%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU671^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:27:09 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 62 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 1104 ( 95 equ; 0 cnn)
% Maximal formula atoms : 284 ( 17 avg)
% Number of connectives : 2503 ( 95 ~; 111 |; 244 &;1328 @)
% ( 36 <=>; 689 =>; 0 <=; 0 <~>)
% Maximal formula depth : 286 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 220 ( 218 usr; 193 con; 0-3 aty)
% Number of variables : 423 ( 81 ^; 312 !; 30 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_25,type,
setextAx: $o ).
thf(decl_26,type,
emptyset: $i ).
thf(decl_27,type,
emptysetAx: $o ).
thf(decl_28,type,
setadjoin: $i > $i > $i ).
thf(decl_29,type,
setadjoinAx: $o ).
thf(decl_31,type,
powersetAx: $o ).
thf(decl_32,type,
setunion: $i > $i ).
thf(decl_33,type,
setunionAx: $o ).
thf(decl_35,type,
omega0Ax: $o ).
thf(decl_36,type,
omegaSAx: $o ).
thf(decl_37,type,
omegaIndAx: $o ).
thf(decl_38,type,
replAx: $o ).
thf(decl_39,type,
foundationAx: $o ).
thf(decl_40,type,
wellorderingAx: $o ).
thf(decl_42,type,
descrp: $o ).
thf(decl_43,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_44,type,
dsetconstrI: $o ).
thf(decl_45,type,
dsetconstrEL: $o ).
thf(decl_46,type,
dsetconstrER: $o ).
thf(decl_47,type,
exuE1: $o ).
thf(decl_49,type,
prop2setE: $o ).
thf(decl_50,type,
emptysetE: $o ).
thf(decl_51,type,
emptysetimpfalse: $o ).
thf(decl_52,type,
notinemptyset: $o ).
thf(decl_53,type,
exuE3e: $o ).
thf(decl_54,type,
setext: $o ).
thf(decl_55,type,
emptyI: $o ).
thf(decl_56,type,
noeltsimpempty: $o ).
thf(decl_57,type,
setbeta: $o ).
thf(decl_59,type,
nonemptyE1: $o ).
thf(decl_60,type,
nonemptyI: $o ).
thf(decl_61,type,
nonemptyI1: $o ).
thf(decl_62,type,
setadjoinIL: $o ).
thf(decl_63,type,
emptyinunitempty: $o ).
thf(decl_64,type,
setadjoinIR: $o ).
thf(decl_65,type,
setadjoinE: $o ).
thf(decl_66,type,
setadjoinOr: $o ).
thf(decl_67,type,
setoftrueEq: $o ).
thf(decl_68,type,
powersetI: $o ).
thf(decl_69,type,
emptyinPowerset: $o ).
thf(decl_70,type,
emptyInPowerset: $o ).
thf(decl_71,type,
powersetE: $o ).
thf(decl_72,type,
setunionI: $o ).
thf(decl_73,type,
setunionE: $o ).
thf(decl_74,type,
subPowSU: $o ).
thf(decl_75,type,
exuE2: $o ).
thf(decl_76,type,
nonemptyImpWitness: $o ).
thf(decl_77,type,
uniqinunit: $o ).
thf(decl_78,type,
notinsingleton: $o ).
thf(decl_79,type,
eqinunit: $o ).
thf(decl_80,type,
singletonsswitch: $o ).
thf(decl_81,type,
upairsetE: $o ).
thf(decl_82,type,
upairsetIL: $o ).
thf(decl_83,type,
upairsetIR: $o ).
thf(decl_84,type,
emptyE1: $o ).
thf(decl_85,type,
vacuousDall: $o ).
thf(decl_86,type,
quantDeMorgan1: $o ).
thf(decl_87,type,
quantDeMorgan2: $o ).
thf(decl_88,type,
quantDeMorgan3: $o ).
thf(decl_89,type,
quantDeMorgan4: $o ).
thf(decl_90,type,
prop2setI: $o ).
thf(decl_92,type,
prop2set2propI: $o ).
thf(decl_93,type,
notdexE: $o ).
thf(decl_94,type,
notdallE: $o ).
thf(decl_95,type,
exuI1: $o ).
thf(decl_96,type,
exuI3: $o ).
thf(decl_97,type,
exuI2: $o ).
thf(decl_98,type,
inCongP: $o ).
thf(decl_99,type,
in__Cong: $o ).
thf(decl_100,type,
exuE3u: $o ).
thf(decl_101,type,
exu__Cong: $o ).
thf(decl_102,type,
emptyset__Cong: $o ).
thf(decl_103,type,
setadjoin__Cong: $o ).
thf(decl_104,type,
powerset__Cong: $o ).
thf(decl_105,type,
setunion__Cong: $o ).
thf(decl_106,type,
omega__Cong: $o ).
thf(decl_107,type,
exuEu: $o ).
thf(decl_108,type,
descr__Cong: $o ).
thf(decl_109,type,
dsetconstr__Cong: $o ).
thf(decl_110,type,
subset: $i > $i > $o ).
thf(decl_113,type,
subsetI1: $o ).
thf(decl_114,type,
eqimpsubset2: $o ).
thf(decl_115,type,
eqimpsubset1: $o ).
thf(decl_116,type,
subsetI2: $o ).
thf(decl_117,type,
emptysetsubset: $o ).
thf(decl_118,type,
subsetE: $o ).
thf(decl_119,type,
subsetE2: $o ).
thf(decl_120,type,
notsubsetI: $o ).
thf(decl_121,type,
notequalI1: $o ).
thf(decl_122,type,
notequalI2: $o ).
thf(decl_123,type,
subsetRefl: $o ).
thf(decl_124,type,
subsetTrans: $o ).
thf(decl_125,type,
setadjoinSub: $o ).
thf(decl_126,type,
setadjoinSub2: $o ).
thf(decl_127,type,
subset2powerset: $o ).
thf(decl_128,type,
setextsub: $o ).
thf(decl_129,type,
subsetemptysetimpeq: $o ).
thf(decl_130,type,
powersetI1: $o ).
thf(decl_131,type,
powersetE1: $o ).
thf(decl_132,type,
inPowerset: $o ).
thf(decl_133,type,
powersetsubset: $o ).
thf(decl_134,type,
sepInPowerset: $o ).
thf(decl_135,type,
sepSubset: $o ).
thf(decl_137,type,
binunionIL: $o ).
thf(decl_138,type,
upairset2IR: $o ).
thf(decl_139,type,
binunionIR: $o ).
thf(decl_140,type,
binunionEcases: $o ).
thf(decl_141,type,
binunionE: $o ).
thf(decl_142,type,
binunionLsub: $o ).
thf(decl_143,type,
binunionRsub: $o ).
thf(decl_145,type,
binintersectI: $o ).
thf(decl_146,type,
binintersectSubset5: $o ).
thf(decl_147,type,
binintersectEL: $o ).
thf(decl_148,type,
binintersectLsub: $o ).
thf(decl_149,type,
binintersectSubset2: $o ).
thf(decl_150,type,
binintersectSubset3: $o ).
thf(decl_151,type,
binintersectER: $o ).
thf(decl_152,type,
disjointsetsI1: $o ).
thf(decl_153,type,
binintersectRsub: $o ).
thf(decl_154,type,
binintersectSubset4: $o ).
thf(decl_155,type,
binintersectSubset1: $o ).
thf(decl_156,type,
bs114d: $o ).
thf(decl_159,type,
setminusI: $o ).
thf(decl_160,type,
setminusEL: $o ).
thf(decl_161,type,
setminusER: $o ).
thf(decl_162,type,
setminusSubset2: $o ).
thf(decl_163,type,
setminusERneg: $o ).
thf(decl_164,type,
setminusELneg: $o ).
thf(decl_165,type,
setminusILneg: $o ).
thf(decl_166,type,
setminusIRneg: $o ).
thf(decl_167,type,
setminusLsub: $o ).
thf(decl_168,type,
setminusSubset1: $o ).
thf(decl_170,type,
symdiffE: $o ).
thf(decl_171,type,
symdiffI1: $o ).
thf(decl_172,type,
symdiffI2: $o ).
thf(decl_173,type,
symdiffIneg1: $o ).
thf(decl_174,type,
symdiffIneg2: $o ).
thf(decl_175,type,
iskpair: $i > $o ).
thf(decl_176,type,
secondinupair: $o ).
thf(decl_177,type,
setukpairIL: $o ).
thf(decl_178,type,
setukpairIR: $o ).
thf(decl_179,type,
kpairiskpair: $o ).
thf(decl_180,type,
kpair: $i > $i > $i ).
thf(decl_181,type,
kpairp: $o ).
thf(decl_182,type,
cartprod: $i > $i > $i ).
thf(decl_183,type,
singletonsubset: $o ).
thf(decl_184,type,
singletoninpowerset: $o ).
thf(decl_185,type,
singletoninpowunion: $o ).
thf(decl_186,type,
upairset2E: $o ).
thf(decl_187,type,
upairsubunion: $o ).
thf(decl_188,type,
upairinpowunion: $o ).
thf(decl_189,type,
ubforcartprodlem1: $o ).
thf(decl_190,type,
ubforcartprodlem2: $o ).
thf(decl_191,type,
ubforcartprodlem3: $o ).
thf(decl_192,type,
cartprodpairin: $o ).
thf(decl_193,type,
cartprodmempair1: $o ).
thf(decl_194,type,
cartprodmempair: $o ).
thf(decl_195,type,
setunionE2: $o ).
thf(decl_196,type,
setunionsingleton1: $o ).
thf(decl_197,type,
setunionsingleton2: $o ).
thf(decl_198,type,
setunionsingleton: $o ).
thf(decl_199,type,
singleton: $i > $o ).
thf(decl_200,type,
singletonprop: $o ).
thf(decl_201,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_202,type,
ex1E1: $o ).
thf(decl_203,type,
ex1I: $o ).
thf(decl_204,type,
ex1I2: $o ).
thf(decl_205,type,
singletonsuniq: $o ).
thf(decl_210,type,
setukpairinjL1: $o ).
thf(decl_211,type,
kfstsingleton: $o ).
thf(decl_212,type,
theprop: $o ).
thf(decl_213,type,
kfst: $i > $i ).
thf(decl_214,type,
kfstpairEq: $o ).
thf(decl_215,type,
cartprodfstin: $o ).
thf(decl_216,type,
setukpairinjL2: $o ).
thf(decl_217,type,
setukpairinjL: $o ).
thf(decl_218,type,
setukpairinjR11: $o ).
thf(decl_219,type,
setukpairinjR12: $o ).
thf(decl_220,type,
setukpairinjR1: $o ).
thf(decl_221,type,
upairequniteq: $o ).
thf(decl_222,type,
setukpairinjR2: $o ).
thf(decl_223,type,
setukpairinjR: $o ).
thf(decl_224,type,
ksndsingleton: $o ).
thf(decl_225,type,
ksnd: $i > $i ).
thf(decl_226,type,
ksndpairEq: $o ).
thf(decl_227,type,
kpairsurjEq: $o ).
thf(decl_228,type,
cartprodsndin: $o ).
thf(decl_229,type,
cartprodpairmemEL: $o ).
thf(decl_230,type,
cartprodpairmemER: $o ).
thf(decl_231,type,
cartprodmempaircEq: $o ).
thf(decl_232,type,
cartprodfstpairEq: $o ).
thf(decl_233,type,
cartprodsndpairEq: $o ).
thf(decl_234,type,
cartprodpairsurjEq: $o ).
thf(decl_235,type,
breln: $i > $i > $i > $o ).
thf(decl_236,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_237,type,
dpsetconstrI: $o ).
thf(decl_238,type,
dpsetconstrSub: $o ).
thf(decl_239,type,
setOfPairsIsBReln: $o ).
thf(decl_240,type,
dpsetconstrERa: $o ).
thf(decl_241,type,
dpsetconstrEL1: $o ).
thf(decl_242,type,
dpsetconstrEL2: $o ).
thf(decl_243,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_244,type,
esk2_2: $i > ( $i > $o ) > $i ).
thf(decl_245,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_246,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_247,type,
esk5_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_248,type,
esk6_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_249,type,
esk7_2: $i > ( $i > $o ) > $i ).
thf(decl_250,type,
esk8_2: $i > ( $i > $o ) > $i ).
thf(decl_251,type,
esk9_2: $i > ( $i > $o ) > $i ).
thf(decl_252,type,
esk10_1: $i > $i ).
thf(decl_253,type,
esk11_1: $i > $i ).
thf(decl_254,type,
esk12_0: $i ).
thf(decl_255,type,
esk13_0: $i ).
thf(decl_256,type,
epred1_0: $i > $i > $o ).
thf(decl_257,type,
esk14_0: $i ).
thf(decl_258,type,
esk15_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.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/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.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/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.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/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',ex1E1) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',ksndsingleton) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',kfstsingleton) ).
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/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',singletonprop) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X25 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',breln) ).
thf(dpsetconstrER,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
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ! [X4: $i,X5: $i,X29: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X29 @ X14 @ X18 ) ) )
=> ( X29 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',dpsetconstrER) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',theprop) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',dpsetconstrEL2) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',dpsetconstrEL1) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( X26 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',dpsetconstrERa) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',dpsetconstrSub) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X23 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X23 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',dpsetconstrI) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',cartprodsndpairEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',cartprodsndin) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',ksndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',cartprodpairsurjEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',cartprodfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',cartprodfstin) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',kfstpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',kpairsurjEq) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',cartprodmempair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.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/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p',kpairiskpair) ).
thf(c_0_28,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X111: $i] :
( ( in @ X111
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X111 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_29,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
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 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_31,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X111: $i] :
( ( in @ X111
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X111 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_32,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_33,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_34,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_35,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_36,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_37,plain,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).
thf(c_0_38,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_39,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
=> ( 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
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ! [X4: $i,X5: $i,X29: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X29 @ X14 @ X18 ) ) )
=> ( X29 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[dpsetconstrER]) ).
thf(c_0_40,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 ) )
=> ? [X114: $i] :
( ( in @ X114
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X114 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_41,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X113: $i] :
( ( in @ X113
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X113 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_32,c_0_31]) ).
thf(c_0_42,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X112: $i] :
( ( in @ X112
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X112 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_33,c_0_31]) ).
thf(c_0_43,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X117: $i] :
( ( in @ X117
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X117 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_34,c_0_29]) ).
thf(c_0_44,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X116: $i] :
( ( in @ X116 @ X21 )
& ( X21
= ( setadjoin @ X116 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_29]) ).
thf(c_0_45,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X115: $i] :
( ( in @ X115
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X115 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_35,c_0_29]) ).
thf(c_0_46,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 ) )
=> ? [X110: $i] :
( ( in @ X110
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X110 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_36,c_0_29]) ).
thf(c_0_47,plain,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X28 @ Z0 @ Z1 ) ) )
=> ( in @ X3 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL2]) ).
thf(c_0_48,plain,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X27 @ Z0 @ Z1 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL1]) ).
thf(c_0_49,plain,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X26 @ Z0 @ Z1 ) ) )
=> ( X26 @ X2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrERa]) ).
thf(c_0_50,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X25: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_51,plain,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).
thf(c_0_52,plain,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X23 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X23 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_53,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
=> ( ! [X118: $i,X119: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X118 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X118 @ ( setadjoin @ X119 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X120: $i,X121: $i] : ( iskpair @ ( kpair @ X120 @ X121 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( ! [X122: $i,X123: $i,X124: $i] :
( ( in @ X124 @ ( cartprod @ X122 @ X123 ) )
=> ( iskpair @ X124 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X125: $i,X126: $i > $o] :
( ! [X127: $i] :
( ( in @ X127 @ X125 )
=> ! [X128: $i] :
( ( in @ X128 @ X125 )
=> ( ( X126 @ X127 )
=> ( ( X126 @ X128 )
=> ( X127 = X128 ) ) ) ) )
=> ( ? [X129: $i] :
( ( in @ X129 @ X125 )
& ( X126 @ X129 ) )
=> ? [X130: $i] :
( ( in @ X130 @ ( dsetconstr @ X125 @ X126 ) )
& ( ( dsetconstr @ X125 @ X126 )
= ( setadjoin @ X130 @ emptyset ) ) ) ) )
=> ( ! [X131: $i,X132: $i > $o] :
( ? [X133: $i] :
( ( in @ X133 @ ( dsetconstr @ X131 @ X132 ) )
& ( ( dsetconstr @ X131 @ X132 )
= ( setadjoin @ X133 @ emptyset ) ) )
=> ? [X134: $i] :
( ( in @ X134 @ X131 )
& ( X132 @ X134 ) ) )
=> ( ! [X135: $i,X136: $i > $o,X137: $i] :
( ( in @ X137 @ X135 )
=> ( ( X136 @ X137 )
=> ( ! [X138: $i] :
( ( in @ X138 @ X135 )
=> ( ( X136 @ X138 )
=> ( X138 = X137 ) ) )
=> ? [X139: $i] :
( ( in @ X139 @ ( dsetconstr @ X135 @ X136 ) )
& ( ( dsetconstr @ X135 @ X136 )
= ( setadjoin @ X139 @ emptyset ) ) ) ) ) )
=> ( ! [X140: $i,X141: $i > $o] :
( ! [X142: $i] :
( ( in @ X142 @ X140 )
=> ! [X143: $i] :
( ( in @ X143 @ X140 )
=> ( ( X141 @ X142 )
=> ( ( X141 @ X143 )
=> ( X142 = X143 ) ) ) ) )
=> ( ? [X144: $i] :
( ( in @ X144 @ X140 )
& ( X141 @ X144 ) )
=> ? [X145: $i] :
( ( in @ X145 @ ( dsetconstr @ X140 @ X141 ) )
& ( ( dsetconstr @ X140 @ X141 )
= ( setadjoin @ X145 @ emptyset ) ) ) ) )
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X146: $i] :
( ( iskpair @ X146 )
=> ? [X147: $i] :
( ( in @ X147
@ ( dsetconstr @ ( setunion @ X146 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X146 ) ) )
& ( ( dsetconstr @ ( setunion @ X146 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X146 ) )
= ( setadjoin @ X147 @ emptyset ) ) ) )
=> ( ! [X148: $i] :
( ? [X149: $i] :
( ( in @ X149 @ X148 )
& ( X148
= ( setadjoin @ X149 @ emptyset ) ) )
=> ( in @ ( setunion @ X148 ) @ X148 ) )
=> ( ! [X150: $i,X151: $i] :
( ( kfst @ ( kpair @ X150 @ X151 ) )
= X150 )
=> ( ! [X152: $i,X153: $i,X154: $i] :
( ( in @ X154 @ ( cartprod @ X152 @ X153 ) )
=> ( in @ ( kfst @ X154 ) @ X152 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X155: $i] :
( ( iskpair @ X155 )
=> ? [X156: $i] :
( ( in @ X156
@ ( dsetconstr @ ( setunion @ X155 )
@ ^ [Z0: $i] :
( X155
= ( kpair @ ( kfst @ X155 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X155 )
@ ^ [Z0: $i] :
( X155
= ( kpair @ ( kfst @ X155 ) @ Z0 ) ) )
= ( setadjoin @ X156 @ emptyset ) ) ) )
=> ( ! [X157: $i,X158: $i] :
( ( ksnd @ ( kpair @ X157 @ X158 ) )
= X158 )
=> ( ! [X159: $i] :
( ( iskpair @ X159 )
=> ( ( kpair @ ( kfst @ X159 ) @ ( ksnd @ X159 ) )
= X159 ) )
=> ( ! [X160: $i,X161: $i,X162: $i] :
( ( in @ X162 @ ( cartprod @ X160 @ X161 ) )
=> ( in @ ( ksnd @ X162 ) @ X161 ) )
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( ! [X163: $i,X164: $i,X165: $i] :
( ( in @ X165 @ X163 )
=> ! [X166: $i] :
( ( in @ X166 @ X164 )
=> ( ( kfst @ ( kpair @ X165 @ X166 ) )
= X165 ) ) )
=> ( ! [X167: $i,X168: $i,X169: $i] :
( ( in @ X169 @ X167 )
=> ! [X170: $i] :
( ( in @ X170 @ X168 )
=> ( ( ksnd @ ( kpair @ X169 @ X170 ) )
= X170 ) ) )
=> ( ! [X171: $i,X172: $i,X173: $i] :
( ( in @ X173 @ ( cartprod @ X171 @ X172 ) )
=> ( ( kpair @ ( kfst @ X173 ) @ ( ksnd @ X173 ) )
= X173 ) )
=> ( ! [X174: $i,X175: $i,X176: $i > $i > $o,X177: $i] :
( ( in @ X177 @ X174 )
=> ! [X178: $i] :
( ( in @ X178 @ X175 )
=> ( ( X176 @ X177 @ X178 )
=> ( in @ ( kpair @ X177 @ X178 ) @ ( dpsetconstr @ X174 @ X175 @ X176 ) ) ) ) )
=> ( ! [X179: $i,X180: $i,X181: $i > $i > $o] : ( subset @ ( dpsetconstr @ X179 @ X180 @ X181 ) @ ( cartprod @ X179 @ X180 ) )
=> ( ! [X182: $i,X183: $i,X184: $i > $i > $o] : ( subset @ ( dpsetconstr @ X182 @ X183 @ X184 ) @ ( cartprod @ X182 @ X183 ) )
=> ( ! [X185: $i,X186: $i,X187: $i > $i > $o,X188: $i] :
( ( in @ X188 @ X185 )
=> ! [X189: $i] :
( ( in @ X189 @ X186 )
=> ( ( in @ ( kpair @ X188 @ X189 ) @ ( dpsetconstr @ X185 @ X186 @ X187 ) )
=> ( X187 @ X188 @ X189 ) ) ) )
=> ( ! [X190: $i,X191: $i,X192: $i > $i > $o,X193: $i,X194: $i] :
( ( in @ ( kpair @ X193 @ X194 ) @ ( dpsetconstr @ X190 @ X191 @ X192 ) )
=> ( in @ X193 @ X190 ) )
=> ( ! [X195: $i,X196: $i,X197: $i > $i > $o,X198: $i,X199: $i] :
( ( in @ ( kpair @ X198 @ X199 ) @ ( dpsetconstr @ X195 @ X196 @ X197 ) )
=> ( in @ X199 @ X196 ) )
=> ! [X4: $i,X5: $i,X29: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X29 ) )
=> ( X29 @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_39]),cartprodsndpairEq]),cartprodsndin]),ksndpairEq]),cartprodpairsurjEq]),cartprodfstpairEq]),cartprodfstin]),kfstpairEq]),kpairsurjEq]),cartprodmempair]),kpairp]),kpairiskpair]),c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_52])]) ).
thf(c_0_54,negated_conjecture,
! [X203: $i,X204: $i,X205: $i,X206: $i,X207: $i,X208: $i,X209: $i,X210: $i,X211: $i > $o,X214: $i,X216: $i,X217: $i > $o,X218: $i,X220: $i,X221: $i > $o,X222: $i,X225: $i,X226: $i > $o,X229: $i,X231: $i,X233: $i,X234: $i,X235: $i,X236: $i,X237: $i,X238: $i,X239: $i,X240: $i,X242: $i,X243: $i,X244: $i,X245: $i,X246: $i,X247: $i,X248: $i,X249: $i,X250: $i,X251: $i,X252: $i,X253: $i,X254: $i,X255: $i,X256: $i,X257: $i,X258: $i,X259: $i,X260: $i,X261: $i > $i > $o,X262: $i,X263: $i,X264: $i,X265: $i,X266: $i > $i > $o,X267: $i,X268: $i,X269: $i > $i > $o,X270: $i,X271: $i,X272: $i > $i > $o,X273: $i,X274: $i,X275: $i,X276: $i,X277: $i > $i > $o,X278: $i,X279: $i,X280: $i,X281: $i,X282: $i > $i > $o,X283: $i,X284: $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
& ( iskpair @ ( setadjoin @ ( setadjoin @ X203 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X203 @ ( setadjoin @ X204 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X205 @ X206 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& cartprodpairin
& cartprodmempair1
& ( ~ ( in @ X209 @ ( cartprod @ X207 @ X208 ) )
| ( iskpair @ X209 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk3_2 @ X210 @ X211 ) @ ( dsetconstr @ X210 @ X211 ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( in @ ( esk1_2 @ X210 @ X211 ) @ X210 ) )
& ( ( ( dsetconstr @ X210 @ X211 )
= ( setadjoin @ ( esk3_2 @ X210 @ X211 ) @ emptyset ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( in @ ( esk1_2 @ X210 @ X211 ) @ X210 ) )
& ( ( in @ ( esk3_2 @ X210 @ X211 ) @ ( dsetconstr @ X210 @ X211 ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( in @ ( esk2_2 @ X210 @ X211 ) @ X210 ) )
& ( ( ( dsetconstr @ X210 @ X211 )
= ( setadjoin @ ( esk3_2 @ X210 @ X211 ) @ emptyset ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( in @ ( esk2_2 @ X210 @ X211 ) @ X210 ) )
& ( ( in @ ( esk3_2 @ X210 @ X211 ) @ ( dsetconstr @ X210 @ X211 ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( X211 @ ( esk1_2 @ X210 @ X211 ) ) )
& ( ( ( dsetconstr @ X210 @ X211 )
= ( setadjoin @ ( esk3_2 @ X210 @ X211 ) @ emptyset ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( X211 @ ( esk1_2 @ X210 @ X211 ) ) )
& ( ( in @ ( esk3_2 @ X210 @ X211 ) @ ( dsetconstr @ X210 @ X211 ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( X211 @ ( esk2_2 @ X210 @ X211 ) ) )
& ( ( ( dsetconstr @ X210 @ X211 )
= ( setadjoin @ ( esk3_2 @ X210 @ X211 ) @ emptyset ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( X211 @ ( esk2_2 @ X210 @ X211 ) ) )
& ( ( in @ ( esk3_2 @ X210 @ X211 ) @ ( dsetconstr @ X210 @ X211 ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( ( esk1_2 @ X210 @ X211 )
!= ( esk2_2 @ X210 @ X211 ) ) )
& ( ( ( dsetconstr @ X210 @ X211 )
= ( setadjoin @ ( esk3_2 @ X210 @ X211 ) @ emptyset ) )
| ~ ( in @ X214 @ X210 )
| ~ ( X211 @ X214 )
| ( ( esk1_2 @ X210 @ X211 )
!= ( esk2_2 @ X210 @ X211 ) ) )
& ( ( in @ ( esk4_2 @ X216 @ X217 ) @ X216 )
| ~ ( in @ X218 @ ( dsetconstr @ X216 @ X217 ) )
| ( ( dsetconstr @ X216 @ X217 )
!= ( setadjoin @ X218 @ emptyset ) ) )
& ( ( X217 @ ( esk4_2 @ X216 @ X217 ) )
| ~ ( in @ X218 @ ( dsetconstr @ X216 @ X217 ) )
| ( ( dsetconstr @ X216 @ X217 )
!= ( setadjoin @ X218 @ emptyset ) ) )
& ( ( in @ ( esk6_3 @ X220 @ X221 @ X222 ) @ ( dsetconstr @ X220 @ X221 ) )
| ( in @ ( esk5_3 @ X220 @ X221 @ X222 ) @ X220 )
| ~ ( X221 @ X222 )
| ~ ( in @ X222 @ X220 ) )
& ( ( ( dsetconstr @ X220 @ X221 )
= ( setadjoin @ ( esk6_3 @ X220 @ X221 @ X222 ) @ emptyset ) )
| ( in @ ( esk5_3 @ X220 @ X221 @ X222 ) @ X220 )
| ~ ( X221 @ X222 )
| ~ ( in @ X222 @ X220 ) )
& ( ( in @ ( esk6_3 @ X220 @ X221 @ X222 ) @ ( dsetconstr @ X220 @ X221 ) )
| ( X221 @ ( esk5_3 @ X220 @ X221 @ X222 ) )
| ~ ( X221 @ X222 )
| ~ ( in @ X222 @ X220 ) )
& ( ( ( dsetconstr @ X220 @ X221 )
= ( setadjoin @ ( esk6_3 @ X220 @ X221 @ X222 ) @ emptyset ) )
| ( X221 @ ( esk5_3 @ X220 @ X221 @ X222 ) )
| ~ ( X221 @ X222 )
| ~ ( in @ X222 @ X220 ) )
& ( ( in @ ( esk6_3 @ X220 @ X221 @ X222 ) @ ( dsetconstr @ X220 @ X221 ) )
| ( ( esk5_3 @ X220 @ X221 @ X222 )
!= X222 )
| ~ ( X221 @ X222 )
| ~ ( in @ X222 @ X220 ) )
& ( ( ( dsetconstr @ X220 @ X221 )
= ( setadjoin @ ( esk6_3 @ X220 @ X221 @ X222 ) @ emptyset ) )
| ( ( esk5_3 @ X220 @ X221 @ X222 )
!= X222 )
| ~ ( X221 @ X222 )
| ~ ( in @ X222 @ X220 ) )
& ( ( in @ ( esk9_2 @ X225 @ X226 ) @ ( dsetconstr @ X225 @ X226 ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( in @ ( esk7_2 @ X225 @ X226 ) @ X225 ) )
& ( ( ( dsetconstr @ X225 @ X226 )
= ( setadjoin @ ( esk9_2 @ X225 @ X226 ) @ emptyset ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( in @ ( esk7_2 @ X225 @ X226 ) @ X225 ) )
& ( ( in @ ( esk9_2 @ X225 @ X226 ) @ ( dsetconstr @ X225 @ X226 ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( in @ ( esk8_2 @ X225 @ X226 ) @ X225 ) )
& ( ( ( dsetconstr @ X225 @ X226 )
= ( setadjoin @ ( esk9_2 @ X225 @ X226 ) @ emptyset ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( in @ ( esk8_2 @ X225 @ X226 ) @ X225 ) )
& ( ( in @ ( esk9_2 @ X225 @ X226 ) @ ( dsetconstr @ X225 @ X226 ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( X226 @ ( esk7_2 @ X225 @ X226 ) ) )
& ( ( ( dsetconstr @ X225 @ X226 )
= ( setadjoin @ ( esk9_2 @ X225 @ X226 ) @ emptyset ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( X226 @ ( esk7_2 @ X225 @ X226 ) ) )
& ( ( in @ ( esk9_2 @ X225 @ X226 ) @ ( dsetconstr @ X225 @ X226 ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( X226 @ ( esk8_2 @ X225 @ X226 ) ) )
& ( ( ( dsetconstr @ X225 @ X226 )
= ( setadjoin @ ( esk9_2 @ X225 @ X226 ) @ emptyset ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( X226 @ ( esk8_2 @ X225 @ X226 ) ) )
& ( ( in @ ( esk9_2 @ X225 @ X226 ) @ ( dsetconstr @ X225 @ X226 ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( ( esk7_2 @ X225 @ X226 )
!= ( esk8_2 @ X225 @ X226 ) ) )
& ( ( ( dsetconstr @ X225 @ X226 )
= ( setadjoin @ ( esk9_2 @ X225 @ X226 ) @ emptyset ) )
| ~ ( in @ X229 @ X225 )
| ~ ( X226 @ X229 )
| ( ( esk7_2 @ X225 @ X226 )
!= ( esk8_2 @ X225 @ X226 ) ) )
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk10_1 @ X231 )
@ ( dsetconstr @ ( setunion @ X231 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X231 ) ) )
| ~ ( iskpair @ X231 ) )
& ( ( ( dsetconstr @ ( setunion @ X231 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X231 ) )
= ( setadjoin @ ( esk10_1 @ X231 ) @ emptyset ) )
| ~ ( iskpair @ X231 ) )
& ( ~ ( in @ X234 @ X233 )
| ( X233
!= ( setadjoin @ X234 @ emptyset ) )
| ( in @ ( setunion @ X233 ) @ X233 ) )
& ( ( kfst @ ( kpair @ X235 @ X236 ) )
= X235 )
& ( ~ ( in @ X239 @ ( cartprod @ X237 @ X238 ) )
| ( in @ ( kfst @ X239 ) @ X237 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk11_1 @ X240 )
@ ( dsetconstr @ ( setunion @ X240 )
@ ^ [Z0: $i] :
( X240
= ( kpair @ ( kfst @ X240 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X240 ) )
& ( ( ( dsetconstr @ ( setunion @ X240 )
@ ^ [Z0: $i] :
( X240
= ( kpair @ ( kfst @ X240 ) @ Z0 ) ) )
= ( setadjoin @ ( esk11_1 @ X240 ) @ emptyset ) )
| ~ ( iskpair @ X240 ) )
& ( ( ksnd @ ( kpair @ X242 @ X243 ) )
= X243 )
& ( ~ ( iskpair @ X244 )
| ( ( kpair @ ( kfst @ X244 ) @ ( ksnd @ X244 ) )
= X244 ) )
& ( ~ ( in @ X247 @ ( cartprod @ X245 @ X246 ) )
| ( in @ ( ksnd @ X247 ) @ X246 ) )
& cartprodpairmemEL
& cartprodpairmemER
& cartprodmempaircEq
& ( ~ ( in @ X250 @ X248 )
| ~ ( in @ X251 @ X249 )
| ( ( kfst @ ( kpair @ X250 @ X251 ) )
= X250 ) )
& ( ~ ( in @ X254 @ X252 )
| ~ ( in @ X255 @ X253 )
| ( ( ksnd @ ( kpair @ X254 @ X255 ) )
= X255 ) )
& ( ~ ( in @ X258 @ ( cartprod @ X256 @ X257 ) )
| ( ( kpair @ ( kfst @ X258 ) @ ( ksnd @ X258 ) )
= X258 ) )
& ( ~ ( in @ X262 @ X259 )
| ~ ( in @ X263 @ X260 )
| ~ ( X261 @ X262 @ X263 )
| ( in @ ( kpair @ X262 @ X263 ) @ ( dpsetconstr @ X259 @ X260 @ X261 ) ) )
& ( subset @ ( dpsetconstr @ X264 @ X265 @ X266 ) @ ( cartprod @ X264 @ X265 ) )
& ( subset @ ( dpsetconstr @ X267 @ X268 @ X269 ) @ ( cartprod @ X267 @ X268 ) )
& ( ~ ( in @ X273 @ X270 )
| ~ ( in @ X274 @ X271 )
| ~ ( in @ ( kpair @ X273 @ X274 ) @ ( dpsetconstr @ X270 @ X271 @ X272 ) )
| ( X272 @ X273 @ X274 ) )
& ( ~ ( in @ ( kpair @ X278 @ X279 ) @ ( dpsetconstr @ X275 @ X276 @ X277 ) )
| ( in @ X278 @ X275 ) )
& ( ~ ( in @ ( kpair @ X283 @ X284 ) @ ( dpsetconstr @ X280 @ X281 @ X282 ) )
| ( in @ X284 @ X281 ) )
& ( in @ ( kpair @ esk14_0 @ esk15_0 ) @ ( dpsetconstr @ esk12_0 @ esk13_0 @ epred1_0 ) )
& ~ ( epred1_0 @ esk14_0 @ esk15_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_53])])])])])]) ).
thf(c_0_55,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( X6 @ X2 @ X4 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X5 )
| ~ ( in @ ( kpair @ X2 @ X4 ) @ ( dpsetconstr @ X3 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_56,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( in @ X2 @ X4 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_57,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( in @ X3 @ X5 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_58,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i > $i > $o] :
( ( X6 @ X2 @ X3 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ X4 @ X5 @ X6 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
thf(c_0_59,negated_conjecture,
in @ ( kpair @ esk14_0 @ esk15_0 ) @ ( dpsetconstr @ esk12_0 @ esk13_0 @ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_60,negated_conjecture,
~ ( epred1_0 @ esk14_0 @ esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU671^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n014.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:06:45 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.26 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/tmp/tmp.Ouy58mMU7h/E---3.1_2713776.p
% 0.23/0.33 % Version: 3.5.1-ho
% 0.23/0.33 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.23/0.33 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.23/0.33 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.33 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.23/0.33 % Starting full_lambda_10 with 300s (1) cores
% 0.23/0.33 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.23/0.33 % pre_casc_3 with pid 2713817 completed with status 0
% 0.23/0.33 % Result found by pre_casc_3
% 0.23/0.33 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.23/0.33 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.23/0.33 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.23/0.33 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.23/0.33 % Search class: HGUSM-FFMM32-MHSMMSBN
% 0.23/0.33 % partial match(3): HGHSM-FSLM32-MHSMMSBN
% 0.23/0.33 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.33 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.33 % SubtermCWHack with pid 2713831 completed with status 0
% 0.23/0.33 % Result found by SubtermCWHack
% 0.23/0.33 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.23/0.33 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.23/0.33 % Starting pre_casc_3 with 300s (1) cores
% 0.23/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.23/0.33 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.23/0.33 % Search class: HGUSM-FFMM32-MHSMMSBN
% 0.23/0.33 % partial match(3): HGHSM-FSLM32-MHSMMSBN
% 0.23/0.33 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.33 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.33 % Preprocessing time : 0.003 s
% 0.23/0.33
% 0.23/0.33 % Proof found!
% 0.23/0.33 % SZS status Theorem
% 0.23/0.33 % SZS output start CNFRefutation
% See solution above
% 0.23/0.33 % Parsed axioms : 414
% 0.23/0.33 % Removed by relevancy pruning/SinE : 385
% 0.23/0.33 % Initial clauses : 225
% 0.23/0.33 % Removed in clause preprocessing : 0
% 0.23/0.33 % Initial clauses in saturation : 225
% 0.23/0.33 % Processed clauses : 291
% 0.23/0.33 % ...of these trivial : 3
% 0.23/0.33 % ...subsumed : 19
% 0.23/0.33 % ...remaining for further processing : 269
% 0.23/0.33 % Other redundant clauses eliminated : 1
% 0.23/0.33 % Clauses deleted for lack of memory : 0
% 0.23/0.33 % Backward-subsumed : 0
% 0.23/0.33 % Backward-rewritten : 0
% 0.23/0.33 % Generated clauses : 681
% 0.23/0.33 % ...of the previous two non-redundant : 654
% 0.23/0.33 % ...aggressively subsumed : 0
% 0.23/0.33 % Contextual simplify-reflections : 2
% 0.23/0.33 % Paramodulations : 678
% 0.23/0.33 % Factorizations : 0
% 0.23/0.33 % NegExts : 0
% 0.23/0.33 % Equation resolutions : 3
% 0.23/0.33 % Disequality decompositions : 0
% 0.23/0.33 % Total rewrite steps : 38
% 0.23/0.33 % ...of those cached : 25
% 0.23/0.33 % Propositional unsat checks : 0
% 0.23/0.33 % Propositional check models : 0
% 0.23/0.33 % Propositional check unsatisfiable : 0
% 0.23/0.33 % Propositional clauses : 0
% 0.23/0.33 % Propositional clauses after purity: 0
% 0.23/0.33 % Propositional unsat core size : 0
% 0.23/0.33 % Propositional preprocessing time : 0.000
% 0.23/0.33 % Propositional encoding time : 0.000
% 0.23/0.33 % Propositional solver time : 0.000
% 0.23/0.33 % Success case prop preproc time : 0.000
% 0.23/0.33 % Success case prop encoding time : 0.000
% 0.23/0.33 % Success case prop solver time : 0.000
% 0.23/0.33 % Current number of processed clauses : 268
% 0.23/0.33 % Positive orientable unit clauses : 173
% 0.23/0.33 % Positive unorientable unit clauses: 0
% 0.23/0.33 % Negative unit clauses : 1
% 0.23/0.33 % Non-unit-clauses : 94
% 0.23/0.33 % Current number of unprocessed clauses: 586
% 0.23/0.33 % ...number of literals in the above : 2533
% 0.23/0.33 % Current number of archived formulas : 0
% 0.23/0.33 % Current number of archived clauses : 0
% 0.23/0.33 % Clause-clause subsumption calls (NU) : 1866
% 0.23/0.33 % Rec. Clause-clause subsumption calls : 1322
% 0.23/0.33 % Non-unit clause-clause subsumptions : 21
% 0.23/0.33 % Unit Clause-clause subsumption calls : 9
% 0.23/0.33 % Rewrite failures with RHS unbound : 0
% 0.23/0.33 % BW rewrite match attempts : 0
% 0.23/0.33 % BW rewrite match successes : 0
% 0.23/0.33 % Condensation attempts : 0
% 0.23/0.33 % Condensation successes : 0
% 0.23/0.33 % Termbank termtop insertions : 32207
% 0.23/0.33 % Search garbage collected termcells : 6882
% 0.23/0.33
% 0.23/0.33 % -------------------------------------------------
% 0.23/0.33 % User time : 0.039 s
% 0.23/0.33 % System time : 0.009 s
% 0.23/0.33 % Total time : 0.048 s
% 0.23/0.33 % Maximum resident set size: 6104 pages
% 0.23/0.33
% 0.23/0.33 % -------------------------------------------------
% 0.23/0.33 % User time : 0.049 s
% 0.23/0.33 % System time : 0.014 s
% 0.23/0.33 % Total time : 0.063 s
% 0.23/0.33 % Maximum resident set size: 5376 pages
% 0.23/0.33 % E exiting
%------------------------------------------------------------------------------