @ X839 ) )
| ~ ( exu @ ( X838 @ ( esk5_2 @ X838 @ X839 ) ) ) )
& ( ~ ( in @ X845 @ X839 )
| ~ ( X838 @ X845 @ X844 )
| ( in @ X844 @ ( esk6_2 @ X838 @ X839 ) )
| ~ ( exu @ ( X838 @ ( esk5_2 @ X838 @ X839 ) ) ) )
& ( ( in @ ( esk8_1 @ X846 ) @ X846 )
| ~ ( in @ X847 @ X846 ) )
& ( ~ ( in @ X849 @ ( esk8_1 @ X846 ) )
| ~ ( in @ X849 @ X846 )
| ~ ( in @ X847 @ X846 ) )
& epred1_0
& ( ~ ( exu @ X850 )
| ( X850 @ ( descr @ X850 ) ) )
& ( ~ ( in @ X853 @ X851 )
| ~ ( X852 @ X853 )
| ( in @ X853 @ ( dsetconstr @ X851 @ X852 ) ) )
& ( ~ ( in @ X856 @ ( dsetconstr @ X854 @ X855 ) )
| ( in @ X856 @ X854 ) )
& ( ~ ( in @ X859 @ ( dsetconstr @ X857 @ X858 ) )
| ( X858 @ X859 ) )
& ( ( X860 @ ( esk9_1 @ X860 ) )
| ~ ( exu @ X860 ) )
& ( ~ ( X860 @ X862 )
| ( ( esk9_1 @ X860 )
= X862 )
| ~ ( exu @ X860 ) )
& ( ~ ( in @ X864 @ ( prop2set @ X863 ) )
| X863 )
& ( ~ ( in @ X865 @ emptyset )
| X866 )
& ( ~ ( in @ X867 @ emptyset )
| ~ $true )
& ~ ( in @ X868 @ emptyset )
& ( ~ ( exu @ X869 )
| ( X869 @ ( esk10_1 @ X869 ) ) )
& ( ( in @ ( esk12_2 @ X871 @ X872 ) @ X872 )
| ( X871 = X872 )
| ( in @ ( esk11_2 @ X871 @ X872 ) @ X871 ) )
& ( ~ ( in @ ( esk12_2 @ X871 @ X872 ) @ X871 )
| ( X871 = X872 )
| ( in @ ( esk11_2 @ X871 @ X872 ) @ X871 ) )
& ( ( in @ ( esk12_2 @ X871 @ X872 ) @ X872 )
| ( X871 = X872 )
| ~ ( in @ ( esk11_2 @ X871 @ X872 ) @ X872 ) )
& ( ~ ( in @ ( esk12_2 @ X871 @ X872 ) @ X871 )
| ( X871 = X872 )
| ~ ( in @ ( esk11_2 @ X871 @ X872 ) @ X872 ) )
& ( ( in @ ( esk13_1 @ X875 ) @ X875 )
| ( X875 = emptyset ) )
& ( ( in @ ( esk14_1 @ X877 ) @ X877 )
| ( X877 = emptyset ) )
& ( ~ ( in @ X881 @ ( dsetconstr @ X879 @ X880 ) )
| ( X880 @ X881 )
| ~ ( in @ X881 @ X879 ) )
& ( ~ ( X880 @ X881 )
| ( in @ X881 @ ( dsetconstr @ X879 @ X880 ) )
| ~ ( in @ X881 @ X879 ) )
& ( ~ ( nonempty @ X882 )
| ( in @ ( esk15_1 @ X882 ) @ X882 ) )
& ( ~ ( in @ X886 @ X884 )
| ~ ( X885 @ X886 )
| ( nonempty @ ( dsetconstr @ X884 @ X885 ) ) )
& ( ~ ( in @ X888 @ X887 )
| ( nonempty @ X887 ) )
& ( in @ X889 @ ( setadjoin @ X889 @ X890 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X893 @ X892 )
| ( in @ X893 @ ( setadjoin @ X891 @ X892 ) ) )
& ( ( in @ X896 @ X895 )
| X897
| ( X896 = X894 )
| ~ ( in @ X896 @ ( setadjoin @ X894 @ X895 ) ) )
& ( ~ X897
| X897
| ( X896 = X894 )
| ~ ( in @ X896 @ ( setadjoin @ X894 @ X895 ) ) )
& ( ( in @ X896 @ X895 )
| X897
| ~ X897
| ~ ( in @ X896 @ ( setadjoin @ X894 @ X895 ) ) )
& ( ~ X897
| X897
| ~ X897
| ~ ( in @ X896 @ ( setadjoin @ X894 @ X895 ) ) )
& ( ~ ( in @ X900 @ ( setadjoin @ X898 @ X899 ) )
| ( X900 = X898 )
| ( in @ X900 @ X899 ) )
& ( ( dsetconstr @ X901
@ ^ [Z0: $i] : $true )
= X901 )
& ( ( in @ ( esk16_2 @ X902 @ X903 ) @ X903 )
| ( in @ X903 @ ( powerset @ X902 ) ) )
& ( ~ ( in @ ( esk16_2 @ X902 @ X903 ) @ X902 )
| ( in @ X903 @ ( powerset @ X902 ) ) )
& ( in @ emptyset @ ( powerset @ X905 ) )
& ( in @ emptyset @ ( powerset @ X906 ) )
& ( ~ ( in @ X908 @ ( powerset @ X907 ) )
| ~ ( in @ X909 @ X908 )
| ( in @ X909 @ X907 ) )
& ( ~ ( in @ X911 @ X912 )
| ~ ( in @ X912 @ X910 )
| ( in @ X911 @ ( setunion @ X910 ) ) )
& ( ( in @ X914 @ ( esk17_3 @ X913 @ X914 @ X915 ) )
| X915
| ~ ( in @ X914 @ ( setunion @ X913 ) ) )
& ( ( in @ ( esk17_3 @ X913 @ X914 @ X915 ) @ X913 )
| X915
| ~ ( in @ X914 @ ( setunion @ X913 ) ) )
& ( ~ X915
| X915
| ~ ( in @ X914 @ ( setunion @ X913 ) ) )
& ( ~ ( in @ X918 @ X917 )
| ( in @ X918 @ ( powerset @ ( setunion @ X917 ) ) ) )
& ( ~ ( X919 @ X921 )
| ( X921
= ( esk18_1 @ X919 ) )
| ~ ( exu @ X919 ) )
& ( ( X922
!= ( esk18_1 @ X919 ) )
| ( X919 @ X922 )
| ~ ( exu @ X919 ) )
& ( ( in @ ( esk19_1 @ X923 ) @ X923 )
| ~ ( nonempty @ X923 ) )
& ( $true
| ~ ( nonempty @ X923 ) )
& ( ~ ( in @ X925 @ ( setadjoin @ X926 @ emptyset ) )
| ( X925 = X926 ) )
& ( ( X927 = X928 )
| ~ ( in @ X928 @ ( setadjoin @ X927 @ emptyset ) ) )
& ( ( X929 != X930 )
| ( in @ X929 @ ( setadjoin @ X930 @ emptyset ) ) )
& ( ~ ( in @ X931 @ ( setadjoin @ X932 @ emptyset ) )
| ( in @ X932 @ ( setadjoin @ X931 @ emptyset ) ) )
& ( ~ ( in @ X935 @ ( setadjoin @ X933 @ ( setadjoin @ X934 @ emptyset ) ) )
| ( X935 = X933 )
| ( X935 = X934 ) )
& ( in @ X936 @ ( setadjoin @ X936 @ ( setadjoin @ X937 @ emptyset ) ) )
& ( in @ X939 @ ( setadjoin @ X938 @ ( setadjoin @ X939 @ emptyset ) ) )
& ( ~ ( in @ X942 @ X940 )
| ~ ( X941 @ X942 )
| ( ( dsetconstr @ X940 @ X941 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X944 @ emptyset )
| ( X943 @ X944 ) )
& ( ( in @ ( esk20_2 @ X945 @ X946 ) @ X945 )
| ~ ( in @ X947 @ X945 )
| ( X946 @ X947 ) )
& ( ~ ( X946 @ ( esk20_2 @ X945 @ X946 ) )
| ~ ( in @ X947 @ X945 )
| ( X946 @ X947 ) )
& ( ( in @ ( esk21_2 @ X949 @ X950 ) @ X949 )
| ~ ( in @ X952 @ X949 )
| ~ ( X950 @ X952 ) )
& ( ( X950 @ ( esk21_2 @ X949 @ X950 ) )
| ~ ( in @ X952 @ X949 )
| ~ ( X950 @ X952 ) )
& ( ( in @ ( esk22_2 @ X953 @ X954 ) @ X953 )
| ~ ( in @ X956 @ X953 )
| ~ ( X954 @ X956 ) )
& ( ( X954 @ ( esk22_2 @ X953 @ X954 ) )
| ~ ( in @ X956 @ X953 )
| ~ ( X954 @ X956 ) )
& ( ( in @ ( esk23_2 @ X957 @ X958 ) @ X957 )
| ~ ( in @ X959 @ X957 )
| ( X958 @ X959 ) )
& ( ~ ( X958 @ ( esk23_2 @ X957 @ X958 ) )
| ~ ( in @ X959 @ X957 )
| ( X958 @ X959 ) )
& ( ~ X961
| ( in @ emptyset @ ( prop2set @ X961 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X962 @ X963 ) @ X962 )
| ~ ( in @ X965 @ X962 )
| ~ ( X963 @ X965 ) )
& ( ( X963 @ ( esk24_2 @ X962 @ X963 ) )
| ~ ( in @ X965 @ X962 )
| ~ ( X963 @ X965 ) )
& ( ( in @ ( esk25_2 @ X966 @ X967 ) @ X966 )
| ~ ( in @ X968 @ X966 )
| ( X967 @ X968 ) )
& ( ~ ( X967 @ ( esk25_2 @ X966 @ X967 ) )
| ~ ( in @ X968 @ X966 )
| ( X967 @ X968 ) )
& ( ( X970 @ ( esk26_2 @ X970 @ X971 ) )
| ~ ( X970 @ X971 )
| ( exu @ X970 ) )
& ( ( X971
!= ( esk26_2 @ X970 @ X971 ) )
| ~ ( X970 @ X971 )
| ( exu @ X970 ) )
& ( ( X973 @ ( esk27_1 @ X973 ) )
| ( exu @ X973 )
| ~ ( X973 @ X974 ) )
& ( ( X973 @ ( esk28_1 @ X973 ) )
| ( exu @ X973 )
| ~ ( X973 @ X974 ) )
& ( ( ( esk27_1 @ X973 )
!= ( esk28_1 @ X973 ) )
| ( exu @ X973 )
| ~ ( X973 @ X974 ) )
& ( ~ ( X977 @ ( esk29_2 @ X977 @ X978 ) )
| ( ( esk29_2 @ X977 @ X978 )
!= X978 )
| ( exu @ X977 ) )
& ( ( X977 @ ( esk29_2 @ X977 @ X978 ) )
| ( ( esk29_2 @ X977 @ X978 )
= X978 )
| ( exu @ X977 ) )
& ( ( X980 != X981 )
| ( X982 != X983 )
| ~ ( in @ X982 @ X980 )
| ( in @ X983 @ X981 ) )
& ( ~ ( in @ X986 @ X984 )
| ( in @ X987 @ X985 )
| ( X986 != X987 )
| ( X984 != X985 ) )
& ( ~ ( in @ X987 @ X985 )
| ( in @ X986 @ X984 )
| ( X986 != X987 )
| ( X984 != X985 ) )
& ( ~ ( exu @ X988 )
| ~ ( X988 @ X989 )
| ~ ( X988 @ X990 )
| ( X989 = X990 ) )
& ( ~ ( exu @ X991 )
| ( exu @ X992 )
| ( ( esk30_2 @ X991 @ X992 )
= ( esk31_2 @ X991 @ X992 ) ) )
& ( ~ ( exu @ X992 )
| ( exu @ X991 )
| ( ( esk30_2 @ X991 @ X992 )
= ( esk31_2 @ X991 @ X992 ) ) )
& ( ~ ( exu @ X991 )
| ( exu @ X992 )
| ~ ( X991 @ ( esk30_2 @ X991 @ X992 ) )
| ~ ( X992 @ ( esk31_2 @ X991 @ X992 ) ) )
& ( ~ ( exu @ X992 )
| ( exu @ X991 )
| ~ ( X991 @ ( esk30_2 @ X991 @ X992 ) )
| ~ ( X992 @ ( esk31_2 @ X991 @ X992 ) ) )
& ( ~ ( exu @ X991 )
| ( exu @ X992 )
| ( X991 @ ( esk30_2 @ X991 @ X992 ) )
| ( X992 @ ( esk31_2 @ X991 @ X992 ) ) )
& ( ~ ( exu @ X992 )
| ( exu @ X991 )
| ( X991 @ ( esk30_2 @ X991 @ X992 ) )
| ( X992 @ ( esk31_2 @ X991 @ X992 ) ) )
& ( emptyset = emptyset )
& ( ( X995 != X996 )
| ( X997 != X998 )
| ( ( setadjoin @ X995 @ X997 )
= ( setadjoin @ X996 @ X998 ) ) )
& ( ( X999 != X1000 )
| ( ( powerset @ X999 )
= ( powerset @ X1000 ) ) )
& ( ( X1001 != X1002 )
| ( ( setunion @ X1001 )
= ( setunion @ X1002 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1003 )
| ~ ( X1003 @ X1004 )
| ~ ( X1003 @ X1005 )
| ( X1004 = X1005 ) )
& ( ( ( esk32_2 @ X1006 @ X1007 )
= ( esk33_2 @ X1006 @ X1007 ) )
| ~ ( exu @ X1006 )
| ~ ( exu @ X1007 )
| ( ( descr @ X1006 )
= ( descr @ X1007 ) ) )
& ( ~ ( X1006 @ ( esk32_2 @ X1006 @ X1007 ) )
| ~ ( X1007 @ ( esk33_2 @ X1006 @ X1007 ) )
| ~ ( exu @ X1006 )
| ~ ( exu @ X1007 )
| ( ( descr @ X1006 )
= ( descr @ X1007 ) ) )
& ( ( X1006 @ ( esk32_2 @ X1006 @ X1007 ) )
| ( X1007 @ ( esk33_2 @ X1006 @ X1007 ) )
| ~ ( exu @ X1006 )
| ~ ( exu @ X1007 )
| ( ( descr @ X1006 )
= ( descr @ X1007 ) ) )
& ( ( in @ ( esk34_4 @ X1010 @ X1011 @ X1012 @ X1013 ) @ X1010 )
| ( ( dsetconstr @ X1010 @ X1012 )
= ( dsetconstr @ X1011 @ X1013 ) )
| ( X1010 != X1011 ) )
& ( ( in @ ( esk35_4 @ X1010 @ X1011 @ X1012 @ X1013 ) @ X1011 )
| ( ( dsetconstr @ X1010 @ X1012 )
= ( dsetconstr @ X1011 @ X1013 ) )
| ( X1010 != X1011 ) )
& ( ( ( esk34_4 @ X1010 @ X1011 @ X1012 @ X1013 )
= ( esk35_4 @ X1010 @ X1011 @ X1012 @ X1013 ) )
| ( ( dsetconstr @ X1010 @ X1012 )
= ( dsetconstr @ X1011 @ X1013 ) )
| ( X1010 != X1011 ) )
& ( ~ ( X1012 @ ( esk34_4 @ X1010 @ X1011 @ X1012 @ X1013 ) )
| ~ ( X1013 @ ( esk35_4 @ X1010 @ X1011 @ X1012 @ X1013 ) )
| ( ( dsetconstr @ X1010 @ X1012 )
= ( dsetconstr @ X1011 @ X1013 ) )
| ( X1010 != X1011 ) )
& ( ( X1012 @ ( esk34_4 @ X1010 @ X1011 @ X1012 @ X1013 ) )
| ( X1013 @ ( esk35_4 @ X1010 @ X1011 @ X1012 @ X1013 ) )
| ( ( dsetconstr @ X1010 @ X1012 )
= ( dsetconstr @ X1011 @ X1013 ) )
| ( X1010 != X1011 ) )
& ( ( in @ ( esk36_2 @ X1016 @ X1017 ) @ X1016 )
| ( subset @ X1016 @ X1017 ) )
& ( ~ ( in @ ( esk36_2 @ X1016 @ X1017 ) @ X1017 )
| ( subset @ X1016 @ X1017 ) )
& ( ( X1019 != X1020 )
| ( subset @ X1020 @ X1019 ) )
& ( ( X1021 != X1022 )
| ( subset @ X1021 @ X1022 ) )
& ( ( in @ ( esk37_2 @ X1023 @ X1024 ) @ X1023 )
| ( subset @ X1023 @ X1024 ) )
& ( ~ ( in @ ( esk37_2 @ X1023 @ X1024 ) @ X1024 )
| ( subset @ X1023 @ X1024 ) )
& ( subset @ emptyset @ X1026 )
& ( ~ ( subset @ X1027 @ X1028 )
| ~ ( in @ X1029 @ X1027 )
| ( in @ X1029 @ X1028 ) )
& ( ~ ( subset @ X1030 @ X1031 )
| ( in @ X1032 @ X1031 )
| ~ ( in @ X1032 @ X1030 ) )
& ( ~ ( in @ X1035 @ X1033 )
| ( in @ X1035 @ X1034 )
| ~ ( subset @ X1033 @ X1034 ) )
& ( ( subset @ X1036 @ X1037 )
| ( X1036 != X1037 ) )
& ( ~ ( in @ X1040 @ X1038 )
| ( in @ X1040 @ X1039 )
| ( X1038 != X1039 ) )
& ( subset @ X1041 @ X1041 )
& ( ~ ( subset @ X1042 @ X1043 )
| ~ ( subset @ X1043 @ X1044 )
| ( subset @ X1042 @ X1044 ) )
& ( subset @ X1046 @ ( setadjoin @ X1045 @ X1046 ) )
& ( ~ ( subset @ X1047 @ X1049 )
| ( subset @ X1047 @ ( setadjoin @ X1048 @ X1049 ) ) )
& ( ~ ( subset @ X1050 @ X1051 )
| ( in @ X1050 @ ( powerset @ X1051 ) ) )
& ( ~ ( subset @ X1052 @ X1053 )
| ~ ( subset @ X1053 @ X1052 )
| ( X1052 = X1053 ) )
& ( ~ ( subset @ X1054 @ emptyset )
| ( X1054 = emptyset ) )
& ( ~ ( subset @ X1056 @ X1055 )
| ( in @ X1056 @ ( powerset @ X1055 ) ) )
& ( ~ ( in @ X1058 @ ( powerset @ X1057 ) )
| ( subset @ X1058 @ X1057 ) )
& ( in @ X1059 @ ( powerset @ X1059 ) )
& ( ~ ( subset @ X1060 @ X1061 )
| ( subset @ ( powerset @ X1060 ) @ ( powerset @ X1061 ) ) )
& ( in @ ( dsetconstr @ X1062 @ X1063 ) @ ( powerset @ X1062 ) )
& ( subset @ ( dsetconstr @ X1064 @ X1065 ) @ X1064 )
& ( ~ ( in @ X1068 @ X1066 )
| ( in @ X1068 @ ( binunion @ X1066 @ X1067 ) ) )
& ( in @ X1070 @ ( setadjoin @ X1069 @ ( setadjoin @ X1070 @ emptyset ) ) )
& ( ~ ( in @ X1073 @ X1072 )
| ( in @ X1073 @ ( binunion @ X1071 @ X1072 ) ) )
& ( ( in @ X1076 @ X1075 )
| X1077
| ( in @ X1076 @ X1074 )
| ~ ( in @ X1076 @ ( binunion @ X1074 @ X1075 ) ) )
& ( ~ X1077
| X1077
| ( in @ X1076 @ X1074 )
| ~ ( in @ X1076 @ ( binunion @ X1074 @ X1075 ) ) )
& ( ( in @ X1076 @ X1075 )
| X1077
| ~ X1077
| ~ ( in @ X1076 @ ( binunion @ X1074 @ X1075 ) ) )
& ( ~ X1077
| X1077
| ~ X1077
| ~ ( in @ X1076 @ ( binunion @ X1074 @ X1075 ) ) )
& ( ~ ( in @ X1080 @ ( binunion @ X1078 @ X1079 ) )
| ( in @ X1080 @ X1078 )
| ( in @ X1080 @ X1079 ) )
& ( subset @ X1081 @ ( binunion @ X1081 @ X1082 ) )
& ( subset @ X1084 @ ( binunion @ X1083 @ X1084 ) )
& ( ~ ( in @ X1087 @ X1085 )
| ~ ( in @ X1087 @ X1086 )
| ( in @ X1087 @ ( binintersect @ X1085 @ X1086 ) ) )
& ( ~ ( subset @ X1090 @ X1088 )
| ~ ( subset @ X1090 @ X1089 )
| ( subset @ X1090 @ ( binintersect @ X1088 @ X1089 ) ) )
& ( ~ ( in @ X1093 @ ( binintersect @ X1091 @ X1092 ) )
| ( in @ X1093 @ X1091 ) )
& ( subset @ ( binintersect @ X1094 @ X1095 ) @ X1094 )
& ( ~ ( subset @ X1096 @ X1097 )
| ( ( binintersect @ X1096 @ X1097 )
= X1096 ) )
& ( ( ( binintersect @ X1098 @ X1099 )
!= X1099 )
| ( subset @ X1099 @ X1098 ) )
& ( ~ ( in @ X1102 @ ( binintersect @ X1100 @ X1101 ) )
| ( in @ X1102 @ X1101 ) )
& ( ( in @ ( esk38_2 @ X1103 @ X1104 ) @ X1103 )
| ( ( binintersect @ X1103 @ X1104 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1103 @ X1104 ) @ X1104 )
| ( ( binintersect @ X1103 @ X1104 )
= emptyset ) )
& ( subset @ ( binintersect @ X1106 @ X1107 ) @ X1107 )
& ( ~ ( subset @ X1109 @ X1108 )
| ( ( binintersect @ X1108 @ X1109 )
= X1109 ) )
& ( ( ( binintersect @ X1110 @ X1111 )
!= X1110 )
| ( subset @ X1110 @ X1111 ) )
& ( ( binintersect @ X1112 @ ( binunion @ X1113 @ X1114 ) )
= ( binunion @ ( binintersect @ X1112 @ X1113 ) @ ( binintersect @ X1112 @ X1114 ) ) )
& ( ~ ( in @ X1117 @ X1115 )
| ( in @ X1117 @ X1116 )
| ( in @ X1117 @ ( setminus @ X1115 @ X1116 ) ) )
& ( ~ ( in @ X1120 @ ( setminus @ X1118 @ X1119 ) )
| ( in @ X1120 @ X1118 ) )
& ( ~ ( in @ X1123 @ ( setminus @ X1121 @ X1122 ) )
| ~ ( in @ X1123 @ X1122 ) )
& ( ~ ( subset @ X1124 @ X1125 )
| ( ( setminus @ X1124 @ X1125 )
= emptyset ) )
& ( ( in @ X1128 @ ( setminus @ X1126 @ X1127 ) )
| ~ ( in @ X1128 @ X1126 )
| ( in @ X1128 @ X1127 ) )
& ( ( in @ X1131 @ ( setminus @ X1129 @ X1130 ) )
| ( in @ X1131 @ X1130 )
| ~ ( in @ X1131 @ X1129 ) )
& ( ( in @ X1134 @ X1132 )
| ~ ( in @ X1134 @ ( setminus @ X1132 @ X1133 ) ) )
& ( ~ ( in @ X1137 @ X1136 )
| ~ ( in @ X1137 @ ( setminus @ X1135 @ X1136 ) ) )
& ( subset @ ( setminus @ X1138 @ X1139 ) @ X1138 )
& ( ( ( setminus @ X1140 @ X1141 )
!= emptyset )
| ( subset @ X1140 @ X1141 ) )
& ( ~ ( in @ X1144 @ X1142 )
| X1145
| ( in @ X1144 @ X1142 )
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ( in @ X1144 @ X1143 )
| X1145
| ( in @ X1144 @ X1142 )
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ~ X1145
| X1145
| ( in @ X1144 @ X1142 )
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ~ ( in @ X1144 @ X1142 )
| X1145
| ~ ( in @ X1144 @ X1143 )
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ( in @ X1144 @ X1143 )
| X1145
| ~ ( in @ X1144 @ X1143 )
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ~ X1145
| X1145
| ~ ( in @ X1144 @ X1143 )
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ~ ( in @ X1144 @ X1142 )
| X1145
| ~ X1145
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ( in @ X1144 @ X1143 )
| X1145
| ~ X1145
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ~ X1145
| X1145
| ~ X1145
| ~ ( in @ X1144 @ ( symdiff @ X1142 @ X1143 ) ) )
& ( ~ ( in @ X1148 @ X1146 )
| ( in @ X1148 @ X1147 )
| ( in @ X1148 @ ( symdiff @ X1146 @ X1147 ) ) )
& ( ( in @ X1151 @ X1149 )
| ~ ( in @ X1151 @ X1150 )
| ( in @ X1151 @ ( symdiff @ X1149 @ X1150 ) ) )
& ( ~ ( in @ X1154 @ X1152 )
| ~ ( in @ X1154 @ X1153 )
| ~ ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) )
& ( ( in @ X1157 @ X1155 )
| ( in @ X1157 @ X1156 )
| ~ ( in @ X1157 @ ( symdiff @ X1155 @ X1156 ) ) )
& ( in @ X1159 @ ( setadjoin @ X1158 @ ( setadjoin @ X1159 @ emptyset ) ) )
& ( in @ X1160 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1160 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1160 @ ( setadjoin @ X1161 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1163 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1162 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1162 @ ( setadjoin @ X1163 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1164 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1164 @ ( setadjoin @ X1165 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1166 @ X1167 ) )
& ( ~ ( in @ X1169 @ X1168 )
| ( subset @ ( setadjoin @ X1169 @ emptyset ) @ X1168 ) )
& ( ~ ( in @ X1171 @ X1170 )
| ( in @ ( setadjoin @ X1171 @ emptyset ) @ ( powerset @ X1170 ) ) )
& ( ~ ( in @ X1174 @ X1172 )
| ( in @ ( setadjoin @ X1174 @ emptyset ) @ ( powerset @ ( binunion @ X1172 @ X1173 ) ) ) )
& ( ~ ( in @ X1177 @ ( setadjoin @ X1175 @ ( setadjoin @ X1176 @ emptyset ) ) )
| ( X1177 = X1175 )
| ( X1177 = X1176 ) )
& ( ~ ( in @ X1180 @ X1178 )
| ~ ( in @ X1181 @ X1179 )
| ( subset @ ( setadjoin @ X1180 @ ( setadjoin @ X1181 @ emptyset ) ) @ ( binunion @ X1178 @ X1179 ) ) )
& ( ~ ( in @ X1184 @ X1182 )
| ~ ( in @ X1185 @ X1183 )
| ( in @ ( setadjoin @ X1184 @ ( setadjoin @ X1185 @ emptyset ) ) @ ( powerset @ ( binunion @ X1182 @ X1183 ) ) ) )
& ( ~ ( in @ X1188 @ X1186 )
| ~ ( in @ X1189 @ X1187 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1188 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1188 @ ( setadjoin @ X1189 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1186 @ X1187 ) ) ) )
& ( ~ ( in @ X1192 @ X1190 )
| ~ ( in @ X1193 @ X1191 )
| ( in @ ( setadjoin @ ( setadjoin @ X1192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1192 @ ( setadjoin @ X1193 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1190 @ X1191 ) ) ) ) )
& ( ~ ( in @ X1196 @ X1194 )
| ~ ( in @ X1197 @ X1195 )
| ( in @ ( kpair @ X1196 @ X1197 ) @ ( powerset @ ( powerset @ ( binunion @ X1194 @ X1195 ) ) ) ) )
& ( in @ esk41_0 @ esk39_0 )
& ( in @ esk42_0 @ esk40_0 )
& ~ ( in @ ( kpair @ esk41_0 @ esk42_0 ) @ ( cartprod @ esk39_0 @ esk40_0 ) ) ),
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_170])])])])])])]) ).
thf(c_0_173,plain,
! [X1202: $i,X1203: $i] :
( ( cartprod @ X1202 @ X1203 )
= ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1202 @ X1203 ) ) )
@ ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ X1202 )
& ? [X14: $i] :
( ( in @ X14 @ X1203 )
& ( Z0
= ( kpair @ X3 @ X14 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_171]) ).
thf(c_0_174,plain,
! [X1228: $i,X2: $i,X3: $i] :
( ( epred3_2 @ X3 @ X2 @ X1228 )
<=> ? [X1226: $i] :
( ( in @ X1226 @ X2 )
& ? [X1227: $i] :
( ( in @ X1227 @ X3 )
& ( X1228
= ( kpair @ X1226 @ X1227 ) ) ) ) ),
introduced(definition) ).
thf(c_0_175,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
| ~ ( X1 @ X2 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_176,plain,
! [X3: $i,X2: $i] :
( ( cartprod @ X2 @ X3 )
= ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X2 @ X3 ) ) ) @ ( epred3_2 @ X3 @ X2 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_173]),c_0_174]) ).
thf(c_0_177,negated_conjecture,
~ ( in @ ( kpair @ esk41_0 @ esk42_0 ) @ ( cartprod @ esk39_0 @ esk40_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_178,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X3 @ X4 ) )
| ~ ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X3 @ X4 ) ) ) )
| ~ ( epred3_2 @ X4 @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
thf(c_0_179,plain,
! [X1230: $i,X1231: $i,X1232: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i] :
( ( ( in @ ( esk48_3 @ X1230 @ X1231 @ X1232 ) @ X1231 )
| ~ ( epred3_2 @ X1232 @ X1231 @ X1230 ) )
& ( ( in @ ( esk49_3 @ X1230 @ X1231 @ X1232 ) @ X1232 )
| ~ ( epred3_2 @ X1232 @ X1231 @ X1230 ) )
& ( ( X1230
= ( kpair @ ( esk48_3 @ X1230 @ X1231 @ X1232 ) @ ( esk49_3 @ X1230 @ X1231 @ X1232 ) ) )
| ~ ( epred3_2 @ X1232 @ X1231 @ X1230 ) )
& ( ~ ( in @ X1238 @ X1236 )
| ~ ( in @ X1239 @ X1237 )
| ( X1235
!= ( kpair @ X1238 @ X1239 ) )
| ( epred3_2 @ X1237 @ X1236 @ X1235 ) ) ),
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)],[])])])])])])]) ).
thf(c_0_180,negated_conjecture,
( ~ ( in @ ( kpair @ esk41_0 @ esk42_0 ) @ ( powerset @ ( powerset @ ( binunion @ esk39_0 @ esk40_0 ) ) ) )
| ~ ( epred3_2 @ esk40_0 @ esk39_0 @ ( kpair @ esk41_0 @ esk42_0 ) ) ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
thf(c_0_181,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i] :
( ( in @ ( kpair @ X2 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X3 @ X5 ) ) ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_182,negated_conjecture,
in @ esk42_0 @ esk40_0,
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_183,negated_conjecture,
in @ esk41_0 @ esk39_0,
inference(split_conjunct,[status(thm)],[c_0_172]) ).
thf(c_0_184,plain,
! [X3: $i,X2: $i,X7: $i,X5: $i,X4: $i] :
( ( epred3_2 @ X5 @ X3 @ X7 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X5 )
| ( X7
!= ( kpair @ X2 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
thf(c_0_185,negated_conjecture,
~ ( epred3_2 @ esk40_0 @ esk39_0 @ ( kpair @ esk41_0 @ esk42_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182]),c_0_183])]) ).
thf(c_0_186,plain,
! [X2: $i,X5: $i,X4: $i,X3: $i] :
( ( epred3_2 @ X2 @ X3 @ ( kpair @ X4 @ X5 ) )
| ~ ( in @ X5 @ X2 )
| ~ ( in @ X4 @ X3 ) ),
inference(er,[status(thm)],[c_0_184]) ).
thf(c_0_187,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_182]),c_0_183])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SEU630^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 17:26:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 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
% 68.68/9.18 # Version: 3.1.0-ho
% 68.68/9.18 # Preprocessing class: HSLMSLSSLLLCHFA.
% 68.68/9.18 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 68.68/9.18 # Starting ehoh_best5 with 300s (1) cores
% 68.68/9.18 # Starting almost_fo_3_lam with 300s (1) cores
% 68.68/9.18 # Starting new_bool_5 with 300s (1) cores
% 68.68/9.18 # Starting pre_casc_3 with 300s (1) cores
% 68.68/9.18 # Starting ho_unfolding_8 with 300s (1) cores
% 68.68/9.18 # Starting new_ho_10_cnf2 with 300s (1) cores
% 68.68/9.18 # Starting new_bool_3 with 300s (1) cores
% 68.68/9.18 # Starting new_ho_5 with 300s (1) cores
% 68.68/9.18 # new_bool_5 with pid 17598 completed with status 0
% 68.68/9.18 # Result found by new_bool_5
% 68.68/9.18 # Preprocessing class: HSLMSLSSLLLCHFA.
% 68.68/9.18 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 68.68/9.18 # Starting ehoh_best5 with 300s (1) cores
% 68.68/9.18 # Starting almost_fo_3_lam with 300s (1) cores
% 68.68/9.18 # Starting new_bool_5 with 300s (1) cores
% 68.68/9.18 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 68.68/9.18 # Search class: HGHSM-FSLM31-MHFMMSBN
% 68.68/9.18 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 68.68/9.18 # Starting new_ho_10_cnf2 with 163s (1) cores
% 68.68/9.18 # new_ho_10_cnf2 with pid 17615 completed with status 0
% 68.68/9.18 # Result found by new_ho_10_cnf2
% 68.68/9.18 # Preprocessing class: HSLMSLSSLLLCHFA.
% 68.68/9.18 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 68.68/9.18 # Starting ehoh_best5 with 300s (1) cores
% 68.68/9.18 # Starting almost_fo_3_lam with 300s (1) cores
% 68.68/9.18 # Starting new_bool_5 with 300s (1) cores
% 68.68/9.18 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 68.68/9.18 # Search class: HGHSM-FSLM31-MHFMMSBN
% 68.68/9.18 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 68.68/9.18 # Starting new_ho_10_cnf2 with 163s (1) cores
% 68.68/9.18 # Preprocessing time : 0.007 s
% 68.68/9.18 # Presaturation interreduction done
% 68.68/9.18
% 68.68/9.18 # Proof found!
% 68.68/9.18 # SZS status Theorem
% 68.68/9.18 # SZS output start CNFRefutation
% See solution above
% 68.68/9.18 # Parsed axioms : 321
% 68.68/9.18 # Removed by relevancy pruning/SinE : 173
% 68.68/9.18 # Initial clauses : 234
% 68.68/9.18 # Removed in clause preprocessing : 25
% 68.68/9.18 # Initial clauses in saturation : 209
% 68.68/9.18 # Processed clauses : 4727
% 68.68/9.18 # ...of these trivial : 118
% 68.68/9.18 # ...subsumed : 1560
% 68.68/9.18 # ...remaining for further processing : 3049
% 68.68/9.18 # Other redundant clauses eliminated : 90
% 68.68/9.18 # Clauses deleted for lack of memory : 0
% 68.68/9.18 # Backward-subsumed : 435
% 68.68/9.18 # Backward-rewritten : 47
% 68.68/9.18 # Generated clauses : 496151
% 68.68/9.18 # ...of the previous two non-redundant : 491749
% 68.68/9.18 # ...aggressively subsumed : 0
% 68.68/9.18 # Contextual simplify-reflections : 11
% 68.68/9.18 # Paramodulations : 495940
% 68.68/9.18 # Factorizations : 110
% 68.68/9.18 # NegExts : 0
% 68.68/9.18 # Equation resolutions : 90
% 68.68/9.18 # Disequality decompositions : 0
% 68.68/9.18 # Total rewrite steps : 8988
% 68.68/9.18 # ...of those cached : 8008
% 68.68/9.18 # Propositional unsat checks : 0
% 68.68/9.18 # Propositional check models : 0
% 68.68/9.18 # Propositional check unsatisfiable : 0
% 68.68/9.18 # Propositional clauses : 0
% 68.68/9.18 # Propositional clauses after purity: 0
% 68.68/9.18 # Propositional unsat core size : 0
% 68.68/9.18 # Propositional preprocessing time : 0.000
% 68.68/9.18 # Propositional encoding time : 0.000
% 68.68/9.18 # Propositional solver time : 0.000
% 68.68/9.18 # Success case prop preproc time : 0.000
% 68.68/9.18 # Success case prop encoding time : 0.000
% 68.68/9.18 # Success case prop solver time : 0.000
% 68.68/9.18 # Current number of processed clauses : 2371
% 68.68/9.18 # Positive orientable unit clauses : 171
% 68.68/9.18 # Positive unorientable unit clauses: 0
% 68.68/9.18 # Negative unit clauses : 125
% 68.68/9.18 # Non-unit-clauses : 2075
% 68.68/9.18 # Current number of unprocessed clauses: 485893
% 68.68/9.18 # ...number of literals in the above : 2110235
% 68.68/9.18 # Current number of archived formulas : 0
% 68.68/9.18 # Current number of archived clauses : 666
% 68.68/9.18 # Clause-clause subsumption calls (NU) : 598670
% 68.68/9.18 # Rec. Clause-clause subsumption calls : 303220
% 68.68/9.18 # Non-unit clause-clause subsumptions : 710
% 68.68/9.18 # Unit Clause-clause subsumption calls : 21183
% 68.68/9.18 # Rewrite failures with RHS unbound : 0
% 68.68/9.18 # BW rewrite match attempts : 268
% 68.68/9.18 # BW rewrite match successes : 44
% 68.68/9.18 # Condensation attempts : 4727
% 68.68/9.18 # Condensation successes : 26
% 68.68/9.18 # Termbank termtop insertions : 9960932
% 68.68/9.18 # Search garbage collected termcells : 12858
% 68.68/9.18
% 68.68/9.18 # -------------------------------------------------
% 68.68/9.18 # User time : 8.190 s
% 68.68/9.18 # System time : 0.298 s
% 68.68/9.18 # Total time : 8.488 s
% 68.68/9.18 # Maximum resident set size: 5012 pages
% 68.68/9.18
% 68.68/9.18 # -------------------------------------------------
% 68.68/9.18 # User time : 8.204 s
% 68.68/9.18 # System time : 0.302 s
% 68.68/9.18 # Total time : 8.506 s
% 68.68/9.18 # Maximum resident set size: 2120 pages
% 68.68/9.18 % E---3.1 exiting
% 68.68/9.18 % E exiting
%------------------------------------------------------------------------------