%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU639^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:46 EDT 2024
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 173
% Syntax : Number of formulae : 225 ( 15 unt; 168 typ; 0 def)
% Number of atoms : 713 ( 67 equ; 0 cnn)
% Maximal formula atoms : 192 ( 12 avg)
% Number of connectives : 1442 ( 73 ~; 108 |; 185 &; 724 @)
% ( 4 <=>; 348 =>; 0 <=; 0 <~>)
% Maximal formula depth : 182 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 170 ( 168 usr; 159 con; 0-2 aty)
% Number of variables : 121 ( 22 ^ 82 !; 17 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_203,type,
esk2_2: $i > ( $i > $o ) > $i ).
thf(decl_204,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_205,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_206,type,
esk5_0: $i ).
thf(decl_207,type,
epred1_0: $i > $o ).
thf(decl_208,type,
esk6_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(c_0_5,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X35: $i] :
( ( in @ X35
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X35 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_6,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_7,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_8,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X35: $i] :
( ( in @ X35
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X35 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,plain,
( singletonprop
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X34: $i] :
( ( in @ X34
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X34 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_6]) ).
thf(c_0_11,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X36: $i] :
( ( in @ X36
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X36 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X37: $i,X38: $i > $o] :
( ! [X39: $i] :
( ( in @ X39 @ X37 )
=> ! [X40: $i] :
( ( in @ X40 @ X37 )
=> ( ( X38 @ X39 )
=> ( ( X38 @ X40 )
=> ( X39 = X40 ) ) ) ) )
=> ( ? [X41: $i] :
( ( in @ X41 @ X37 )
& ( X38 @ X41 ) )
=> ? [X42: $i] :
( ( in @ X42 @ ( dsetconstr @ X37 @ X38 ) )
& ( ( dsetconstr @ X37 @ X38 )
= ( setadjoin @ X42 @ emptyset ) ) ) ) )
=> ( ! [X43: $i,X44: $i > $o] :
( ? [X45: $i] :
( ( in @ X45 @ ( dsetconstr @ X43 @ X44 ) )
& ( ( dsetconstr @ X43 @ X44 )
= ( setadjoin @ X45 @ emptyset ) ) )
=> ? [X46: $i] :
( ( in @ X46 @ X43 )
& ( X44 @ X46 ) ) )
=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X47: $i] :
( ( in @ X47 @ ( dsetconstr @ X4 @ X1 ) )
& ( ( dsetconstr @ X4 @ X1 )
= ( setadjoin @ X47 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[ex1I])]),c_0_9]),c_0_10]),c_0_11])]) ).
thf(c_0_13,negated_conjecture,
! [X48: $i,X49: $i > $o,X52: $i,X54: $i,X55: $i > $o,X56: $i,X61: $i,X62: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& descrp
& dsetconstrI
& dsetconstrEL
& dsetconstrER
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& setbeta
& nonemptyE1
& nonemptyI
& nonemptyI1
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& nonemptyImpWitness
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& emptyE1
& vacuousDall
& quantDeMorgan1
& quantDeMorgan2
& quantDeMorgan3
& quantDeMorgan4
& prop2setI
& prop2set2propI
& notdexE
& notdallE
& exuI1
& exuI3
& exuI2
& inCongP
& in__Cong
& exuE3u
& exu__Cong
& emptyset__Cong
& setadjoin__Cong
& powerset__Cong
& setunion__Cong
& omega__Cong
& exuEu
& descr__Cong
& dsetconstr__Cong
& subsetI1
& eqimpsubset2
& eqimpsubset1
& subsetI2
& emptysetsubset
& subsetE
& subsetE2
& notsubsetI
& notequalI1
& notequalI2
& subsetRefl
& subsetTrans
& setadjoinSub
& setadjoinSub2
& subset2powerset
& setextsub
& subsetemptysetimpeq
& powersetI1
& powersetE1
& inPowerset
& powersetsubset
& sepInPowerset
& sepSubset
& binunionIL
& upairset2IR
& binunionIR
& binunionEcases
& binunionE
& binunionLsub
& binunionRsub
& binintersectI
& binintersectSubset5
& binintersectEL
& binintersectLsub
& binintersectSubset2
& binintersectSubset3
& binintersectER
& disjointsetsI1
& binintersectRsub
& binintersectSubset4
& binintersectSubset1
& bs114d
& setminusI
& setminusEL
& setminusER
& setminusSubset2
& setminusERneg
& setminusELneg
& setminusILneg
& setminusIRneg
& setminusLsub
& setminusSubset1
& symdiffE
& symdiffI1
& symdiffI2
& symdiffIneg1
& symdiffIneg2
& secondinupair
& setukpairIL
& setukpairIR
& kpairiskpair
& kpairp
& singletonsubset
& singletoninpowerset
& singletoninpowunion
& upairset2E
& upairsubunion
& upairinpowunion
& ubforcartprodlem1
& ubforcartprodlem2
& ubforcartprodlem3
& cartprodpairin
& cartprodmempair1
& cartprodmempair
& setunionE2
& setunionsingleton1
& setunionsingleton2
& setunionsingleton
& ( ( in @ ( esk3_2 @ X48 @ X49 ) @ ( dsetconstr @ X48 @ X49 ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( in @ ( esk1_2 @ X48 @ X49 ) @ X48 ) )
& ( ( ( dsetconstr @ X48 @ X49 )
= ( setadjoin @ ( esk3_2 @ X48 @ X49 ) @ emptyset ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( in @ ( esk1_2 @ X48 @ X49 ) @ X48 ) )
& ( ( in @ ( esk3_2 @ X48 @ X49 ) @ ( dsetconstr @ X48 @ X49 ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( in @ ( esk2_2 @ X48 @ X49 ) @ X48 ) )
& ( ( ( dsetconstr @ X48 @ X49 )
= ( setadjoin @ ( esk3_2 @ X48 @ X49 ) @ emptyset ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( in @ ( esk2_2 @ X48 @ X49 ) @ X48 ) )
& ( ( in @ ( esk3_2 @ X48 @ X49 ) @ ( dsetconstr @ X48 @ X49 ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( X49 @ ( esk1_2 @ X48 @ X49 ) ) )
& ( ( ( dsetconstr @ X48 @ X49 )
= ( setadjoin @ ( esk3_2 @ X48 @ X49 ) @ emptyset ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( X49 @ ( esk1_2 @ X48 @ X49 ) ) )
& ( ( in @ ( esk3_2 @ X48 @ X49 ) @ ( dsetconstr @ X48 @ X49 ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( X49 @ ( esk2_2 @ X48 @ X49 ) ) )
& ( ( ( dsetconstr @ X48 @ X49 )
= ( setadjoin @ ( esk3_2 @ X48 @ X49 ) @ emptyset ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( X49 @ ( esk2_2 @ X48 @ X49 ) ) )
& ( ( in @ ( esk3_2 @ X48 @ X49 ) @ ( dsetconstr @ X48 @ X49 ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( ( esk1_2 @ X48 @ X49 )
!= ( esk2_2 @ X48 @ X49 ) ) )
& ( ( ( dsetconstr @ X48 @ X49 )
= ( setadjoin @ ( esk3_2 @ X48 @ X49 ) @ emptyset ) )
| ~ ( in @ X52 @ X48 )
| ~ ( X49 @ X52 )
| ( ( esk1_2 @ X48 @ X49 )
!= ( esk2_2 @ X48 @ X49 ) ) )
& ( ( in @ ( esk4_2 @ X54 @ X55 ) @ X54 )
| ~ ( in @ X56 @ ( dsetconstr @ X54 @ X55 ) )
| ( ( dsetconstr @ X54 @ X55 )
!= ( setadjoin @ X56 @ emptyset ) ) )
& ( ( X55 @ ( esk4_2 @ X54 @ X55 ) )
| ~ ( in @ X56 @ ( dsetconstr @ X54 @ X55 ) )
| ( ( dsetconstr @ X54 @ X55 )
!= ( setadjoin @ X56 @ emptyset ) ) )
& ( in @ esk6_0 @ esk5_0 )
& ( epred1_0 @ esk6_0 )
& ( ~ ( in @ X61 @ esk5_0 )
| ~ ( epred1_0 @ X61 )
| ( X61 = esk6_0 ) )
& ( ~ ( in @ X62 @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( ( dsetconstr @ esk5_0 @ epred1_0 )
!= ( setadjoin @ X62 @ emptyset ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk3_2 @ X2 @ X1 ) @ emptyset ) )
| ( in @ ( esk1_2 @ X2 @ X1 ) @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
in @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk3_2 @ X2 @ X1 ) @ emptyset ) )
| ( in @ ( esk2_2 @ X2 @ X1 ) @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk3_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( in @ ( esk1_2 @ X2 @ X1 ) @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk3_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk3_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( in @ ( esk2_2 @ X2 @ X1 ) @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ ( esk3_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ( X1 @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ X1 ) )
| ( in @ ( esk1_2 @ esk5_0 @ X1 ) @ esk5_0 )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_22,negated_conjecture,
epred1_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk3_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk1_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ X1 ) )
| ( in @ ( esk2_2 @ esk5_0 @ X1 ) @ esk5_0 )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk3_2 @ X2 @ X1 ) @ emptyset ) )
| ( X1 @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk3_2 @ esk5_0 @ X1 ) @ ( dsetconstr @ esk5_0 @ X1 ) )
| ( in @ ( esk1_2 @ esk5_0 @ X1 ) @ esk5_0 )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk3_2 @ esk5_0 @ X1 ) @ ( dsetconstr @ esk5_0 @ X1 ) )
| ( X1 @ ( esk1_2 @ esk5_0 @ X1 ) )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk3_2 @ esk5_0 @ X1 ) @ ( dsetconstr @ esk5_0 @ X1 ) )
| ( in @ ( esk2_2 @ esk5_0 @ X1 ) @ esk5_0 )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk3_2 @ esk5_0 @ X1 ) @ ( dsetconstr @ esk5_0 @ X1 ) )
| ( X1 @ ( esk2_2 @ esk5_0 @ X1 ) )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( in @ ( esk3_2 @ X2 @ X1 ) @ ( dsetconstr @ X2 @ X1 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk1_2 @ X2 @ X1 )
!= ( esk2_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i] :
( ( X2 = esk6_0 )
| ~ ( in @ X2 @ esk5_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_32,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( in @ ( esk1_2 @ esk5_0 @ epred1_0 ) @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ X1 ) )
| ( X1 @ ( esk1_2 @ esk5_0 @ X1 ) )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
thf(c_0_34,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( in @ ( esk2_2 @ esk5_0 @ epred1_0 ) @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ X1 ) )
| ( X1 @ ( esk2_2 @ esk5_0 @ X1 ) )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
thf(c_0_36,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( ( dsetconstr @ X2 @ X1 )
= ( setadjoin @ ( esk3_2 @ X2 @ X1 ) @ emptyset ) )
| ~ ( in @ X3 @ X2 )
| ~ ( X1 @ X3 )
| ( ( esk1_2 @ X2 @ X1 )
!= ( esk2_2 @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_37,negated_conjecture,
( ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( in @ ( esk1_2 @ esk5_0 @ epred1_0 ) @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
thf(c_0_38,negated_conjecture,
( ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk1_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
thf(c_0_39,negated_conjecture,
( ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( in @ ( esk2_2 @ esk5_0 @ epred1_0 ) @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
thf(c_0_40,negated_conjecture,
( ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk2_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i > $o] :
( ( in @ ( esk3_2 @ esk5_0 @ X1 ) @ ( dsetconstr @ esk5_0 @ X1 ) )
| ( ( esk2_2 @ esk5_0 @ X1 )
!= ( esk1_2 @ esk5_0 @ X1 ) )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_15]) ).
thf(c_0_42,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( esk6_0
= ( esk1_2 @ esk5_0 @ epred1_0 ) )
| ~ ( epred1_0 @ ( esk1_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_43,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk1_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
thf(c_0_44,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( esk6_0
= ( esk2_2 @ esk5_0 @ epred1_0 ) )
| ~ ( epred1_0 @ ( esk2_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
thf(c_0_45,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk2_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i > $o] :
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ X1 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ X1 ) )
| ( ( esk2_2 @ esk5_0 @ X1 )
!= ( esk1_2 @ esk5_0 @ X1 ) )
| ~ ( X1 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_15]) ).
thf(c_0_47,negated_conjecture,
( ( esk6_0
= ( esk1_2 @ esk5_0 @ epred1_0 ) )
| ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_37]),c_0_38]) ).
thf(c_0_48,negated_conjecture,
( ( esk6_0
= ( esk2_2 @ esk5_0 @ epred1_0 ) )
| ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_40]) ).
thf(c_0_49,negated_conjecture,
( ( in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( ( esk2_2 @ esk5_0 @ epred1_0 )
!= ( esk1_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
thf(c_0_50,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( esk6_0
= ( esk1_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_51,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( esk6_0
= ( esk2_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_52,negated_conjecture,
( ( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( ( esk2_2 @ esk5_0 @ epred1_0 )
!= ( esk1_2 @ esk5_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_46,c_0_22]) ).
thf(c_0_53,negated_conjecture,
! [X2: $i] :
( ~ ( in @ X2 @ ( dsetconstr @ esk5_0 @ epred1_0 ) )
| ( ( dsetconstr @ esk5_0 @ epred1_0 )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_54,negated_conjecture,
in @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ ( dsetconstr @ esk5_0 @ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
thf(c_0_55,negated_conjecture,
( ( setadjoin @ ( esk3_2 @ esk5_0 @ epred1_0 ) @ emptyset )
= ( dsetconstr @ esk5_0 @ epred1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
thf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU639^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 15:59:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.46 Running higher-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 # Version: 3.1.0-ho
% 0.18/0.51 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.18/0.51 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.51 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.18/0.51 # Starting pre_casc_3 with 300s (1) cores
% 0.18/0.51 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.18/0.51 # Starting full_lambda_10 with 300s (1) cores
% 0.18/0.51 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.18/0.51 # full_lambda_10 with pid 23013 completed with status 0
% 0.18/0.51 # Result found by full_lambda_10
% 0.18/0.51 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.18/0.51 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.51 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.18/0.51 # Starting pre_casc_3 with 300s (1) cores
% 0.18/0.51 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.18/0.51 # Starting full_lambda_10 with 300s (1) cores
% 0.18/0.51 # SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.18/0.51 # Search class: HGHSF-FFMM22-SHSMMFBN
% 0.18/0.51 # partial match(3): HGHSF-FFMM21-SHSFFFBN
% 0.18/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.51 # Starting ho_unfolding_3 with 163s (1) cores
% 0.18/0.51 # ho_unfolding_3 with pid 23015 completed with status 0
% 0.18/0.51 # Result found by ho_unfolding_3
% 0.18/0.51 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.18/0.51 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.51 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.18/0.51 # Starting pre_casc_3 with 300s (1) cores
% 0.18/0.51 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.18/0.51 # Starting full_lambda_10 with 300s (1) cores
% 0.18/0.51 # SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.18/0.51 # Search class: HGHSF-FFMM22-SHSMMFBN
% 0.18/0.51 # partial match(3): HGHSF-FFMM21-SHSFFFBN
% 0.18/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.51 # Starting ho_unfolding_3 with 163s (1) cores
% 0.18/0.51 # Preprocessing time : 0.002 s
% 0.18/0.51 # Presaturation interreduction done
% 0.18/0.51
% 0.18/0.51 # Proof found!
% 0.18/0.51 # SZS status Theorem
% 0.18/0.51 # SZS output start CNFRefutation
% See solution above
% 0.18/0.51 # Parsed axioms : 342
% 0.18/0.51 # Removed by relevancy pruning/SinE : 337
% 0.18/0.51 # Initial clauses : 169
% 0.18/0.51 # Removed in clause preprocessing : 0
% 0.18/0.51 # Initial clauses in saturation : 169
% 0.18/0.51 # Processed clauses : 378
% 0.18/0.51 # ...of these trivial : 0
% 0.18/0.51 # ...subsumed : 5
% 0.18/0.51 # ...remaining for further processing : 373
% 0.18/0.51 # Other redundant clauses eliminated : 5
% 0.18/0.51 # Clauses deleted for lack of memory : 0
% 0.18/0.51 # Backward-subsumed : 2
% 0.18/0.51 # Backward-rewritten : 15
% 0.18/0.51 # Generated clauses : 159
% 0.18/0.51 # ...of the previous two non-redundant : 153
% 0.18/0.51 # ...aggressively subsumed : 0
% 0.18/0.51 # Contextual simplify-reflections : 4
% 0.18/0.51 # Paramodulations : 135
% 0.18/0.51 # Factorizations : 0
% 0.18/0.51 # NegExts : 3
% 0.18/0.51 # Equation resolutions : 6
% 0.18/0.51 # Disequality decompositions : 0
% 0.18/0.51 # Total rewrite steps : 18
% 0.18/0.51 # ...of those cached : 16
% 0.18/0.51 # Propositional unsat checks : 0
% 0.18/0.51 # Propositional check models : 0
% 0.18/0.51 # Propositional check unsatisfiable : 0
% 0.18/0.51 # Propositional clauses : 0
% 0.18/0.51 # Propositional clauses after purity: 0
% 0.18/0.51 # Propositional unsat core size : 0
% 0.18/0.51 # Propositional preprocessing time : 0.000
% 0.18/0.51 # Propositional encoding time : 0.000
% 0.18/0.51 # Propositional solver time : 0.000
% 0.18/0.51 # Success case prop preproc time : 0.000
% 0.18/0.51 # Success case prop encoding time : 0.000
% 0.18/0.51 # Success case prop solver time : 0.000
% 0.18/0.51 # Current number of processed clauses : 186
% 0.18/0.51 # Positive orientable unit clauses : 157
% 0.18/0.51 # Positive unorientable unit clauses: 0
% 0.18/0.51 # Negative unit clauses : 0
% 0.18/0.51 # Non-unit-clauses : 29
% 0.18/0.51 # Current number of unprocessed clauses: 96
% 0.18/0.51 # ...number of literals in the above : 373
% 0.18/0.51 # Current number of archived formulas : 0
% 0.18/0.51 # Current number of archived clauses : 187
% 0.18/0.51 # Clause-clause subsumption calls (NU) : 92
% 0.18/0.51 # Rec. Clause-clause subsumption calls : 37
% 0.18/0.51 # Non-unit clause-clause subsumptions : 11
% 0.18/0.51 # Unit Clause-clause subsumption calls : 0
% 0.18/0.51 # Rewrite failures with RHS unbound : 0
% 0.18/0.51 # BW rewrite match attempts : 2
% 0.18/0.51 # BW rewrite match successes : 2
% 0.18/0.51 # Condensation attempts : 378
% 0.18/0.51 # Condensation successes : 0
% 0.18/0.51 # Termbank termtop insertions : 15030
% 0.18/0.51 # Search garbage collected termcells : 4317
% 0.18/0.51
% 0.18/0.51 # -------------------------------------------------
% 0.18/0.51 # User time : 0.025 s
% 0.18/0.51 # System time : 0.008 s
% 0.18/0.51 # Total time : 0.033 s
% 0.18/0.51 # Maximum resident set size: 3076 pages
% 0.18/0.51
% 0.18/0.51 # -------------------------------------------------
% 0.18/0.51 # User time : 0.034 s
% 0.18/0.51 # System time : 0.011 s
% 0.18/0.51 # Total time : 0.045 s
% 0.18/0.51 # Maximum resident set size: 2076 pages
% 0.18/0.51 % E---3.1 exiting
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------