%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU619^1 : 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 08:24:45 AM UTC 2026
% Result : Theorem 12.47s 2.12s
% Output : CNFRefutation 12.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 746 ( 63 equ; 0 cnn)
% Maximal formula atoms : 177 ( 15 avg)
% Number of connectives : 1558 ( 59 ~; 48 |; 159 &; 780 @)
% ( 38 <=>; 474 =>; 0 <=; 0 <~>)
% Maximal formula depth : 199 ( 21 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 155 ( 152 usr; 140 con; 0-4 aty)
% Number of variables : 244 ( 29 ^; 195 !; 20 ?; 244 :)
% 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_30,type,
powerset: $i > $i ).
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_58,type,
nonempty: $i > $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,
esk1_2: $i > $i > $i ).
thf(decl_180,type,
esk2_1: $i > $i ).
thf(decl_181,type,
esk3_3: $i > $i > $o > $i ).
thf(decl_182,type,
esk4_1: $i > $i ).
thf(decl_183,type,
esk5_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_184,type,
esk6_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_185,type,
esk7_0: $i ).
thf(decl_186,type,
esk8_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',nonemptyI) ).
thf(kpairiskpair,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
=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',kpairiskpair) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',nonemptyE1) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X4 ) )
& ( X4
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',iskpair) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',sepSubset) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',sepInPowerset) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',dsetconstr__Cong) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',emptyE1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setoftrueEq) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setbeta) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',dsetconstrI) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',nonemptyImpWitness) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',nonemptyI1) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setukpairIR) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setukpairIL) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setunion__Cong) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setunionI) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PMLS1J7Vtm/E---3.1_1708807.p',setunionAx) ).
thf(c_0_23,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_24,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_25,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
=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[kpairiskpair]) ).
thf(c_0_26,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_23]) ).
thf(c_0_27,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_28,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_29,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_30,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_31,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_32,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_33,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_34,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_35,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_36,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_37,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_23]) ).
thf(c_0_38,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_23]) ).
thf(c_0_39,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_23]) ).
thf(c_0_40,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( ! [X76: $i,X77: $i] :
( ( in @ X77 @ ( setunion @ X76 ) )
<=> ? [X78: $i] :
( ( in @ X77 @ X78 )
& ( in @ X78 @ X76 ) ) )
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( ! [X79: $i,X80: $i > $o,X81: $i] :
( ( in @ X81 @ X79 )
=> ( ( X80 @ X81 )
=> ( in @ X81 @ ( dsetconstr @ X79 @ X80 ) ) ) )
=> ( ! [X82: $i,X83: $i > $o,X84: $i] :
( ( in @ X84 @ ( dsetconstr @ X82 @ X83 ) )
=> ( in @ X84 @ X82 ) )
=> ( ! [X85: $i,X86: $i > $o,X87: $i] :
( ( in @ X87 @ ( dsetconstr @ X85 @ X86 ) )
=> ( X86 @ X87 ) )
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( ! [X88: $i,X89: $i > $o,X90: $i] :
( ( in @ X90 @ X88 )
=> ( ( in @ X90 @ ( dsetconstr @ X88 @ X89 ) )
<=> ( X89 @ X90 ) ) )
=> ( ! [X91: $i] :
( ( X91 != emptyset )
=> ? [X92: $i] : ( in @ X92 @ X91 ) )
=> ( ! [X93: $i,X94: $i > $o,X95: $i] :
( ( in @ X95 @ X93 )
=> ( ( X94 @ X95 )
=> ( ( dsetconstr @ X93 @ X94 )
!= emptyset ) ) )
=> ( ! [X96: $i] :
( ? [X97: $i] : ( in @ X97 @ X96 )
=> ( X96 != emptyset ) )
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( ! [X98: $i] :
( ( dsetconstr @ X98
@ ^ [Z0: $i] : $true )
= X98 )
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( ! [X99: $i,X100: $i,X101: $i] :
( ( in @ X100 @ X101 )
=> ( ( in @ X101 @ X99 )
=> ( in @ X100 @ ( setunion @ X99 ) ) ) )
=> ( ! [X102: $i,X103: $i] :
( ( in @ X103 @ ( setunion @ X102 ) )
=> ! [X104: $o] :
( ! [X105: $i] :
( ( in @ X103 @ X105 )
=> ( ( in @ X105 @ X102 )
=> X104 ) )
=> X104 ) )
=> ( ! [X106: $i,X107: $i] :
( ( in @ X107 @ X106 )
=> ( in @ X107 @ ( powerset @ ( setunion @ X106 ) ) ) )
=> ( exuE2
=> ( ! [X108: $i] :
( ( X108 != emptyset )
=> ? [X109: $i] :
( ( in @ X109 @ X108 )
& $true ) )
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( ! [X110: $i,X111: $i > $o] :
( ? [X112: $i] :
( ( in @ X112 @ X110 )
& ( X111 @ X112 ) )
=> ( ( ( dsetconstr @ X110 @ X111 )
= emptyset )
=> ~ $true ) )
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( ! [X113: $i,X114: $i] :
( ( X113 = X114 )
=> ( ( setunion @ X113 )
= ( setunion @ X114 ) ) )
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( ! [X115: $i,X116: $i] :
( ( X115 = X116 )
=> ! [X117: $i > $o,X118: $i > $o] :
( ! [X119: $i] :
( ( in @ X119 @ X115 )
=> ! [X120: $i] :
( ( in @ X120 @ X116 )
=> ( ( X119 = X120 )
=> ( ( X117 @ X119 )
<=> ( X118 @ X120 ) ) ) ) )
=> ( ( dsetconstr @ X115 @ X117 )
= ( dsetconstr @ X116 @ X118 ) ) ) )
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( ! [X121: $i,X122: $i > $o] : ( in @ ( dsetconstr @ X121 @ X122 ) @ ( powerset @ X121 ) )
=> ( ! [X123: $i,X124: $i > $o] : ( subset @ ( dsetconstr @ X123 @ X124 ) @ X123 )
=> ( 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
=> ( ! [X125: $i,X126: $i] : ( in @ X125 @ ( setunion @ ( setadjoin @ ( setadjoin @ X125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X125 @ ( setadjoin @ X126 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X127: $i,X128: $i] : ( in @ X128 @ ( setunion @ ( setadjoin @ ( setadjoin @ X127 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X127 @ ( setadjoin @ X128 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X2: $i,X3: $i] :
? [X129: $i] :
( ( in @ X129 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X130: $i] :
( ( in @ X130 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X129 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X129 @ ( setadjoin @ X130 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_26]),setukpairIR]),setukpairIL]),setunion__Cong]),subPowSU]),setunionE]),setunionI]),setunionAx]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39])])]) ).
thf(c_0_41,negated_conjecture,
! [X131: $i,X132: $i,X134: $i,X135: $i,X136: $i,X137: $i,X138: $i > $o,X139: $i,X140: $i,X141: $i > $o,X142: $i,X143: $i,X144: $i > $o,X145: $i,X146: $i,X147: $i > $o,X148: $i,X149: $i,X151: $i,X152: $i > $o,X153: $i,X154: $i,X155: $i,X156: $i,X157: $i,X158: $i,X159: $i,X160: $i,X161: $i,X162: $o,X164: $i,X165: $i,X166: $i,X168: $i,X169: $i > $o,X170: $i,X171: $i,X172: $i,X173: $i,X174: $i,X175: $i > $o,X176: $i > $o,X179: $i,X180: $i > $o,X181: $i,X182: $i > $o,X183: $i,X184: $i,X185: $i,X186: $i,X189: $i,X190: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& ( ( in @ X132 @ ( esk1_2 @ X131 @ X132 ) )
| ~ ( in @ X132 @ ( setunion @ X131 ) ) )
& ( ( in @ ( esk1_2 @ X131 @ X132 ) @ X131 )
| ~ ( in @ X132 @ ( setunion @ X131 ) ) )
& ( ~ ( in @ X135 @ X136 )
| ~ ( in @ X136 @ X134 )
| ( in @ X135 @ ( setunion @ X134 ) ) )
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& descrp
& ( ~ ( in @ X139 @ X137 )
| ~ ( X138 @ X139 )
| ( in @ X139 @ ( dsetconstr @ X137 @ X138 ) ) )
& ( ~ ( in @ X142 @ ( dsetconstr @ X140 @ X141 ) )
| ( in @ X142 @ X140 ) )
& ( ~ ( in @ X145 @ ( dsetconstr @ X143 @ X144 ) )
| ( X144 @ X145 ) )
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& ( ~ ( in @ X148 @ ( dsetconstr @ X146 @ X147 ) )
| ( X147 @ X148 )
| ~ ( in @ X148 @ X146 ) )
& ( ~ ( X147 @ X148 )
| ( in @ X148 @ ( dsetconstr @ X146 @ X147 ) )
| ~ ( in @ X148 @ X146 ) )
& ( ( X149 = emptyset )
| ( in @ ( esk2_1 @ X149 ) @ X149 ) )
& ( ~ ( in @ X153 @ X151 )
| ~ ( X152 @ X153 )
| ( ( dsetconstr @ X151 @ X152 )
!= emptyset ) )
& ( ~ ( in @ X155 @ X154 )
| ( X154 != emptyset ) )
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& ( ( dsetconstr @ X156
@ ^ [Z0: $i] : $true )
= X156 )
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& ( ~ ( in @ X158 @ X159 )
| ~ ( in @ X159 @ X157 )
| ( in @ X158 @ ( setunion @ X157 ) ) )
& ( ( in @ X161 @ ( esk3_3 @ X160 @ X161 @ X162 ) )
| X162
| ~ ( in @ X161 @ ( setunion @ X160 ) ) )
& ( ( in @ ( esk3_3 @ X160 @ X161 @ X162 ) @ X160 )
| X162
| ~ ( in @ X161 @ ( setunion @ X160 ) ) )
& ( ~ X162
| X162
| ~ ( in @ X161 @ ( setunion @ X160 ) ) )
& ( ~ ( in @ X165 @ X164 )
| ( in @ X165 @ ( powerset @ ( setunion @ X164 ) ) ) )
& exuE2
& ( ( in @ ( esk4_1 @ X166 ) @ X166 )
| ( X166 = emptyset ) )
& ( $true
| ( X166 = emptyset ) )
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& ( ~ ( in @ X170 @ X168 )
| ~ ( X169 @ X170 )
| ( ( dsetconstr @ X168 @ X169 )
!= emptyset )
| ~ $true )
& vacuousDall
& quantDeMorgan1
& quantDeMorgan2
& quantDeMorgan3
& quantDeMorgan4
& prop2setI
& prop2set2propI
& notdexE
& notdallE
& exuI1
& exuI3
& exuI2
& inCongP
& in__Cong
& exuE3u
& exu__Cong
& emptyset__Cong
& setadjoin__Cong
& powerset__Cong
& ( ( X171 != X172 )
| ( ( setunion @ X171 )
= ( setunion @ X172 ) ) )
& omega__Cong
& exuEu
& descr__Cong
& ( ( in @ ( esk5_4 @ X173 @ X174 @ X175 @ X176 ) @ X173 )
| ( ( dsetconstr @ X173 @ X175 )
= ( dsetconstr @ X174 @ X176 ) )
| ( X173 != X174 ) )
& ( ( in @ ( esk6_4 @ X173 @ X174 @ X175 @ X176 ) @ X174 )
| ( ( dsetconstr @ X173 @ X175 )
= ( dsetconstr @ X174 @ X176 ) )
| ( X173 != X174 ) )
& ( ( ( esk5_4 @ X173 @ X174 @ X175 @ X176 )
= ( esk6_4 @ X173 @ X174 @ X175 @ X176 ) )
| ( ( dsetconstr @ X173 @ X175 )
= ( dsetconstr @ X174 @ X176 ) )
| ( X173 != X174 ) )
& ( ~ ( X175 @ ( esk5_4 @ X173 @ X174 @ X175 @ X176 ) )
| ~ ( X176 @ ( esk6_4 @ X173 @ X174 @ X175 @ X176 ) )
| ( ( dsetconstr @ X173 @ X175 )
= ( dsetconstr @ X174 @ X176 ) )
| ( X173 != X174 ) )
& ( ( X175 @ ( esk5_4 @ X173 @ X174 @ X175 @ X176 ) )
| ( X176 @ ( esk6_4 @ X173 @ X174 @ X175 @ X176 ) )
| ( ( dsetconstr @ X173 @ X175 )
= ( dsetconstr @ X174 @ X176 ) )
| ( X173 != X174 ) )
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& ( in @ ( dsetconstr @ X179 @ X180 ) @ ( powerset @ X179 ) )
& ( subset @ ( dsetconstr @ X181 @ X182 ) @ X181 )
& 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
& ( in @ X183 @ ( setunion @ ( setadjoin @ ( setadjoin @ X183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X183 @ ( setadjoin @ X184 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X186 @ ( setunion @ ( setadjoin @ ( setadjoin @ X185 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X185 @ ( setadjoin @ X186 @ emptyset ) ) @ emptyset ) ) ) )
& ( ~ ( in @ X189 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X190 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X189 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X189 @ ( setadjoin @ X190 @ emptyset ) ) @ 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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])])]) ).
thf(c_0_42,negated_conjecture,
! [X2: $i,X3: $i] :
( ~ ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_43,negated_conjecture,
! [X3: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_44,negated_conjecture,
! [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk7_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk7_0 @ ( setadjoin @ esk8_0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_46,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_44,c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU619^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n005.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:58:31 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.26 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.PMLS1J7Vtm/E---3.1_1708807.p
% 12.47/2.12 % Version: 3.5.1-ho
% 12.47/2.12 % Preprocessing class: HSLMSLSSLLLCHFA.
% 12.47/2.12 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 12.47/2.12 % Starting ehoh_best5 with 300s (1) cores
% 12.47/2.12 % Starting almost_fo_3_lam with 300s (1) cores
% 12.47/2.12 % Starting new_bool_5 with 300s (1) cores
% 12.47/2.12 % Starting pre_casc_3 with 300s (1) cores
% 12.47/2.12 % Starting ho_unfolding_8 with 300s (1) cores
% 12.47/2.12 % Starting new_ho_10_cnf2 with 300s (1) cores
% 12.47/2.12 % Starting new_bool_3 with 300s (1) cores
% 12.47/2.12 % Starting new_ho_5 with 300s (1) cores
% 12.47/2.12 % new_ho_5 with pid 1708849 completed with status 9
% 12.47/2.12 % pre_casc_3 with pid 1708845 completed with status 0
% 12.47/2.12 % Result found by pre_casc_3
% 12.47/2.12 % Preprocessing class: HSLMSLSSLLLCHFA.
% 12.47/2.12 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 12.47/2.12 % Starting ehoh_best5 with 300s (1) cores
% 12.47/2.12 % Starting almost_fo_3_lam with 300s (1) cores
% 12.47/2.12 % Starting new_bool_5 with 300s (1) cores
% 12.47/2.12 % Starting pre_casc_3 with 300s (1) cores
% 12.47/2.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 12.47/2.12 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 12.47/2.12 % Search class: HGHSM-FFMM32-MHFMMFBN
% 12.47/2.12 % partial match(3): HGHSM-FSLM32-MHFMMSBN
% 12.47/2.12 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 12.47/2.12 % Starting SubtermCWHack with 31s (1) cores
% 12.47/2.12 % SubtermCWHack with pid 1708856 completed with status 0
% 12.47/2.12 % Result found by SubtermCWHack
% 12.47/2.12 % Preprocessing class: HSLMSLSSLLLCHFA.
% 12.47/2.12 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 12.47/2.12 % Starting ehoh_best5 with 300s (1) cores
% 12.47/2.12 % Starting almost_fo_3_lam with 300s (1) cores
% 12.47/2.12 % Starting new_bool_5 with 300s (1) cores
% 12.47/2.12 % Starting pre_casc_3 with 300s (1) cores
% 12.47/2.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 12.47/2.12 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 12.47/2.12 % Search class: HGHSM-FFMM32-MHFMMFBN
% 12.47/2.12 % partial match(3): HGHSM-FSLM32-MHFMMSBN
% 12.47/2.12 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 12.47/2.12 % Starting SubtermCWHack with 31s (1) cores
% 12.47/2.12 % Preprocessing time : 0.003 s
% 12.47/2.12
% 12.47/2.12 % Proof found!
% 12.47/2.12 % SZS status Theorem
% 12.47/2.12 % SZS output start CNFRefutation
% See solution above
% 12.47/2.12 % Parsed axioms : 295
% 12.47/2.12 % Removed by relevancy pruning/SinE : 272
% 12.47/2.12 % Initial clauses : 148
% 12.47/2.12 % Removed in clause preprocessing : 4
% 12.47/2.12 % Initial clauses in saturation : 144
% 12.47/2.12 % Processed clauses : 3641
% 12.47/2.12 % ...of these trivial : 4
% 12.47/2.12 % ...subsumed : 2588
% 12.47/2.12 % ...remaining for further processing : 1049
% 12.47/2.12 % Other redundant clauses eliminated : 7
% 12.47/2.12 % Clauses deleted for lack of memory : 0
% 12.47/2.12 % Backward-subsumed : 24
% 12.47/2.12 % Backward-rewritten : 3
% 12.47/2.12 % Generated clauses : 100368
% 12.47/2.12 % ...of the previous two non-redundant : 98218
% 12.47/2.12 % ...aggressively subsumed : 0
% 12.47/2.12 % Contextual simplify-reflections : 0
% 12.47/2.12 % Paramodulations : 100361
% 12.47/2.12 % Factorizations : 0
% 12.47/2.12 % NegExts : 0
% 12.47/2.12 % Equation resolutions : 7
% 12.47/2.12 % Disequality decompositions : 0
% 12.47/2.12 % Total rewrite steps : 6819
% 12.47/2.12 % ...of those cached : 6738
% 12.47/2.12 % Propositional unsat checks : 0
% 12.47/2.12 % Propositional check models : 0
% 12.47/2.12 % Propositional check unsatisfiable : 0
% 12.47/2.12 % Propositional clauses : 0
% 12.47/2.12 % Propositional clauses after purity: 0
% 12.47/2.12 % Propositional unsat core size : 0
% 12.47/2.12 % Propositional preprocessing time : 0.000
% 12.47/2.12 % Propositional encoding time : 0.000
% 12.47/2.12 % Propositional solver time : 0.000
% 12.47/2.12 % Success case prop preproc time : 0.000
% 12.47/2.12 % Success case prop encoding time : 0.000
% 12.47/2.12 % Success case prop solver time : 0.000
% 12.47/2.12 % Current number of processed clauses : 1016
% 12.47/2.12 % Positive orientable unit clauses : 198
% 12.47/2.12 % Positive unorientable unit clauses: 0
% 12.47/2.12 % Negative unit clauses : 1
% 12.47/2.12 % Non-unit-clauses : 817
% 12.47/2.12 % Current number of unprocessed clauses: 93953
% 12.47/2.12 % ...number of literals in the above : 294067
% 12.47/2.12 % Current number of archived formulas : 0
% 12.47/2.12 % Current number of archived clauses : 27
% 12.47/2.12 % Clause-clause subsumption calls (NU) : 124902
% 12.47/2.12 % Rec. Clause-clause subsumption calls : 112807
% 12.47/2.12 % Non-unit clause-clause subsumptions : 2295
% 12.47/2.12 % Unit Clause-clause subsumption calls : 246
% 12.47/2.12 % Rewrite failures with RHS unbound : 0
% 12.47/2.12 % BW rewrite match attempts : 4968
% 12.47/2.12 % BW rewrite match successes : 3
% 12.47/2.12 % Condensation attempts : 0
% 12.47/2.12 % Condensation successes : 0
% 12.47/2.12 % Termbank termtop insertions : 2113530
% 12.47/2.12 % Search garbage collected termcells : 4514
% 12.47/2.12
% 12.47/2.12 % -------------------------------------------------
% 12.47/2.12 % User time : 1.730 s
% 12.47/2.12 % System time : 0.060 s
% 12.47/2.12 % Total time : 1.790 s
% 12.47/2.12 % Maximum resident set size: 4692 pages
% 12.47/2.12
% 12.47/2.12 % -------------------------------------------------
% 12.47/2.12 % User time : 1.821 s
% 12.47/2.12 % System time : 0.112 s
% 12.47/2.12 % Total time : 1.933 s
% 12.47/2.12 % Maximum resident set size: 5120 pages
% 12.47/2.12 % E exiting
%------------------------------------------------------------------------------