%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU607^1 : 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 : n012.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 08:24:42 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 594 ( 24 equ; 0 cnn)
% Maximal formula atoms : 140 ( 23 avg)
% Number of connectives : 822 ( 45 ~; 16 |; 128 &; 215 @)
% ( 11 <=>; 407 =>; 0 <=; 0 <~>)
% Maximal formula depth : 150 ( 27 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 137 ( 134 usr; 129 con; 0-2 aty)
% Number of variables : 105 ( 5 ^; 91 !; 9 ?; 105 :)
% 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_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_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_158,type,
setminus: $i > $i > $i ).
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,
esk1_1: $i > $i ).
thf(decl_166,type,
esk2_1: $i > $i ).
thf(decl_167,type,
esk3_0: $i ).
thf(decl_168,type,
esk4_0: $i ).
thf(decl_169,type,
esk5_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.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.iMy3aUTfwD/E---3.1_146293.p',nonemptyI) ).
thf(setminusILneg,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
=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusILneg) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',nonemptyImpWitness) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',nonemptyE1) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusELneg) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusERneg) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusSubset2) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusER) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusEL) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iMy3aUTfwD/E---3.1_146293.p',setminusI) ).
thf(c_0_12,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_13,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_14,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
=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setminusILneg]) ).
thf(c_0_15,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_12]) ).
thf(c_0_16,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_12]) ).
thf(c_0_17,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_13,c_0_12]) ).
thf(c_0_18,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_12]) ).
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
=> ( ! [X49: $i] :
( ( X49 != emptyset )
=> ? [X50: $i] : ( in @ X50 @ X49 ) )
=> ( ! [X51: $i,X52: $i > $o,X53: $i] :
( ( in @ X53 @ X51 )
=> ( ( X52 @ X53 )
=> ( ( dsetconstr @ X51 @ X52 )
!= emptyset ) ) )
=> ( ! [X54: $i] :
( ? [X55: $i] : ( in @ X55 @ X54 )
=> ( X54 != emptyset ) )
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( ! [X56: $i] :
( ( X56 != emptyset )
=> ? [X57: $i] :
( ( in @ X57 @ X56 )
& $true ) )
=> ( 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
=> ( ! [X58: $i,X59: $i,X60: $i] :
( ( in @ X60 @ X58 )
=> ( ~ ( in @ X60 @ X59 )
=> ( in @ X60 @ ( setminus @ X58 @ X59 ) ) ) )
=> ( ! [X61: $i,X62: $i,X63: $i] :
( ( in @ X63 @ ( setminus @ X61 @ X62 ) )
=> ( in @ X63 @ X61 ) )
=> ( ! [X64: $i,X65: $i,X66: $i] :
( ( in @ X66 @ ( setminus @ X64 @ X65 ) )
=> ~ ( in @ X66 @ X65 ) )
=> ( ! [X67: $i,X68: $i] :
( ( subset @ X67 @ X68 )
=> ( ( setminus @ X67 @ X68 )
= emptyset ) )
=> ( ! [X69: $i,X70: $i,X71: $i] :
( ~ ( in @ X71 @ ( setminus @ X69 @ X70 ) )
=> ( ( in @ X71 @ X69 )
=> ( in @ X71 @ X70 ) ) )
=> ( ! [X72: $i,X73: $i,X74: $i] :
( ~ ( in @ X74 @ ( setminus @ X72 @ X73 ) )
=> ( ~ ( in @ X74 @ X73 )
=> ~ ( in @ X74 @ X72 ) ) )
=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18]),setminusELneg]),setminusERneg]),setminusSubset2]),setminusER]),setminusEL]),setminusI])])]) ).
thf(c_0_20,negated_conjecture,
! [X75: $i,X77: $i,X78: $i > $o,X79: $i,X80: $i,X81: $i,X82: $i,X84: $i,X85: $i,X86: $i,X87: $i,X88: $i,X89: $i,X90: $i,X91: $i,X92: $i,X93: $i,X94: $i,X95: $i,X96: $i,X97: $i,X98: $i,X99: $i,X100: $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
& ( ( X75 = emptyset )
| ( in @ ( esk1_1 @ X75 ) @ X75 ) )
& ( ~ ( in @ X79 @ X77 )
| ~ ( X78 @ X79 )
| ( ( dsetconstr @ X77 @ X78 )
!= emptyset ) )
& ( ~ ( in @ X81 @ X80 )
| ( X80 != emptyset ) )
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& ( ( in @ ( esk2_1 @ X82 ) @ X82 )
| ( X82 = emptyset ) )
& ( $true
| ( X82 = emptyset ) )
& 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
& ( ~ ( in @ X86 @ X84 )
| ( in @ X86 @ X85 )
| ( in @ X86 @ ( setminus @ X84 @ X85 ) ) )
& ( ~ ( in @ X89 @ ( setminus @ X87 @ X88 ) )
| ( in @ X89 @ X87 ) )
& ( ~ ( in @ X92 @ ( setminus @ X90 @ X91 ) )
| ~ ( in @ X92 @ X91 ) )
& ( ~ ( subset @ X93 @ X94 )
| ( ( setminus @ X93 @ X94 )
= emptyset ) )
& ( ( in @ X97 @ ( setminus @ X95 @ X96 ) )
| ~ ( in @ X97 @ X95 )
| ( in @ X97 @ X96 ) )
& ( ( in @ X100 @ ( setminus @ X98 @ X99 ) )
| ( in @ X100 @ X99 )
| ~ ( in @ X100 @ X98 ) )
& ~ ( in @ esk5_0 @ esk3_0 )
& ( in @ esk5_0 @ ( setminus @ esk3_0 @ esk4_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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ X3 )
| ~ ( in @ X2 @ ( setminus @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_22,negated_conjecture,
in @ esk5_0 @ ( setminus @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
~ ( in @ esk5_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU607^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Sep 29 13:57:03 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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.iMy3aUTfwD/E---3.1_146293.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.15 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.15 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.15 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.15 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.15 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.15 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.15 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.15 % Starting new_ho_5 with 300s (1) cores
% 0.08/0.15 % new_ho_5 with pid 146313 completed with status 0
% 0.08/0.15 % Result found by new_ho_5
% 0.08/0.15 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.15 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.15 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.15 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.15 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.15 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.15 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.15 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.15 % Starting new_ho_5 with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.08/0.15 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.08/0.15 % Search class: HGHSF-FFMM21-SHFMMFBN
% 0.08/0.15 % partial match(2): HGHSF-FFMM21-SHFFFFBN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % SubtermCWHack with pid 146314 completed with status 0
% 0.08/0.15 % Result found by SubtermCWHack
% 0.08/0.15 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.15 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.15 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.15 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.15 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.15 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.15 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.15 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.15 % Starting new_ho_5 with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true))
% 0.08/0.15 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.08/0.15 % Search class: HGHSF-FFMM21-SHFMMFBN
% 0.08/0.15 % partial match(2): HGHSF-FFMM21-SHFFFFBN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 268
% 0.08/0.15 % Removed by relevancy pruning/SinE : 256
% 0.08/0.15 % Initial clauses : 126
% 0.08/0.15 % Removed in clause preprocessing : 1
% 0.08/0.15 % Initial clauses in saturation : 125
% 0.08/0.15 % Processed clauses : 122
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 0
% 0.08/0.15 % ...remaining for further processing : 122
% 0.08/0.15 % Other redundant clauses eliminated : 1
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 0
% 0.08/0.15 % Backward-rewritten : 0
% 0.08/0.15 % Generated clauses : 4
% 0.08/0.15 % ...of the previous two non-redundant : 1
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 0
% 0.08/0.15 % Paramodulations : 3
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 1
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 0
% 0.08/0.15 % ...of those cached : 0
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 121
% 0.08/0.15 % Positive orientable unit clauses : 114
% 0.08/0.15 % Positive unorientable unit clauses: 0
% 0.08/0.15 % Negative unit clauses : 2
% 0.08/0.15 % Non-unit-clauses : 5
% 0.08/0.15 % Current number of unprocessed clauses: 4
% 0.08/0.15 % ...number of literals in the above : 11
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 0
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.15 % Non-unit clause-clause subsumptions : 0
% 0.08/0.15 % Unit Clause-clause subsumption calls : 0
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 0
% 0.08/0.15 % BW rewrite match successes : 0
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 8158
% 0.08/0.15 % Search garbage collected termcells : 3342
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.006 s
% 0.08/0.15 % System time : 0.001 s
% 0.08/0.15 % Total time : 0.008 s
% 0.08/0.15 % Maximum resident set size: 4668 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.010 s
% 0.08/0.15 % System time : 0.004 s
% 0.08/0.15 % Total time : 0.014 s
% 0.08/0.15 % Maximum resident set size: 5120 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------