TSTP Solution File: SEU547^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU547^1 : 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 03:28:06 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 179
% Syntax : Number of formulae : 214 ( 21 unt; 114 typ; 0 def)
% Number of atoms : 760 ( 154 equ; 0 cnn)
% Maximal formula atoms : 209 ( 7 avg)
% Number of connectives : 2689 ( 223 ~; 214 |; 193 &;1592 @)
% ( 101 <=>; 366 =>; 0 <=; 0 <~>)
% Maximal formula depth : 264 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 189 ( 189 >; 0 *; 0 +; 0 <<)
% Number of symbols : 117 ( 114 usr; 72 con; 0-3 aty)
% Number of variables : 654 ( 48 ^ 516 !; 90 ?; 654 :)
% 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_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,
epred1_0: $o ).
thf(decl_98,type,
esk1_2: $i > $i > $i ).
thf(decl_99,type,
esk2_2: $i > $i > $i ).
thf(decl_100,type,
esk3_2: $i > $i > $i ).
thf(decl_101,type,
esk4_1: $i > $i ).
thf(decl_102,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_103,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_104,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_105,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_106,type,
esk9_1: $i > $i ).
thf(decl_107,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_108,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_109,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_110,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_111,type,
esk14_2: $i > $i > $i ).
thf(decl_112,type,
esk15_2: $i > $i > $i ).
thf(decl_113,type,
esk16_1: $i > $i ).
thf(decl_114,type,
esk17_1: $i > $i ).
thf(decl_115,type,
esk18_1: $i > $i ).
thf(decl_116,type,
esk19_2: $i > $i > $i ).
thf(decl_117,type,
esk20_3: $i > $i > $o > $i ).
thf(decl_118,type,
esk21_2: ( $i > $o ) > $i > $i ).
thf(decl_119,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_120,type,
esk23_1: $i > $i ).
thf(decl_121,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_122,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_123,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_124,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_125,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_126,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_127,type,
esk30_2: ( $i > $o ) > $i > $i ).
thf(decl_128,type,
esk31_1: ( $i > $o ) > $i ).
thf(decl_129,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_130,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_131,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_132,type,
esk35_2: ( $i > $o ) > $i > $i ).
thf(decl_133,type,
esk36_1: ( $i > $o ) > $i ).
thf(decl_134,type,
esk37_0: $i ).
thf(decl_135,type,
esk38_0: $i ).
thf(decl_136,type,
esk39_0: $i ).
thf(decl_137,type,
esk40_0: $i ).
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/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
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/sandbox2/benchmark/theBenchmark.p',exuI1) ).
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/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
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/sandbox2/benchmark/theBenchmark.p',exuE1) ).
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/sandbox2/benchmark/theBenchmark.p',replAx) ).
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/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
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/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(inCongP,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
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
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/sandbox2/benchmark/theBenchmark.p',setext) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
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/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionI) ).
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/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_64,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_65,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_66,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_67,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_68,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_69,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_70,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_71,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_72,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_73,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_74,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_75,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X207: $i] :
( ( X1 @ X207 )
& ! [X208: $i] :
( ( X1 @ X208 )
=> ( X207 = X208 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_76,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_77,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X199: $i] :
( ( X1 @ X199 )
& ! [X200: $i] :
( ( X1 @ X200 )
=> ( X199 = X200 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_68,c_0_67]) ).
thf(c_0_78,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X203: $i] :
( ( X1 @ X203 )
& ! [X204: $i] :
( ( X1 @ X204 )
=> ( X203 = X204 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_69,c_0_67]) ).
thf(c_0_79,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X205: $i] :
( ( X1 @ X205 )
& ! [X206: $i] :
( ( X1 @ X206 )
=> ( X205 = X206 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_70,c_0_67]) ).
thf(c_0_80,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_81,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_65]) ).
thf(c_0_82,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_65]) ).
thf(c_0_83,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_84,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X201: $i] :
( ( X1 @ X201 )
& ! [X202: $i] :
( ( X1 @ X202 )
=> ( X201 = X202 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_71,c_0_67]) ).
thf(c_0_85,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_65]) ).
thf(c_0_86,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X197: $i] :
( ( X1 @ X197 )
& ! [X198: $i] :
( ( X1 @ X198 )
=> ( X197 = X198 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_72,c_0_67]) ).
thf(c_0_87,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_88,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_89,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_90,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X195: $i] :
( ( X6 @ X2 @ X195 )
& ! [X196: $i] :
( ( X6 @ X2 @ X196 )
=> ( X195 = X196 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_73,c_0_67]) ).
thf(c_0_91,plain,
( epred1_0
<=> ! [X238: $i] :
? [X239: $i] :
( ! [X240: $i] :
( ( in @ X240 @ X239 )
=> ! [X241: $i] :
( ( in @ X241 @ X240 )
=> ( in @ X241 @ X238 ) ) )
& ! [X242: $i,X243: $i] :
( ( ( in @ X242 @ X238 )
& ( in @ X243 @ X238 ) )
=> ( ! [X244: $i] :
( ( in @ X244 @ X239 )
=> ( ( in @ X242 @ X244 )
<=> ( in @ X243 @ X244 ) ) )
=> ( X242 = X243 ) ) )
& ! [X245: $i,X246: $i] :
( ( ( in @ X245 @ X239 )
& ( in @ X246 @ X239 ) )
=> ( ! [X247: $i] :
( ( in @ X247 @ X245 )
=> ( in @ X247 @ X246 ) )
| ! [X248: $i] :
( ( in @ X248 @ X246 )
=> ( in @ X248 @ X245 ) ) ) )
& ! [X249: $i] :
( ( ! [X250: $i] :
( ( in @ X250 @ X249 )
=> ( in @ X250 @ X238 ) )
& ? [X251: $i] : ( in @ X251 @ X249 ) )
=> ? [X252: $i,X253: $i] :
( ( in @ X252 @ X239 )
& ( in @ X253 @ X249 )
& ~ ? [X254: $i] :
( ( in @ X254 @ X252 )
& ( in @ X254 @ X249 ) )
& ! [X255: $i] :
( ( in @ X255 @ X239 )
=> ( ! [X256: $i] :
( ( in @ X256 @ X255 )
=> ( in @ X256 @ X252 ) )
| ( in @ X253 @ X255 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_92,negated_conjecture,
~ ( ! [X209: $i,X210: $i] :
( ! [X211: $i] :
( ( in @ X211 @ X209 )
<=> ( in @ X211 @ X210 ) )
=> ( X209 = X210 ) )
=> ( ! [X212: $i] :
~ ( in @ X212 @ emptyset )
=> ( ! [X213: $i,X214: $i,X215: $i] :
( ( in @ X215 @ ( setadjoin @ X213 @ X214 ) )
<=> ( ( X215 = X213 )
| ( in @ X215 @ X214 ) ) )
=> ( ! [X216: $i,X217: $i] :
( ( in @ X217 @ ( powerset @ X216 ) )
<=> ! [X218: $i] :
( ( in @ X218 @ X217 )
=> ( in @ X218 @ X216 ) ) )
=> ( ! [X219: $i,X220: $i] :
( ( in @ X220 @ ( setunion @ X219 ) )
<=> ? [X221: $i] :
( ( in @ X220 @ X221 )
& ( in @ X221 @ X219 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X222: $i] :
( ( in @ X222 @ omega )
=> ( in @ ( setadjoin @ X222 @ X222 ) @ omega ) )
=> ( ! [X223: $i] :
( ( ( in @ emptyset @ X223 )
& ! [X224: $i] :
( ( ( in @ X224 @ omega )
& ( in @ X224 @ X223 ) )
=> ( in @ ( setadjoin @ X224 @ X224 ) @ X223 ) ) )
=> ! [X225: $i] :
( ( in @ X225 @ omega )
=> ( in @ X225 @ X223 ) ) )
=> ( ! [X226: $i > $i > $o,X227: $i] :
( ! [X228: $i] :
( ( in @ X228 @ X227 )
=> ? [X229: $i] :
( ( X226 @ X228 @ X229 )
& ! [X230: $i] :
( ( X226 @ X228 @ X230 )
=> ( X229 = X230 ) ) ) )
=> ? [X231: $i] :
! [X232: $i] :
( ( in @ X232 @ X231 )
<=> ? [X233: $i] :
( ( in @ X233 @ X227 )
& ( X226 @ X233 @ X232 ) ) ) )
=> ( ! [X234: $i] :
( ? [X235: $i] : ( in @ X235 @ X234 )
=> ? [X236: $i] :
( ( in @ X236 @ X234 )
& ~ ? [X237: $i] :
( ( in @ X237 @ X236 )
& ( in @ X237 @ X234 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X257: $i,X258: $i > $o,X259: $i] :
( ( in @ X259 @ X257 )
=> ( ( X258 @ X259 )
=> ( in @ X259
@ ( dsetconstr @ X257
@ ^ [Z0: $i] : ( X258 @ Z0 ) ) ) ) )
=> ( ! [X260: $i,X261: $i > $o,X262: $i] :
( ( in @ X262
@ ( dsetconstr @ X260
@ ^ [Z0: $i] : ( X261 @ Z0 ) ) )
=> ( in @ X262 @ X260 ) )
=> ( ! [X263: $i,X264: $i > $o,X265: $i] :
( ( in @ X265
@ ( dsetconstr @ X263
@ ^ [Z0: $i] : ( X264 @ Z0 ) ) )
=> ( X264 @ X265 ) )
=> ( ! [X266: $i > $o] :
( ? [X267: $i] :
( ( X266 @ X267 )
& ! [X268: $i] :
( ( X266 @ X268 )
=> ( X267 = X268 ) ) )
=> ? [X269: $i] :
( ( X266 @ X269 )
& ! [X270: $i] :
( ( X266 @ X270 )
=> ( X269 = X270 ) ) ) )
=> ( ! [X271: $o,X272: $i] :
( ( in @ X272 @ ( prop2set @ X271 ) )
=> X271 )
=> ( ! [X273: $i] :
( ( in @ X273 @ emptyset )
=> ! [X274: $o] : X274 )
=> ( ! [X275: $i] :
~ ( in @ X275 @ emptyset )
=> ( ! [X276: $i] :
~ ( in @ X276 @ emptyset )
=> ( ! [X277: $i > $o] :
( ? [X278: $i] :
( ( X277 @ X278 )
& ! [X279: $i] :
( ( X277 @ X279 )
=> ( X278 = X279 ) ) )
=> ? [X280: $i] : ( X277 @ X280 ) )
=> ( ! [X281: $i,X282: $i] :
( ! [X283: $i] :
( ( in @ X283 @ X281 )
=> ( in @ X283 @ X282 ) )
=> ( ! [X284: $i] :
( ( in @ X284 @ X282 )
=> ( in @ X284 @ X281 ) )
=> ( X281 = X282 ) ) )
=> ( ! [X285: $i] :
( ! [X286: $i] :
~ ( in @ X286 @ X285 )
=> ( X285 = emptyset ) )
=> ( ! [X287: $i] :
( ! [X288: $i] :
~ ( in @ X288 @ X287 )
=> ( X287 = emptyset ) )
=> ( ! [X289: $i,X290: $i > $o,X291: $i] :
( ( in @ X291 @ X289 )
=> ( ( in @ X291
@ ( dsetconstr @ X289
@ ^ [Z0: $i] : ( X290 @ Z0 ) ) )
<=> ( X290 @ X291 ) ) )
=> ( ! [X292: $i] :
( ( X292 != emptyset )
=> ? [X293: $i] : ( in @ X293 @ X292 ) )
=> ( ! [X294: $i,X295: $i > $o,X296: $i] :
( ( in @ X296 @ X294 )
=> ( ( X295 @ X296 )
=> ( ( dsetconstr @ X294
@ ^ [Z0: $i] : ( X295 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X297: $i] :
( ? [X298: $i] : ( in @ X298 @ X297 )
=> ( X297 != emptyset ) )
=> ( ! [X299: $i,X300: $i] : ( in @ X299 @ ( setadjoin @ X299 @ X300 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X301: $i,X302: $i,X303: $i] :
( ( in @ X303 @ X302 )
=> ( in @ X303 @ ( setadjoin @ X301 @ X302 ) ) )
=> ( ! [X304: $i,X305: $i,X306: $i] :
( ( in @ X306 @ ( setadjoin @ X304 @ X305 ) )
=> ! [X307: $o] :
( ( ( X306 = X304 )
=> X307 )
=> ( ( ( in @ X306 @ X305 )
=> X307 )
=> X307 ) ) )
=> ( ! [X308: $i,X309: $i,X310: $i] :
( ( in @ X310 @ ( setadjoin @ X308 @ X309 ) )
=> ( ( X310 = X308 )
| ( in @ X310 @ X309 ) ) )
=> ( ! [X311: $i] :
( ( dsetconstr @ X311
@ ^ [Z0: $i] : $true )
= X311 )
=> ( ! [X312: $i,X313: $i] :
( ! [X314: $i] :
( ( in @ X314 @ X313 )
=> ( in @ X314 @ X312 ) )
=> ( in @ X313 @ ( powerset @ X312 ) ) )
=> ( ! [X315: $i] : ( in @ emptyset @ ( powerset @ X315 ) )
=> ( ! [X316: $i] : ( in @ emptyset @ ( powerset @ X316 ) )
=> ( ! [X317: $i,X318: $i,X319: $i] :
( ( in @ X318 @ ( powerset @ X317 ) )
=> ( ( in @ X319 @ X318 )
=> ( in @ X319 @ X317 ) ) )
=> ( ! [X320: $i,X321: $i,X322: $i] :
( ( in @ X321 @ X322 )
=> ( ( in @ X322 @ X320 )
=> ( in @ X321 @ ( setunion @ X320 ) ) ) )
=> ( ! [X323: $i,X324: $i] :
( ( in @ X324 @ ( setunion @ X323 ) )
=> ! [X325: $o] :
( ! [X326: $i] :
( ( in @ X324 @ X326 )
=> ( ( in @ X326 @ X323 )
=> X325 ) )
=> X325 ) )
=> ( ! [X327: $i,X328: $i] :
( ( in @ X328 @ X327 )
=> ( in @ X328 @ ( powerset @ ( setunion @ X327 ) ) ) )
=> ( ! [X329: $i > $o] :
( ? [X330: $i] :
( ( X329 @ X330 )
& ! [X331: $i] :
( ( X329 @ X331 )
=> ( X330 = X331 ) ) )
=> ? [X332: $i] :
! [X333: $i] :
( ( X329 @ X333 )
<=> ( X333 = X332 ) ) )
=> ( ! [X334: $i] :
( ( X334 != emptyset )
=> ? [X335: $i] : ( in @ X335 @ X334 ) )
=> ( ! [X336: $i,X337: $i] :
( ( in @ X336 @ ( setadjoin @ X337 @ emptyset ) )
=> ( X336 = X337 ) )
=> ( ! [X338: $i,X339: $i] :
( ( X338 != X339 )
=> ~ ( in @ X339 @ ( setadjoin @ X338 @ emptyset ) ) )
=> ( ! [X340: $i,X341: $i] :
( ( X340 = X341 )
=> ( in @ X340 @ ( setadjoin @ X341 @ emptyset ) ) )
=> ( ! [X342: $i,X343: $i] :
( ( in @ X342 @ ( setadjoin @ X343 @ emptyset ) )
=> ( in @ X343 @ ( setadjoin @ X342 @ emptyset ) ) )
=> ( ! [X344: $i,X345: $i,X346: $i] :
( ( in @ X346 @ ( setadjoin @ X344 @ ( setadjoin @ X345 @ emptyset ) ) )
=> ( ( X346 = X344 )
| ( X346 = X345 ) ) )
=> ( ! [X347: $i,X348: $i] : ( in @ X347 @ ( setadjoin @ X347 @ ( setadjoin @ X348 @ emptyset ) ) )
=> ( ! [X349: $i,X350: $i] : ( in @ X350 @ ( setadjoin @ X349 @ ( setadjoin @ X350 @ emptyset ) ) )
=> ( ! [X351: $i,X352: $i > $o] :
( ? [X353: $i] :
( ( in @ X353 @ X351 )
& ( X352 @ X353 ) )
=> ( ( dsetconstr @ X351
@ ^ [Z0: $i] : ( X352 @ Z0 ) )
!= emptyset ) )
=> ( ! [X354: $i > $o,X355: $i] :
( ( in @ X355 @ emptyset )
=> ( X354 @ X355 ) )
=> ( ! [X356: $i,X357: $i > $o] :
( ~ ! [X358: $i] :
( ( in @ X358 @ X356 )
=> ( X357 @ X358 ) )
=> ? [X359: $i] :
( ( in @ X359 @ X356 )
& ~ ( X357 @ X359 ) ) )
=> ( ! [X360: $i,X361: $i > $o] :
( ! [X362: $i] :
( ( in @ X362 @ X360 )
=> ~ ( X361 @ X362 ) )
=> ~ ? [X363: $i] :
( ( in @ X363 @ X360 )
& ( X361 @ X363 ) ) )
=> ( ! [X364: $i,X365: $i > $o] :
( ~ ? [X366: $i] :
( ( in @ X366 @ X364 )
& ( X365 @ X366 ) )
=> ! [X367: $i] :
( ( in @ X367 @ X364 )
=> ~ ( X365 @ X367 ) ) )
=> ( ! [X368: $i,X369: $i > $o] :
( ? [X370: $i] :
( ( in @ X370 @ X368 )
& ~ ( X369 @ X370 ) )
=> ~ ! [X371: $i] :
( ( in @ X371 @ X368 )
=> ( X369 @ X371 ) ) )
=> ( ! [X372: $o] :
( X372
=> ( in @ emptyset @ ( prop2set @ X372 ) ) )
=> ( prop2set2propI
=> ( ! [X373: $i,X374: $i > $o] :
( ~ ? [X375: $i] :
( ( in @ X375 @ X373 )
& ( X374 @ X375 ) )
=> ! [X376: $i] :
( ( in @ X376 @ X373 )
=> ~ ( X374 @ X376 ) ) )
=> ( ! [X377: $i,X378: $i > $o] :
( ~ ! [X379: $i] :
( ( in @ X379 @ X377 )
=> ( X378 @ X379 ) )
=> ? [X380: $i] :
( ( in @ X380 @ X377 )
& ~ ( X378 @ X380 ) ) )
=> ( ! [X381: $i > $o] :
( ? [X382: $i] :
( ( X381 @ X382 )
& ! [X383: $i] :
( ( X381 @ X383 )
=> ( X382 = X383 ) ) )
=> ? [X384: $i] :
( ( X381 @ X384 )
& ! [X385: $i] :
( ( X381 @ X385 )
=> ( X384 = X385 ) ) ) )
=> ( ! [X386: $i > $o] :
( ? [X387: $i] : ( X386 @ X387 )
=> ( ! [X388: $i,X389: $i] :
( ( X386 @ X388 )
=> ( ( X386 @ X389 )
=> ( X388 = X389 ) ) )
=> ? [X390: $i] :
( ( X386 @ X390 )
& ! [X391: $i] :
( ( X386 @ X391 )
=> ( X390 = X391 ) ) ) ) )
=> ( ! [X392: $i > $o] :
( ? [X393: $i] :
! [X394: $i] :
( ( X392 @ X394 )
<=> ( X394 = X393 ) )
=> ? [X395: $i] :
( ( X392 @ X395 )
& ! [X396: $i] :
( ( X392 @ X396 )
=> ( X395 = X396 ) ) ) )
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[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)],[inCongP]),c_0_74]),c_0_75]),upairsetE]),emptysetE]),upairsetIL]),upairsetIR]),c_0_76]),emptysetimpfalse]),vacuousDall]),quantDeMorgan1]),notinemptyset]),quantDeMorgan2]),quantDeMorgan3]),c_0_77]),quantDeMorgan4]),prop2setI]),setext]),notdexE]),notdallE]),emptyI]),c_0_78]),c_0_79]),noeltsimpempty]),c_0_80]),c_0_81]),notinsingleton]),c_0_82]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_83]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_84]),c_0_85]),uniqinunit]),eqinunit]),singletonsswitch]),prop2setE]),c_0_86]),c_0_87]),c_0_88]),c_0_89]),wellorderingAx]),foundationAx]),c_0_90]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_91]) ).
thf(c_0_93,negated_conjecture,
! [X397: $i,X398: $i,X400: $i,X401: $i,X402: $i,X403: $i,X404: $i,X405: $i,X406: $i,X407: $i,X408: $i,X410: $i,X411: $i,X413: $i,X414: $i,X415: $i,X416: $i,X417: $i,X419: $i,X420: $i > $i > $o,X421: $i,X423: $i,X426: $i,X428: $i,X429: $i,X430: $i,X431: $i,X433: $i,X434: $i,X435: $i > $o,X436: $i,X437: $i,X438: $i > $o,X439: $i,X440: $i,X441: $i > $o,X442: $i,X443: $i > $o,X444: $i,X447: $i,X448: $o,X449: $i,X450: $i,X451: $o,X452: $i,X453: $i,X454: $i > $o,X455: $i,X458: $i,X459: $i,X462: $i,X464: $i,X466: $i,X467: $i > $o,X468: $i,X469: $i,X471: $i,X472: $i > $o,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i,X478: $i,X479: $i,X480: $i,X481: $i,X482: $i,X483: $i,X484: $o,X485: $i,X486: $i,X487: $i,X488: $i,X489: $i,X490: $i,X492: $i,X493: $i,X494: $i,X495: $i,X496: $i,X497: $i,X498: $i,X499: $i,X500: $i,X501: $i,X502: $o,X504: $i,X505: $i,X506: $i > $o,X507: $i,X510: $i,X511: $i,X512: $i,X514: $i,X515: $i,X516: $i,X517: $i,X518: $i,X519: $i,X520: $i,X521: $i,X522: $i,X523: $i,X524: $i,X525: $i,X526: $i,X527: $i,X528: $i,X529: $i,X530: $i > $o,X531: $i,X532: $i > $o,X533: $i,X534: $i,X535: $i > $o,X536: $i,X538: $i,X539: $i > $o,X541: $i,X542: $i,X543: $i > $o,X545: $i,X546: $i,X547: $i > $o,X548: $i,X550: $o,X551: $i,X552: $i > $o,X554: $i,X555: $i,X556: $i > $o,X557: $i,X559: $i > $o,X560: $i,X563: $i,X564: $i > $o,X565: $i,X569: $i,X570: $i > $o,X571: $i,X574: $i] :
( ( ~ ( in @ ( esk1_2 @ X397 @ X398 ) @ X397 )
| ~ ( in @ ( esk1_2 @ X397 @ X398 ) @ X398 )
| ( X397 = X398 ) )
& ( ( in @ ( esk1_2 @ X397 @ X398 ) @ X397 )
| ( in @ ( esk1_2 @ X397 @ X398 ) @ X398 )
| ( X397 = X398 ) )
& ~ ( in @ X400 @ emptyset )
& ( ~ ( in @ X403 @ ( setadjoin @ X401 @ X402 ) )
| ( X403 = X401 )
| ( in @ X403 @ X402 ) )
& ( ( X403 != X401 )
| ( in @ X403 @ ( setadjoin @ X401 @ X402 ) ) )
& ( ~ ( in @ X403 @ X402 )
| ( in @ X403 @ ( setadjoin @ X401 @ X402 ) ) )
& ( ~ ( in @ X405 @ ( powerset @ X404 ) )
| ~ ( in @ X406 @ X405 )
| ( in @ X406 @ X404 ) )
& ( ( in @ ( esk2_2 @ X407 @ X408 ) @ X408 )
| ( in @ X408 @ ( powerset @ X407 ) ) )
& ( ~ ( in @ ( esk2_2 @ X407 @ X408 ) @ X407 )
| ( in @ X408 @ ( powerset @ X407 ) ) )
& ( ( in @ X411 @ ( esk3_2 @ X410 @ X411 ) )
| ~ ( in @ X411 @ ( setunion @ X410 ) ) )
& ( ( in @ ( esk3_2 @ X410 @ X411 ) @ X410 )
| ~ ( in @ X411 @ ( setunion @ X410 ) ) )
& ( ~ ( in @ X414 @ X415 )
| ~ ( in @ X415 @ X413 )
| ( in @ X414 @ ( setunion @ X413 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X416 @ omega )
| ( in @ ( setadjoin @ X416 @ X416 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X417 ) @ omega )
| ~ ( in @ emptyset @ X417 )
| ~ ( in @ X419 @ omega )
| ( in @ X419 @ X417 ) )
& ( ( in @ ( esk4_1 @ X417 ) @ X417 )
| ~ ( in @ emptyset @ X417 )
| ~ ( in @ X419 @ omega )
| ( in @ X419 @ X417 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X417 ) @ ( esk4_1 @ X417 ) ) @ X417 )
| ~ ( in @ emptyset @ X417 )
| ~ ( in @ X419 @ omega )
| ( in @ X419 @ X417 ) )
& ( ( in @ ( esk8_3 @ X420 @ X421 @ X426 ) @ X421 )
| ~ ( in @ X426 @ ( esk7_2 @ X420 @ X421 ) )
| ( in @ ( esk5_2 @ X420 @ X421 ) @ X421 ) )
& ( ( X420 @ ( esk8_3 @ X420 @ X421 @ X426 ) @ X426 )
| ~ ( in @ X426 @ ( esk7_2 @ X420 @ X421 ) )
| ( in @ ( esk5_2 @ X420 @ X421 ) @ X421 ) )
& ( ~ ( in @ X429 @ X421 )
| ~ ( X420 @ X429 @ X428 )
| ( in @ X428 @ ( esk7_2 @ X420 @ X421 ) )
| ( in @ ( esk5_2 @ X420 @ X421 ) @ X421 ) )
& ( ( in @ ( esk8_3 @ X420 @ X421 @ X426 ) @ X421 )
| ~ ( in @ X426 @ ( esk7_2 @ X420 @ X421 ) )
| ( X420 @ ( esk5_2 @ X420 @ X421 ) @ ( esk6_3 @ X420 @ X421 @ X423 ) )
| ~ ( X420 @ ( esk5_2 @ X420 @ X421 ) @ X423 ) )
& ( ( X420 @ ( esk8_3 @ X420 @ X421 @ X426 ) @ X426 )
| ~ ( in @ X426 @ ( esk7_2 @ X420 @ X421 ) )
| ( X420 @ ( esk5_2 @ X420 @ X421 ) @ ( esk6_3 @ X420 @ X421 @ X423 ) )
| ~ ( X420 @ ( esk5_2 @ X420 @ X421 ) @ X423 ) )
& ( ~ ( in @ X429 @ X421 )
| ~ ( X420 @ X429 @ X428 )
| ( in @ X428 @ ( esk7_2 @ X420 @ X421 ) )
| ( X420 @ ( esk5_2 @ X420 @ X421 ) @ ( esk6_3 @ X420 @ X421 @ X423 ) )
| ~ ( X420 @ ( esk5_2 @ X420 @ X421 ) @ X423 ) )
& ( ( in @ ( esk8_3 @ X420 @ X421 @ X426 ) @ X421 )
| ~ ( in @ X426 @ ( esk7_2 @ X420 @ X421 ) )
| ( X423
!= ( esk6_3 @ X420 @ X421 @ X423 ) )
| ~ ( X420 @ ( esk5_2 @ X420 @ X421 ) @ X423 ) )
& ( ( X420 @ ( esk8_3 @ X420 @ X421 @ X426 ) @ X426 )
| ~ ( in @ X426 @ ( esk7_2 @ X420 @ X421 ) )
| ( X423
!= ( esk6_3 @ X420 @ X421 @ X423 ) )
| ~ ( X420 @ ( esk5_2 @ X420 @ X421 ) @ X423 ) )
& ( ~ ( in @ X429 @ X421 )
| ~ ( X420 @ X429 @ X428 )
| ( in @ X428 @ ( esk7_2 @ X420 @ X421 ) )
| ( X423
!= ( esk6_3 @ X420 @ X421 @ X423 ) )
| ~ ( X420 @ ( esk5_2 @ X420 @ X421 ) @ X423 ) )
& ( ( in @ ( esk9_1 @ X430 ) @ X430 )
| ~ ( in @ X431 @ X430 ) )
& ( ~ ( in @ X433 @ ( esk9_1 @ X430 ) )
| ~ ( in @ X433 @ X430 )
| ~ ( in @ X431 @ X430 ) )
& epred1_0
& descrp
& ( ~ ( in @ X436 @ X434 )
| ~ ( X435 @ X436 )
| ( in @ X436
@ ( dsetconstr @ X434
@ ^ [Z0: $i] : ( X435 @ Z0 ) ) ) )
& ( ~ ( in @ X439
@ ( dsetconstr @ X437
@ ^ [Z0: $i] : ( X438 @ Z0 ) ) )
| ( in @ X439 @ X437 ) )
& ( ~ ( in @ X442
@ ( dsetconstr @ X440
@ ^ [Z0: $i] : ( X441 @ Z0 ) ) )
| ( X441 @ X442 ) )
& ( ( X443 @ ( esk11_1 @ X443 ) )
| ( X443 @ ( esk10_2 @ X443 @ X444 ) )
| ~ ( X443 @ X444 ) )
& ( ~ ( X443 @ X447 )
| ( ( esk11_1 @ X443 )
= X447 )
| ( X443 @ ( esk10_2 @ X443 @ X444 ) )
| ~ ( X443 @ X444 ) )
& ( ( X443 @ ( esk11_1 @ X443 ) )
| ( X444
!= ( esk10_2 @ X443 @ X444 ) )
| ~ ( X443 @ X444 ) )
& ( ~ ( X443 @ X447 )
| ( ( esk11_1 @ X443 )
= X447 )
| ( X444
!= ( esk10_2 @ X443 @ X444 ) )
| ~ ( X443 @ X444 ) )
& ( ~ ( in @ X449 @ ( prop2set @ X448 ) )
| X448 )
& ( ~ ( in @ X450 @ emptyset )
| X451 )
& ~ ( in @ X452 @ emptyset )
& ~ ( in @ X453 @ emptyset )
& ( ( X454 @ ( esk12_2 @ X454 @ X455 ) )
| ~ ( X454 @ X455 )
| ( X454 @ ( esk13_1 @ X454 ) ) )
& ( ( X455
!= ( esk12_2 @ X454 @ X455 ) )
| ~ ( X454 @ X455 )
| ( X454 @ ( esk13_1 @ X454 ) ) )
& ( ( in @ ( esk15_2 @ X458 @ X459 ) @ X459 )
| ( X458 = X459 )
| ( in @ ( esk14_2 @ X458 @ X459 ) @ X458 ) )
& ( ~ ( in @ ( esk15_2 @ X458 @ X459 ) @ X458 )
| ( X458 = X459 )
| ( in @ ( esk14_2 @ X458 @ X459 ) @ X458 ) )
& ( ( in @ ( esk15_2 @ X458 @ X459 ) @ X459 )
| ( X458 = X459 )
| ~ ( in @ ( esk14_2 @ X458 @ X459 ) @ X459 ) )
& ( ~ ( in @ ( esk15_2 @ X458 @ X459 ) @ X458 )
| ( X458 = X459 )
| ~ ( in @ ( esk14_2 @ X458 @ X459 ) @ X459 ) )
& ( ( in @ ( esk16_1 @ X462 ) @ X462 )
| ( X462 = emptyset ) )
& ( ( in @ ( esk17_1 @ X464 ) @ X464 )
| ( X464 = emptyset ) )
& ( ~ ( in @ X468
@ ( dsetconstr @ X466
@ ^ [Z0: $i] : ( X467 @ Z0 ) ) )
| ( X467 @ X468 )
| ~ ( in @ X468 @ X466 ) )
& ( ~ ( X467 @ X468 )
| ( in @ X468
@ ( dsetconstr @ X466
@ ^ [Z0: $i] : ( X467 @ Z0 ) ) )
| ~ ( in @ X468 @ X466 ) )
& ( ( X469 = emptyset )
| ( in @ ( esk18_1 @ X469 ) @ X469 ) )
& ( ~ ( in @ X473 @ X471 )
| ~ ( X472 @ X473 )
| ( ( dsetconstr @ X471
@ ^ [Z0: $i] : ( X472 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X475 @ X474 )
| ( X474 != emptyset ) )
& ( in @ X476 @ ( setadjoin @ X476 @ X477 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X480 @ X479 )
| ( in @ X480 @ ( setadjoin @ X478 @ X479 ) ) )
& ( ( in @ X483 @ X482 )
| X484
| ( X483 = X481 )
| ~ ( in @ X483 @ ( setadjoin @ X481 @ X482 ) ) )
& ( ~ X484
| X484
| ( X483 = X481 )
| ~ ( in @ X483 @ ( setadjoin @ X481 @ X482 ) ) )
& ( ( in @ X483 @ X482 )
| X484
| ~ X484
| ~ ( in @ X483 @ ( setadjoin @ X481 @ X482 ) ) )
& ( ~ X484
| X484
| ~ X484
| ~ ( in @ X483 @ ( setadjoin @ X481 @ X482 ) ) )
& ( ~ ( in @ X487 @ ( setadjoin @ X485 @ X486 ) )
| ( X487 = X485 )
| ( in @ X487 @ X486 ) )
& ( ( dsetconstr @ X488
@ ^ [Z0: $i] : $true )
= X488 )
& ( ( in @ ( esk19_2 @ X489 @ X490 ) @ X490 )
| ( in @ X490 @ ( powerset @ X489 ) ) )
& ( ~ ( in @ ( esk19_2 @ X489 @ X490 ) @ X489 )
| ( in @ X490 @ ( powerset @ X489 ) ) )
& ( in @ emptyset @ ( powerset @ X492 ) )
& ( in @ emptyset @ ( powerset @ X493 ) )
& ( ~ ( in @ X495 @ ( powerset @ X494 ) )
| ~ ( in @ X496 @ X495 )
| ( in @ X496 @ X494 ) )
& ( ~ ( in @ X498 @ X499 )
| ~ ( in @ X499 @ X497 )
| ( in @ X498 @ ( setunion @ X497 ) ) )
& ( ( in @ X501 @ ( esk20_3 @ X500 @ X501 @ X502 ) )
| X502
| ~ ( in @ X501 @ ( setunion @ X500 ) ) )
& ( ( in @ ( esk20_3 @ X500 @ X501 @ X502 ) @ X500 )
| X502
| ~ ( in @ X501 @ ( setunion @ X500 ) ) )
& ( ~ X502
| X502
| ~ ( in @ X501 @ ( setunion @ X500 ) ) )
& ( ~ ( in @ X505 @ X504 )
| ( in @ X505 @ ( powerset @ ( setunion @ X504 ) ) ) )
& ( ~ ( X506 @ X510 )
| ( X510
= ( esk22_1 @ X506 ) )
| ( X506 @ ( esk21_2 @ X506 @ X507 ) )
| ~ ( X506 @ X507 ) )
& ( ( X511
!= ( esk22_1 @ X506 ) )
| ( X506 @ X511 )
| ( X506 @ ( esk21_2 @ X506 @ X507 ) )
| ~ ( X506 @ X507 ) )
& ( ~ ( X506 @ X510 )
| ( X510
= ( esk22_1 @ X506 ) )
| ( X507
!= ( esk21_2 @ X506 @ X507 ) )
| ~ ( X506 @ X507 ) )
& ( ( X511
!= ( esk22_1 @ X506 ) )
| ( X506 @ X511 )
| ( X507
!= ( esk21_2 @ X506 @ X507 ) )
| ~ ( X506 @ X507 ) )
& ( ( X512 = emptyset )
| ( in @ ( esk23_1 @ X512 ) @ X512 ) )
& ( ~ ( in @ X514 @ ( setadjoin @ X515 @ emptyset ) )
| ( X514 = X515 ) )
& ( ( X516 = X517 )
| ~ ( in @ X517 @ ( setadjoin @ X516 @ emptyset ) ) )
& ( ( X518 != X519 )
| ( in @ X518 @ ( setadjoin @ X519 @ emptyset ) ) )
& ( ~ ( in @ X520 @ ( setadjoin @ X521 @ emptyset ) )
| ( in @ X521 @ ( setadjoin @ X520 @ emptyset ) ) )
& ( ~ ( in @ X524 @ ( setadjoin @ X522 @ ( setadjoin @ X523 @ emptyset ) ) )
| ( X524 = X522 )
| ( X524 = X523 ) )
& ( in @ X525 @ ( setadjoin @ X525 @ ( setadjoin @ X526 @ emptyset ) ) )
& ( in @ X528 @ ( setadjoin @ X527 @ ( setadjoin @ X528 @ emptyset ) ) )
& ( ~ ( in @ X531 @ X529 )
| ~ ( X530 @ X531 )
| ( ( dsetconstr @ X529
@ ^ [Z0: $i] : ( X530 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X533 @ emptyset )
| ( X532 @ X533 ) )
& ( ( in @ ( esk24_2 @ X534 @ X535 ) @ X534 )
| ~ ( in @ X536 @ X534 )
| ( X535 @ X536 ) )
& ( ~ ( X535 @ ( esk24_2 @ X534 @ X535 ) )
| ~ ( in @ X536 @ X534 )
| ( X535 @ X536 ) )
& ( ( in @ ( esk25_2 @ X538 @ X539 ) @ X538 )
| ~ ( in @ X541 @ X538 )
| ~ ( X539 @ X541 ) )
& ( ( X539 @ ( esk25_2 @ X538 @ X539 ) )
| ~ ( in @ X541 @ X538 )
| ~ ( X539 @ X541 ) )
& ( ( in @ ( esk26_2 @ X542 @ X543 ) @ X542 )
| ~ ( in @ X545 @ X542 )
| ~ ( X543 @ X545 ) )
& ( ( X543 @ ( esk26_2 @ X542 @ X543 ) )
| ~ ( in @ X545 @ X542 )
| ~ ( X543 @ X545 ) )
& ( ( in @ ( esk27_2 @ X546 @ X547 ) @ X546 )
| ~ ( in @ X548 @ X546 )
| ( X547 @ X548 ) )
& ( ~ ( X547 @ ( esk27_2 @ X546 @ X547 ) )
| ~ ( in @ X548 @ X546 )
| ( X547 @ X548 ) )
& ( ~ X550
| ( in @ emptyset @ ( prop2set @ X550 ) ) )
& prop2set2propI
& ( ( in @ ( esk28_2 @ X551 @ X552 ) @ X551 )
| ~ ( in @ X554 @ X551 )
| ~ ( X552 @ X554 ) )
& ( ( X552 @ ( esk28_2 @ X551 @ X552 ) )
| ~ ( in @ X554 @ X551 )
| ~ ( X552 @ X554 ) )
& ( ( in @ ( esk29_2 @ X555 @ X556 ) @ X555 )
| ~ ( in @ X557 @ X555 )
| ( X556 @ X557 ) )
& ( ~ ( X556 @ ( esk29_2 @ X555 @ X556 ) )
| ~ ( in @ X557 @ X555 )
| ( X556 @ X557 ) )
& ( ( X559 @ ( esk31_1 @ X559 ) )
| ( X559 @ ( esk30_2 @ X559 @ X560 ) )
| ~ ( X559 @ X560 ) )
& ( ~ ( X559 @ X563 )
| ( ( esk31_1 @ X559 )
= X563 )
| ( X559 @ ( esk30_2 @ X559 @ X560 ) )
| ~ ( X559 @ X560 ) )
& ( ( X559 @ ( esk31_1 @ X559 ) )
| ( X560
!= ( esk30_2 @ X559 @ X560 ) )
| ~ ( X559 @ X560 ) )
& ( ~ ( X559 @ X563 )
| ( ( esk31_1 @ X559 )
= X563 )
| ( X560
!= ( esk30_2 @ X559 @ X560 ) )
| ~ ( X559 @ X560 ) )
& ( ( X564 @ ( esk34_1 @ X564 ) )
| ( X564 @ ( esk32_1 @ X564 ) )
| ~ ( X564 @ X565 ) )
& ( ~ ( X564 @ X569 )
| ( ( esk34_1 @ X564 )
= X569 )
| ( X564 @ ( esk32_1 @ X564 ) )
| ~ ( X564 @ X565 ) )
& ( ( X564 @ ( esk34_1 @ X564 ) )
| ( X564 @ ( esk33_1 @ X564 ) )
| ~ ( X564 @ X565 ) )
& ( ~ ( X564 @ X569 )
| ( ( esk34_1 @ X564 )
= X569 )
| ( X564 @ ( esk33_1 @ X564 ) )
| ~ ( X564 @ X565 ) )
& ( ( X564 @ ( esk34_1 @ X564 ) )
| ( ( esk32_1 @ X564 )
!= ( esk33_1 @ X564 ) )
| ~ ( X564 @ X565 ) )
& ( ~ ( X564 @ X569 )
| ( ( esk34_1 @ X564 )
= X569 )
| ( ( esk32_1 @ X564 )
!= ( esk33_1 @ X564 ) )
| ~ ( X564 @ X565 ) )
& ( ( X570 @ ( esk36_1 @ X570 ) )
| ~ ( X570 @ ( esk35_2 @ X570 @ X571 ) )
| ( ( esk35_2 @ X570 @ X571 )
!= X571 ) )
& ( ~ ( X570 @ X574 )
| ( ( esk36_1 @ X570 )
= X574 )
| ~ ( X570 @ ( esk35_2 @ X570 @ X571 ) )
| ( ( esk35_2 @ X570 @ X571 )
!= X571 ) )
& ( ( X570 @ ( esk36_1 @ X570 ) )
| ( X570 @ ( esk35_2 @ X570 @ X571 ) )
| ( ( esk35_2 @ X570 @ X571 )
= X571 ) )
& ( ~ ( X570 @ X574 )
| ( ( esk36_1 @ X570 )
= X574 )
| ( X570 @ ( esk35_2 @ X570 @ X571 ) )
| ( ( esk35_2 @ X570 @ X571 )
= X571 ) )
& ( esk37_0 = esk38_0 )
& ( esk39_0 = esk40_0 )
& ( in @ esk39_0 @ esk37_0 )
& ~ ( in @ esk40_0 @ esk38_0 ) ),
inference(distribute,[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_92])])])])])]) ).
thf(c_0_94,negated_conjecture,
~ ( in @ esk40_0 @ esk38_0 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_95,negated_conjecture,
esk37_0 = esk38_0,
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_96,negated_conjecture,
in @ esk39_0 @ esk37_0,
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_97,negated_conjecture,
esk39_0 = esk40_0,
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_98,negated_conjecture,
~ ( in @ esk40_0 @ esk37_0 ),
inference(rw,[status(thm)],[c_0_94,c_0_95]) ).
thf(c_0_99,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU547^1 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 16:13:38 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 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
% 0.21/0.51 # Version: 3.1.0-ho
% 0.21/0.51 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51 # new_bool_2 with pid 18382 completed with status 0
% 0.21/0.51 # Result found by new_bool_2
% 0.21/0.51 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51 # Search class: HGHSM-FFMM31-SHFMMSBN
% 0.21/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting new_ho_10 with 181s (1) cores
% 0.21/0.51 # new_ho_10 with pid 18384 completed with status 0
% 0.21/0.51 # Result found by new_ho_10
% 0.21/0.51 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51 # Search class: HGHSM-FFMM31-SHFMMSBN
% 0.21/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting new_ho_10 with 181s (1) cores
% 0.21/0.51 # Preprocessing time : 0.002 s
% 0.21/0.51 # Presaturation interreduction done
% 0.21/0.51
% 0.21/0.51 # Proof found!
% 0.21/0.51 # SZS status Theorem
% 0.21/0.51 # SZS output start CNFRefutation
% See solution above
% 0.21/0.51 # Parsed axioms : 141
% 0.21/0.51 # Removed by relevancy pruning/SinE : 77
% 0.21/0.51 # Initial clauses : 132
% 0.21/0.51 # Removed in clause preprocessing : 4
% 0.21/0.51 # Initial clauses in saturation : 128
% 0.21/0.51 # Processed clauses : 8
% 0.21/0.51 # ...of these trivial : 0
% 0.21/0.51 # ...subsumed : 0
% 0.21/0.51 # ...remaining for further processing : 7
% 0.21/0.51 # Other redundant clauses eliminated : 0
% 0.21/0.51 # Clauses deleted for lack of memory : 0
% 0.21/0.51 # Backward-subsumed : 0
% 0.21/0.51 # Backward-rewritten : 0
% 0.21/0.51 # Generated clauses : 0
% 0.21/0.51 # ...of the previous two non-redundant : 0
% 0.21/0.51 # ...aggressively subsumed : 0
% 0.21/0.51 # Contextual simplify-reflections : 0
% 0.21/0.51 # Paramodulations : 0
% 0.21/0.51 # Factorizations : 0
% 0.21/0.51 # NegExts : 0
% 0.21/0.51 # Equation resolutions : 0
% 0.21/0.51 # Disequality decompositions : 0
% 0.21/0.51 # Total rewrite steps : 2
% 0.21/0.51 # ...of those cached : 0
% 0.21/0.51 # Propositional unsat checks : 0
% 0.21/0.51 # Propositional check models : 0
% 0.21/0.51 # Propositional check unsatisfiable : 0
% 0.21/0.51 # Propositional clauses : 0
% 0.21/0.51 # Propositional clauses after purity: 0
% 0.21/0.51 # Propositional unsat core size : 0
% 0.21/0.51 # Propositional preprocessing time : 0.000
% 0.21/0.51 # Propositional encoding time : 0.000
% 0.21/0.51 # Propositional solver time : 0.000
% 0.21/0.51 # Success case prop preproc time : 0.000
% 0.21/0.51 # Success case prop encoding time : 0.000
% 0.21/0.51 # Success case prop solver time : 0.000
% 0.21/0.51 # Current number of processed clauses : 7
% 0.21/0.51 # Positive orientable unit clauses : 6
% 0.21/0.51 # Positive unorientable unit clauses: 0
% 0.21/0.51 # Negative unit clauses : 1
% 0.21/0.51 # Non-unit-clauses : 0
% 0.21/0.51 # Current number of unprocessed clauses: 120
% 0.21/0.51 # ...number of literals in the above : 362
% 0.21/0.51 # Current number of archived formulas : 0
% 0.21/0.51 # Current number of archived clauses : 0
% 0.21/0.51 # Clause-clause subsumption calls (NU) : 0
% 0.21/0.51 # Rec. Clause-clause subsumption calls : 0
% 0.21/0.51 # Non-unit clause-clause subsumptions : 0
% 0.21/0.51 # Unit Clause-clause subsumption calls : 0
% 0.21/0.51 # Rewrite failures with RHS unbound : 0
% 0.21/0.51 # BW rewrite match attempts : 0
% 0.21/0.51 # BW rewrite match successes : 0
% 0.21/0.51 # Condensation attempts : 8
% 0.21/0.51 # Condensation successes : 0
% 0.21/0.51 # Termbank termtop insertions : 14322
% 0.21/0.51 # Search garbage collected termcells : 5681
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.011 s
% 0.21/0.51 # System time : 0.004 s
% 0.21/0.51 # Total time : 0.016 s
% 0.21/0.51 # Maximum resident set size: 3668 pages
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.016 s
% 0.21/0.51 # System time : 0.006 s
% 0.21/0.51 # Total time : 0.022 s
% 0.21/0.51 # Maximum resident set size: 1916 pages
% 0.21/0.51 % E---3.1 exiting
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------