TSTP Solution File: SEU540^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU540^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 03:28:03 EDT 2024
% Result : Theorem 0.37s 0.53s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 155
% Syntax : Number of formulae : 187 ( 18 unt; 95 typ; 0 def)
% Number of atoms : 683 ( 113 equ; 0 cnn)
% Maximal formula atoms : 185 ( 7 avg)
% Number of connectives : 2352 ( 184 ~; 174 |; 157 &;1444 @)
% ( 88 <=>; 305 =>; 0 <=; 0 <~>)
% Maximal formula depth : 228 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 147 ( 147 >; 0 *; 0 +; 0 <<)
% Number of symbols : 98 ( 95 usr; 62 con; 0-3 aty)
% Number of variables : 576 ( 52 ^ 456 !; 68 ?; 576 :)
% 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,
epred1_0: $o ).
thf(decl_90,type,
esk1_2: $i > $i > $i ).
thf(decl_91,type,
esk2_2: $i > $i > $i ).
thf(decl_92,type,
esk3_2: $i > $i > $i ).
thf(decl_93,type,
esk4_1: $i > $i ).
thf(decl_94,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_95,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_96,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_97,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_98,type,
esk9_1: $i > $i ).
thf(decl_99,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_100,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_101,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_102,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_103,type,
esk14_2: $i > $i > $i ).
thf(decl_104,type,
esk15_2: $i > $i > $i ).
thf(decl_105,type,
esk16_1: $i > $i ).
thf(decl_106,type,
esk17_1: $i > $i ).
thf(decl_107,type,
esk18_1: $i > $i ).
thf(decl_108,type,
esk19_2: $i > $i > $i ).
thf(decl_109,type,
esk20_3: $i > $i > $o > $i ).
thf(decl_110,type,
esk21_2: ( $i > $o ) > $i > $i ).
thf(decl_111,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_112,type,
esk23_1: $i > $i ).
thf(decl_113,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_114,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_115,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_116,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_117,type,
epred2_0: $o ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
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(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(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(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(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
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(prop2setI,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
=> ! [X16: $o] :
( X16
=> ( in @ emptyset @ ( prop2set @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X13: $o] :
( ( ( X3 = X2 )
=> X13 )
=> ( ( ( in @ X3 @ X4 )
=> X13 )
=> X13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X15: $i] :
( ( in @ X15 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X15 = X2 )
| ( X15 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
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(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
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(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(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(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 ) )
=> ! [X14: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X14 ) )
=> X14 ) ) ),
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(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
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(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(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
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_59,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_60,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_61,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_62,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_63,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_64,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_65,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_66,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_67,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_68,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_69,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_59]) ).
thf(c_0_70,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_60]) ).
thf(c_0_71,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_61,c_0_59]) ).
thf(c_0_72,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_59]) ).
thf(c_0_73,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_74,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X179: $i] :
( ( X1 @ X179 )
& ! [X180: $i] :
( ( X1 @ X180 )
=> ( X179 = X180 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_75,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_59]) ).
thf(c_0_76,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X177: $i] :
( ( X1 @ X177 )
& ! [X178: $i] :
( ( X1 @ X178 )
=> ( X177 = X178 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_64,c_0_63]) ).
thf(c_0_77,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X175: $i] :
( ( X1 @ X175 )
& ! [X176: $i] :
( ( X1 @ X176 )
=> ( X175 = X176 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_65,c_0_63]) ).
thf(c_0_78,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_79,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_80,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_81,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X173: $i] :
( ( X6 @ X2 @ X173 )
& ! [X174: $i] :
( ( X6 @ X2 @ X174 )
=> ( X173 = X174 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_66,c_0_63]) ).
thf(c_0_82,plain,
( epred1_0
<=> ! [X210: $i] :
? [X211: $i] :
( ! [X212: $i] :
( ( in @ X212 @ X211 )
=> ! [X213: $i] :
( ( in @ X213 @ X212 )
=> ( in @ X213 @ X210 ) ) )
& ! [X214: $i,X215: $i] :
( ( ( in @ X214 @ X210 )
& ( in @ X215 @ X210 ) )
=> ( ! [X216: $i] :
( ( in @ X216 @ X211 )
=> ( ( in @ X214 @ X216 )
<=> ( in @ X215 @ X216 ) ) )
=> ( X214 = X215 ) ) )
& ! [X217: $i,X218: $i] :
( ( ( in @ X217 @ X211 )
& ( in @ X218 @ X211 ) )
=> ( ! [X219: $i] :
( ( in @ X219 @ X217 )
=> ( in @ X219 @ X218 ) )
| ! [X220: $i] :
( ( in @ X220 @ X218 )
=> ( in @ X220 @ X217 ) ) ) )
& ! [X221: $i] :
( ( ! [X222: $i] :
( ( in @ X222 @ X221 )
=> ( in @ X222 @ X210 ) )
& ? [X223: $i] : ( in @ X223 @ X221 ) )
=> ? [X224: $i,X225: $i] :
( ( in @ X224 @ X211 )
& ( in @ X225 @ X221 )
& ~ ? [X226: $i] :
( ( in @ X226 @ X224 )
& ( in @ X226 @ X221 ) )
& ! [X227: $i] :
( ( in @ X227 @ X211 )
=> ( ! [X228: $i] :
( ( in @ X228 @ X227 )
=> ( in @ X228 @ X224 ) )
| ( in @ X225 @ X227 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_83,negated_conjecture,
~ ( ! [X181: $i,X182: $i] :
( ! [X183: $i] :
( ( in @ X183 @ X181 )
<=> ( in @ X183 @ X182 ) )
=> ( X181 = X182 ) )
=> ( ! [X184: $i] :
~ ( in @ X184 @ emptyset )
=> ( ! [X185: $i,X186: $i,X187: $i] :
( ( in @ X187 @ ( setadjoin @ X185 @ X186 ) )
<=> ( ( X187 = X185 )
| ( in @ X187 @ X186 ) ) )
=> ( ! [X188: $i,X189: $i] :
( ( in @ X189 @ ( powerset @ X188 ) )
<=> ! [X190: $i] :
( ( in @ X190 @ X189 )
=> ( in @ X190 @ X188 ) ) )
=> ( ! [X191: $i,X192: $i] :
( ( in @ X192 @ ( setunion @ X191 ) )
<=> ? [X193: $i] :
( ( in @ X192 @ X193 )
& ( in @ X193 @ X191 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X194: $i] :
( ( in @ X194 @ omega )
=> ( in @ ( setadjoin @ X194 @ X194 ) @ omega ) )
=> ( ! [X195: $i] :
( ( ( in @ emptyset @ X195 )
& ! [X196: $i] :
( ( ( in @ X196 @ omega )
& ( in @ X196 @ X195 ) )
=> ( in @ ( setadjoin @ X196 @ X196 ) @ X195 ) ) )
=> ! [X197: $i] :
( ( in @ X197 @ omega )
=> ( in @ X197 @ X195 ) ) )
=> ( ! [X198: $i > $i > $o,X199: $i] :
( ! [X200: $i] :
( ( in @ X200 @ X199 )
=> ? [X201: $i] :
( ( X198 @ X200 @ X201 )
& ! [X202: $i] :
( ( X198 @ X200 @ X202 )
=> ( X201 = X202 ) ) ) )
=> ? [X203: $i] :
! [X204: $i] :
( ( in @ X204 @ X203 )
<=> ? [X205: $i] :
( ( in @ X205 @ X199 )
& ( X198 @ X205 @ X204 ) ) ) )
=> ( ! [X206: $i] :
( ? [X207: $i] : ( in @ X207 @ X206 )
=> ? [X208: $i] :
( ( in @ X208 @ X206 )
& ~ ? [X209: $i] :
( ( in @ X209 @ X208 )
& ( in @ X209 @ X206 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X229: $i,X230: $i > $o,X231: $i] :
( ( in @ X231 @ X229 )
=> ( ( X230 @ X231 )
=> ( in @ X231
@ ( dsetconstr @ X229
@ ^ [Z0: $i] : ( X230 @ Z0 ) ) ) ) )
=> ( ! [X232: $i,X233: $i > $o,X234: $i] :
( ( in @ X234
@ ( dsetconstr @ X232
@ ^ [Z0: $i] : ( X233 @ Z0 ) ) )
=> ( in @ X234 @ X232 ) )
=> ( ! [X235: $i,X236: $i > $o,X237: $i] :
( ( in @ X237
@ ( dsetconstr @ X235
@ ^ [Z0: $i] : ( X236 @ Z0 ) ) )
=> ( X236 @ X237 ) )
=> ( ! [X238: $i > $o] :
( ? [X239: $i] :
( ( X238 @ X239 )
& ! [X240: $i] :
( ( X238 @ X240 )
=> ( X239 = X240 ) ) )
=> ? [X241: $i] :
( ( X238 @ X241 )
& ! [X242: $i] :
( ( X238 @ X242 )
=> ( X241 = X242 ) ) ) )
=> ( ! [X243: $o,X244: $i] :
( ( in @ X244
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X243 ) )
=> X243 )
=> ( ! [X245: $i] :
( ( in @ X245 @ emptyset )
=> ! [X246: $o] : X246 )
=> ( ! [X247: $i] :
~ ( in @ X247 @ emptyset )
=> ( ! [X248: $i] :
~ ( in @ X248 @ emptyset )
=> ( ! [X249: $i > $o] :
( ? [X250: $i] :
( ( X249 @ X250 )
& ! [X251: $i] :
( ( X249 @ X251 )
=> ( X250 = X251 ) ) )
=> ? [X252: $i] : ( X249 @ X252 ) )
=> ( ! [X253: $i,X254: $i] :
( ! [X255: $i] :
( ( in @ X255 @ X253 )
=> ( in @ X255 @ X254 ) )
=> ( ! [X256: $i] :
( ( in @ X256 @ X254 )
=> ( in @ X256 @ X253 ) )
=> ( X253 = X254 ) ) )
=> ( ! [X257: $i] :
( ! [X258: $i] :
~ ( in @ X258 @ X257 )
=> ( X257 = emptyset ) )
=> ( ! [X259: $i] :
( ! [X260: $i] :
~ ( in @ X260 @ X259 )
=> ( X259 = emptyset ) )
=> ( ! [X261: $i,X262: $i > $o,X263: $i] :
( ( in @ X263 @ X261 )
=> ( ( in @ X263
@ ( dsetconstr @ X261
@ ^ [Z0: $i] : ( X262 @ Z0 ) ) )
<=> ( X262 @ X263 ) ) )
=> ( ! [X264: $i] :
( ( X264 != emptyset )
=> ? [X265: $i] : ( in @ X265 @ X264 ) )
=> ( ! [X266: $i,X267: $i > $o,X268: $i] :
( ( in @ X268 @ X266 )
=> ( ( X267 @ X268 )
=> ( ( dsetconstr @ X266
@ ^ [Z0: $i] : ( X267 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X269: $i] :
( ? [X270: $i] : ( in @ X270 @ X269 )
=> ( X269 != emptyset ) )
=> ( ! [X271: $i,X272: $i] : ( in @ X271 @ ( setadjoin @ X271 @ X272 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X273: $i,X274: $i,X275: $i] :
( ( in @ X275 @ X274 )
=> ( in @ X275 @ ( setadjoin @ X273 @ X274 ) ) )
=> ( ! [X276: $i,X277: $i,X278: $i] :
( ( in @ X278 @ ( setadjoin @ X276 @ X277 ) )
=> ! [X279: $o] :
( ( ( X278 = X276 )
=> X279 )
=> ( ( ( in @ X278 @ X277 )
=> X279 )
=> X279 ) ) )
=> ( ! [X280: $i,X281: $i,X282: $i] :
( ( in @ X282 @ ( setadjoin @ X280 @ X281 ) )
=> ( ( X282 = X280 )
| ( in @ X282 @ X281 ) ) )
=> ( ! [X283: $i] :
( ( dsetconstr @ X283
@ ^ [Z0: $i] : $true )
= X283 )
=> ( ! [X284: $i,X285: $i] :
( ! [X286: $i] :
( ( in @ X286 @ X285 )
=> ( in @ X286 @ X284 ) )
=> ( in @ X285 @ ( powerset @ X284 ) ) )
=> ( ! [X287: $i] : ( in @ emptyset @ ( powerset @ X287 ) )
=> ( ! [X288: $i] : ( in @ emptyset @ ( powerset @ X288 ) )
=> ( ! [X289: $i,X290: $i,X291: $i] :
( ( in @ X290 @ ( powerset @ X289 ) )
=> ( ( in @ X291 @ X290 )
=> ( in @ X291 @ X289 ) ) )
=> ( ! [X292: $i,X293: $i,X294: $i] :
( ( in @ X293 @ X294 )
=> ( ( in @ X294 @ X292 )
=> ( in @ X293 @ ( setunion @ X292 ) ) ) )
=> ( ! [X295: $i,X296: $i] :
( ( in @ X296 @ ( setunion @ X295 ) )
=> ! [X297: $o] :
( ! [X298: $i] :
( ( in @ X296 @ X298 )
=> ( ( in @ X298 @ X295 )
=> X297 ) )
=> X297 ) )
=> ( ! [X299: $i,X300: $i] :
( ( in @ X300 @ X299 )
=> ( in @ X300 @ ( powerset @ ( setunion @ X299 ) ) ) )
=> ( ! [X301: $i > $o] :
( ? [X302: $i] :
( ( X301 @ X302 )
& ! [X303: $i] :
( ( X301 @ X303 )
=> ( X302 = X303 ) ) )
=> ? [X304: $i] :
! [X305: $i] :
( ( X301 @ X305 )
<=> ( X305 = X304 ) ) )
=> ( ! [X306: $i] :
( ( X306 != emptyset )
=> ? [X307: $i] : ( in @ X307 @ X306 ) )
=> ( ! [X308: $i,X309: $i] :
( ( in @ X308 @ ( setadjoin @ X309 @ emptyset ) )
=> ( X308 = X309 ) )
=> ( ! [X310: $i,X311: $i] :
( ( X310 != X311 )
=> ~ ( in @ X311 @ ( setadjoin @ X310 @ emptyset ) ) )
=> ( ! [X312: $i,X313: $i] :
( ( X312 = X313 )
=> ( in @ X312 @ ( setadjoin @ X313 @ emptyset ) ) )
=> ( ! [X314: $i,X315: $i] :
( ( in @ X314 @ ( setadjoin @ X315 @ emptyset ) )
=> ( in @ X315 @ ( setadjoin @ X314 @ emptyset ) ) )
=> ( ! [X316: $i,X317: $i,X318: $i] :
( ( in @ X318 @ ( setadjoin @ X316 @ ( setadjoin @ X317 @ emptyset ) ) )
=> ( ( X318 = X316 )
| ( X318 = X317 ) ) )
=> ( ! [X319: $i,X320: $i] : ( in @ X319 @ ( setadjoin @ X319 @ ( setadjoin @ X320 @ emptyset ) ) )
=> ( ! [X321: $i,X322: $i] : ( in @ X322 @ ( setadjoin @ X321 @ ( setadjoin @ X322 @ emptyset ) ) )
=> ( ! [X323: $i,X324: $i > $o] :
( ? [X325: $i] :
( ( in @ X325 @ X323 )
& ( X324 @ X325 ) )
=> ( ( dsetconstr @ X323
@ ^ [Z0: $i] : ( X324 @ Z0 ) )
!= emptyset ) )
=> ( ! [X326: $i > $o,X327: $i] :
( ( in @ X327 @ emptyset )
=> ( X326 @ X327 ) )
=> ( ! [X328: $i,X329: $i > $o] :
( ~ ! [X330: $i] :
( ( in @ X330 @ X328 )
=> ( X329 @ X330 ) )
=> ? [X331: $i] :
( ( in @ X331 @ X328 )
& ~ ( X329 @ X331 ) ) )
=> ( ! [X332: $i,X333: $i > $o] :
( ! [X334: $i] :
( ( in @ X334 @ X332 )
=> ~ ( X333 @ X334 ) )
=> ~ ? [X335: $i] :
( ( in @ X335 @ X332 )
& ( X333 @ X335 ) ) )
=> ( ! [X336: $i,X337: $i > $o] :
( ~ ? [X338: $i] :
( ( in @ X338 @ X336 )
& ( X337 @ X338 ) )
=> ! [X339: $i] :
( ( in @ X339 @ X336 )
=> ~ ( X337 @ X339 ) ) )
=> ( ! [X340: $i,X341: $i > $o] :
( ? [X342: $i] :
( ( in @ X342 @ X340 )
& ~ ( X341 @ X342 ) )
=> ~ ! [X343: $i] :
( ( in @ X343 @ X340 )
=> ( X341 @ X343 ) ) )
=> ! [X16: $o] :
( X16
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[prop2setI]),setadjoinE]),c_0_60]),upairsetE]),emptyI]),upairsetIL]),upairsetIR]),c_0_67]),noeltsimpempty]),vacuousDall]),quantDeMorgan1]),c_0_68]),quantDeMorgan2]),quantDeMorgan3]),c_0_69]),quantDeMorgan4]),c_0_70]),c_0_71]),c_0_72]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinOr]),c_0_73]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_74]),c_0_75]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),setext]),c_0_76]),notinemptyset]),emptysetimpfalse]),emptysetE]),c_0_77]),c_0_78]),c_0_79]),c_0_80]),wellorderingAx]),foundationAx]),c_0_81]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_82]) ).
thf(c_0_84,negated_conjecture,
! [X344: $i,X345: $i,X347: $i,X348: $i,X349: $i,X350: $i,X351: $i,X352: $i,X353: $i,X354: $i,X355: $i,X357: $i,X358: $i,X360: $i,X361: $i,X362: $i,X363: $i,X364: $i,X366: $i,X367: $i > $i > $o,X368: $i,X370: $i,X373: $i,X375: $i,X376: $i,X377: $i,X378: $i,X380: $i,X381: $i,X382: $i > $o,X383: $i,X384: $i,X385: $i > $o,X386: $i,X387: $i,X388: $i > $o,X389: $i,X390: $i > $o,X391: $i,X394: $i,X395: $o,X396: $i,X397: $i,X398: $o,X399: $i,X400: $i,X401: $i > $o,X402: $i,X405: $i,X406: $i,X409: $i,X411: $i,X413: $i,X414: $i > $o,X415: $i,X416: $i,X418: $i,X419: $i > $o,X420: $i,X421: $i,X422: $i,X423: $i,X424: $i,X425: $i,X426: $i,X427: $i,X428: $i,X429: $i,X430: $i,X431: $o,X432: $i,X433: $i,X434: $i,X435: $i,X436: $i,X437: $i,X439: $i,X440: $i,X441: $i,X442: $i,X443: $i,X444: $i,X445: $i,X446: $i,X447: $i,X448: $i,X449: $o,X451: $i,X452: $i,X453: $i > $o,X454: $i,X457: $i,X458: $i,X459: $i,X461: $i,X462: $i,X463: $i,X464: $i,X465: $i,X466: $i,X467: $i,X468: $i,X469: $i,X470: $i,X471: $i,X472: $i,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i > $o,X478: $i,X479: $i > $o,X480: $i,X481: $i,X482: $i > $o,X483: $i,X485: $i,X486: $i > $o,X488: $i,X489: $i,X490: $i > $o,X492: $i,X493: $i,X494: $i > $o,X495: $i] :
( ( ~ ( in @ ( esk1_2 @ X344 @ X345 ) @ X344 )
| ~ ( in @ ( esk1_2 @ X344 @ X345 ) @ X345 )
| ( X344 = X345 ) )
& ( ( in @ ( esk1_2 @ X344 @ X345 ) @ X344 )
| ( in @ ( esk1_2 @ X344 @ X345 ) @ X345 )
| ( X344 = X345 ) )
& ~ ( in @ X347 @ emptyset )
& ( ~ ( in @ X350 @ ( setadjoin @ X348 @ X349 ) )
| ( X350 = X348 )
| ( in @ X350 @ X349 ) )
& ( ( X350 != X348 )
| ( in @ X350 @ ( setadjoin @ X348 @ X349 ) ) )
& ( ~ ( in @ X350 @ X349 )
| ( in @ X350 @ ( setadjoin @ X348 @ X349 ) ) )
& ( ~ ( in @ X352 @ ( powerset @ X351 ) )
| ~ ( in @ X353 @ X352 )
| ( in @ X353 @ X351 ) )
& ( ( in @ ( esk2_2 @ X354 @ X355 ) @ X355 )
| ( in @ X355 @ ( powerset @ X354 ) ) )
& ( ~ ( in @ ( esk2_2 @ X354 @ X355 ) @ X354 )
| ( in @ X355 @ ( powerset @ X354 ) ) )
& ( ( in @ X358 @ ( esk3_2 @ X357 @ X358 ) )
| ~ ( in @ X358 @ ( setunion @ X357 ) ) )
& ( ( in @ ( esk3_2 @ X357 @ X358 ) @ X357 )
| ~ ( in @ X358 @ ( setunion @ X357 ) ) )
& ( ~ ( in @ X361 @ X362 )
| ~ ( in @ X362 @ X360 )
| ( in @ X361 @ ( setunion @ X360 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X363 @ omega )
| ( in @ ( setadjoin @ X363 @ X363 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X364 ) @ omega )
| ~ ( in @ emptyset @ X364 )
| ~ ( in @ X366 @ omega )
| ( in @ X366 @ X364 ) )
& ( ( in @ ( esk4_1 @ X364 ) @ X364 )
| ~ ( in @ emptyset @ X364 )
| ~ ( in @ X366 @ omega )
| ( in @ X366 @ X364 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X364 ) @ ( esk4_1 @ X364 ) ) @ X364 )
| ~ ( in @ emptyset @ X364 )
| ~ ( in @ X366 @ omega )
| ( in @ X366 @ X364 ) )
& ( ( in @ ( esk8_3 @ X367 @ X368 @ X373 ) @ X368 )
| ~ ( in @ X373 @ ( esk7_2 @ X367 @ X368 ) )
| ( in @ ( esk5_2 @ X367 @ X368 ) @ X368 ) )
& ( ( X367 @ ( esk8_3 @ X367 @ X368 @ X373 ) @ X373 )
| ~ ( in @ X373 @ ( esk7_2 @ X367 @ X368 ) )
| ( in @ ( esk5_2 @ X367 @ X368 ) @ X368 ) )
& ( ~ ( in @ X376 @ X368 )
| ~ ( X367 @ X376 @ X375 )
| ( in @ X375 @ ( esk7_2 @ X367 @ X368 ) )
| ( in @ ( esk5_2 @ X367 @ X368 ) @ X368 ) )
& ( ( in @ ( esk8_3 @ X367 @ X368 @ X373 ) @ X368 )
| ~ ( in @ X373 @ ( esk7_2 @ X367 @ X368 ) )
| ( X367 @ ( esk5_2 @ X367 @ X368 ) @ ( esk6_3 @ X367 @ X368 @ X370 ) )
| ~ ( X367 @ ( esk5_2 @ X367 @ X368 ) @ X370 ) )
& ( ( X367 @ ( esk8_3 @ X367 @ X368 @ X373 ) @ X373 )
| ~ ( in @ X373 @ ( esk7_2 @ X367 @ X368 ) )
| ( X367 @ ( esk5_2 @ X367 @ X368 ) @ ( esk6_3 @ X367 @ X368 @ X370 ) )
| ~ ( X367 @ ( esk5_2 @ X367 @ X368 ) @ X370 ) )
& ( ~ ( in @ X376 @ X368 )
| ~ ( X367 @ X376 @ X375 )
| ( in @ X375 @ ( esk7_2 @ X367 @ X368 ) )
| ( X367 @ ( esk5_2 @ X367 @ X368 ) @ ( esk6_3 @ X367 @ X368 @ X370 ) )
| ~ ( X367 @ ( esk5_2 @ X367 @ X368 ) @ X370 ) )
& ( ( in @ ( esk8_3 @ X367 @ X368 @ X373 ) @ X368 )
| ~ ( in @ X373 @ ( esk7_2 @ X367 @ X368 ) )
| ( X370
!= ( esk6_3 @ X367 @ X368 @ X370 ) )
| ~ ( X367 @ ( esk5_2 @ X367 @ X368 ) @ X370 ) )
& ( ( X367 @ ( esk8_3 @ X367 @ X368 @ X373 ) @ X373 )
| ~ ( in @ X373 @ ( esk7_2 @ X367 @ X368 ) )
| ( X370
!= ( esk6_3 @ X367 @ X368 @ X370 ) )
| ~ ( X367 @ ( esk5_2 @ X367 @ X368 ) @ X370 ) )
& ( ~ ( in @ X376 @ X368 )
| ~ ( X367 @ X376 @ X375 )
| ( in @ X375 @ ( esk7_2 @ X367 @ X368 ) )
| ( X370
!= ( esk6_3 @ X367 @ X368 @ X370 ) )
| ~ ( X367 @ ( esk5_2 @ X367 @ X368 ) @ X370 ) )
& ( ( in @ ( esk9_1 @ X377 ) @ X377 )
| ~ ( in @ X378 @ X377 ) )
& ( ~ ( in @ X380 @ ( esk9_1 @ X377 ) )
| ~ ( in @ X380 @ X377 )
| ~ ( in @ X378 @ X377 ) )
& epred1_0
& descrp
& ( ~ ( in @ X383 @ X381 )
| ~ ( X382 @ X383 )
| ( in @ X383
@ ( dsetconstr @ X381
@ ^ [Z0: $i] : ( X382 @ Z0 ) ) ) )
& ( ~ ( in @ X386
@ ( dsetconstr @ X384
@ ^ [Z0: $i] : ( X385 @ Z0 ) ) )
| ( in @ X386 @ X384 ) )
& ( ~ ( in @ X389
@ ( dsetconstr @ X387
@ ^ [Z0: $i] : ( X388 @ Z0 ) ) )
| ( X388 @ X389 ) )
& ( ( X390 @ ( esk11_1 @ X390 ) )
| ( X390 @ ( esk10_2 @ X390 @ X391 ) )
| ~ ( X390 @ X391 ) )
& ( ~ ( X390 @ X394 )
| ( ( esk11_1 @ X390 )
= X394 )
| ( X390 @ ( esk10_2 @ X390 @ X391 ) )
| ~ ( X390 @ X391 ) )
& ( ( X390 @ ( esk11_1 @ X390 ) )
| ( X391
!= ( esk10_2 @ X390 @ X391 ) )
| ~ ( X390 @ X391 ) )
& ( ~ ( X390 @ X394 )
| ( ( esk11_1 @ X390 )
= X394 )
| ( X391
!= ( esk10_2 @ X390 @ X391 ) )
| ~ ( X390 @ X391 ) )
& ( ~ ( in @ X396
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X395 ) )
| X395 )
& ( ~ ( in @ X397 @ emptyset )
| X398 )
& ~ ( in @ X399 @ emptyset )
& ~ ( in @ X400 @ emptyset )
& ( ( X401 @ ( esk12_2 @ X401 @ X402 ) )
| ~ ( X401 @ X402 )
| ( X401 @ ( esk13_1 @ X401 ) ) )
& ( ( X402
!= ( esk12_2 @ X401 @ X402 ) )
| ~ ( X401 @ X402 )
| ( X401 @ ( esk13_1 @ X401 ) ) )
& ( ( in @ ( esk15_2 @ X405 @ X406 ) @ X406 )
| ( X405 = X406 )
| ( in @ ( esk14_2 @ X405 @ X406 ) @ X405 ) )
& ( ~ ( in @ ( esk15_2 @ X405 @ X406 ) @ X405 )
| ( X405 = X406 )
| ( in @ ( esk14_2 @ X405 @ X406 ) @ X405 ) )
& ( ( in @ ( esk15_2 @ X405 @ X406 ) @ X406 )
| ( X405 = X406 )
| ~ ( in @ ( esk14_2 @ X405 @ X406 ) @ X406 ) )
& ( ~ ( in @ ( esk15_2 @ X405 @ X406 ) @ X405 )
| ( X405 = X406 )
| ~ ( in @ ( esk14_2 @ X405 @ X406 ) @ X406 ) )
& ( ( in @ ( esk16_1 @ X409 ) @ X409 )
| ( X409 = emptyset ) )
& ( ( in @ ( esk17_1 @ X411 ) @ X411 )
| ( X411 = emptyset ) )
& ( ~ ( in @ X415
@ ( dsetconstr @ X413
@ ^ [Z0: $i] : ( X414 @ Z0 ) ) )
| ( X414 @ X415 )
| ~ ( in @ X415 @ X413 ) )
& ( ~ ( X414 @ X415 )
| ( in @ X415
@ ( dsetconstr @ X413
@ ^ [Z0: $i] : ( X414 @ Z0 ) ) )
| ~ ( in @ X415 @ X413 ) )
& ( ( X416 = emptyset )
| ( in @ ( esk18_1 @ X416 ) @ X416 ) )
& ( ~ ( in @ X420 @ X418 )
| ~ ( X419 @ X420 )
| ( ( dsetconstr @ X418
@ ^ [Z0: $i] : ( X419 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X422 @ X421 )
| ( X421 != emptyset ) )
& ( in @ X423 @ ( setadjoin @ X423 @ X424 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X427 @ X426 )
| ( in @ X427 @ ( setadjoin @ X425 @ X426 ) ) )
& ( ( in @ X430 @ X429 )
| X431
| ( X430 = X428 )
| ~ ( in @ X430 @ ( setadjoin @ X428 @ X429 ) ) )
& ( ~ X431
| X431
| ( X430 = X428 )
| ~ ( in @ X430 @ ( setadjoin @ X428 @ X429 ) ) )
& ( ( in @ X430 @ X429 )
| X431
| ~ X431
| ~ ( in @ X430 @ ( setadjoin @ X428 @ X429 ) ) )
& ( ~ X431
| X431
| ~ X431
| ~ ( in @ X430 @ ( setadjoin @ X428 @ X429 ) ) )
& ( ~ ( in @ X434 @ ( setadjoin @ X432 @ X433 ) )
| ( X434 = X432 )
| ( in @ X434 @ X433 ) )
& ( ( dsetconstr @ X435
@ ^ [Z0: $i] : $true )
= X435 )
& ( ( in @ ( esk19_2 @ X436 @ X437 ) @ X437 )
| ( in @ X437 @ ( powerset @ X436 ) ) )
& ( ~ ( in @ ( esk19_2 @ X436 @ X437 ) @ X436 )
| ( in @ X437 @ ( powerset @ X436 ) ) )
& ( in @ emptyset @ ( powerset @ X439 ) )
& ( in @ emptyset @ ( powerset @ X440 ) )
& ( ~ ( in @ X442 @ ( powerset @ X441 ) )
| ~ ( in @ X443 @ X442 )
| ( in @ X443 @ X441 ) )
& ( ~ ( in @ X445 @ X446 )
| ~ ( in @ X446 @ X444 )
| ( in @ X445 @ ( setunion @ X444 ) ) )
& ( ( in @ X448 @ ( esk20_3 @ X447 @ X448 @ X449 ) )
| X449
| ~ ( in @ X448 @ ( setunion @ X447 ) ) )
& ( ( in @ ( esk20_3 @ X447 @ X448 @ X449 ) @ X447 )
| X449
| ~ ( in @ X448 @ ( setunion @ X447 ) ) )
& ( ~ X449
| X449
| ~ ( in @ X448 @ ( setunion @ X447 ) ) )
& ( ~ ( in @ X452 @ X451 )
| ( in @ X452 @ ( powerset @ ( setunion @ X451 ) ) ) )
& ( ~ ( X453 @ X457 )
| ( X457
= ( esk22_1 @ X453 ) )
| ( X453 @ ( esk21_2 @ X453 @ X454 ) )
| ~ ( X453 @ X454 ) )
& ( ( X458
!= ( esk22_1 @ X453 ) )
| ( X453 @ X458 )
| ( X453 @ ( esk21_2 @ X453 @ X454 ) )
| ~ ( X453 @ X454 ) )
& ( ~ ( X453 @ X457 )
| ( X457
= ( esk22_1 @ X453 ) )
| ( X454
!= ( esk21_2 @ X453 @ X454 ) )
| ~ ( X453 @ X454 ) )
& ( ( X458
!= ( esk22_1 @ X453 ) )
| ( X453 @ X458 )
| ( X454
!= ( esk21_2 @ X453 @ X454 ) )
| ~ ( X453 @ X454 ) )
& ( ( X459 = emptyset )
| ( in @ ( esk23_1 @ X459 ) @ X459 ) )
& ( ~ ( in @ X461 @ ( setadjoin @ X462 @ emptyset ) )
| ( X461 = X462 ) )
& ( ( X463 = X464 )
| ~ ( in @ X464 @ ( setadjoin @ X463 @ emptyset ) ) )
& ( ( X465 != X466 )
| ( in @ X465 @ ( setadjoin @ X466 @ emptyset ) ) )
& ( ~ ( in @ X467 @ ( setadjoin @ X468 @ emptyset ) )
| ( in @ X468 @ ( setadjoin @ X467 @ emptyset ) ) )
& ( ~ ( in @ X471 @ ( setadjoin @ X469 @ ( setadjoin @ X470 @ emptyset ) ) )
| ( X471 = X469 )
| ( X471 = X470 ) )
& ( in @ X472 @ ( setadjoin @ X472 @ ( setadjoin @ X473 @ emptyset ) ) )
& ( in @ X475 @ ( setadjoin @ X474 @ ( setadjoin @ X475 @ emptyset ) ) )
& ( ~ ( in @ X478 @ X476 )
| ~ ( X477 @ X478 )
| ( ( dsetconstr @ X476
@ ^ [Z0: $i] : ( X477 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X480 @ emptyset )
| ( X479 @ X480 ) )
& ( ( in @ ( esk24_2 @ X481 @ X482 ) @ X481 )
| ~ ( in @ X483 @ X481 )
| ( X482 @ X483 ) )
& ( ~ ( X482 @ ( esk24_2 @ X481 @ X482 ) )
| ~ ( in @ X483 @ X481 )
| ( X482 @ X483 ) )
& ( ( in @ ( esk25_2 @ X485 @ X486 ) @ X485 )
| ~ ( in @ X488 @ X485 )
| ~ ( X486 @ X488 ) )
& ( ( X486 @ ( esk25_2 @ X485 @ X486 ) )
| ~ ( in @ X488 @ X485 )
| ~ ( X486 @ X488 ) )
& ( ( in @ ( esk26_2 @ X489 @ X490 ) @ X489 )
| ~ ( in @ X492 @ X489 )
| ~ ( X490 @ X492 ) )
& ( ( X490 @ ( esk26_2 @ X489 @ X490 ) )
| ~ ( in @ X492 @ X489 )
| ~ ( X490 @ X492 ) )
& ( ( in @ ( esk27_2 @ X493 @ X494 ) @ X493 )
| ~ ( in @ X495 @ X493 )
| ( X494 @ X495 ) )
& ( ~ ( X494 @ ( esk27_2 @ X493 @ X494 ) )
| ~ ( in @ X495 @ X493 )
| ( X494 @ X495 ) )
& epred2_0
& ~ ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : epred2_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_83])])])])])]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i,X2: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ ( esk2_2 @ X2 @ X3 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_86,negated_conjecture,
! [X3: $i,X2: $i] :
( ( in @ ( esk2_2 @ X2 @ X3 ) @ X3 )
| ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_87,negated_conjecture,
~ ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
| ~ ( X1 @ X2 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_89,negated_conjecture,
! [X2: $i] : ( in @ X2 @ ( powerset @ X2 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_90,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_91,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_90])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU540^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun May 19 17:52:38 EDT 2024
% 0.13/0.36 % 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
% 0.37/0.53 # Version: 3.1.0-ho
% 0.37/0.53 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.37/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.37/0.53 # Starting sh5l with 300s (1) cores
% 0.37/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.37/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.37/0.53 # new_bool_2 with pid 27024 completed with status 0
% 0.37/0.53 # Result found by new_bool_2
% 0.37/0.53 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.37/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.37/0.53 # Starting sh5l with 300s (1) cores
% 0.37/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.37/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.37/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/0.53 # Search class: HGHSM-FFMS31-SHFSMSBN
% 0.37/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.53 # Starting new_ho_10 with 181s (1) cores
% 0.37/0.53 # new_ho_10 with pid 27025 completed with status 0
% 0.37/0.53 # Result found by new_ho_10
% 0.37/0.53 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.37/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.37/0.53 # Starting sh5l with 300s (1) cores
% 0.37/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.37/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.37/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/0.53 # Search class: HGHSM-FFMS31-SHFSMSBN
% 0.37/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.53 # Starting new_ho_10 with 181s (1) cores
% 0.37/0.53 # Preprocessing time : 0.006 s
% 0.37/0.53 # Presaturation interreduction done
% 0.37/0.53
% 0.37/0.53 # Proof found!
% 0.37/0.53 # SZS status Theorem
% 0.37/0.53 # SZS output start CNFRefutation
% See solution above
% 0.37/0.53 # Parsed axioms : 127
% 0.37/0.53 # Removed by relevancy pruning/SinE : 68
% 0.37/0.53 # Initial clauses : 110
% 0.37/0.53 # Removed in clause preprocessing : 4
% 0.37/0.53 # Initial clauses in saturation : 106
% 0.37/0.53 # Processed clauses : 171
% 0.37/0.53 # ...of these trivial : 5
% 0.37/0.53 # ...subsumed : 21
% 0.37/0.53 # ...remaining for further processing : 145
% 0.37/0.53 # Other redundant clauses eliminated : 6
% 0.37/0.53 # Clauses deleted for lack of memory : 0
% 0.37/0.53 # Backward-subsumed : 0
% 0.37/0.53 # Backward-rewritten : 3
% 0.37/0.53 # Generated clauses : 194
% 0.37/0.53 # ...of the previous two non-redundant : 178
% 0.37/0.53 # ...aggressively subsumed : 0
% 0.37/0.53 # Contextual simplify-reflections : 0
% 0.37/0.53 # Paramodulations : 188
% 0.37/0.53 # Factorizations : 0
% 0.37/0.53 # NegExts : 0
% 0.37/0.53 # Equation resolutions : 6
% 0.37/0.53 # Disequality decompositions : 0
% 0.37/0.53 # Total rewrite steps : 30
% 0.37/0.53 # ...of those cached : 18
% 0.37/0.53 # Propositional unsat checks : 0
% 0.37/0.53 # Propositional check models : 0
% 0.37/0.53 # Propositional check unsatisfiable : 0
% 0.37/0.53 # Propositional clauses : 0
% 0.37/0.53 # Propositional clauses after purity: 0
% 0.37/0.53 # Propositional unsat core size : 0
% 0.37/0.53 # Propositional preprocessing time : 0.000
% 0.37/0.53 # Propositional encoding time : 0.000
% 0.37/0.53 # Propositional solver time : 0.000
% 0.37/0.53 # Success case prop preproc time : 0.000
% 0.37/0.53 # Success case prop encoding time : 0.000
% 0.37/0.53 # Success case prop solver time : 0.000
% 0.37/0.53 # Current number of processed clauses : 50
% 0.37/0.53 # Positive orientable unit clauses : 12
% 0.37/0.53 # Positive unorientable unit clauses: 0
% 0.37/0.53 # Negative unit clauses : 2
% 0.37/0.53 # Non-unit-clauses : 36
% 0.37/0.53 # Current number of unprocessed clauses: 184
% 0.37/0.53 # ...number of literals in the above : 511
% 0.37/0.53 # Current number of archived formulas : 0
% 0.37/0.53 # Current number of archived clauses : 90
% 0.37/0.53 # Clause-clause subsumption calls (NU) : 2130
% 0.37/0.53 # Rec. Clause-clause subsumption calls : 1047
% 0.37/0.53 # Non-unit clause-clause subsumptions : 12
% 0.37/0.53 # Unit Clause-clause subsumption calls : 26
% 0.37/0.53 # Rewrite failures with RHS unbound : 0
% 0.37/0.53 # BW rewrite match attempts : 12
% 0.37/0.53 # BW rewrite match successes : 3
% 0.37/0.53 # Condensation attempts : 171
% 0.37/0.53 # Condensation successes : 3
% 0.37/0.53 # Termbank termtop insertions : 17028
% 0.37/0.53 # Search garbage collected termcells : 4776
% 0.37/0.53
% 0.37/0.53 # -------------------------------------------------
% 0.37/0.53 # User time : 0.029 s
% 0.37/0.53 # System time : 0.005 s
% 0.37/0.53 # Total time : 0.034 s
% 0.37/0.53 # Maximum resident set size: 3328 pages
% 0.37/0.53
% 0.37/0.53 # -------------------------------------------------
% 0.37/0.53 # User time : 0.031 s
% 0.37/0.53 # System time : 0.009 s
% 0.37/0.53 # Total time : 0.040 s
% 0.37/0.53 # Maximum resident set size: 1856 pages
% 0.37/0.53 % E---3.1 exiting
% 0.37/0.53 % E exiting
%------------------------------------------------------------------------------