%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU608^1 : 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 : n017.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 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 44 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 689 ( 52 equ; 0 cnn)
% Maximal formula atoms : 161 ( 15 avg)
% Number of connectives : 1241 ( 68 ~; 40 |; 137 &; 512 @)
% ( 36 <=>; 448 =>; 0 <=; 0 <~>)
% Maximal formula depth : 183 ( 20 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 141 ( 138 usr; 130 con; 0-4 aty)
% Number of variables : 238 ( 27 ^; 199 !; 12 ?; 238 :)
% 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_30,type,
powerset: $i > $i ).
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,
setminusILneg: $o ).
thf(decl_166,type,
esk1_1: $i > $i ).
thf(decl_167,type,
esk2_1: $i > $i ).
thf(decl_168,type,
esk3_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_169,type,
esk4_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_170,type,
esk5_0: $i ).
thf(decl_171,type,
esk6_0: $i ).
thf(decl_172,type,
esk7_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.p',nonemptyI) ).
thf(setminusIRneg,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
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.p',setminusIRneg) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.p',emptyE1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.p',dsetconstrI) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.p',nonemptyImpWitness) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.p',nonemptyE1) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.p',setminusILneg) ).
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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.p',setminusERneg) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.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.1gLZI3f2Mb/E---3.1_375054.p',setminusI) ).
thf(c_0_22,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_23,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_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
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setminusIRneg]) ).
thf(c_0_25,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_26,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_27,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_28,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_29,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_30,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_31,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_32,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_33,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_34,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_22]) ).
thf(c_0_35,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_22]) ).
thf(c_0_36,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_23,c_0_22]) ).
thf(c_0_37,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_22]) ).
thf(c_0_38,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( ! [X78: $i,X79: $i > $o,X80: $i] :
( ( in @ X80 @ X78 )
=> ( ( X79 @ X80 )
=> ( in @ X80 @ ( dsetconstr @ X78 @ X79 ) ) ) )
=> ( ! [X81: $i,X82: $i > $o,X83: $i] :
( ( in @ X83 @ ( dsetconstr @ X81 @ X82 ) )
=> ( in @ X83 @ X81 ) )
=> ( ! [X84: $i,X85: $i > $o,X86: $i] :
( ( in @ X86 @ ( dsetconstr @ X84 @ X85 ) )
=> ( X85 @ X86 ) )
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( ! [X87: $i,X88: $i > $o,X89: $i] :
( ( in @ X89 @ X87 )
=> ( ( in @ X89 @ ( dsetconstr @ X87 @ X88 ) )
<=> ( X88 @ X89 ) ) )
=> ( ! [X90: $i] :
( ( X90 != emptyset )
=> ? [X91: $i] : ( in @ X91 @ X90 ) )
=> ( ! [X92: $i,X93: $i > $o,X94: $i] :
( ( in @ X94 @ X92 )
=> ( ( X93 @ X94 )
=> ( ( dsetconstr @ X92 @ X93 )
!= emptyset ) ) )
=> ( ! [X95: $i] :
( ? [X96: $i] : ( in @ X96 @ X95 )
=> ( X95 != emptyset ) )
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( ! [X97: $i] :
( ( dsetconstr @ X97
@ ^ [Z0: $i] : $true )
= X97 )
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( ! [X98: $i] :
( ( X98 != emptyset )
=> ? [X99: $i] :
( ( in @ X99 @ X98 )
& $true ) )
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( ! [X100: $i,X101: $i > $o] :
( ? [X102: $i] :
( ( in @ X102 @ X100 )
& ( X101 @ X102 ) )
=> ( ( ( dsetconstr @ X100 @ X101 )
= 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
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( ! [X103: $i,X104: $i] :
( ( X103 = X104 )
=> ! [X105: $i > $o,X106: $i > $o] :
( ! [X107: $i] :
( ( in @ X107 @ X103 )
=> ! [X108: $i] :
( ( in @ X108 @ X104 )
=> ( ( X107 = X108 )
=> ( ( X105 @ X107 )
<=> ( X106 @ X108 ) ) ) ) )
=> ( ( dsetconstr @ X103 @ X105 )
= ( dsetconstr @ X104 @ X106 ) ) ) )
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( ! [X109: $i,X110: $i > $o] : ( in @ ( dsetconstr @ X109 @ X110 ) @ ( powerset @ X109 ) )
=> ( ! [X111: $i,X112: $i > $o] : ( subset @ ( dsetconstr @ X111 @ X112 ) @ X111 )
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( ! [X113: $i,X114: $i,X115: $i] :
( ( in @ X115 @ X113 )
=> ( ~ ( in @ X115 @ X114 )
=> ( in @ X115 @ ( setminus @ X113 @ X114 ) ) ) )
=> ( ! [X116: $i,X117: $i,X118: $i] :
( ( in @ X118 @ ( setminus @ X116 @ X117 ) )
=> ( in @ X118 @ X116 ) )
=> ( ! [X119: $i,X120: $i,X121: $i] :
( ( in @ X121 @ ( setminus @ X119 @ X120 ) )
=> ~ ( in @ X121 @ X120 ) )
=> ( ! [X122: $i,X123: $i] :
( ( subset @ X122 @ X123 )
=> ( ( setminus @ X122 @ X123 )
= emptyset ) )
=> ( ! [X124: $i,X125: $i,X126: $i] :
( ~ ( in @ X126 @ ( setminus @ X124 @ X125 ) )
=> ( ( in @ X126 @ X124 )
=> ( in @ X126 @ X125 ) ) )
=> ( ! [X127: $i,X128: $i,X129: $i] :
( ~ ( in @ X129 @ ( setminus @ X127 @ X128 ) )
=> ( ~ ( in @ X129 @ X128 )
=> ~ ( in @ X129 @ X127 ) ) )
=> ( ! [X130: $i,X131: $i,X132: $i] :
( ~ ( in @ X132 @ X130 )
=> ~ ( in @ X132 @ ( setminus @ X130 @ X131 ) ) )
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( 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)],[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_24,c_0_25]),c_0_26]),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]),setminusILneg]),setminusELneg]),setminusERneg]),setminusSubset2]),setminusER]),setminusEL]),setminusI])])]) ).
thf(c_0_39,negated_conjecture,
! [X133: $i,X134: $i > $o,X135: $i,X136: $i,X137: $i > $o,X138: $i,X139: $i,X140: $i > $o,X141: $i,X142: $i,X143: $i > $o,X144: $i,X145: $i,X147: $i,X148: $i > $o,X149: $i,X150: $i,X151: $i,X152: $i,X153: $i,X155: $i,X156: $i > $o,X157: $i,X158: $i,X159: $i,X160: $i > $o,X161: $i > $o,X164: $i,X165: $i > $o,X166: $i,X167: $i > $o,X168: $i,X169: $i,X170: $i,X171: $i,X172: $i,X173: $i,X174: $i,X175: $i,X176: $i,X177: $i,X178: $i,X179: $i,X180: $i,X181: $i,X182: $i,X183: $i,X184: $i,X185: $i,X186: $i,X187: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& descrp
& ( ~ ( in @ X135 @ X133 )
| ~ ( X134 @ X135 )
| ( in @ X135 @ ( dsetconstr @ X133 @ X134 ) ) )
& ( ~ ( in @ X138 @ ( dsetconstr @ X136 @ X137 ) )
| ( in @ X138 @ X136 ) )
& ( ~ ( in @ X141 @ ( dsetconstr @ X139 @ X140 ) )
| ( X140 @ X141 ) )
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& ( ~ ( in @ X144 @ ( dsetconstr @ X142 @ X143 ) )
| ( X143 @ X144 )
| ~ ( in @ X144 @ X142 ) )
& ( ~ ( X143 @ X144 )
| ( in @ X144 @ ( dsetconstr @ X142 @ X143 ) )
| ~ ( in @ X144 @ X142 ) )
& ( ( X145 = emptyset )
| ( in @ ( esk1_1 @ X145 ) @ X145 ) )
& ( ~ ( in @ X149 @ X147 )
| ~ ( X148 @ X149 )
| ( ( dsetconstr @ X147 @ X148 )
!= emptyset ) )
& ( ~ ( in @ X151 @ X150 )
| ( X150 != emptyset ) )
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& ( ( dsetconstr @ X152
@ ^ [Z0: $i] : $true )
= X152 )
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& ( ( in @ ( esk2_1 @ X153 ) @ X153 )
| ( X153 = emptyset ) )
& ( $true
| ( X153 = emptyset ) )
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& ( ~ ( in @ X157 @ X155 )
| ~ ( X156 @ X157 )
| ( ( dsetconstr @ X155 @ X156 )
!= 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
& setunion__Cong
& omega__Cong
& exuEu
& descr__Cong
& ( ( in @ ( esk3_4 @ X158 @ X159 @ X160 @ X161 ) @ X158 )
| ( ( dsetconstr @ X158 @ X160 )
= ( dsetconstr @ X159 @ X161 ) )
| ( X158 != X159 ) )
& ( ( in @ ( esk4_4 @ X158 @ X159 @ X160 @ X161 ) @ X159 )
| ( ( dsetconstr @ X158 @ X160 )
= ( dsetconstr @ X159 @ X161 ) )
| ( X158 != X159 ) )
& ( ( ( esk3_4 @ X158 @ X159 @ X160 @ X161 )
= ( esk4_4 @ X158 @ X159 @ X160 @ X161 ) )
| ( ( dsetconstr @ X158 @ X160 )
= ( dsetconstr @ X159 @ X161 ) )
| ( X158 != X159 ) )
& ( ~ ( X160 @ ( esk3_4 @ X158 @ X159 @ X160 @ X161 ) )
| ~ ( X161 @ ( esk4_4 @ X158 @ X159 @ X160 @ X161 ) )
| ( ( dsetconstr @ X158 @ X160 )
= ( dsetconstr @ X159 @ X161 ) )
| ( X158 != X159 ) )
& ( ( X160 @ ( esk3_4 @ X158 @ X159 @ X160 @ X161 ) )
| ( X161 @ ( esk4_4 @ X158 @ X159 @ X160 @ X161 ) )
| ( ( dsetconstr @ X158 @ X160 )
= ( dsetconstr @ X159 @ X161 ) )
| ( X158 != X159 ) )
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& ( in @ ( dsetconstr @ X164 @ X165 ) @ ( powerset @ X164 ) )
& ( subset @ ( dsetconstr @ X166 @ X167 ) @ X166 )
& binunionIL
& upairset2IR
& binunionIR
& binunionEcases
& binunionE
& binunionLsub
& binunionRsub
& binintersectI
& binintersectSubset5
& binintersectEL
& binintersectLsub
& binintersectSubset2
& binintersectSubset3
& binintersectER
& disjointsetsI1
& binintersectRsub
& binintersectSubset4
& binintersectSubset1
& bs114d
& ( ~ ( in @ X170 @ X168 )
| ( in @ X170 @ X169 )
| ( in @ X170 @ ( setminus @ X168 @ X169 ) ) )
& ( ~ ( in @ X173 @ ( setminus @ X171 @ X172 ) )
| ( in @ X173 @ X171 ) )
& ( ~ ( in @ X176 @ ( setminus @ X174 @ X175 ) )
| ~ ( in @ X176 @ X175 ) )
& ( ~ ( subset @ X177 @ X178 )
| ( ( setminus @ X177 @ X178 )
= emptyset ) )
& ( ( in @ X181 @ ( setminus @ X179 @ X180 ) )
| ~ ( in @ X181 @ X179 )
| ( in @ X181 @ X180 ) )
& ( ( in @ X184 @ ( setminus @ X182 @ X183 ) )
| ( in @ X184 @ X183 )
| ~ ( in @ X184 @ X182 ) )
& ( ( in @ X187 @ X185 )
| ~ ( in @ X187 @ ( setminus @ X185 @ X186 ) ) )
& ( in @ esk7_0 @ esk6_0 )
& ( in @ esk7_0 @ ( setminus @ esk5_0 @ esk6_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_38])])])])])])]) ).
thf(c_0_40,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ~ ( in @ X2 @ ( setminus @ X3 @ X4 ) )
| ~ ( in @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_41,negated_conjecture,
in @ esk7_0 @ ( setminus @ esk5_0 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_42,negated_conjecture,
in @ esk7_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU608^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.15 % Computer : n017.cluster.edu
% 0.11/0.15 % Model : x86_64 x86_64
% 0.11/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.15 % Memory : 8046.5625MB
% 0.11/0.15 % OS : Linux 6.8.0-71-generic
% 0.11/0.15 % CPULimit : 300
% 0.11/0.15 % WCLimit : 300
% 0.11/0.15 % DateTime : Tue Sep 29 13:52:52 UTC 2026
% 0.11/0.15 % CPUTime :
% 0.11/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 Running higher-order theorem proving
% 0.11/0.21 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.1gLZI3f2Mb/E---3.1_375054.p
% 0.11/0.25 % Version: 3.5.1-ho
% 0.11/0.25 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.11/0.25 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting ehoh_best5 with 300s (1) cores
% 0.11/0.25 % Starting almost_fo_3_lam with 300s (1) cores
% 0.11/0.25 % Starting new_bool_5 with 300s (1) cores
% 0.11/0.25 % Starting pre_casc_3 with 300s (1) cores
% 0.11/0.25 % Starting ho_unfolding_8 with 300s (1) cores
% 0.11/0.25 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.11/0.25 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.25 % Starting new_ho_5 with 300s (1) cores
% 0.11/0.25 % pre_casc_3 with pid 375070 completed with status 0
% 0.11/0.25 % Result found by pre_casc_3
% 0.11/0.25 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.11/0.25 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting ehoh_best5 with 300s (1) cores
% 0.11/0.25 % Starting almost_fo_3_lam with 300s (1) cores
% 0.11/0.25 % Starting new_bool_5 with 300s (1) cores
% 0.11/0.25 % Starting pre_casc_3 with 300s (1) cores
% 0.11/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.11/0.25 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.11/0.25 % Search class: HGHSM-FFMM32-SHFMMFBN
% 0.11/0.25 % partial match(2): HGHSM-FFMM31-SHFMMSBN
% 0.11/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.25 % SubtermCWHack with pid 375076 completed with status 0
% 0.11/0.25 % Result found by SubtermCWHack
% 0.11/0.25 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.11/0.25 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting ehoh_best5 with 300s (1) cores
% 0.11/0.25 % Starting almost_fo_3_lam with 300s (1) cores
% 0.11/0.25 % Starting new_bool_5 with 300s (1) cores
% 0.11/0.25 % Starting pre_casc_3 with 300s (1) cores
% 0.11/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,10,,5,20000,3.0,true))
% 0.11/0.25 % SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 0.11/0.25 % Search class: HGHSM-FFMM32-SHFMMFBN
% 0.11/0.25 % partial match(2): HGHSM-FFMM31-SHFMMSBN
% 0.11/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.25 % Preprocessing time : 0.002 s
% 0.11/0.25
% 0.11/0.25 % Proof found!
% 0.11/0.25 % SZS status Theorem
% 0.11/0.25 % SZS output start CNFRefutation
% See solution above
% 0.11/0.25 % Parsed axioms : 270
% 0.11/0.25 % Removed by relevancy pruning/SinE : 248
% 0.11/0.25 % Initial clauses : 134
% 0.11/0.25 % Removed in clause preprocessing : 2
% 0.11/0.25 % Initial clauses in saturation : 132
% 0.11/0.25 % Processed clauses : 128
% 0.11/0.25 % ...of these trivial : 0
% 0.11/0.25 % ...subsumed : 3
% 0.11/0.25 % ...remaining for further processing : 125
% 0.11/0.25 % Other redundant clauses eliminated : 2
% 0.11/0.25 % Clauses deleted for lack of memory : 0
% 0.11/0.25 % Backward-subsumed : 0
% 0.11/0.25 % Backward-rewritten : 0
% 0.11/0.25 % Generated clauses : 24
% 0.11/0.25 % ...of the previous two non-redundant : 17
% 0.11/0.25 % ...aggressively subsumed : 0
% 0.11/0.25 % Contextual simplify-reflections : 0
% 0.11/0.25 % Paramodulations : 22
% 0.11/0.25 % Factorizations : 0
% 0.11/0.25 % NegExts : 0
% 0.11/0.25 % Equation resolutions : 2
% 0.11/0.25 % Disequality decompositions : 0
% 0.11/0.25 % Total rewrite steps : 4
% 0.11/0.25 % ...of those cached : 0
% 0.11/0.25 % Propositional unsat checks : 0
% 0.11/0.25 % Propositional check models : 0
% 0.11/0.25 % Propositional check unsatisfiable : 0
% 0.11/0.25 % Propositional clauses : 0
% 0.11/0.25 % Propositional clauses after purity: 0
% 0.11/0.25 % Propositional unsat core size : 0
% 0.11/0.25 % Propositional preprocessing time : 0.000
% 0.11/0.25 % Propositional encoding time : 0.000
% 0.11/0.25 % Propositional solver time : 0.000
% 0.11/0.25 % Success case prop preproc time : 0.000
% 0.11/0.25 % Success case prop encoding time : 0.000
% 0.11/0.25 % Success case prop solver time : 0.000
% 0.11/0.25 % Current number of processed clauses : 124
% 0.11/0.25 % Positive orientable unit clauses : 115
% 0.11/0.25 % Positive unorientable unit clauses: 0
% 0.11/0.25 % Negative unit clauses : 1
% 0.11/0.25 % Non-unit-clauses : 8
% 0.11/0.25 % Current number of unprocessed clauses: 19
% 0.11/0.25 % ...number of literals in the above : 52
% 0.11/0.25 % Current number of archived formulas : 0
% 0.11/0.25 % Current number of archived clauses : 0
% 0.11/0.25 % Clause-clause subsumption calls (NU) : 6
% 0.11/0.25 % Rec. Clause-clause subsumption calls : 6
% 0.11/0.25 % Non-unit clause-clause subsumptions : 1
% 0.11/0.25 % Unit Clause-clause subsumption calls : 4
% 0.11/0.25 % Rewrite failures with RHS unbound : 0
% 0.11/0.25 % BW rewrite match attempts : 4
% 0.11/0.25 % BW rewrite match successes : 0
% 0.11/0.25 % Condensation attempts : 0
% 0.11/0.25 % Condensation successes : 0
% 0.11/0.25 % Termbank termtop insertions : 10522
% 0.11/0.25 % Search garbage collected termcells : 4346
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.014 s
% 0.11/0.25 % System time : 0.004 s
% 0.11/0.25 % Total time : 0.018 s
% 0.11/0.25 % Maximum resident set size: 4924 pages
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.022 s
% 0.11/0.25 % System time : 0.008 s
% 0.11/0.25 % Total time : 0.030 s
% 0.11/0.25 % Maximum resident set size: 5120 pages
% 0.11/0.25 % E exiting
%------------------------------------------------------------------------------