%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU657^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 03:28:54 EDT 2024
% Result : Theorem 0.21s 0.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 227
% Syntax : Number of formulae : 261 ( 30 unt; 207 typ; 0 def)
% Number of atoms : 869 ( 124 equ; 0 cnn)
% Maximal formula atoms : 281 ( 16 avg)
% Number of connectives : 2412 ( 89 ~; 105 |; 270 &;1485 @)
% ( 21 <=>; 442 =>; 0 <=; 0 <~>)
% Maximal formula depth : 254 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 209 ( 207 usr; 178 con; 0-3 aty)
% Number of variables : 278 ( 49 ^ 169 !; 60 ?; 278 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $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_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
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_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_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_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_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_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_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_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_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
esk1_2: $i > $i > $i ).
thf(decl_227,type,
esk2_2: $i > $i > $i ).
thf(decl_228,type,
esk3_2: $i > $i > $i ).
thf(decl_229,type,
esk4_2: $i > $i > $i ).
thf(decl_230,type,
esk5_3: $i > $i > $i > $i ).
thf(decl_231,type,
esk6_3: $i > $i > $i > $i ).
thf(decl_232,type,
esk7_3: $i > $i > $i > $i ).
thf(decl_233,type,
esk8_3: $i > $i > $i > $i ).
thf(decl_234,type,
esk9_2: $i > ( $i > $o ) > $i ).
thf(decl_235,type,
esk10_2: $i > ( $i > $o ) > $i ).
thf(decl_236,type,
esk11_2: $i > ( $i > $o ) > $i ).
thf(decl_237,type,
esk12_2: $i > ( $i > $o ) > $i ).
thf(decl_238,type,
esk13_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_239,type,
esk14_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_240,type,
esk15_2: $i > ( $i > $o ) > $i ).
thf(decl_241,type,
esk16_2: $i > ( $i > $o ) > $i ).
thf(decl_242,type,
esk17_2: $i > ( $i > $o ) > $i ).
thf(decl_243,type,
esk18_1: $i > $i ).
thf(decl_244,type,
esk19_1: $i > $i ).
thf(decl_245,type,
esk20_0: $i ).
thf(decl_246,type,
esk21_0: $i ).
thf(decl_247,type,
esk22_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X4 ) )
& ( X4
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairsurjEq,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(c_0_20,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X73: $i] :
( ( in @ X73
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X73 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_21,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_22,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_23,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X73: $i] :
( ( in @ X73
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X73 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_25,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_26,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_27,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_28,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_29,plain,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ksndsingleton]) ).
thf(c_0_30,plain,
( ex1I2
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X76: $i] :
( ( in @ X76
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X76 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_31,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X75: $i] :
( ( in @ X75
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X75 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_23]) ).
thf(c_0_32,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X74: $i] :
( ( in @ X74
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X74 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_23]) ).
thf(c_0_33,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X80: $i] :
( ( in @ X80 @ X21 )
& ( X21
= ( setadjoin @ X80 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_21]) ).
thf(c_0_34,plain,
( singletonprop
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X72: $i] :
( ( in @ X72
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X72 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_26,c_0_21]) ).
thf(c_0_35,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ? [X77: $i] :
( ( in @ X77 @ ( setunion @ X18 ) )
& ? [X78: $i] :
( ( in @ X78 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X77 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X77 @ ( setadjoin @ X78 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X79: $i] :
( ( in @ X79
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X79 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_21]),c_0_28]) ).
thf(c_0_36,axiom,
( cartprodmempair
= ( ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X70: $i] :
( ( in @ X70 @ ( setunion @ X18 ) )
& ? [X71: $i] :
( ( in @ X71 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X70 @ ( setadjoin @ X71 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[cartprodmempair,c_0_28]) ).
thf(c_0_37,axiom,
( kpairp
= ( ! [X2: $i,X3: $i] :
? [X68: $i] :
( ( in @ X68 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
& ? [X69: $i] :
( ( in @ X69 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
& ( ( kpair @ X2 @ X3 )
= ( setadjoin @ ( setadjoin @ X68 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X68 @ ( setadjoin @ X69 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairp,c_0_28]) ).
thf(c_0_38,axiom,
( kpairiskpair
= ( ! [X2: $i,X3: $i] :
? [X66: $i] :
( ( in @ X66 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X67: $i] :
( ( in @ X67 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X66 @ ( setadjoin @ X67 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairiskpair,c_0_28]) ).
thf(c_0_39,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ? [X81: $i] :
( ( in @ X81 @ ( setunion @ X18 ) )
& ? [X82: $i] :
( ( in @ X82 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X81 @ ( setadjoin @ X82 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X83: $i] :
( ( in @ X83
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X83 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_21]),c_0_28]) ).
thf(c_0_40,negated_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
=> ( ! [X84: $i,X85: $i] :
? [X86: $i] :
( ( in @ X86 @ ( setunion @ ( setadjoin @ ( setadjoin @ X84 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X84 @ ( setadjoin @ X85 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X87: $i] :
( ( in @ X87 @ ( setunion @ ( setadjoin @ ( setadjoin @ X84 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X84 @ ( setadjoin @ X85 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X84 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X84 @ ( setadjoin @ X85 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X86 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X86 @ ( setadjoin @ X87 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X88: $i,X89: $i] :
? [X90: $i] :
( ( in @ X90 @ ( setunion @ ( kpair @ X88 @ X89 ) ) )
& ? [X91: $i] :
( ( in @ X91 @ ( setunion @ ( kpair @ X88 @ X89 ) ) )
& ( ( kpair @ X88 @ X89 )
= ( setadjoin @ ( setadjoin @ X90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X90 @ ( setadjoin @ X91 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X92: $i,X93: $i,X94: $i] :
( ( in @ X94 @ X92 )
=> ! [X95: $i] :
( ( in @ X95 @ X93 )
=> ( in @ ( kpair @ X94 @ X95 ) @ ( cartprod @ X92 @ X93 ) ) ) )
=> ( ! [X96: $i,X97: $i,X98: $i] :
( ( in @ X98 @ ( cartprod @ X96 @ X97 ) )
=> ? [X99: $i] :
( ( in @ X99 @ X96 )
& ? [X100: $i] :
( ( in @ X100 @ X97 )
& ( X98
= ( kpair @ X99 @ X100 ) ) ) ) )
=> ( ! [X101: $i,X102: $i,X103: $i] :
( ( in @ X103 @ ( cartprod @ X101 @ X102 ) )
=> ? [X104: $i] :
( ( in @ X104 @ ( setunion @ X103 ) )
& ? [X105: $i] :
( ( in @ X105 @ ( setunion @ X103 ) )
& ( X103
= ( setadjoin @ ( setadjoin @ X104 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X104 @ ( setadjoin @ X105 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X106: $i,X107: $i > $o] :
( ! [X108: $i] :
( ( in @ X108 @ X106 )
=> ! [X109: $i] :
( ( in @ X109 @ X106 )
=> ( ( X107 @ X108 )
=> ( ( X107 @ X109 )
=> ( X108 = X109 ) ) ) ) )
=> ( ? [X110: $i] :
( ( in @ X110 @ X106 )
& ( X107 @ X110 ) )
=> ? [X111: $i] :
( ( in @ X111 @ ( dsetconstr @ X106 @ X107 ) )
& ( ( dsetconstr @ X106 @ X107 )
= ( setadjoin @ X111 @ emptyset ) ) ) ) )
=> ( ! [X112: $i,X113: $i > $o] :
( ? [X114: $i] :
( ( in @ X114 @ ( dsetconstr @ X112 @ X113 ) )
& ( ( dsetconstr @ X112 @ X113 )
= ( setadjoin @ X114 @ emptyset ) ) )
=> ? [X115: $i] :
( ( in @ X115 @ X112 )
& ( X113 @ X115 ) ) )
=> ( ! [X116: $i,X117: $i > $o,X118: $i] :
( ( in @ X118 @ X116 )
=> ( ( X117 @ X118 )
=> ( ! [X119: $i] :
( ( in @ X119 @ X116 )
=> ( ( X117 @ X119 )
=> ( X119 = X118 ) ) )
=> ? [X120: $i] :
( ( in @ X120 @ ( dsetconstr @ X116 @ X117 ) )
& ( ( dsetconstr @ X116 @ X117 )
= ( setadjoin @ X120 @ emptyset ) ) ) ) ) )
=> ( ! [X121: $i,X122: $i > $o] :
( ! [X123: $i] :
( ( in @ X123 @ X121 )
=> ! [X124: $i] :
( ( in @ X124 @ X121 )
=> ( ( X122 @ X123 )
=> ( ( X122 @ X124 )
=> ( X123 = X124 ) ) ) ) )
=> ( ? [X125: $i] :
( ( in @ X125 @ X121 )
& ( X122 @ X125 ) )
=> ? [X126: $i] :
( ( in @ X126 @ ( dsetconstr @ X121 @ X122 ) )
& ( ( dsetconstr @ X121 @ X122 )
= ( setadjoin @ X126 @ emptyset ) ) ) ) )
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X127: $i] :
( ? [X128: $i] :
( ( in @ X128 @ ( setunion @ X127 ) )
& ? [X129: $i] :
( ( in @ X129 @ ( setunion @ X127 ) )
& ( X127
= ( setadjoin @ ( setadjoin @ X128 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X128 @ ( setadjoin @ X129 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X130: $i] :
( ( in @ X130
@ ( dsetconstr @ ( setunion @ X127 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X127 ) ) )
& ( ( dsetconstr @ ( setunion @ X127 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X127 ) )
= ( setadjoin @ X130 @ emptyset ) ) ) )
=> ( ! [X131: $i] :
( ? [X132: $i] :
( ( in @ X132 @ X131 )
& ( X131
= ( setadjoin @ X132 @ emptyset ) ) )
=> ( in @ ( setunion @ X131 ) @ X131 ) )
=> ( ! [X133: $i,X134: $i] :
( ( kfst @ ( kpair @ X133 @ X134 ) )
= X133 )
=> ( ! [X135: $i,X136: $i,X137: $i] :
( ( in @ X137 @ ( cartprod @ X135 @ X136 ) )
=> ( in @ ( kfst @ X137 ) @ X135 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X138: $i] :
( ? [X139: $i] :
( ( in @ X139 @ ( setunion @ X138 ) )
& ? [X140: $i] :
( ( in @ X140 @ ( setunion @ X138 ) )
& ( X138
= ( setadjoin @ ( setadjoin @ X139 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X139 @ ( setadjoin @ X140 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X141: $i] :
( ( in @ X141
@ ( dsetconstr @ ( setunion @ X138 )
@ ^ [Z0: $i] :
( X138
= ( kpair @ ( kfst @ X138 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X138 )
@ ^ [Z0: $i] :
( X138
= ( kpair @ ( kfst @ X138 ) @ Z0 ) ) )
= ( setadjoin @ X141 @ emptyset ) ) ) )
=> ( ! [X142: $i,X143: $i] :
( ( ksnd @ ( kpair @ X142 @ X143 ) )
= X143 )
=> ! [X18: $i] :
( ? [X144: $i] :
( ( in @ X144 @ ( setunion @ X18 ) )
& ? [X145: $i] :
( ( in @ X145 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X144 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X144 @ ( setadjoin @ X145 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[kpairsurjEq]),ksndpairEq]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34]),cartprodmempair1]),cartprodpairin]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_28]),c_0_39]),cartprodfstin]),kfstpairEq])]) ).
thf(c_0_41,plain,
! [X146: $i,X147: $i] :
( ( kpair @ X146 @ X147 )
= ( setadjoin @ ( setadjoin @ X146 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X146 @ ( setadjoin @ X147 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_42,negated_conjecture,
! [X148: $i,X149: $i,X152: $i,X153: $i,X156: $i,X157: $i,X158: $i,X159: $i,X160: $i,X161: $i,X162: $i,X165: $i,X166: $i,X167: $i,X170: $i,X171: $i > $o,X174: $i,X176: $i,X177: $i > $o,X178: $i,X180: $i,X181: $i > $o,X182: $i,X185: $i,X186: $i > $o,X189: $i,X191: $i,X192: $i,X193: $i,X195: $i,X196: $i,X197: $i,X198: $i,X199: $i,X200: $i,X201: $i,X202: $i,X203: $i,X204: $i,X206: $i,X207: $i] :
( 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
& ( in @ ( esk1_2 @ X148 @ X149 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X148 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X148 @ ( setadjoin @ X149 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk2_2 @ X148 @ X149 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X148 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X148 @ ( setadjoin @ X149 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X148 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X148 @ ( setadjoin @ X149 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X148 @ X149 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X148 @ X149 ) @ ( setadjoin @ ( esk2_2 @ X148 @ X149 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( esk3_2 @ X152 @ X153 ) @ ( setunion @ ( kpair @ X152 @ X153 ) ) )
& ( in @ ( esk4_2 @ X152 @ X153 ) @ ( setunion @ ( kpair @ X152 @ X153 ) ) )
& ( ( kpair @ X152 @ X153 )
= ( setadjoin @ ( setadjoin @ ( esk3_2 @ X152 @ X153 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk3_2 @ X152 @ X153 ) @ ( setadjoin @ ( esk4_2 @ X152 @ X153 ) @ emptyset ) ) @ emptyset ) ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X158 @ X156 )
| ~ ( in @ X159 @ X157 )
| ( in @ ( kpair @ X158 @ X159 ) @ ( cartprod @ X156 @ X157 ) ) )
& ( ( in @ ( esk5_3 @ X160 @ X161 @ X162 ) @ X160 )
| ~ ( in @ X162 @ ( cartprod @ X160 @ X161 ) ) )
& ( ( in @ ( esk6_3 @ X160 @ X161 @ X162 ) @ X161 )
| ~ ( in @ X162 @ ( cartprod @ X160 @ X161 ) ) )
& ( ( X162
= ( kpair @ ( esk5_3 @ X160 @ X161 @ X162 ) @ ( esk6_3 @ X160 @ X161 @ X162 ) ) )
| ~ ( in @ X162 @ ( cartprod @ X160 @ X161 ) ) )
& ( ( in @ ( esk7_3 @ X165 @ X166 @ X167 ) @ ( setunion @ X167 ) )
| ~ ( in @ X167 @ ( cartprod @ X165 @ X166 ) ) )
& ( ( in @ ( esk8_3 @ X165 @ X166 @ X167 ) @ ( setunion @ X167 ) )
| ~ ( in @ X167 @ ( cartprod @ X165 @ X166 ) ) )
& ( ( X167
= ( setadjoin @ ( setadjoin @ ( esk7_3 @ X165 @ X166 @ X167 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk7_3 @ X165 @ X166 @ X167 ) @ ( setadjoin @ ( esk8_3 @ X165 @ X166 @ X167 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X167 @ ( cartprod @ X165 @ X166 ) ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk11_2 @ X170 @ X171 ) @ ( dsetconstr @ X170 @ X171 ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( in @ ( esk9_2 @ X170 @ X171 ) @ X170 ) )
& ( ( ( dsetconstr @ X170 @ X171 )
= ( setadjoin @ ( esk11_2 @ X170 @ X171 ) @ emptyset ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( in @ ( esk9_2 @ X170 @ X171 ) @ X170 ) )
& ( ( in @ ( esk11_2 @ X170 @ X171 ) @ ( dsetconstr @ X170 @ X171 ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( in @ ( esk10_2 @ X170 @ X171 ) @ X170 ) )
& ( ( ( dsetconstr @ X170 @ X171 )
= ( setadjoin @ ( esk11_2 @ X170 @ X171 ) @ emptyset ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( in @ ( esk10_2 @ X170 @ X171 ) @ X170 ) )
& ( ( in @ ( esk11_2 @ X170 @ X171 ) @ ( dsetconstr @ X170 @ X171 ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( X171 @ ( esk9_2 @ X170 @ X171 ) ) )
& ( ( ( dsetconstr @ X170 @ X171 )
= ( setadjoin @ ( esk11_2 @ X170 @ X171 ) @ emptyset ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( X171 @ ( esk9_2 @ X170 @ X171 ) ) )
& ( ( in @ ( esk11_2 @ X170 @ X171 ) @ ( dsetconstr @ X170 @ X171 ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( X171 @ ( esk10_2 @ X170 @ X171 ) ) )
& ( ( ( dsetconstr @ X170 @ X171 )
= ( setadjoin @ ( esk11_2 @ X170 @ X171 ) @ emptyset ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( X171 @ ( esk10_2 @ X170 @ X171 ) ) )
& ( ( in @ ( esk11_2 @ X170 @ X171 ) @ ( dsetconstr @ X170 @ X171 ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( ( esk9_2 @ X170 @ X171 )
!= ( esk10_2 @ X170 @ X171 ) ) )
& ( ( ( dsetconstr @ X170 @ X171 )
= ( setadjoin @ ( esk11_2 @ X170 @ X171 ) @ emptyset ) )
| ~ ( in @ X174 @ X170 )
| ~ ( X171 @ X174 )
| ( ( esk9_2 @ X170 @ X171 )
!= ( esk10_2 @ X170 @ X171 ) ) )
& ( ( in @ ( esk12_2 @ X176 @ X177 ) @ X176 )
| ~ ( in @ X178 @ ( dsetconstr @ X176 @ X177 ) )
| ( ( dsetconstr @ X176 @ X177 )
!= ( setadjoin @ X178 @ emptyset ) ) )
& ( ( X177 @ ( esk12_2 @ X176 @ X177 ) )
| ~ ( in @ X178 @ ( dsetconstr @ X176 @ X177 ) )
| ( ( dsetconstr @ X176 @ X177 )
!= ( setadjoin @ X178 @ emptyset ) ) )
& ( ( in @ ( esk14_3 @ X180 @ X181 @ X182 ) @ ( dsetconstr @ X180 @ X181 ) )
| ( in @ ( esk13_3 @ X180 @ X181 @ X182 ) @ X180 )
| ~ ( X181 @ X182 )
| ~ ( in @ X182 @ X180 ) )
& ( ( ( dsetconstr @ X180 @ X181 )
= ( setadjoin @ ( esk14_3 @ X180 @ X181 @ X182 ) @ emptyset ) )
| ( in @ ( esk13_3 @ X180 @ X181 @ X182 ) @ X180 )
| ~ ( X181 @ X182 )
| ~ ( in @ X182 @ X180 ) )
& ( ( in @ ( esk14_3 @ X180 @ X181 @ X182 ) @ ( dsetconstr @ X180 @ X181 ) )
| ( X181 @ ( esk13_3 @ X180 @ X181 @ X182 ) )
| ~ ( X181 @ X182 )
| ~ ( in @ X182 @ X180 ) )
& ( ( ( dsetconstr @ X180 @ X181 )
= ( setadjoin @ ( esk14_3 @ X180 @ X181 @ X182 ) @ emptyset ) )
| ( X181 @ ( esk13_3 @ X180 @ X181 @ X182 ) )
| ~ ( X181 @ X182 )
| ~ ( in @ X182 @ X180 ) )
& ( ( in @ ( esk14_3 @ X180 @ X181 @ X182 ) @ ( dsetconstr @ X180 @ X181 ) )
| ( ( esk13_3 @ X180 @ X181 @ X182 )
!= X182 )
| ~ ( X181 @ X182 )
| ~ ( in @ X182 @ X180 ) )
& ( ( ( dsetconstr @ X180 @ X181 )
= ( setadjoin @ ( esk14_3 @ X180 @ X181 @ X182 ) @ emptyset ) )
| ( ( esk13_3 @ X180 @ X181 @ X182 )
!= X182 )
| ~ ( X181 @ X182 )
| ~ ( in @ X182 @ X180 ) )
& ( ( in @ ( esk17_2 @ X185 @ X186 ) @ ( dsetconstr @ X185 @ X186 ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( in @ ( esk15_2 @ X185 @ X186 ) @ X185 ) )
& ( ( ( dsetconstr @ X185 @ X186 )
= ( setadjoin @ ( esk17_2 @ X185 @ X186 ) @ emptyset ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( in @ ( esk15_2 @ X185 @ X186 ) @ X185 ) )
& ( ( in @ ( esk17_2 @ X185 @ X186 ) @ ( dsetconstr @ X185 @ X186 ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( in @ ( esk16_2 @ X185 @ X186 ) @ X185 ) )
& ( ( ( dsetconstr @ X185 @ X186 )
= ( setadjoin @ ( esk17_2 @ X185 @ X186 ) @ emptyset ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( in @ ( esk16_2 @ X185 @ X186 ) @ X185 ) )
& ( ( in @ ( esk17_2 @ X185 @ X186 ) @ ( dsetconstr @ X185 @ X186 ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( X186 @ ( esk15_2 @ X185 @ X186 ) ) )
& ( ( ( dsetconstr @ X185 @ X186 )
= ( setadjoin @ ( esk17_2 @ X185 @ X186 ) @ emptyset ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( X186 @ ( esk15_2 @ X185 @ X186 ) ) )
& ( ( in @ ( esk17_2 @ X185 @ X186 ) @ ( dsetconstr @ X185 @ X186 ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( X186 @ ( esk16_2 @ X185 @ X186 ) ) )
& ( ( ( dsetconstr @ X185 @ X186 )
= ( setadjoin @ ( esk17_2 @ X185 @ X186 ) @ emptyset ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( X186 @ ( esk16_2 @ X185 @ X186 ) ) )
& ( ( in @ ( esk17_2 @ X185 @ X186 ) @ ( dsetconstr @ X185 @ X186 ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( ( esk15_2 @ X185 @ X186 )
!= ( esk16_2 @ X185 @ X186 ) ) )
& ( ( ( dsetconstr @ X185 @ X186 )
= ( setadjoin @ ( esk17_2 @ X185 @ X186 ) @ emptyset ) )
| ~ ( in @ X189 @ X185 )
| ~ ( X186 @ X189 )
| ( ( esk15_2 @ X185 @ X186 )
!= ( esk16_2 @ X185 @ X186 ) ) )
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk18_1 @ X191 )
@ ( dsetconstr @ ( setunion @ X191 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X191 ) ) )
| ~ ( in @ X192 @ ( setunion @ X191 ) )
| ~ ( in @ X193 @ ( setunion @ X191 ) )
| ( X191
!= ( setadjoin @ ( setadjoin @ X192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X192 @ ( setadjoin @ X193 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ( dsetconstr @ ( setunion @ X191 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X191 ) )
= ( setadjoin @ ( esk18_1 @ X191 ) @ emptyset ) )
| ~ ( in @ X192 @ ( setunion @ X191 ) )
| ~ ( in @ X193 @ ( setunion @ X191 ) )
| ( X191
!= ( setadjoin @ ( setadjoin @ X192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X192 @ ( setadjoin @ X193 @ emptyset ) ) @ emptyset ) ) ) )
& ( ~ ( in @ X196 @ X195 )
| ( X195
!= ( setadjoin @ X196 @ emptyset ) )
| ( in @ ( setunion @ X195 ) @ X195 ) )
& ( ( kfst @ ( kpair @ X197 @ X198 ) )
= X197 )
& ( ~ ( in @ X201 @ ( cartprod @ X199 @ X200 ) )
| ( in @ ( kfst @ X201 ) @ X199 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk19_1 @ X202 )
@ ( dsetconstr @ ( setunion @ X202 )
@ ^ [Z0: $i] :
( X202
= ( kpair @ ( kfst @ X202 ) @ Z0 ) ) ) )
| ~ ( in @ X203 @ ( setunion @ X202 ) )
| ~ ( in @ X204 @ ( setunion @ X202 ) )
| ( X202
!= ( setadjoin @ ( setadjoin @ X203 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X203 @ ( setadjoin @ X204 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ( dsetconstr @ ( setunion @ X202 )
@ ^ [Z0: $i] :
( X202
= ( kpair @ ( kfst @ X202 ) @ Z0 ) ) )
= ( setadjoin @ ( esk19_1 @ X202 ) @ emptyset ) )
| ~ ( in @ X203 @ ( setunion @ X202 ) )
| ~ ( in @ X204 @ ( setunion @ X202 ) )
| ( X202
!= ( setadjoin @ ( setadjoin @ X203 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X203 @ ( setadjoin @ X204 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ksnd @ ( kpair @ X206 @ X207 ) )
= X207 )
& ( in @ esk21_0 @ ( setunion @ esk20_0 ) )
& ( in @ esk22_0 @ ( setunion @ esk20_0 ) )
& ( esk20_0
= ( setadjoin @ ( setadjoin @ esk21_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk21_0 @ ( setadjoin @ esk22_0 @ emptyset ) ) @ emptyset ) ) )
& ( ( kpair @ ( kfst @ esk20_0 ) @ ( ksnd @ esk20_0 ) )
!= esk20_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(fof_nnf,[status(thm)],[c_0_40])])])])])]) ).
thf(c_0_43,plain,
! [X211: $i,X212: $i] :
( ( kpair @ X211 @ X212 )
= ( setadjoin @ ( setadjoin @ X211 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X211 @ ( setadjoin @ X212 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_41]) ).
thf(c_0_44,negated_conjecture,
( esk20_0
= ( setadjoin @ ( setadjoin @ esk21_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk21_0 @ ( setadjoin @ esk22_0 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_45,plain,
! [X2: $i,X3: $i] :
( ( kpair @ X2 @ X3 )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_46,negated_conjecture,
! [X3: $i,X2: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_47,negated_conjecture,
( ( kpair @ esk21_0 @ esk22_0 )
= esk20_0 ),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_48,negated_conjecture,
( ( kpair @ ( kfst @ esk20_0 ) @ ( ksnd @ esk20_0 ) )
!= esk20_0 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_49,negated_conjecture,
( ( kfst @ esk20_0 )
= esk21_0 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_50,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_51,negated_conjecture,
( ( kpair @ esk21_0 @ ( ksnd @ esk20_0 ) )
!= esk20_0 ),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_52,negated_conjecture,
( ( ksnd @ esk20_0 )
= esk22_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
thf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU657^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:18:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.53 # Version: 3.1.0-ho
% 0.21/0.53 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.53 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.53 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.53 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.53 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.53 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.53 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.53 # new_ho_5 with pid 22244 completed with status 0
% 0.21/0.53 # Result found by new_ho_5
% 0.21/0.53 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.53 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.53 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.53 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.53 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.53 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.53 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.53 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.21/0.53 # Search class: HGUSM-FFMM32-MHFMMSBN
% 0.21/0.53 # partial match(2): HGUSM-FFMF31-MHFMMSBN
% 0.21/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53 # Starting new_ho_10 with 55s (1) cores
% 0.21/0.53 # new_ho_10 with pid 22245 completed with status 0
% 0.21/0.53 # Result found by new_ho_10
% 0.21/0.53 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.53 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.53 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.53 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.53 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.53 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.53 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.53 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.21/0.53 # Search class: HGUSM-FFMM32-MHFMMSBN
% 0.21/0.53 # partial match(2): HGUSM-FFMF31-MHFMMSBN
% 0.21/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53 # Starting new_ho_10 with 55s (1) cores
% 0.21/0.53 # Preprocessing time : 0.003 s
% 0.21/0.53 # Presaturation interreduction done
% 0.21/0.53
% 0.21/0.53 # Proof found!
% 0.21/0.53 # SZS status Theorem
% 0.21/0.53 # SZS output start CNFRefutation
% See solution above
% 0.21/0.53 # Parsed axioms : 384
% 0.21/0.53 # Removed by relevancy pruning/SinE : 364
% 0.21/0.53 # Initial clauses : 216
% 0.21/0.53 # Removed in clause preprocessing : 0
% 0.21/0.53 # Initial clauses in saturation : 216
% 0.21/0.53 # Processed clauses : 396
% 0.21/0.53 # ...of these trivial : 0
% 0.21/0.53 # ...subsumed : 0
% 0.21/0.53 # ...remaining for further processing : 396
% 0.21/0.53 # Other redundant clauses eliminated : 5
% 0.21/0.53 # Clauses deleted for lack of memory : 0
% 0.21/0.53 # Backward-subsumed : 0
% 0.21/0.53 # Backward-rewritten : 3
% 0.21/0.53 # Generated clauses : 20
% 0.21/0.53 # ...of the previous two non-redundant : 20
% 0.21/0.53 # ...aggressively subsumed : 0
% 0.21/0.53 # Contextual simplify-reflections : 0
% 0.21/0.53 # Paramodulations : 15
% 0.21/0.53 # Factorizations : 0
% 0.21/0.53 # NegExts : 0
% 0.21/0.53 # Equation resolutions : 5
% 0.21/0.53 # Disequality decompositions : 0
% 0.21/0.53 # Total rewrite steps : 14
% 0.21/0.53 # ...of those cached : 5
% 0.21/0.53 # Propositional unsat checks : 0
% 0.21/0.53 # Propositional check models : 0
% 0.21/0.53 # Propositional check unsatisfiable : 0
% 0.21/0.53 # Propositional clauses : 0
% 0.21/0.53 # Propositional clauses after purity: 0
% 0.21/0.53 # Propositional unsat core size : 0
% 0.21/0.53 # Propositional preprocessing time : 0.000
% 0.21/0.53 # Propositional encoding time : 0.000
% 0.21/0.53 # Propositional solver time : 0.000
% 0.21/0.53 # Success case prop preproc time : 0.000
% 0.21/0.53 # Success case prop encoding time : 0.000
% 0.21/0.53 # Success case prop solver time : 0.000
% 0.21/0.53 # Current number of processed clauses : 172
% 0.21/0.53 # Positive orientable unit clauses : 167
% 0.21/0.53 # Positive unorientable unit clauses: 0
% 0.21/0.53 # Negative unit clauses : 0
% 0.21/0.53 # Non-unit-clauses : 5
% 0.21/0.53 # Current number of unprocessed clauses: 55
% 0.21/0.53 # ...number of literals in the above : 162
% 0.21/0.53 # Current number of archived formulas : 0
% 0.21/0.53 # Current number of archived clauses : 219
% 0.21/0.53 # Clause-clause subsumption calls (NU) : 359
% 0.21/0.53 # Rec. Clause-clause subsumption calls : 233
% 0.21/0.53 # Non-unit clause-clause subsumptions : 0
% 0.21/0.53 # Unit Clause-clause subsumption calls : 0
% 0.21/0.53 # Rewrite failures with RHS unbound : 0
% 0.21/0.53 # BW rewrite match attempts : 3
% 0.21/0.53 # BW rewrite match successes : 3
% 0.21/0.53 # Condensation attempts : 396
% 0.21/0.53 # Condensation successes : 0
% 0.21/0.53 # Termbank termtop insertions : 16259
% 0.21/0.53 # Search garbage collected termcells : 5793
% 0.21/0.53
% 0.21/0.53 # -------------------------------------------------
% 0.21/0.53 # User time : 0.022 s
% 0.21/0.53 # System time : 0.007 s
% 0.21/0.53 # Total time : 0.029 s
% 0.21/0.53 # Maximum resident set size: 3660 pages
% 0.21/0.53
% 0.21/0.53 # -------------------------------------------------
% 0.21/0.53 # User time : 0.031 s
% 0.21/0.53 # System time : 0.010 s
% 0.21/0.53 # Total time : 0.041 s
% 0.21/0.53 # Maximum resident set size: 2116 pages
% 0.21/0.53 % E---3.1 exiting
% 0.21/0.54 % E exiting
%------------------------------------------------------------------------------