%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU658^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:27:06 AM UTC 2026
% Result : Theorem 0.37s 0.28s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 878 ( 53 equ; 0 cnn)
% Maximal formula atoms : 221 ( 25 avg)
% Number of connectives : 1520 ( 44 ~; 48 |; 206 &; 634 @)
% ( 16 <=>; 572 =>; 0 <=; 0 <~>)
% Maximal formula depth : 218 ( 28 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 197 ( 195 usr; 179 con; 0-3 aty)
% Number of variables : 163 ( 22 ^; 123 !; 18 ?; 163 :)
% 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_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_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,
esk1_3: $i > $i > $i > $i ).
thf(decl_229,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_230,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_231,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_232,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_233,type,
esk6_1: $i > $i ).
thf(decl_234,type,
esk7_1: $i > $i ).
thf(decl_235,type,
esk8_0: $i ).
thf(decl_236,type,
esk9_0: $i ).
thf(decl_237,type,
esk10_0: $i ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',singleton) ).
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/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',singletonprop) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',ksndsingleton) ).
thf(cartprodsndin,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
=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',cartprodsndin) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',theprop) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.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/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',kpairiskpair) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',cartprodfstin) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',cartprodmempair) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',cartprodmempair1) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',cartprodpairin) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',kpairsurjEq) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p',ksndpairEq) ).
thf(c_0_15,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_16,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_17,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_18,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_19,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
=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodsndin]) ).
thf(c_0_20,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X60: $i] :
( ( in @ X60 @ X21 )
& ( X21
= ( setadjoin @ X60 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_15]) ).
thf(c_0_21,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 ) )
=> ? [X57: $i] :
( ( in @ X57
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X57 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_22,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X59: $i] :
( ( in @ X59
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X59 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_15]) ).
thf(c_0_23,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X61: $i] :
( ( in @ X61
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X61 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_15]) ).
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
=> ( ! [X62: $i,X63: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X62 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X62 @ ( setadjoin @ X63 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X64: $i,X65: $i] : ( iskpair @ ( kpair @ X64 @ X65 ) )
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( ! [X66: $i,X67: $i,X68: $i] :
( ( in @ X68 @ X66 )
=> ! [X69: $i] :
( ( in @ X69 @ X67 )
=> ( in @ ( kpair @ X68 @ X69 ) @ ( cartprod @ X66 @ X67 ) ) ) )
=> ( ! [X70: $i,X71: $i,X72: $i] :
( ( in @ X72 @ ( cartprod @ X70 @ X71 ) )
=> ? [X73: $i] :
( ( in @ X73 @ X70 )
& ? [X74: $i] :
( ( in @ X74 @ X71 )
& ( X72
= ( kpair @ X73 @ X74 ) ) ) ) )
=> ( ! [X75: $i,X76: $i,X77: $i] :
( ( in @ X77 @ ( cartprod @ X75 @ X76 ) )
=> ( iskpair @ X77 ) )
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X78: $i,X79: $i > $o] :
( ! [X80: $i] :
( ( in @ X80 @ X78 )
=> ! [X81: $i] :
( ( in @ X81 @ X78 )
=> ( ( X79 @ X80 )
=> ( ( X79 @ X81 )
=> ( X80 = X81 ) ) ) ) )
=> ( ? [X82: $i] :
( ( in @ X82 @ X78 )
& ( X79 @ X82 ) )
=> ? [X83: $i] :
( ( in @ X83 @ ( dsetconstr @ X78 @ X79 ) )
& ( ( dsetconstr @ X78 @ X79 )
= ( setadjoin @ X83 @ emptyset ) ) ) ) )
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( ! [X84: $i] :
( ( iskpair @ X84 )
=> ? [X85: $i] :
( ( in @ X85
@ ( dsetconstr @ ( setunion @ X84 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X84 ) ) )
& ( ( dsetconstr @ ( setunion @ X84 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X84 ) )
= ( setadjoin @ X85 @ emptyset ) ) ) )
=> ( ! [X86: $i] :
( ? [X87: $i] :
( ( in @ X87 @ X86 )
& ( X86
= ( setadjoin @ X87 @ emptyset ) ) )
=> ( in @ ( setunion @ X86 ) @ X86 ) )
=> ( ! [X88: $i,X89: $i] :
( ( kfst @ ( kpair @ X88 @ X89 ) )
= X88 )
=> ( ! [X90: $i,X91: $i,X92: $i] :
( ( in @ X92 @ ( cartprod @ X90 @ X91 ) )
=> ( in @ ( kfst @ X92 ) @ X90 ) )
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ! [X93: $i] :
( ( iskpair @ X93 )
=> ? [X94: $i] :
( ( in @ X94
@ ( dsetconstr @ ( setunion @ X93 )
@ ^ [Z0: $i] :
( X93
= ( kpair @ ( kfst @ X93 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X93 )
@ ^ [Z0: $i] :
( X93
= ( kpair @ ( kfst @ X93 ) @ Z0 ) ) )
= ( setadjoin @ X94 @ emptyset ) ) ) )
=> ( ! [X95: $i,X96: $i] :
( ( ksnd @ ( kpair @ X95 @ X96 ) )
= X96 )
=> ( ! [X97: $i] :
( ( iskpair @ X97 )
=> ( ( kpair @ ( kfst @ X97 ) @ ( ksnd @ X97 ) )
= X97 ) )
=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),kpairp]),kpairiskpair]),c_0_23]),kfstpairEq]),cartprodfstin]),cartprodmempair]),cartprodmempair1]),cartprodpairin]),kpairsurjEq]),ksndpairEq])]) ).
thf(c_0_25,negated_conjecture,
! [X98: $i,X99: $i,X100: $i,X101: $i,X102: $i,X103: $i,X104: $i,X105: $i,X106: $i,X107: $i,X108: $i,X111: $i,X112: $i,X113: $i,X114: $i,X115: $i > $o,X118: $i,X120: $i,X122: $i,X123: $i,X124: $i,X125: $i,X126: $i,X127: $i,X128: $i,X129: $i,X131: $i,X132: $i,X133: $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 @ X98 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X98 @ ( setadjoin @ X99 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X100 @ X101 ) )
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& ( ~ ( in @ X104 @ X102 )
| ~ ( in @ X105 @ X103 )
| ( in @ ( kpair @ X104 @ X105 ) @ ( cartprod @ X102 @ X103 ) ) )
& ( ( in @ ( esk1_3 @ X106 @ X107 @ X108 ) @ X106 )
| ~ ( in @ X108 @ ( cartprod @ X106 @ X107 ) ) )
& ( ( in @ ( esk2_3 @ X106 @ X107 @ X108 ) @ X107 )
| ~ ( in @ X108 @ ( cartprod @ X106 @ X107 ) ) )
& ( ( X108
= ( kpair @ ( esk1_3 @ X106 @ X107 @ X108 ) @ ( esk2_3 @ X106 @ X107 @ X108 ) ) )
| ~ ( in @ X108 @ ( cartprod @ X106 @ X107 ) ) )
& ( ~ ( in @ X113 @ ( cartprod @ X111 @ X112 ) )
| ( iskpair @ X113 ) )
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk5_2 @ X114 @ X115 ) @ ( dsetconstr @ X114 @ X115 ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( in @ ( esk3_2 @ X114 @ X115 ) @ X114 ) )
& ( ( ( dsetconstr @ X114 @ X115 )
= ( setadjoin @ ( esk5_2 @ X114 @ X115 ) @ emptyset ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( in @ ( esk3_2 @ X114 @ X115 ) @ X114 ) )
& ( ( in @ ( esk5_2 @ X114 @ X115 ) @ ( dsetconstr @ X114 @ X115 ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( in @ ( esk4_2 @ X114 @ X115 ) @ X114 ) )
& ( ( ( dsetconstr @ X114 @ X115 )
= ( setadjoin @ ( esk5_2 @ X114 @ X115 ) @ emptyset ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( in @ ( esk4_2 @ X114 @ X115 ) @ X114 ) )
& ( ( in @ ( esk5_2 @ X114 @ X115 ) @ ( dsetconstr @ X114 @ X115 ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( X115 @ ( esk3_2 @ X114 @ X115 ) ) )
& ( ( ( dsetconstr @ X114 @ X115 )
= ( setadjoin @ ( esk5_2 @ X114 @ X115 ) @ emptyset ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( X115 @ ( esk3_2 @ X114 @ X115 ) ) )
& ( ( in @ ( esk5_2 @ X114 @ X115 ) @ ( dsetconstr @ X114 @ X115 ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( X115 @ ( esk4_2 @ X114 @ X115 ) ) )
& ( ( ( dsetconstr @ X114 @ X115 )
= ( setadjoin @ ( esk5_2 @ X114 @ X115 ) @ emptyset ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( X115 @ ( esk4_2 @ X114 @ X115 ) ) )
& ( ( in @ ( esk5_2 @ X114 @ X115 ) @ ( dsetconstr @ X114 @ X115 ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( ( esk3_2 @ X114 @ X115 )
!= ( esk4_2 @ X114 @ X115 ) ) )
& ( ( ( dsetconstr @ X114 @ X115 )
= ( setadjoin @ ( esk5_2 @ X114 @ X115 ) @ emptyset ) )
| ~ ( in @ X118 @ X114 )
| ~ ( X115 @ X118 )
| ( ( esk3_2 @ X114 @ X115 )
!= ( esk4_2 @ X114 @ X115 ) ) )
& ex1E1
& ex1I
& ex1I2
& singletonsuniq
& setukpairinjL1
& ( ( in @ ( esk6_1 @ X120 )
@ ( dsetconstr @ ( setunion @ X120 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X120 ) ) )
| ~ ( iskpair @ X120 ) )
& ( ( ( dsetconstr @ ( setunion @ X120 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X120 ) )
= ( setadjoin @ ( esk6_1 @ X120 ) @ emptyset ) )
| ~ ( iskpair @ X120 ) )
& ( ~ ( in @ X123 @ X122 )
| ( X122
!= ( setadjoin @ X123 @ emptyset ) )
| ( in @ ( setunion @ X122 ) @ X122 ) )
& ( ( kfst @ ( kpair @ X124 @ X125 ) )
= X124 )
& ( ~ ( in @ X128 @ ( cartprod @ X126 @ X127 ) )
| ( in @ ( kfst @ X128 ) @ X126 ) )
& setukpairinjL2
& setukpairinjL
& setukpairinjR11
& setukpairinjR12
& setukpairinjR1
& upairequniteq
& setukpairinjR2
& setukpairinjR
& ( ( in @ ( esk7_1 @ X129 )
@ ( dsetconstr @ ( setunion @ X129 )
@ ^ [Z0: $i] :
( X129
= ( kpair @ ( kfst @ X129 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X129 ) )
& ( ( ( dsetconstr @ ( setunion @ X129 )
@ ^ [Z0: $i] :
( X129
= ( kpair @ ( kfst @ X129 ) @ Z0 ) ) )
= ( setadjoin @ ( esk7_1 @ X129 ) @ emptyset ) )
| ~ ( iskpair @ X129 ) )
& ( ( ksnd @ ( kpair @ X131 @ X132 ) )
= X132 )
& ( ~ ( iskpair @ X133 )
| ( ( kpair @ ( kfst @ X133 ) @ ( ksnd @ X133 ) )
= X133 ) )
& ( in @ esk10_0 @ ( cartprod @ esk8_0 @ esk9_0 ) )
& ~ ( in @ ( ksnd @ esk10_0 ) @ esk9_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_24])])])])])]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( X2
= ( kpair @ ( esk1_3 @ X3 @ X4 @ X2 ) @ ( esk2_3 @ X3 @ X4 @ X2 ) ) )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk2_3 @ X2 @ X3 @ X4 ) @ X3 )
| ~ ( in @ X4 @ ( cartprod @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( ( esk2_3 @ X2 @ X3 @ X4 )
= ( ksnd @ X4 ) )
| ~ ( in @ X4 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ ( ksnd @ X2 ) @ X3 )
| ~ ( in @ X2 @ ( cartprod @ X4 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_31,negated_conjecture,
in @ esk10_0 @ ( cartprod @ esk8_0 @ esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_32,negated_conjecture,
~ ( in @ ( ksnd @ esk10_0 ) @ esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU658^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 % Computer : n005.cluster.edu
% 0.09/0.14 % Model : x86_64 x86_64
% 0.09/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.14 % Memory : 8046.5625MB
% 0.09/0.14 % OS : Linux 6.8.0-71-generic
% 0.09/0.14 % CPULimit : 300
% 0.09/0.14 % WCLimit : 300
% 0.09/0.14 % DateTime : Tue Sep 29 14:03:16 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.JvwCQjAzTU/E---3.1_1719537.p
% 0.37/0.28 % Version: 3.5.1-ho
% 0.37/0.28 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.37/0.28 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.28 % Starting ehoh_best5 with 300s (1) cores
% 0.37/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.37/0.28 % Starting new_bool_5 with 300s (1) cores
% 0.37/0.28 % Starting pre_casc_3 with 300s (1) cores
% 0.37/0.28 % Starting ho_unfolding_8 with 300s (1) cores
% 0.37/0.28 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.37/0.28 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.28 % Starting new_ho_5 with 300s (1) cores
% 0.37/0.28 % new_ho_5 with pid 1719557 completed with status 0
% 0.37/0.28 % Result found by new_ho_5
% 0.37/0.28 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.37/0.28 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.28 % Starting ehoh_best5 with 300s (1) cores
% 0.37/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.37/0.28 % Starting new_bool_5 with 300s (1) cores
% 0.37/0.28 % Starting pre_casc_3 with 300s (1) cores
% 0.37/0.28 % Starting ho_unfolding_8 with 300s (1) cores
% 0.37/0.28 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.37/0.28 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.28 % Starting new_ho_5 with 300s (1) cores
% 0.37/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.37/0.28 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.37/0.28 % Search class: HGUSM-FFMM31-MHFMMFBN
% 0.37/0.28 % partial match(2): HGUSM-FFMS31-MHFMMMBN
% 0.37/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.37/0.28 % SubtermCWHack with pid 1719558 completed with status 0
% 0.37/0.28 % Result found by SubtermCWHack
% 0.37/0.28 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.37/0.28 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.28 % Starting ehoh_best5 with 300s (1) cores
% 0.37/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.37/0.28 % Starting new_bool_5 with 300s (1) cores
% 0.37/0.28 % Starting pre_casc_3 with 300s (1) cores
% 0.37/0.28 % Starting ho_unfolding_8 with 300s (1) cores
% 0.37/0.28 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.37/0.28 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.28 % Starting new_ho_5 with 300s (1) cores
% 0.37/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.37/0.28 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.37/0.28 % Search class: HGUSM-FFMM31-MHFMMFBN
% 0.37/0.28 % partial match(2): HGUSM-FFMS31-MHFMMMBN
% 0.37/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.37/0.28 % Preprocessing time : 0.003 s
% 0.37/0.28
% 0.37/0.28 % Proof found!
% 0.37/0.28 % SZS status Theorem
% 0.37/0.28 % SZS output start CNFRefutation
% See solution above
% 0.37/0.28 % Parsed axioms : 384
% 0.37/0.28 % Removed by relevancy pruning/SinE : 368
% 0.37/0.28 % Initial clauses : 193
% 0.37/0.28 % Removed in clause preprocessing : 0
% 0.37/0.28 % Initial clauses in saturation : 193
% 0.37/0.28 % Processed clauses : 247
% 0.37/0.28 % ...of these trivial : 0
% 0.37/0.28 % ...subsumed : 25
% 0.37/0.28 % ...remaining for further processing : 222
% 0.37/0.28 % Other redundant clauses eliminated : 1
% 0.37/0.28 % Clauses deleted for lack of memory : 0
% 0.37/0.28 % Backward-subsumed : 0
% 0.37/0.28 % Backward-rewritten : 0
% 0.37/0.28 % Generated clauses : 186
% 0.37/0.28 % ...of the previous two non-redundant : 164
% 0.37/0.28 % ...aggressively subsumed : 0
% 0.37/0.28 % Contextual simplify-reflections : 0
% 0.37/0.28 % Paramodulations : 184
% 0.37/0.28 % Factorizations : 0
% 0.37/0.28 % NegExts : 0
% 0.37/0.28 % Equation resolutions : 2
% 0.37/0.28 % Disequality decompositions : 0
% 0.37/0.28 % Total rewrite steps : 26
% 0.37/0.28 % ...of those cached : 19
% 0.37/0.28 % Propositional unsat checks : 0
% 0.37/0.28 % Propositional check models : 0
% 0.37/0.28 % Propositional check unsatisfiable : 0
% 0.37/0.28 % Propositional clauses : 0
% 0.37/0.28 % Propositional clauses after purity: 0
% 0.37/0.28 % Propositional unsat core size : 0
% 0.37/0.28 % Propositional preprocessing time : 0.000
% 0.37/0.28 % Propositional encoding time : 0.000
% 0.37/0.28 % Propositional solver time : 0.000
% 0.37/0.28 % Success case prop preproc time : 0.000
% 0.37/0.28 % Success case prop encoding time : 0.000
% 0.37/0.28 % Success case prop solver time : 0.000
% 0.37/0.28 % Current number of processed clauses : 221
% 0.37/0.28 % Positive orientable unit clauses : 170
% 0.37/0.28 % Positive unorientable unit clauses: 0
% 0.37/0.28 % Negative unit clauses : 1
% 0.37/0.28 % Non-unit-clauses : 50
% 0.37/0.28 % Current number of unprocessed clauses: 110
% 0.37/0.28 % ...number of literals in the above : 414
% 0.37/0.28 % Current number of archived formulas : 0
% 0.37/0.28 % Current number of archived clauses : 0
% 0.37/0.28 % Clause-clause subsumption calls (NU) : 694
% 0.37/0.28 % Rec. Clause-clause subsumption calls : 499
% 0.37/0.28 % Non-unit clause-clause subsumptions : 25
% 0.37/0.28 % Unit Clause-clause subsumption calls : 0
% 0.37/0.28 % Rewrite failures with RHS unbound : 0
% 0.37/0.28 % BW rewrite match attempts : 0
% 0.37/0.28 % BW rewrite match successes : 0
% 0.37/0.28 % Condensation attempts : 0
% 0.37/0.28 % Condensation successes : 0
% 0.37/0.28 % Termbank termtop insertions : 15521
% 0.37/0.28 % Search garbage collected termcells : 4835
% 0.37/0.28
% 0.37/0.28 % -------------------------------------------------
% 0.37/0.28 % User time : 0.020 s
% 0.37/0.28 % System time : 0.007 s
% 0.37/0.28 % Total time : 0.027 s
% 0.37/0.28 % Maximum resident set size: 5552 pages
% 0.37/0.28
% 0.37/0.28 % -------------------------------------------------
% 0.37/0.28 % User time : 0.030 s
% 0.37/0.28 % System time : 0.012 s
% 0.37/0.28 % Total time : 0.042 s
% 0.37/0.28 % Maximum resident set size: 5376 pages
% 0.37/0.28 % E exiting
%------------------------------------------------------------------------------