TSTP Solution File: SEU588^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU588^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 03:28:23 EDT 2024
% Result : Theorem 2.55s 0.87s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 262
% Syntax : Number of formulae : 293 ( 3 unt; 157 typ; 0 def)
% Number of atoms : 1119 ( 176 equ; 0 cnn)
% Maximal formula atoms : 327 ( 8 avg)
% Number of connectives : 3632 ( 274 ~; 271 |; 215 &;2162 @)
% ( 162 <=>; 548 =>; 0 <=; 0 <~>)
% Maximal formula depth : 396 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 240 ( 240 >; 0 *; 0 +; 0 <<)
% Number of symbols : 160 ( 157 usr; 111 con; 0-4 aty)
% Number of variables : 930 ( 59 ^ 808 !; 63 ?; 930 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $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_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
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_40,type,
descr: ( $i > $o ) > $i ).
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_47,type,
prop2set: $o > $i ).
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_57,type,
nonempty: $i > $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_109,type,
subset: $i > $i > $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_135,type,
binunion: $i > $i > $i ).
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,
epred1_0: $o ).
thf(decl_143,type,
esk1_2: $i > $i > $i ).
thf(decl_144,type,
esk2_2: $i > $i > $i ).
thf(decl_145,type,
esk3_2: $i > $i > $i ).
thf(decl_146,type,
esk4_1: $i > $i ).
thf(decl_147,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_148,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_149,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_150,type,
esk8_1: $i > $i ).
thf(decl_151,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_152,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_153,type,
esk11_2: $i > $i > $i ).
thf(decl_154,type,
esk12_2: $i > $i > $i ).
thf(decl_155,type,
esk13_1: $i > $i ).
thf(decl_156,type,
esk14_1: $i > $i ).
thf(decl_157,type,
esk15_1: $i > $i ).
thf(decl_158,type,
esk16_2: $i > $i > $i ).
thf(decl_159,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_160,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_161,type,
esk19_1: $i > $i ).
thf(decl_162,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_163,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_164,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_165,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_166,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_167,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_168,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_169,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_170,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_171,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_172,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_173,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_174,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_175,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_176,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_177,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_178,type,
esk36_2: $i > $i > $i ).
thf(decl_179,type,
esk37_2: $i > $i > $i ).
thf(decl_180,type,
esk38_0: $i ).
thf(decl_181,type,
esk39_0: $i ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
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/benchmark/theBenchmark.p',emptyE1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
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/benchmark/theBenchmark.p',dsetconstr__Cong) ).
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/benchmark/theBenchmark.p',nonemptyI) ).
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/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(binunionRsub,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
=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_104,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_105,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_106,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_107,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_108,plain,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE2]) ).
thf(c_0_109,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_110,plain,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI3]) ).
thf(c_0_111,plain,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI2]) ).
thf(c_0_112,plain,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE3u]) ).
thf(c_0_113,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_114,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu]) ).
thf(c_0_115,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_116,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_117,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_118,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_119,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_120,plain,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE1]) ).
thf(c_0_121,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_122,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_123,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_124,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_125,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_126,plain,
( epred1_0
<=> ! [X327: $i] :
? [X328: $i] :
( ! [X329: $i] :
( ( in @ X329 @ X328 )
=> ! [X330: $i] :
( ( in @ X330 @ X329 )
=> ( in @ X330 @ X327 ) ) )
& ! [X331: $i,X332: $i] :
( ( ( in @ X331 @ X327 )
& ( in @ X332 @ X327 ) )
=> ( ! [X333: $i] :
( ( in @ X333 @ X328 )
=> ( ( in @ X331 @ X333 )
<=> ( in @ X332 @ X333 ) ) )
=> ( X331 = X332 ) ) )
& ! [X334: $i,X335: $i] :
( ( ( in @ X334 @ X328 )
& ( in @ X335 @ X328 ) )
=> ( ! [X336: $i] :
( ( in @ X336 @ X334 )
=> ( in @ X336 @ X335 ) )
| ! [X337: $i] :
( ( in @ X337 @ X335 )
=> ( in @ X337 @ X334 ) ) ) )
& ! [X338: $i] :
( ( ! [X339: $i] :
( ( in @ X339 @ X338 )
=> ( in @ X339 @ X327 ) )
& ? [X340: $i] : ( in @ X340 @ X338 ) )
=> ? [X341: $i,X342: $i] :
( ( in @ X341 @ X328 )
& ( in @ X342 @ X338 )
& ~ ? [X343: $i] :
( ( in @ X343 @ X341 )
& ( in @ X343 @ X338 ) )
& ! [X344: $i] :
( ( in @ X344 @ X328 )
=> ( ! [X345: $i] :
( ( in @ X345 @ X344 )
=> ( in @ X345 @ X341 ) )
| ( in @ X342 @ X344 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_127,negated_conjecture,
~ ( ! [X300: $i,X301: $i] :
( ! [X302: $i] :
( ( in @ X302 @ X300 )
<=> ( in @ X302 @ X301 ) )
=> ( X300 = X301 ) )
=> ( ! [X303: $i] :
~ ( in @ X303 @ emptyset )
=> ( ! [X304: $i,X305: $i,X306: $i] :
( ( in @ X306 @ ( setadjoin @ X304 @ X305 ) )
<=> ( ( X306 = X304 )
| ( in @ X306 @ X305 ) ) )
=> ( ! [X307: $i,X308: $i] :
( ( in @ X308 @ ( powerset @ X307 ) )
<=> ! [X309: $i] :
( ( in @ X309 @ X308 )
=> ( in @ X309 @ X307 ) ) )
=> ( ! [X310: $i,X311: $i] :
( ( in @ X311 @ ( setunion @ X310 ) )
<=> ? [X312: $i] :
( ( in @ X311 @ X312 )
& ( in @ X312 @ X310 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X313: $i] :
( ( in @ X313 @ omega )
=> ( in @ ( setadjoin @ X313 @ X313 ) @ omega ) )
=> ( ! [X314: $i] :
( ( ( in @ emptyset @ X314 )
& ! [X315: $i] :
( ( ( in @ X315 @ omega )
& ( in @ X315 @ X314 ) )
=> ( in @ ( setadjoin @ X315 @ X315 ) @ X314 ) ) )
=> ! [X316: $i] :
( ( in @ X316 @ omega )
=> ( in @ X316 @ X314 ) ) )
=> ( ! [X317: $i > $i > $o,X318: $i] :
( ! [X319: $i] :
( ( in @ X319 @ X318 )
=> ( exu @ ( X317 @ X319 ) ) )
=> ? [X320: $i] :
! [X321: $i] :
( ( in @ X321 @ X320 )
<=> ? [X322: $i] :
( ( in @ X322 @ X318 )
& ( X317 @ X322 @ X321 ) ) ) )
=> ( ! [X323: $i] :
( ? [X324: $i] : ( in @ X324 @ X323 )
=> ? [X325: $i] :
( ( in @ X325 @ X323 )
& ~ ? [X326: $i] :
( ( in @ X326 @ X325 )
& ( in @ X326 @ X323 ) ) ) )
=> ( epred1_0
=> ( ! [X346: $i > $o] :
( ( exu @ X346 )
=> ( X346
@ ( descr
@ ^ [Z0: $i] : ( X346 @ Z0 ) ) ) )
=> ( ! [X347: $i,X348: $i > $o,X349: $i] :
( ( in @ X349 @ X347 )
=> ( ( X348 @ X349 )
=> ( in @ X349 @ ( dsetconstr @ X347 @ X348 ) ) ) )
=> ( ! [X350: $i,X351: $i > $o,X352: $i] :
( ( in @ X352 @ ( dsetconstr @ X350 @ X351 ) )
=> ( in @ X352 @ X350 ) )
=> ( ! [X353: $i,X354: $i > $o,X355: $i] :
( ( in @ X355 @ ( dsetconstr @ X353 @ X354 ) )
=> ( X354 @ X355 ) )
=> ( ! [X356: $i > $o] :
( ( exu @ X356 )
=> ? [X357: $i] :
( ( X356 @ X357 )
& ! [X358: $i] :
( ( X356 @ X358 )
=> ( X357 = X358 ) ) ) )
=> ( ! [X359: $o,X360: $i] :
( ( in @ X360 @ ( prop2set @ X359 ) )
=> X359 )
=> ( ! [X361: $i] :
( ( in @ X361 @ emptyset )
=> ! [X362: $o] : X362 )
=> ( ! [X363: $i] :
( ( in @ X363 @ emptyset )
=> ~ $true )
=> ( ! [X364: $i] :
~ ( in @ X364 @ emptyset )
=> ( ! [X365: $i > $o] :
( ( exu @ X365 )
=> ? [X366: $i] : ( X365 @ X366 ) )
=> ( ! [X367: $i,X368: $i] :
( ! [X369: $i] :
( ( in @ X369 @ X367 )
=> ( in @ X369 @ X368 ) )
=> ( ! [X370: $i] :
( ( in @ X370 @ X368 )
=> ( in @ X370 @ X367 ) )
=> ( X367 = X368 ) ) )
=> ( ! [X371: $i] :
( ! [X372: $i] :
~ ( in @ X372 @ X371 )
=> ( X371 = emptyset ) )
=> ( ! [X373: $i] :
( ! [X374: $i] :
~ ( in @ X374 @ X373 )
=> ( X373 = emptyset ) )
=> ( ! [X375: $i,X376: $i > $o,X377: $i] :
( ( in @ X377 @ X375 )
=> ( ( in @ X377 @ ( dsetconstr @ X375 @ X376 ) )
<=> ( X376 @ X377 ) ) )
=> ( ! [X378: $i] :
( ( nonempty @ X378 )
=> ? [X379: $i] : ( in @ X379 @ X378 ) )
=> ( ! [X380: $i,X381: $i > $o,X382: $i] :
( ( in @ X382 @ X380 )
=> ( ( X381 @ X382 )
=> ( nonempty @ ( dsetconstr @ X380 @ X381 ) ) ) )
=> ( ! [X383: $i] :
( ? [X384: $i] : ( in @ X384 @ X383 )
=> ( nonempty @ X383 ) )
=> ( ! [X385: $i,X386: $i] : ( in @ X385 @ ( setadjoin @ X385 @ X386 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X387: $i,X388: $i,X389: $i] :
( ( in @ X389 @ X388 )
=> ( in @ X389 @ ( setadjoin @ X387 @ X388 ) ) )
=> ( ! [X390: $i,X391: $i,X392: $i] :
( ( in @ X392 @ ( setadjoin @ X390 @ X391 ) )
=> ! [X393: $o] :
( ( ( X392 = X390 )
=> X393 )
=> ( ( ( in @ X392 @ X391 )
=> X393 )
=> X393 ) ) )
=> ( ! [X394: $i,X395: $i,X396: $i] :
( ( in @ X396 @ ( setadjoin @ X394 @ X395 ) )
=> ( ( X396 = X394 )
| ( in @ X396 @ X395 ) ) )
=> ( ! [X397: $i] :
( ( dsetconstr @ X397
@ ^ [Z0: $i] : $true )
= X397 )
=> ( ! [X398: $i,X399: $i] :
( ! [X400: $i] :
( ( in @ X400 @ X399 )
=> ( in @ X400 @ X398 ) )
=> ( in @ X399 @ ( powerset @ X398 ) ) )
=> ( ! [X401: $i] : ( in @ emptyset @ ( powerset @ X401 ) )
=> ( ! [X402: $i] : ( in @ emptyset @ ( powerset @ X402 ) )
=> ( ! [X403: $i,X404: $i,X405: $i] :
( ( in @ X404 @ ( powerset @ X403 ) )
=> ( ( in @ X405 @ X404 )
=> ( in @ X405 @ X403 ) ) )
=> ( ! [X406: $i,X407: $i,X408: $i] :
( ( in @ X407 @ X408 )
=> ( ( in @ X408 @ X406 )
=> ( in @ X407 @ ( setunion @ X406 ) ) ) )
=> ( ! [X409: $i,X410: $i] :
( ( in @ X410 @ ( setunion @ X409 ) )
=> ! [X411: $o] :
( ! [X412: $i] :
( ( in @ X410 @ X412 )
=> ( ( in @ X412 @ X409 )
=> X411 ) )
=> X411 ) )
=> ( ! [X413: $i,X414: $i] :
( ( in @ X414 @ X413 )
=> ( in @ X414 @ ( powerset @ ( setunion @ X413 ) ) ) )
=> ( ! [X415: $i > $o] :
( ( exu @ X415 )
=> ? [X416: $i] :
! [X417: $i] :
( ( X415 @ X417 )
<=> ( X417 = X416 ) ) )
=> ( ! [X418: $i] :
( ( nonempty @ X418 )
=> ? [X419: $i] :
( ( in @ X419 @ X418 )
& $true ) )
=> ( ! [X420: $i,X421: $i] :
( ( in @ X420 @ ( setadjoin @ X421 @ emptyset ) )
=> ( X420 = X421 ) )
=> ( ! [X422: $i,X423: $i] :
( ( X422 != X423 )
=> ~ ( in @ X423 @ ( setadjoin @ X422 @ emptyset ) ) )
=> ( ! [X424: $i,X425: $i] :
( ( X424 = X425 )
=> ( in @ X424 @ ( setadjoin @ X425 @ emptyset ) ) )
=> ( ! [X426: $i,X427: $i] :
( ( in @ X426 @ ( setadjoin @ X427 @ emptyset ) )
=> ( in @ X427 @ ( setadjoin @ X426 @ emptyset ) ) )
=> ( ! [X428: $i,X429: $i,X430: $i] :
( ( in @ X430 @ ( setadjoin @ X428 @ ( setadjoin @ X429 @ emptyset ) ) )
=> ( ( X430 = X428 )
| ( X430 = X429 ) ) )
=> ( ! [X431: $i,X432: $i] : ( in @ X431 @ ( setadjoin @ X431 @ ( setadjoin @ X432 @ emptyset ) ) )
=> ( ! [X433: $i,X434: $i] : ( in @ X434 @ ( setadjoin @ X433 @ ( setadjoin @ X434 @ emptyset ) ) )
=> ( ! [X435: $i,X436: $i > $o] :
( ? [X437: $i] :
( ( in @ X437 @ X435 )
& ( X436 @ X437 ) )
=> ( ( ( dsetconstr @ X435 @ X436 )
= emptyset )
=> ~ $true ) )
=> ( ! [X438: $i > $o,X439: $i] :
( ( in @ X439 @ emptyset )
=> ( X438 @ X439 ) )
=> ( ! [X440: $i,X441: $i > $o] :
( ~ ! [X442: $i] :
( ( in @ X442 @ X440 )
=> ( X441 @ X442 ) )
=> ? [X443: $i] :
( ( in @ X443 @ X440 )
& ~ ( X441 @ X443 ) ) )
=> ( ! [X444: $i,X445: $i > $o] :
( ! [X446: $i] :
( ( in @ X446 @ X444 )
=> ~ ( X445 @ X446 ) )
=> ~ ? [X447: $i] :
( ( in @ X447 @ X444 )
& ( X445 @ X447 ) ) )
=> ( ! [X448: $i,X449: $i > $o] :
( ~ ? [X450: $i] :
( ( in @ X450 @ X448 )
& ( X449 @ X450 ) )
=> ! [X451: $i] :
( ( in @ X451 @ X448 )
=> ~ ( X449 @ X451 ) ) )
=> ( ! [X452: $i,X453: $i > $o] :
( ? [X454: $i] :
( ( in @ X454 @ X452 )
& ~ ( X453 @ X454 ) )
=> ~ ! [X455: $i] :
( ( in @ X455 @ X452 )
=> ( X453 @ X455 ) ) )
=> ( ! [X456: $o] :
( X456
=> ( in @ emptyset @ ( prop2set @ X456 ) ) )
=> ( prop2set2propI
=> ( ! [X457: $i,X458: $i > $o] :
( ~ ? [X459: $i] :
( ( in @ X459 @ X457 )
& ( X458 @ X459 ) )
=> ! [X460: $i] :
( ( in @ X460 @ X457 )
=> ~ ( X458 @ X460 ) ) )
=> ( ! [X461: $i,X462: $i > $o] :
( ~ ! [X463: $i] :
( ( in @ X463 @ X461 )
=> ( X462 @ X463 ) )
=> ? [X464: $i] :
( ( in @ X464 @ X461 )
& ~ ( X462 @ X464 ) ) )
=> ( ! [X465: $i > $o] :
( ? [X466: $i] :
( ( X465 @ X466 )
& ! [X467: $i] :
( ( X465 @ X467 )
=> ( X466 = X467 ) ) )
=> ( exu @ X465 ) )
=> ( ! [X468: $i > $o] :
( ? [X469: $i] : ( X468 @ X469 )
=> ( ! [X470: $i,X471: $i] :
( ( X468 @ X470 )
=> ( ( X468 @ X471 )
=> ( X470 = X471 ) ) )
=> ( exu @ X468 ) ) )
=> ( ! [X472: $i > $o] :
( ? [X473: $i] :
! [X474: $i] :
( ( X472 @ X474 )
<=> ( X474 = X473 ) )
=> ( exu @ X472 ) )
=> ( ! [X475: $i,X476: $i] :
( ( X475 = X476 )
=> ! [X477: $i,X478: $i] :
( ( X477 = X478 )
=> ( ( in @ X477 @ X475 )
=> ( in @ X478 @ X476 ) ) ) )
=> ( ! [X479: $i,X480: $i] :
( ( X479 = X480 )
=> ! [X481: $i,X482: $i] :
( ( X481 = X482 )
=> ( ( in @ X481 @ X479 )
<=> ( in @ X482 @ X480 ) ) ) )
=> ( ! [X483: $i > $o] :
( ( exu @ X483 )
=> ! [X484: $i,X485: $i] :
( ( X483 @ X484 )
=> ( ( X483 @ X485 )
=> ( X484 = X485 ) ) ) )
=> ( ! [X486: $i > $o,X487: $i > $o] :
( ! [X488: $i,X489: $i] :
( ( X488 = X489 )
=> ( ( X486 @ X488 )
<=> ( X487 @ X489 ) ) )
=> ( ( exu @ X486 )
<=> ( exu @ X487 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X490: $i,X491: $i] :
( ( X490 = X491 )
=> ! [X492: $i,X493: $i] :
( ( X492 = X493 )
=> ( ( setadjoin @ X490 @ X492 )
= ( setadjoin @ X491 @ X493 ) ) ) )
=> ( ! [X494: $i,X495: $i] :
( ( X494 = X495 )
=> ( ( powerset @ X494 )
= ( powerset @ X495 ) ) )
=> ( ! [X496: $i,X497: $i] :
( ( X496 = X497 )
=> ( ( setunion @ X496 )
= ( setunion @ X497 ) ) )
=> ( ( omega = omega )
=> ( ! [X498: $i > $o] :
( ( exu @ X498 )
=> ! [X499: $i,X500: $i] :
( ( X498 @ X499 )
=> ( ( X498 @ X500 )
=> ( X499 = X500 ) ) ) )
=> ( ! [X501: $i > $o,X502: $i > $o] :
( ! [X503: $i,X504: $i] :
( ( X503 = X504 )
=> ( ( X501 @ X503 )
<=> ( X502 @ X504 ) ) )
=> ( ( exu @ X501 )
=> ( ( exu @ X502 )
=> ( ( descr @ X501 )
= ( descr @ X502 ) ) ) ) )
=> ( ! [X505: $i,X506: $i] :
( ( X505 = X506 )
=> ! [X507: $i > $o,X508: $i > $o] :
( ! [X509: $i] :
( ( in @ X509 @ X505 )
=> ! [X510: $i] :
( ( in @ X510 @ X506 )
=> ( ( X509 = X510 )
=> ( ( X507 @ X509 )
<=> ( X508 @ X510 ) ) ) ) )
=> ( ( dsetconstr @ X505 @ X507 )
= ( dsetconstr @ X506 @ X508 ) ) ) )
=> ( ! [X511: $i,X512: $i] :
( ! [X513: $i] :
( ( in @ X513 @ X511 )
=> ( in @ X513 @ X512 ) )
=> ( subset @ X511 @ X512 ) )
=> ( ! [X514: $i,X515: $i] :
( ( X514 = X515 )
=> ( subset @ X515 @ X514 ) )
=> ( ! [X516: $i,X517: $i] :
( ( X516 = X517 )
=> ( subset @ X516 @ X517 ) )
=> ( ! [X518: $i,X519: $i] :
( ! [X520: $i] :
( ( in @ X520 @ X518 )
=> ( in @ X520 @ X519 ) )
=> ( subset @ X518 @ X519 ) )
=> ( ! [X521: $i] : ( subset @ emptyset @ X521 )
=> ( ! [X522: $i,X523: $i,X524: $i] :
( ( subset @ X522 @ X523 )
=> ( ( in @ X524 @ X522 )
=> ( in @ X524 @ X523 ) ) )
=> ( ! [X525: $i,X526: $i,X527: $i] :
( ( subset @ X525 @ X526 )
=> ( ~ ( in @ X527 @ X526 )
=> ~ ( in @ X527 @ X525 ) ) )
=> ( ! [X528: $i,X529: $i,X530: $i] :
( ( in @ X530 @ X528 )
=> ( ~ ( in @ X530 @ X529 )
=> ~ ( subset @ X528 @ X529 ) ) )
=> ( ! [X531: $i,X532: $i] :
( ~ ( subset @ X531 @ X532 )
=> ( X531 != X532 ) )
=> ( ! [X533: $i,X534: $i,X535: $i] :
( ( in @ X535 @ X533 )
=> ( ~ ( in @ X535 @ X534 )
=> ( X533 != X534 ) ) )
=> ( ! [X536: $i] : ( subset @ X536 @ X536 )
=> ( ! [X537: $i,X538: $i,X539: $i] :
( ( subset @ X537 @ X538 )
=> ( ( subset @ X538 @ X539 )
=> ( subset @ X537 @ X539 ) ) )
=> ( ! [X540: $i,X541: $i] : ( subset @ X541 @ ( setadjoin @ X540 @ X541 ) )
=> ( ! [X542: $i,X543: $i,X544: $i] :
( ( subset @ X542 @ X544 )
=> ( subset @ X542 @ ( setadjoin @ X543 @ X544 ) ) )
=> ( ! [X545: $i,X546: $i] :
( ( subset @ X545 @ X546 )
=> ( in @ X545 @ ( powerset @ X546 ) ) )
=> ( ! [X547: $i,X548: $i] :
( ( subset @ X547 @ X548 )
=> ( ( subset @ X548 @ X547 )
=> ( X547 = X548 ) ) )
=> ( ! [X549: $i] :
( ( subset @ X549 @ emptyset )
=> ( X549 = emptyset ) )
=> ( ! [X550: $i,X551: $i] :
( ( subset @ X551 @ X550 )
=> ( in @ X551 @ ( powerset @ X550 ) ) )
=> ( ! [X552: $i,X553: $i] :
( ( in @ X553 @ ( powerset @ X552 ) )
=> ( subset @ X553 @ X552 ) )
=> ( ! [X554: $i] : ( in @ X554 @ ( powerset @ X554 ) )
=> ( ! [X555: $i,X556: $i] :
( ( subset @ X555 @ X556 )
=> ( subset @ ( powerset @ X555 ) @ ( powerset @ X556 ) ) )
=> ( ! [X557: $i,X558: $i > $o] : ( in @ ( dsetconstr @ X557 @ X558 ) @ ( powerset @ X557 ) )
=> ( ! [X559: $i,X560: $i > $o] : ( subset @ ( dsetconstr @ X559 @ X560 ) @ X559 )
=> ( ! [X561: $i,X562: $i,X563: $i] :
( ( in @ X563 @ X561 )
=> ( in @ X563 @ ( binunion @ X561 @ X562 ) ) )
=> ( ! [X564: $i,X565: $i] : ( in @ X565 @ ( setadjoin @ X564 @ ( setadjoin @ X565 @ emptyset ) ) )
=> ( ! [X566: $i,X567: $i,X568: $i] :
( ( in @ X568 @ X567 )
=> ( in @ X568 @ ( binunion @ X566 @ X567 ) ) )
=> ( ! [X569: $i,X570: $i,X571: $i,X572: $o] :
( ( in @ X571 @ ( binunion @ X569 @ X570 ) )
=> ( ( ( in @ X571 @ X569 )
=> X572 )
=> ( ( ( in @ X571 @ X570 )
=> X572 )
=> X572 ) ) )
=> ( ! [X573: $i,X574: $i,X575: $i] :
( ( in @ X575 @ ( binunion @ X573 @ X574 ) )
=> ( ( in @ X575 @ X573 )
| ( in @ X575 @ X574 ) ) )
=> ( ! [X576: $i,X577: $i] : ( subset @ X576 @ ( binunion @ X576 @ X577 ) )
=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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(assume_negation,[status(cth)],[binunionRsub]),binunionLsub]),notequalI1]),setadjoinE]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinOr]),setadjoinSub]),setadjoinSub2]),c_0_104]),subset2powerset]),setextsub]),powersetI]),subsetemptysetimpeq]),powersetI1]),emptyinPowerset]),powersetE1]),inPowerset]),emptyInPowerset]),powersetsubset]),c_0_105]),powersetE]),c_0_106]),setunionI]),binunionIL]),upairset2IR]),binunionIR]),setunionE]),binunionEcases]),binunionE]),subPowSU]),c_0_107]),c_0_108]),nonemptyImpWitness]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_109]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_110]),c_0_111]),inCongP]),in__Cong]),c_0_112]),c_0_113]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_114]),c_0_115]),c_0_116]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_117]),nonemptyE1]),c_0_118]),noeltsimpempty]),emptyI]),setext]),c_0_119]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_120]),c_0_121]),c_0_122]),c_0_123]),c_0_124]),wellorderingAx]),foundationAx]),c_0_125]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_126]) ).
thf(c_0_128,negated_conjecture,
! [X578: $i,X579: $i,X581: $i,X582: $i,X583: $i,X584: $i,X585: $i,X586: $i,X587: $i,X588: $i,X589: $i,X591: $i,X592: $i,X594: $i,X595: $i,X596: $i,X597: $i,X598: $i,X600: $i,X601: $i > $i > $o,X602: $i,X605: $i,X607: $i,X608: $i,X609: $i,X610: $i,X612: $i,X613: $i > $o,X614: $i,X615: $i > $o,X616: $i,X617: $i,X618: $i > $o,X619: $i,X620: $i,X621: $i > $o,X622: $i,X623: $i > $o,X625: $i,X626: $o,X627: $i,X628: $i,X629: $o,X630: $i,X631: $i,X632: $i > $o,X634: $i,X635: $i,X638: $i,X640: $i,X642: $i,X643: $i > $o,X644: $i,X645: $i,X647: $i,X648: $i > $o,X649: $i,X650: $i,X651: $i,X652: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i,X660: $o,X661: $i,X662: $i,X663: $i,X664: $i,X665: $i,X666: $i,X668: $i,X669: $i,X670: $i,X671: $i,X672: $i,X673: $i,X674: $i,X675: $i,X676: $i,X677: $i,X678: $o,X680: $i,X681: $i,X682: $i > $o,X684: $i,X685: $i,X686: $i,X688: $i,X689: $i,X690: $i,X691: $i,X692: $i,X693: $i,X694: $i,X695: $i,X696: $i,X697: $i,X698: $i,X699: $i,X700: $i,X701: $i,X702: $i,X703: $i,X704: $i > $o,X705: $i,X706: $i > $o,X707: $i,X708: $i,X709: $i > $o,X710: $i,X712: $i,X713: $i > $o,X715: $i,X716: $i,X717: $i > $o,X719: $i,X720: $i,X721: $i > $o,X722: $i,X724: $o,X725: $i,X726: $i > $o,X728: $i,X729: $i,X730: $i > $o,X731: $i,X733: $i > $o,X734: $i,X736: $i > $o,X737: $i,X740: $i > $o,X741: $i,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X749: $i,X750: $i,X751: $i > $o,X752: $i,X753: $i,X754: $i > $o,X755: $i > $o,X758: $i,X759: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i > $o,X767: $i,X768: $i,X769: $i > $o,X770: $i > $o,X773: $i,X774: $i,X775: $i > $o,X776: $i > $o,X779: $i,X780: $i,X782: $i,X783: $i,X784: $i,X785: $i,X786: $i,X787: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i,X814: $i,X815: $i,X816: $i,X817: $i,X818: $i,X819: $i,X820: $i,X821: $i,X822: $i,X823: $i,X824: $i,X825: $i,X826: $i > $o,X827: $i,X828: $i > $o,X829: $i,X830: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X838: $i,X839: $i,X840: $o,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i] :
( ( ~ ( in @ ( esk1_2 @ X578 @ X579 ) @ X578 )
| ~ ( in @ ( esk1_2 @ X578 @ X579 ) @ X579 )
| ( X578 = X579 ) )
& ( ( in @ ( esk1_2 @ X578 @ X579 ) @ X578 )
| ( in @ ( esk1_2 @ X578 @ X579 ) @ X579 )
| ( X578 = X579 ) )
& ~ ( in @ X581 @ emptyset )
& ( ~ ( in @ X584 @ ( setadjoin @ X582 @ X583 ) )
| ( X584 = X582 )
| ( in @ X584 @ X583 ) )
& ( ( X584 != X582 )
| ( in @ X584 @ ( setadjoin @ X582 @ X583 ) ) )
& ( ~ ( in @ X584 @ X583 )
| ( in @ X584 @ ( setadjoin @ X582 @ X583 ) ) )
& ( ~ ( in @ X586 @ ( powerset @ X585 ) )
| ~ ( in @ X587 @ X586 )
| ( in @ X587 @ X585 ) )
& ( ( in @ ( esk2_2 @ X588 @ X589 ) @ X589 )
| ( in @ X589 @ ( powerset @ X588 ) ) )
& ( ~ ( in @ ( esk2_2 @ X588 @ X589 ) @ X588 )
| ( in @ X589 @ ( powerset @ X588 ) ) )
& ( ( in @ X592 @ ( esk3_2 @ X591 @ X592 ) )
| ~ ( in @ X592 @ ( setunion @ X591 ) ) )
& ( ( in @ ( esk3_2 @ X591 @ X592 ) @ X591 )
| ~ ( in @ X592 @ ( setunion @ X591 ) ) )
& ( ~ ( in @ X595 @ X596 )
| ~ ( in @ X596 @ X594 )
| ( in @ X595 @ ( setunion @ X594 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X597 @ omega )
| ( in @ ( setadjoin @ X597 @ X597 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X598 ) @ omega )
| ~ ( in @ emptyset @ X598 )
| ~ ( in @ X600 @ omega )
| ( in @ X600 @ X598 ) )
& ( ( in @ ( esk4_1 @ X598 ) @ X598 )
| ~ ( in @ emptyset @ X598 )
| ~ ( in @ X600 @ omega )
| ( in @ X600 @ X598 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X598 ) @ ( esk4_1 @ X598 ) ) @ X598 )
| ~ ( in @ emptyset @ X598 )
| ~ ( in @ X600 @ omega )
| ( in @ X600 @ X598 ) )
& ( ( in @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X602 )
| ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
| ( in @ ( esk5_2 @ X601 @ X602 ) @ X602 ) )
& ( ( X601 @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X605 )
| ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
| ( in @ ( esk5_2 @ X601 @ X602 ) @ X602 ) )
& ( ~ ( in @ X608 @ X602 )
| ~ ( X601 @ X608 @ X607 )
| ( in @ X607 @ ( esk6_2 @ X601 @ X602 ) )
| ( in @ ( esk5_2 @ X601 @ X602 ) @ X602 ) )
& ( ( in @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X602 )
| ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
| ~ ( exu @ ( X601 @ ( esk5_2 @ X601 @ X602 ) ) ) )
& ( ( X601 @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X605 )
| ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
| ~ ( exu @ ( X601 @ ( esk5_2 @ X601 @ X602 ) ) ) )
& ( ~ ( in @ X608 @ X602 )
| ~ ( X601 @ X608 @ X607 )
| ( in @ X607 @ ( esk6_2 @ X601 @ X602 ) )
| ~ ( exu @ ( X601 @ ( esk5_2 @ X601 @ X602 ) ) ) )
& ( ( in @ ( esk8_1 @ X609 ) @ X609 )
| ~ ( in @ X610 @ X609 ) )
& ( ~ ( in @ X612 @ ( esk8_1 @ X609 ) )
| ~ ( in @ X612 @ X609 )
| ~ ( in @ X610 @ X609 ) )
& epred1_0
& ( ~ ( exu @ X613 )
| ( X613 @ ( descr @ X613 ) ) )
& ( ~ ( in @ X616 @ X614 )
| ~ ( X615 @ X616 )
| ( in @ X616 @ ( dsetconstr @ X614 @ X615 ) ) )
& ( ~ ( in @ X619 @ ( dsetconstr @ X617 @ X618 ) )
| ( in @ X619 @ X617 ) )
& ( ~ ( in @ X622 @ ( dsetconstr @ X620 @ X621 ) )
| ( X621 @ X622 ) )
& ( ( X623 @ ( esk9_1 @ X623 ) )
| ~ ( exu @ X623 ) )
& ( ~ ( X623 @ X625 )
| ( ( esk9_1 @ X623 )
= X625 )
| ~ ( exu @ X623 ) )
& ( ~ ( in @ X627 @ ( prop2set @ X626 ) )
| X626 )
& ( ~ ( in @ X628 @ emptyset )
| X629 )
& ( ~ ( in @ X630 @ emptyset )
| ~ $true )
& ~ ( in @ X631 @ emptyset )
& ( ~ ( exu @ X632 )
| ( X632 @ ( esk10_1 @ X632 ) ) )
& ( ( in @ ( esk12_2 @ X634 @ X635 ) @ X635 )
| ( X634 = X635 )
| ( in @ ( esk11_2 @ X634 @ X635 ) @ X634 ) )
& ( ~ ( in @ ( esk12_2 @ X634 @ X635 ) @ X634 )
| ( X634 = X635 )
| ( in @ ( esk11_2 @ X634 @ X635 ) @ X634 ) )
& ( ( in @ ( esk12_2 @ X634 @ X635 ) @ X635 )
| ( X634 = X635 )
| ~ ( in @ ( esk11_2 @ X634 @ X635 ) @ X635 ) )
& ( ~ ( in @ ( esk12_2 @ X634 @ X635 ) @ X634 )
| ( X634 = X635 )
| ~ ( in @ ( esk11_2 @ X634 @ X635 ) @ X635 ) )
& ( ( in @ ( esk13_1 @ X638 ) @ X638 )
| ( X638 = emptyset ) )
& ( ( in @ ( esk14_1 @ X640 ) @ X640 )
| ( X640 = emptyset ) )
& ( ~ ( in @ X644 @ ( dsetconstr @ X642 @ X643 ) )
| ( X643 @ X644 )
| ~ ( in @ X644 @ X642 ) )
& ( ~ ( X643 @ X644 )
| ( in @ X644 @ ( dsetconstr @ X642 @ X643 ) )
| ~ ( in @ X644 @ X642 ) )
& ( ~ ( nonempty @ X645 )
| ( in @ ( esk15_1 @ X645 ) @ X645 ) )
& ( ~ ( in @ X649 @ X647 )
| ~ ( X648 @ X649 )
| ( nonempty @ ( dsetconstr @ X647 @ X648 ) ) )
& ( ~ ( in @ X651 @ X650 )
| ( nonempty @ X650 ) )
& ( in @ X652 @ ( setadjoin @ X652 @ X653 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X656 @ X655 )
| ( in @ X656 @ ( setadjoin @ X654 @ X655 ) ) )
& ( ( in @ X659 @ X658 )
| X660
| ( X659 = X657 )
| ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
& ( ~ X660
| X660
| ( X659 = X657 )
| ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
& ( ( in @ X659 @ X658 )
| X660
| ~ X660
| ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
& ( ~ X660
| X660
| ~ X660
| ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
& ( ~ ( in @ X663 @ ( setadjoin @ X661 @ X662 ) )
| ( X663 = X661 )
| ( in @ X663 @ X662 ) )
& ( ( dsetconstr @ X664
@ ^ [Z0: $i] : $true )
= X664 )
& ( ( in @ ( esk16_2 @ X665 @ X666 ) @ X666 )
| ( in @ X666 @ ( powerset @ X665 ) ) )
& ( ~ ( in @ ( esk16_2 @ X665 @ X666 ) @ X665 )
| ( in @ X666 @ ( powerset @ X665 ) ) )
& ( in @ emptyset @ ( powerset @ X668 ) )
& ( in @ emptyset @ ( powerset @ X669 ) )
& ( ~ ( in @ X671 @ ( powerset @ X670 ) )
| ~ ( in @ X672 @ X671 )
| ( in @ X672 @ X670 ) )
& ( ~ ( in @ X674 @ X675 )
| ~ ( in @ X675 @ X673 )
| ( in @ X674 @ ( setunion @ X673 ) ) )
& ( ( in @ X677 @ ( esk17_3 @ X676 @ X677 @ X678 ) )
| X678
| ~ ( in @ X677 @ ( setunion @ X676 ) ) )
& ( ( in @ ( esk17_3 @ X676 @ X677 @ X678 ) @ X676 )
| X678
| ~ ( in @ X677 @ ( setunion @ X676 ) ) )
& ( ~ X678
| X678
| ~ ( in @ X677 @ ( setunion @ X676 ) ) )
& ( ~ ( in @ X681 @ X680 )
| ( in @ X681 @ ( powerset @ ( setunion @ X680 ) ) ) )
& ( ~ ( X682 @ X684 )
| ( X684
= ( esk18_1 @ X682 ) )
| ~ ( exu @ X682 ) )
& ( ( X685
!= ( esk18_1 @ X682 ) )
| ( X682 @ X685 )
| ~ ( exu @ X682 ) )
& ( ( in @ ( esk19_1 @ X686 ) @ X686 )
| ~ ( nonempty @ X686 ) )
& ( $true
| ~ ( nonempty @ X686 ) )
& ( ~ ( in @ X688 @ ( setadjoin @ X689 @ emptyset ) )
| ( X688 = X689 ) )
& ( ( X690 = X691 )
| ~ ( in @ X691 @ ( setadjoin @ X690 @ emptyset ) ) )
& ( ( X692 != X693 )
| ( in @ X692 @ ( setadjoin @ X693 @ emptyset ) ) )
& ( ~ ( in @ X694 @ ( setadjoin @ X695 @ emptyset ) )
| ( in @ X695 @ ( setadjoin @ X694 @ emptyset ) ) )
& ( ~ ( in @ X698 @ ( setadjoin @ X696 @ ( setadjoin @ X697 @ emptyset ) ) )
| ( X698 = X696 )
| ( X698 = X697 ) )
& ( in @ X699 @ ( setadjoin @ X699 @ ( setadjoin @ X700 @ emptyset ) ) )
& ( in @ X702 @ ( setadjoin @ X701 @ ( setadjoin @ X702 @ emptyset ) ) )
& ( ~ ( in @ X705 @ X703 )
| ~ ( X704 @ X705 )
| ( ( dsetconstr @ X703 @ X704 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X707 @ emptyset )
| ( X706 @ X707 ) )
& ( ( in @ ( esk20_2 @ X708 @ X709 ) @ X708 )
| ~ ( in @ X710 @ X708 )
| ( X709 @ X710 ) )
& ( ~ ( X709 @ ( esk20_2 @ X708 @ X709 ) )
| ~ ( in @ X710 @ X708 )
| ( X709 @ X710 ) )
& ( ( in @ ( esk21_2 @ X712 @ X713 ) @ X712 )
| ~ ( in @ X715 @ X712 )
| ~ ( X713 @ X715 ) )
& ( ( X713 @ ( esk21_2 @ X712 @ X713 ) )
| ~ ( in @ X715 @ X712 )
| ~ ( X713 @ X715 ) )
& ( ( in @ ( esk22_2 @ X716 @ X717 ) @ X716 )
| ~ ( in @ X719 @ X716 )
| ~ ( X717 @ X719 ) )
& ( ( X717 @ ( esk22_2 @ X716 @ X717 ) )
| ~ ( in @ X719 @ X716 )
| ~ ( X717 @ X719 ) )
& ( ( in @ ( esk23_2 @ X720 @ X721 ) @ X720 )
| ~ ( in @ X722 @ X720 )
| ( X721 @ X722 ) )
& ( ~ ( X721 @ ( esk23_2 @ X720 @ X721 ) )
| ~ ( in @ X722 @ X720 )
| ( X721 @ X722 ) )
& ( ~ X724
| ( in @ emptyset @ ( prop2set @ X724 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X725 @ X726 ) @ X725 )
| ~ ( in @ X728 @ X725 )
| ~ ( X726 @ X728 ) )
& ( ( X726 @ ( esk24_2 @ X725 @ X726 ) )
| ~ ( in @ X728 @ X725 )
| ~ ( X726 @ X728 ) )
& ( ( in @ ( esk25_2 @ X729 @ X730 ) @ X729 )
| ~ ( in @ X731 @ X729 )
| ( X730 @ X731 ) )
& ( ~ ( X730 @ ( esk25_2 @ X729 @ X730 ) )
| ~ ( in @ X731 @ X729 )
| ( X730 @ X731 ) )
& ( ( X733 @ ( esk26_2 @ X733 @ X734 ) )
| ~ ( X733 @ X734 )
| ( exu @ X733 ) )
& ( ( X734
!= ( esk26_2 @ X733 @ X734 ) )
| ~ ( X733 @ X734 )
| ( exu @ X733 ) )
& ( ( X736 @ ( esk27_1 @ X736 ) )
| ( exu @ X736 )
| ~ ( X736 @ X737 ) )
& ( ( X736 @ ( esk28_1 @ X736 ) )
| ( exu @ X736 )
| ~ ( X736 @ X737 ) )
& ( ( ( esk27_1 @ X736 )
!= ( esk28_1 @ X736 ) )
| ( exu @ X736 )
| ~ ( X736 @ X737 ) )
& ( ~ ( X740 @ ( esk29_2 @ X740 @ X741 ) )
| ( ( esk29_2 @ X740 @ X741 )
!= X741 )
| ( exu @ X740 ) )
& ( ( X740 @ ( esk29_2 @ X740 @ X741 ) )
| ( ( esk29_2 @ X740 @ X741 )
= X741 )
| ( exu @ X740 ) )
& ( ( X743 != X744 )
| ( X745 != X746 )
| ~ ( in @ X745 @ X743 )
| ( in @ X746 @ X744 ) )
& ( ~ ( in @ X749 @ X747 )
| ( in @ X750 @ X748 )
| ( X749 != X750 )
| ( X747 != X748 ) )
& ( ~ ( in @ X750 @ X748 )
| ( in @ X749 @ X747 )
| ( X749 != X750 )
| ( X747 != X748 ) )
& ( ~ ( exu @ X751 )
| ~ ( X751 @ X752 )
| ~ ( X751 @ X753 )
| ( X752 = X753 ) )
& ( ~ ( exu @ X754 )
| ( exu @ X755 )
| ( ( esk30_2 @ X754 @ X755 )
= ( esk31_2 @ X754 @ X755 ) ) )
& ( ~ ( exu @ X755 )
| ( exu @ X754 )
| ( ( esk30_2 @ X754 @ X755 )
= ( esk31_2 @ X754 @ X755 ) ) )
& ( ~ ( exu @ X754 )
| ( exu @ X755 )
| ~ ( X754 @ ( esk30_2 @ X754 @ X755 ) )
| ~ ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
& ( ~ ( exu @ X755 )
| ( exu @ X754 )
| ~ ( X754 @ ( esk30_2 @ X754 @ X755 ) )
| ~ ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
& ( ~ ( exu @ X754 )
| ( exu @ X755 )
| ( X754 @ ( esk30_2 @ X754 @ X755 ) )
| ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
& ( ~ ( exu @ X755 )
| ( exu @ X754 )
| ( X754 @ ( esk30_2 @ X754 @ X755 ) )
| ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
& ( emptyset = emptyset )
& ( ( X758 != X759 )
| ( X760 != X761 )
| ( ( setadjoin @ X758 @ X760 )
= ( setadjoin @ X759 @ X761 ) ) )
& ( ( X762 != X763 )
| ( ( powerset @ X762 )
= ( powerset @ X763 ) ) )
& ( ( X764 != X765 )
| ( ( setunion @ X764 )
= ( setunion @ X765 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X766 )
| ~ ( X766 @ X767 )
| ~ ( X766 @ X768 )
| ( X767 = X768 ) )
& ( ( ( esk32_2 @ X769 @ X770 )
= ( esk33_2 @ X769 @ X770 ) )
| ~ ( exu @ X769 )
| ~ ( exu @ X770 )
| ( ( descr @ X769 )
= ( descr @ X770 ) ) )
& ( ~ ( X769 @ ( esk32_2 @ X769 @ X770 ) )
| ~ ( X770 @ ( esk33_2 @ X769 @ X770 ) )
| ~ ( exu @ X769 )
| ~ ( exu @ X770 )
| ( ( descr @ X769 )
= ( descr @ X770 ) ) )
& ( ( X769 @ ( esk32_2 @ X769 @ X770 ) )
| ( X770 @ ( esk33_2 @ X769 @ X770 ) )
| ~ ( exu @ X769 )
| ~ ( exu @ X770 )
| ( ( descr @ X769 )
= ( descr @ X770 ) ) )
& ( ( in @ ( esk34_4 @ X773 @ X774 @ X775 @ X776 ) @ X773 )
| ( ( dsetconstr @ X773 @ X775 )
= ( dsetconstr @ X774 @ X776 ) )
| ( X773 != X774 ) )
& ( ( in @ ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) @ X774 )
| ( ( dsetconstr @ X773 @ X775 )
= ( dsetconstr @ X774 @ X776 ) )
| ( X773 != X774 ) )
& ( ( ( esk34_4 @ X773 @ X774 @ X775 @ X776 )
= ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) )
| ( ( dsetconstr @ X773 @ X775 )
= ( dsetconstr @ X774 @ X776 ) )
| ( X773 != X774 ) )
& ( ~ ( X775 @ ( esk34_4 @ X773 @ X774 @ X775 @ X776 ) )
| ~ ( X776 @ ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) )
| ( ( dsetconstr @ X773 @ X775 )
= ( dsetconstr @ X774 @ X776 ) )
| ( X773 != X774 ) )
& ( ( X775 @ ( esk34_4 @ X773 @ X774 @ X775 @ X776 ) )
| ( X776 @ ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) )
| ( ( dsetconstr @ X773 @ X775 )
= ( dsetconstr @ X774 @ X776 ) )
| ( X773 != X774 ) )
& ( ( in @ ( esk36_2 @ X779 @ X780 ) @ X779 )
| ( subset @ X779 @ X780 ) )
& ( ~ ( in @ ( esk36_2 @ X779 @ X780 ) @ X780 )
| ( subset @ X779 @ X780 ) )
& ( ( X782 != X783 )
| ( subset @ X783 @ X782 ) )
& ( ( X784 != X785 )
| ( subset @ X784 @ X785 ) )
& ( ( in @ ( esk37_2 @ X786 @ X787 ) @ X786 )
| ( subset @ X786 @ X787 ) )
& ( ~ ( in @ ( esk37_2 @ X786 @ X787 ) @ X787 )
| ( subset @ X786 @ X787 ) )
& ( subset @ emptyset @ X789 )
& ( ~ ( subset @ X790 @ X791 )
| ~ ( in @ X792 @ X790 )
| ( in @ X792 @ X791 ) )
& ( ~ ( subset @ X793 @ X794 )
| ( in @ X795 @ X794 )
| ~ ( in @ X795 @ X793 ) )
& ( ~ ( in @ X798 @ X796 )
| ( in @ X798 @ X797 )
| ~ ( subset @ X796 @ X797 ) )
& ( ( subset @ X799 @ X800 )
| ( X799 != X800 ) )
& ( ~ ( in @ X803 @ X801 )
| ( in @ X803 @ X802 )
| ( X801 != X802 ) )
& ( subset @ X804 @ X804 )
& ( ~ ( subset @ X805 @ X806 )
| ~ ( subset @ X806 @ X807 )
| ( subset @ X805 @ X807 ) )
& ( subset @ X809 @ ( setadjoin @ X808 @ X809 ) )
& ( ~ ( subset @ X810 @ X812 )
| ( subset @ X810 @ ( setadjoin @ X811 @ X812 ) ) )
& ( ~ ( subset @ X813 @ X814 )
| ( in @ X813 @ ( powerset @ X814 ) ) )
& ( ~ ( subset @ X815 @ X816 )
| ~ ( subset @ X816 @ X815 )
| ( X815 = X816 ) )
& ( ~ ( subset @ X817 @ emptyset )
| ( X817 = emptyset ) )
& ( ~ ( subset @ X819 @ X818 )
| ( in @ X819 @ ( powerset @ X818 ) ) )
& ( ~ ( in @ X821 @ ( powerset @ X820 ) )
| ( subset @ X821 @ X820 ) )
& ( in @ X822 @ ( powerset @ X822 ) )
& ( ~ ( subset @ X823 @ X824 )
| ( subset @ ( powerset @ X823 ) @ ( powerset @ X824 ) ) )
& ( in @ ( dsetconstr @ X825 @ X826 ) @ ( powerset @ X825 ) )
& ( subset @ ( dsetconstr @ X827 @ X828 ) @ X827 )
& ( ~ ( in @ X831 @ X829 )
| ( in @ X831 @ ( binunion @ X829 @ X830 ) ) )
& ( in @ X833 @ ( setadjoin @ X832 @ ( setadjoin @ X833 @ emptyset ) ) )
& ( ~ ( in @ X836 @ X835 )
| ( in @ X836 @ ( binunion @ X834 @ X835 ) ) )
& ( ( in @ X839 @ X838 )
| X840
| ( in @ X839 @ X837 )
| ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
& ( ~ X840
| X840
| ( in @ X839 @ X837 )
| ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
& ( ( in @ X839 @ X838 )
| X840
| ~ X840
| ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
& ( ~ X840
| X840
| ~ X840
| ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
& ( ~ ( in @ X843 @ ( binunion @ X841 @ X842 ) )
| ( in @ X843 @ X841 )
| ( in @ X843 @ X842 ) )
& ( subset @ X844 @ ( binunion @ X844 @ X845 ) )
& ~ ( subset @ esk39_0 @ ( binunion @ esk38_0 @ esk39_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_127])])])])])])]) ).
thf(c_0_129,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk37_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_130,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X3 ) )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_131,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ ( binunion @ X3 @ X4 ) )
| ~ ( in @ ( esk37_2 @ X2 @ ( binunion @ X3 @ X4 ) ) @ X4 ) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
thf(c_0_132,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk37_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_133,negated_conjecture,
~ ( subset @ esk39_0 @ ( binunion @ esk38_0 @ esk39_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_134,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
thf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU588^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun May 19 16:06:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 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/benchmark/theBenchmark.p
% 2.55/0.87 # Version: 3.1.0-ho
% 2.55/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.55/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.87 # Starting ehoh_best5 with 300s (1) cores
% 2.55/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 2.55/0.87 # Starting new_bool_5 with 300s (1) cores
% 2.55/0.87 # Starting pre_casc_3 with 300s (1) cores
% 2.55/0.87 # Starting ho_unfolding_8 with 300s (1) cores
% 2.55/0.87 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.55/0.87 # Starting new_bool_3 with 300s (1) cores
% 2.55/0.87 # Starting new_ho_5 with 300s (1) cores
% 2.55/0.87 # new_ho_5 with pid 32634 completed with status 8
% 2.55/0.87 # pre_casc_3 with pid 32630 completed with status 8
% 2.55/0.87 # new_bool_5 with pid 32629 completed with status 0
% 2.55/0.87 # Result found by new_bool_5
% 2.55/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.55/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.87 # Starting ehoh_best5 with 300s (1) cores
% 2.55/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 2.55/0.87 # Starting new_bool_5 with 300s (1) cores
% 2.55/0.87 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.55/0.87 # Search class: HGHSM-FSLS31-SHFMMSBN
% 2.55/0.87 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.55/0.87 # Starting sh3 with 163s (1) cores
% 2.55/0.87 # sh3 with pid 32641 completed with status 0
% 2.55/0.87 # Result found by sh3
% 2.55/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.55/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.87 # Starting ehoh_best5 with 300s (1) cores
% 2.55/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 2.55/0.87 # Starting new_bool_5 with 300s (1) cores
% 2.55/0.87 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.55/0.87 # Search class: HGHSM-FSLS31-SHFMMSBN
% 2.55/0.87 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.55/0.87 # Starting sh3 with 163s (1) cores
% 2.55/0.87 # Preprocessing time : 0.004 s
% 2.55/0.87 # Presaturation interreduction done
% 2.55/0.87
% 2.55/0.87 # Proof found!
% 2.55/0.87 # SZS status Theorem
% 2.55/0.87 # SZS output start CNFRefutation
% See solution above
% 2.55/0.87 # Parsed axioms : 227
% 2.55/0.87 # Removed by relevancy pruning/SinE : 123
% 2.55/0.87 # Initial clauses : 175
% 2.55/0.87 # Removed in clause preprocessing : 18
% 2.55/0.87 # Initial clauses in saturation : 157
% 2.55/0.87 # Processed clauses : 3099
% 2.55/0.87 # ...of these trivial : 80
% 2.55/0.87 # ...subsumed : 1821
% 2.55/0.87 # ...remaining for further processing : 1198
% 2.55/0.87 # Other redundant clauses eliminated : 23
% 2.55/0.87 # Clauses deleted for lack of memory : 0
% 2.55/0.87 # Backward-subsumed : 242
% 2.55/0.87 # Backward-rewritten : 12
% 2.55/0.87 # Generated clauses : 21390
% 2.55/0.87 # ...of the previous two non-redundant : 19695
% 2.55/0.87 # ...aggressively subsumed : 0
% 2.55/0.87 # Contextual simplify-reflections : 11
% 2.55/0.87 # Paramodulations : 21356
% 2.55/0.87 # Factorizations : 4
% 2.55/0.87 # NegExts : 0
% 2.55/0.87 # Equation resolutions : 23
% 2.55/0.87 # Disequality decompositions : 0
% 2.55/0.87 # Total rewrite steps : 2141
% 2.55/0.87 # ...of those cached : 1903
% 2.55/0.87 # Propositional unsat checks : 0
% 2.55/0.87 # Propositional check models : 0
% 2.55/0.87 # Propositional check unsatisfiable : 0
% 2.55/0.87 # Propositional clauses : 0
% 2.55/0.87 # Propositional clauses after purity: 0
% 2.55/0.87 # Propositional unsat core size : 0
% 2.55/0.87 # Propositional preprocessing time : 0.000
% 2.55/0.87 # Propositional encoding time : 0.000
% 2.55/0.87 # Propositional solver time : 0.000
% 2.55/0.87 # Success case prop preproc time : 0.000
% 2.55/0.87 # Success case prop encoding time : 0.000
% 2.55/0.87 # Success case prop solver time : 0.000
% 2.55/0.87 # Current number of processed clauses : 796
% 2.55/0.87 # Positive orientable unit clauses : 97
% 2.55/0.87 # Positive unorientable unit clauses: 0
% 2.55/0.87 # Negative unit clauses : 25
% 2.55/0.87 # Non-unit-clauses : 674
% 2.55/0.87 # Current number of unprocessed clauses: 15913
% 2.55/0.87 # ...number of literals in the above : 49898
% 2.55/0.87 # Current number of archived formulas : 0
% 2.55/0.87 # Current number of archived clauses : 391
% 2.55/0.87 # Clause-clause subsumption calls (NU) : 58322
% 2.55/0.87 # Rec. Clause-clause subsumption calls : 51333
% 2.55/0.87 # Non-unit clause-clause subsumptions : 1159
% 2.55/0.87 # Unit Clause-clause subsumption calls : 1625
% 2.55/0.87 # Rewrite failures with RHS unbound : 0
% 2.55/0.87 # BW rewrite match attempts : 22
% 2.55/0.87 # BW rewrite match successes : 9
% 2.55/0.87 # Condensation attempts : 0
% 2.55/0.87 # Condensation successes : 0
% 2.55/0.87 # Termbank termtop insertions : 320862
% 2.55/0.87 # Search garbage collected termcells : 9626
% 2.55/0.87
% 2.55/0.87 # -------------------------------------------------
% 2.55/0.87 # User time : 0.361 s
% 2.55/0.87 # System time : 0.018 s
% 2.55/0.87 # Total time : 0.379 s
% 2.55/0.87 # Maximum resident set size: 4476 pages
% 2.55/0.87
% 2.55/0.87 # -------------------------------------------------
% 2.55/0.87 # User time : 0.475 s
% 2.55/0.87 # System time : 0.061 s
% 2.55/0.87 # Total time : 0.536 s
% 2.55/0.87 # Maximum resident set size: 2008 pages
% 2.55/0.87 % E---3.1 exiting
% 2.55/0.87 % E exiting
%------------------------------------------------------------------------------