%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU672^1 : 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 : n010.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 08:27:10 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 954 ( 55 equ; 0 cnn)
% Maximal formula atoms : 242 ( 29 avg)
% Number of connectives : 1640 ( 51 ~; 58 |; 233 &; 668 @)
% ( 8 <=>; 622 =>; 0 <=; 0 <~>)
% Maximal formula depth : 222 ( 30 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 213 ( 211 usr; 194 con; 0-3 aty)
% Number of variables : 173 ( 66 ^; 85 !; 22 ?; 173 :)
% 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_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_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_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_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,
dpsetconstrER: $o ).
thf(decl_244,type,
func: $i > $i > $i > $o ).
thf(decl_246,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_247,type,
esk2_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_248,type,
esk3_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_249,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_250,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_251,type,
esk6_2: $i > ( $i > $o ) > $i ).
thf(decl_252,type,
esk7_0: $i ).
thf(decl_253,type,
esk8_0: $i ).
thf(decl_254,type,
esk9_0: $i ).
thf(decl_255,type,
esk10_1: $i > $i ).
thf(decl_256,type,
esk11_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8EWH3qhL1m/E---3.1_2910775.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8EWH3qhL1m/E---3.1_2910775.p',singleton) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8EWH3qhL1m/E---3.1_2910775.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8EWH3qhL1m/E---3.1_2910775.p',breln) ).
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.8EWH3qhL1m/E---3.1_2910775.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.8EWH3qhL1m/E---3.1_2910775.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.8EWH3qhL1m/E---3.1_2910775.p',ex1E1) ).
thf(func,axiom,
( func
= ( ^ [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
& ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8EWH3qhL1m/E---3.1_2910775.p',func) ).
thf(funcImageSingleton,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
=> ( dpsetconstrER
=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8EWH3qhL1m/E---3.1_2910775.p',funcImageSingleton) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X50: $i] :
( ( in @ X50
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X50 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_10,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_11,plain,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).
thf(c_0_12,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_13,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_14,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X50: $i] :
( ( in @ X50
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X50 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_15,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_16,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_17,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X54: $i] :
( ( in @ X54
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X54 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_18,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
=> ( dpsetconstrER
=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcImageSingleton]) ).
thf(c_0_19,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_20,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 ) )
=> ? [X53: $i] :
( ( in @ X53
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X53 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_21,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X52: $i] :
( ( in @ X52
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X52 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_14]) ).
thf(c_0_22,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X51: $i] :
( ( in @ X51
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X51 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_14]) ).
thf(c_0_23,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X54: $i] :
( ( in @ X54
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X54 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_12]),c_0_14]) ).
thf(c_0_24,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
=> ( ! [X55: $i,X56: $i > $o] :
( ? [X57: $i] :
( ( in @ X57 @ ( dsetconstr @ X55 @ X56 ) )
& ( ( dsetconstr @ X55 @ X56 )
= ( setadjoin @ X57 @ emptyset ) ) )
=> ? [X58: $i] :
( ( in @ X58 @ X55 )
& ( X56 @ X58 ) ) )
=> ( ! [X59: $i,X60: $i > $o,X61: $i] :
( ( in @ X61 @ X59 )
=> ( ( X60 @ X61 )
=> ( ! [X62: $i] :
( ( in @ X62 @ X59 )
=> ( ( X60 @ X62 )
=> ( X62 = X61 ) ) )
=> ? [X63: $i] :
( ( in @ X63 @ ( dsetconstr @ X59 @ X60 ) )
& ( ( dsetconstr @ X59 @ X60 )
= ( setadjoin @ X63 @ emptyset ) ) ) ) ) )
=> ( ! [X64: $i,X65: $i > $o] :
( ! [X66: $i] :
( ( in @ X66 @ X64 )
=> ! [X67: $i] :
( ( in @ X67 @ X64 )
=> ( ( X65 @ X66 )
=> ( ( X65 @ X67 )
=> ( X66 = X67 ) ) ) ) )
=> ( ? [X68: $i] :
( ( in @ X68 @ X64 )
& ( X65 @ X68 ) )
=> ? [X69: $i] :
( ( in @ X69 @ ( dsetconstr @ X64 @ X65 ) )
& ( ( dsetconstr @ X64 @ X65 )
= ( setadjoin @ X69 @ emptyset ) ) ) ) )
=> ( 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
=> ( ! [X70: $i,X71: $i,X72: $i > $i > $o] : ( subset @ ( dpsetconstr @ X70 @ X71 @ X72 ) @ ( cartprod @ X70 @ X71 ) )
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X73: $i] :
( ( in @ X73 @ X4 )
=> ? [X74: $i] :
( ( in @ X74
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X73 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X73 @ Z0 ) @ X30 ) )
= ( setadjoin @ X74 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X75: $i] :
( ( in @ X75
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) )
= ( setadjoin @ X75 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_10])]) ).
thf(c_0_25,negated_conjecture,
! [X78: $i,X79: $i > $o,X80: $i,X82: $i,X83: $i > $o,X84: $i,X87: $i,X88: $i > $o,X91: $i,X93: $i,X94: $i,X95: $i > $i > $o,X99: $i,X102: $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
& kpairiskpair
& kpairp
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& cartprodpairin
& cartprodmempair1
& cartprodmempair
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& singletonprop
& ( ( in @ ( esk1_2 @ X78 @ X79 ) @ X78 )
| ~ ( in @ X80 @ ( dsetconstr @ X78 @ X79 ) )
| ( ( dsetconstr @ X78 @ X79 )
!= ( setadjoin @ X80 @ emptyset ) ) )
& ( ( X79 @ ( esk1_2 @ X78 @ X79 ) )
| ~ ( in @ X80 @ ( dsetconstr @ X78 @ X79 ) )
| ( ( dsetconstr @ X78 @ X79 )
!= ( setadjoin @ X80 @ emptyset ) ) )
& ( ( in @ ( esk3_3 @ X82 @ X83 @ X84 ) @ ( dsetconstr @ X82 @ X83 ) )
| ( in @ ( esk2_3 @ X82 @ X83 @ X84 ) @ X82 )
| ~ ( X83 @ X84 )
| ~ ( in @ X84 @ X82 ) )
& ( ( ( dsetconstr @ X82 @ X83 )
= ( setadjoin @ ( esk3_3 @ X82 @ X83 @ X84 ) @ emptyset ) )
| ( in @ ( esk2_3 @ X82 @ X83 @ X84 ) @ X82 )
| ~ ( X83 @ X84 )
| ~ ( in @ X84 @ X82 ) )
& ( ( in @ ( esk3_3 @ X82 @ X83 @ X84 ) @ ( dsetconstr @ X82 @ X83 ) )
| ( X83 @ ( esk2_3 @ X82 @ X83 @ X84 ) )
| ~ ( X83 @ X84 )
| ~ ( in @ X84 @ X82 ) )
& ( ( ( dsetconstr @ X82 @ X83 )
= ( setadjoin @ ( esk3_3 @ X82 @ X83 @ X84 ) @ emptyset ) )
| ( X83 @ ( esk2_3 @ X82 @ X83 @ X84 ) )
| ~ ( X83 @ X84 )
| ~ ( in @ X84 @ X82 ) )
& ( ( in @ ( esk3_3 @ X82 @ X83 @ X84 ) @ ( dsetconstr @ X82 @ X83 ) )
| ( ( esk2_3 @ X82 @ X83 @ X84 )
!= X84 )
| ~ ( X83 @ X84 )
| ~ ( in @ X84 @ X82 ) )
& ( ( ( dsetconstr @ X82 @ X83 )
= ( setadjoin @ ( esk3_3 @ X82 @ X83 @ X84 ) @ emptyset ) )
| ( ( esk2_3 @ X82 @ X83 @ X84 )
!= X84 )
| ~ ( X83 @ X84 )
| ~ ( in @ X84 @ X82 ) )
& ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( in @ ( esk4_2 @ X87 @ X88 ) @ X87 ) )
& ( ( ( dsetconstr @ X87 @ X88 )
= ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( in @ ( esk4_2 @ X87 @ X88 ) @ X87 ) )
& ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( in @ ( esk5_2 @ X87 @ X88 ) @ X87 ) )
& ( ( ( dsetconstr @ X87 @ X88 )
= ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( in @ ( esk5_2 @ X87 @ X88 ) @ X87 ) )
& ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( X88 @ ( esk4_2 @ X87 @ X88 ) ) )
& ( ( ( dsetconstr @ X87 @ X88 )
= ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( X88 @ ( esk4_2 @ X87 @ X88 ) ) )
& ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( X88 @ ( esk5_2 @ X87 @ X88 ) ) )
& ( ( ( dsetconstr @ X87 @ X88 )
= ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( X88 @ ( esk5_2 @ X87 @ X88 ) ) )
& ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( ( esk4_2 @ X87 @ X88 )
!= ( esk5_2 @ X87 @ X88 ) ) )
& ( ( ( dsetconstr @ X87 @ X88 )
= ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
| ~ ( in @ X91 @ X87 )
| ~ ( X88 @ X91 )
| ( ( esk4_2 @ X87 @ X88 )
!= ( esk5_2 @ X87 @ X88 ) ) )
& 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
& ( subset @ ( dpsetconstr @ X93 @ X94 @ X95 ) @ ( cartprod @ X93 @ X94 ) )
& dpsetconstrERa
& dpsetconstrEL1
& dpsetconstrEL2
& dpsetconstrER
& ( subset @ esk9_0 @ ( cartprod @ esk7_0 @ esk8_0 ) )
& ( ( in @ ( esk10_1 @ X99 )
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X99 @ Z0 ) @ esk9_0 ) ) )
| ~ ( in @ X99 @ esk7_0 ) )
& ( ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X99 @ Z0 ) @ esk9_0 ) )
= ( setadjoin @ ( esk10_1 @ X99 ) @ emptyset ) )
| ~ ( in @ X99 @ esk7_0 ) )
& ( in @ esk11_0 @ esk7_0 )
& ( ~ ( in @ X102
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) ) )
| ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) )
!= ( setadjoin @ X102 @ emptyset ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])])]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) ) )
| ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk10_1 @ X2 )
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ esk9_0 ) ) )
| ~ ( in @ X2 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
in @ esk11_0 @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) )
!= ( setadjoin @ ( esk10_1 @ esk11_0 ) @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i] :
( ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ esk9_0 ) )
= ( setadjoin @ ( esk10_1 @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU672^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n010.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:07:18 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.24/0.28 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.8EWH3qhL1m/E---3.1_2910775.p
% 0.24/0.34 % Version: 3.5.1-ho
% 0.24/0.34 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.24/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.34 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.24/0.34 % Starting pre_casc_3 with 300s (1) cores
% 0.24/0.34 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.24/0.34 % Starting full_lambda_10 with 300s (1) cores
% 0.24/0.34 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.24/0.34 % full_lambda_10 with pid 2910830 completed with status 0
% 0.24/0.34 % Result found by full_lambda_10
% 0.24/0.34 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.24/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.34 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.24/0.34 % Starting pre_casc_3 with 300s (1) cores
% 0.24/0.34 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.24/0.34 % Starting full_lambda_10 with 300s (1) cores
% 0.24/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.24/0.34 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.24/0.34 % Search class: HGHSF-FFMM32-DHSMMFBN
% 0.24/0.34 % partial match(4): HGHSM-FMLM32-MHSMMFBN
% 0.24/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.34 % SubtermCWHack with pid 2910837 completed with status 0
% 0.24/0.34 % Result found by SubtermCWHack
% 0.24/0.34 % Preprocessing class: HSLMSLSSLLLCHSA.
% 0.24/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.34 % Starting ho_unfolding_5 with 1200s (4) cores
% 0.24/0.34 % Starting pre_casc_3 with 300s (1) cores
% 0.24/0.34 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.24/0.34 % Starting full_lambda_10 with 300s (1) cores
% 0.24/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.24/0.34 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.24/0.34 % Search class: HGHSF-FFMM32-DHSMMFBN
% 0.24/0.34 % partial match(4): HGHSM-FMLM32-MHSMMFBN
% 0.24/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.34 % Preprocessing time : 0.003 s
% 0.24/0.34
% 0.24/0.34 % Proof found!
% 0.24/0.34 % SZS status Theorem
% 0.24/0.34 % SZS output start CNFRefutation
% See solution above
% 0.24/0.34 % Parsed axioms : 419
% 0.24/0.34 % Removed by relevancy pruning/SinE : 409
% 0.24/0.34 % Initial clauses : 209
% 0.24/0.34 % Removed in clause preprocessing : 0
% 0.24/0.34 % Initial clauses in saturation : 209
% 0.24/0.34 % Processed clauses : 222
% 0.24/0.34 % ...of these trivial : 0
% 0.24/0.34 % ...subsumed : 0
% 0.24/0.34 % ...remaining for further processing : 222
% 0.24/0.34 % Other redundant clauses eliminated : 0
% 0.24/0.34 % Clauses deleted for lack of memory : 0
% 0.24/0.34 % Backward-subsumed : 0
% 0.24/0.34 % Backward-rewritten : 0
% 0.24/0.34 % Generated clauses : 173
% 0.24/0.34 % ...of the previous two non-redundant : 172
% 0.24/0.34 % ...aggressively subsumed : 0
% 0.24/0.34 % Contextual simplify-reflections : 2
% 0.24/0.34 % Paramodulations : 173
% 0.24/0.34 % Factorizations : 0
% 0.24/0.34 % NegExts : 0
% 0.24/0.34 % Equation resolutions : 0
% 0.24/0.34 % Disequality decompositions : 0
% 0.24/0.34 % Total rewrite steps : 3
% 0.24/0.34 % ...of those cached : 2
% 0.24/0.34 % Propositional unsat checks : 0
% 0.24/0.34 % Propositional check models : 0
% 0.24/0.34 % Propositional check unsatisfiable : 0
% 0.24/0.34 % Propositional clauses : 0
% 0.24/0.34 % Propositional clauses after purity: 0
% 0.24/0.34 % Propositional unsat core size : 0
% 0.24/0.34 % Propositional preprocessing time : 0.000
% 0.24/0.34 % Propositional encoding time : 0.000
% 0.24/0.34 % Propositional solver time : 0.000
% 0.24/0.34 % Success case prop preproc time : 0.000
% 0.24/0.34 % Success case prop encoding time : 0.000
% 0.24/0.34 % Success case prop solver time : 0.000
% 0.24/0.34 % Current number of processed clauses : 222
% 0.24/0.34 % Positive orientable unit clauses : 187
% 0.24/0.34 % Positive unorientable unit clauses: 0
% 0.24/0.34 % Negative unit clauses : 1
% 0.24/0.34 % Non-unit-clauses : 34
% 0.24/0.34 % Current number of unprocessed clauses: 159
% 0.24/0.34 % ...number of literals in the above : 781
% 0.24/0.34 % Current number of archived formulas : 0
% 0.24/0.34 % Current number of archived clauses : 0
% 0.24/0.34 % Clause-clause subsumption calls (NU) : 67
% 0.24/0.34 % Rec. Clause-clause subsumption calls : 49
% 0.24/0.34 % Non-unit clause-clause subsumptions : 2
% 0.24/0.34 % Unit Clause-clause subsumption calls : 1
% 0.24/0.34 % Rewrite failures with RHS unbound : 0
% 0.24/0.34 % BW rewrite match attempts : 0
% 0.24/0.34 % BW rewrite match successes : 0
% 0.24/0.34 % Condensation attempts : 0
% 0.24/0.34 % Condensation successes : 0
% 0.24/0.34 % Termbank termtop insertions : 18456
% 0.24/0.34 % Search garbage collected termcells : 5564
% 0.24/0.34
% 0.24/0.34 % -------------------------------------------------
% 0.24/0.34 % User time : 0.024 s
% 0.24/0.34 % System time : 0.006 s
% 0.24/0.34 % Total time : 0.030 s
% 0.24/0.34 % Maximum resident set size: 5600 pages
% 0.24/0.34
% 0.24/0.34 % -------------------------------------------------
% 0.24/0.34 % User time : 0.035 s
% 0.24/0.34 % System time : 0.011 s
% 0.24/0.34 % Total time : 0.046 s
% 0.24/0.34 % Maximum resident set size: 5376 pages
% 0.24/0.34 % E exiting
%------------------------------------------------------------------------------