TSTP Solution File: SEU525^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU525^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 03:27:57 EDT 2024
% Result : Theorem 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 123
% Syntax : Number of formulae : 153 ( 17 unt; 77 typ; 0 def)
% Number of atoms : 558 ( 93 equ; 0 cnn)
% Maximal formula atoms : 154 ( 7 avg)
% Number of connectives : 1867 ( 131 ~; 142 |; 126 &;1156 @)
% ( 71 <=>; 241 =>; 0 <=; 0 <~>)
% Maximal formula depth : 175 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 47 con; 0-3 aty)
% Number of variables : 443 ( 39 ^ 351 !; 53 ?; 443 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
epred1_0: $o ).
thf(decl_75,type,
esk1_2: $i > $i > $i ).
thf(decl_76,type,
esk2_2: $i > $i > $i ).
thf(decl_77,type,
esk3_2: $i > $i > $i ).
thf(decl_78,type,
esk4_1: $i > $i ).
thf(decl_79,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_80,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_81,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_82,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_83,type,
esk9_1: $i > $i ).
thf(decl_84,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_85,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_86,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_87,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_88,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_89,type,
esk15_2: $i > $i > $i ).
thf(decl_90,type,
esk16_2: $i > $i > $i ).
thf(decl_91,type,
esk17_1: $i > $i ).
thf(decl_92,type,
esk18_1: $i > $i ).
thf(decl_93,type,
esk19_1: $i > $i ).
thf(decl_94,type,
esk20_2: $i > $i > $i ).
thf(decl_95,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_96,type,
epred2_0: $i > $o ).
thf(decl_97,type,
esk22_0: $i ).
thf(decl_98,type,
esk23_1: $i > $i ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(exuE2,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
=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(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/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_45,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_46,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_47,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_48,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_49,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_50,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_51,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_52,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_53,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_54,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_55,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X139: $i] :
( ( X1 @ X139 )
& ! [X140: $i] :
( ( X1 @ X140 )
=> ( X139 = X140 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_56,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X137: $i] :
( ( X1 @ X137 )
& ! [X138: $i] :
( ( X1 @ X138 )
=> ( X137 = X138 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_46]) ).
thf(c_0_57,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_58,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X133: $i] :
( ( X6 @ X2 @ X133 )
& ! [X134: $i] :
( ( X6 @ X2 @ X134 )
=> ( X133 = X134 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_48,c_0_46]) ).
thf(c_0_59,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_49]) ).
thf(c_0_60,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_61,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_50]) ).
thf(c_0_62,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_51,c_0_50]) ).
thf(c_0_63,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_50]) ).
thf(c_0_64,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_65,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X135: $i] :
( ( X1 @ X135 )
& ! [X136: $i] :
( ( X1 @ X136 )
=> ( X135 = X136 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_52,c_0_46]) ).
thf(c_0_66,plain,
( epred1_0
<=> ! [X170: $i] :
? [X171: $i] :
( ! [X172: $i] :
( ( in @ X172 @ X171 )
=> ! [X173: $i] :
( ( in @ X173 @ X172 )
=> ( in @ X173 @ X170 ) ) )
& ! [X174: $i,X175: $i] :
( ( ( in @ X174 @ X170 )
& ( in @ X175 @ X170 ) )
=> ( ! [X176: $i] :
( ( in @ X176 @ X171 )
=> ( ( in @ X174 @ X176 )
<=> ( in @ X175 @ X176 ) ) )
=> ( X174 = X175 ) ) )
& ! [X177: $i,X178: $i] :
( ( ( in @ X177 @ X171 )
& ( in @ X178 @ X171 ) )
=> ( ! [X179: $i] :
( ( in @ X179 @ X177 )
=> ( in @ X179 @ X178 ) )
| ! [X180: $i] :
( ( in @ X180 @ X178 )
=> ( in @ X180 @ X177 ) ) ) )
& ! [X181: $i] :
( ( ! [X182: $i] :
( ( in @ X182 @ X181 )
=> ( in @ X182 @ X170 ) )
& ? [X183: $i] : ( in @ X183 @ X181 ) )
=> ? [X184: $i,X185: $i] :
( ( in @ X184 @ X171 )
& ( in @ X185 @ X181 )
& ~ ? [X186: $i] :
( ( in @ X186 @ X184 )
& ( in @ X186 @ X181 ) )
& ! [X187: $i] :
( ( in @ X187 @ X171 )
=> ( ! [X188: $i] :
( ( in @ X188 @ X187 )
=> ( in @ X188 @ X184 ) )
| ( in @ X185 @ X187 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_67,negated_conjecture,
~ ( ! [X141: $i,X142: $i] :
( ! [X143: $i] :
( ( in @ X143 @ X141 )
<=> ( in @ X143 @ X142 ) )
=> ( X141 = X142 ) )
=> ( ! [X144: $i] :
~ ( in @ X144 @ emptyset )
=> ( ! [X145: $i,X146: $i,X147: $i] :
( ( in @ X147 @ ( setadjoin @ X145 @ X146 ) )
<=> ( ( X147 = X145 )
| ( in @ X147 @ X146 ) ) )
=> ( ! [X148: $i,X149: $i] :
( ( in @ X149 @ ( powerset @ X148 ) )
<=> ! [X150: $i] :
( ( in @ X150 @ X149 )
=> ( in @ X150 @ X148 ) ) )
=> ( ! [X151: $i,X152: $i] :
( ( in @ X152 @ ( setunion @ X151 ) )
<=> ? [X153: $i] :
( ( in @ X152 @ X153 )
& ( in @ X153 @ X151 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X154: $i] :
( ( in @ X154 @ omega )
=> ( in @ ( setadjoin @ X154 @ X154 ) @ omega ) )
=> ( ! [X155: $i] :
( ( ( in @ emptyset @ X155 )
& ! [X156: $i] :
( ( ( in @ X156 @ omega )
& ( in @ X156 @ X155 ) )
=> ( in @ ( setadjoin @ X156 @ X156 ) @ X155 ) ) )
=> ! [X157: $i] :
( ( in @ X157 @ omega )
=> ( in @ X157 @ X155 ) ) )
=> ( ! [X158: $i > $i > $o,X159: $i] :
( ! [X160: $i] :
( ( in @ X160 @ X159 )
=> ? [X161: $i] :
( ( X158 @ X160 @ X161 )
& ! [X162: $i] :
( ( X158 @ X160 @ X162 )
=> ( X161 = X162 ) ) ) )
=> ? [X163: $i] :
! [X164: $i] :
( ( in @ X164 @ X163 )
<=> ? [X165: $i] :
( ( in @ X165 @ X159 )
& ( X158 @ X165 @ X164 ) ) ) )
=> ( ! [X166: $i] :
( ? [X167: $i] : ( in @ X167 @ X166 )
=> ? [X168: $i] :
( ( in @ X168 @ X166 )
& ~ ? [X169: $i] :
( ( in @ X169 @ X168 )
& ( in @ X169 @ X166 ) ) ) )
=> ( epred1_0
=> ( ! [X189: $i > $o] :
( ? [X190: $i] :
( ( X189 @ X190 )
& ! [X191: $i] :
( ( X189 @ X191 )
=> ( X190 = X191 ) ) )
=> ( X189
@ ( descr
@ ^ [Z0: $i] : ( X189 @ Z0 ) ) ) )
=> ( ! [X192: $i,X193: $i > $o,X194: $i] :
( ( in @ X194 @ X192 )
=> ( ( X193 @ X194 )
=> ( in @ X194 @ ( dsetconstr @ X192 @ X193 ) ) ) )
=> ( ! [X195: $i,X196: $i > $o,X197: $i] :
( ( in @ X197 @ ( dsetconstr @ X195 @ X196 ) )
=> ( in @ X197 @ X195 ) )
=> ( ! [X198: $i,X199: $i > $o,X200: $i] :
( ( in @ X200 @ ( dsetconstr @ X198 @ X199 ) )
=> ( X199 @ X200 ) )
=> ( ! [X201: $i > $o] :
( ? [X202: $i] :
( ( X201 @ X202 )
& ! [X203: $i] :
( ( X201 @ X203 )
=> ( X202 = X203 ) ) )
=> ? [X204: $i] :
( ( X201 @ X204 )
& ! [X205: $i] :
( ( X201 @ X205 )
=> ( X204 = X205 ) ) ) )
=> ( ! [X206: $o,X207: $i] :
( ( in @ X207
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X206 ) )
=> X206 )
=> ( ! [X208: $i] :
( ( in @ X208 @ emptyset )
=> ! [X209: $o] : X209 )
=> ( ! [X210: $i] :
( ( in @ X210 @ emptyset )
=> ~ $true )
=> ( ! [X211: $i] :
~ ( in @ X211 @ emptyset )
=> ( ! [X212: $i > $o] :
( ? [X213: $i] :
( ( X212 @ X213 )
& ! [X214: $i] :
( ( X212 @ X214 )
=> ( X213 = X214 ) ) )
=> ? [X215: $i] : ( X212 @ X215 ) )
=> ( ! [X216: $i,X217: $i] :
( ! [X218: $i] :
( ( in @ X218 @ X216 )
=> ( in @ X218 @ X217 ) )
=> ( ! [X219: $i] :
( ( in @ X219 @ X217 )
=> ( in @ X219 @ X216 ) )
=> ( X216 = X217 ) ) )
=> ( ! [X220: $i] :
( ! [X221: $i] :
~ ( in @ X221 @ X220 )
=> ( X220 = emptyset ) )
=> ( ! [X222: $i] :
( ! [X223: $i] :
~ ( in @ X223 @ X222 )
=> ( X222 = emptyset ) )
=> ( ! [X224: $i,X225: $i > $o,X226: $i] :
( ( in @ X226 @ X224 )
=> ( ( in @ X226 @ ( dsetconstr @ X224 @ X225 ) )
<=> ( X225 @ X226 ) ) )
=> ( ! [X227: $i] :
( ( X227 != emptyset )
=> ? [X228: $i] : ( in @ X228 @ X227 ) )
=> ( ! [X229: $i,X230: $i > $o,X231: $i] :
( ( in @ X231 @ X229 )
=> ( ( X230 @ X231 )
=> ( ( dsetconstr @ X229 @ X230 )
!= emptyset ) ) )
=> ( ! [X232: $i] :
( ? [X233: $i] : ( in @ X233 @ X232 )
=> ( X232 != emptyset ) )
=> ( ! [X234: $i,X235: $i] : ( in @ X234 @ ( setadjoin @ X234 @ X235 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X236: $i,X237: $i,X238: $i] :
( ( in @ X238 @ X237 )
=> ( in @ X238 @ ( setadjoin @ X236 @ X237 ) ) )
=> ( ! [X239: $i,X240: $i,X241: $i] :
( ( in @ X241 @ ( setadjoin @ X239 @ X240 ) )
=> ! [X242: $o] :
( ( ( X241 = X239 )
=> X242 )
=> ( ( ( in @ X241 @ X240 )
=> X242 )
=> X242 ) ) )
=> ( ! [X243: $i,X244: $i,X245: $i] :
( ( in @ X245 @ ( setadjoin @ X243 @ X244 ) )
=> ( ( X245 = X243 )
| ( in @ X245 @ X244 ) ) )
=> ( ! [X246: $i] :
( ( dsetconstr @ X246
@ ^ [Z0: $i] : $true )
= X246 )
=> ( ! [X247: $i,X248: $i] :
( ! [X249: $i] :
( ( in @ X249 @ X248 )
=> ( in @ X249 @ X247 ) )
=> ( in @ X248 @ ( powerset @ X247 ) ) )
=> ( ! [X250: $i] : ( in @ emptyset @ ( powerset @ X250 ) )
=> ( ! [X251: $i] : ( in @ emptyset @ ( powerset @ X251 ) )
=> ( ! [X252: $i,X253: $i,X254: $i] :
( ( in @ X253 @ ( powerset @ X252 ) )
=> ( ( in @ X254 @ X253 )
=> ( in @ X254 @ X252 ) ) )
=> ( ! [X255: $i,X256: $i,X257: $i] :
( ( in @ X256 @ X257 )
=> ( ( in @ X257 @ X255 )
=> ( in @ X256 @ ( setunion @ X255 ) ) ) )
=> ( ! [X258: $i,X259: $i] :
( ( in @ X259 @ ( setunion @ X258 ) )
=> ! [X260: $o] :
( ! [X261: $i] :
( ( in @ X259 @ X261 )
=> ( ( in @ X261 @ X258 )
=> X260 ) )
=> X260 ) )
=> ( ! [X262: $i,X263: $i] :
( ( in @ X263 @ X262 )
=> ( in @ X263 @ ( powerset @ ( setunion @ X262 ) ) ) )
=> ! [X1: $i > $o] :
( ? [X264: $i] :
( ( X1 @ X264 )
& ! [X265: $i] :
( ( X1 @ X265 )
=> ( X264 = X265 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[exuE2])]),c_0_46]),emptyInPowerset]),powersetE]),setunionI]),c_0_53]),setunionE]),subPowSU]),c_0_54]),c_0_55]),c_0_56]),c_0_57]),c_0_58]),c_0_59]),emptysetE]),emptysetimpfalse]),notinemptyset]),setext]),emptyI]),noeltsimpempty]),c_0_60]),c_0_61]),c_0_62]),c_0_63]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_64]),powersetI]),emptyinPowerset]),c_0_65]),wellorderingAx]),foundationAx]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_66]) ).
thf(c_0_68,negated_conjecture,
! [X266: $i,X267: $i,X269: $i,X270: $i,X271: $i,X272: $i,X273: $i,X274: $i,X275: $i,X276: $i,X277: $i,X279: $i,X280: $i,X282: $i,X283: $i,X284: $i,X285: $i,X286: $i,X288: $i,X289: $i > $i > $o,X290: $i,X292: $i,X295: $i,X297: $i,X298: $i,X299: $i,X300: $i,X302: $i,X303: $i > $o,X304: $i,X306: $i,X307: $i > $o,X308: $i,X309: $i,X310: $i > $o,X311: $i,X312: $i,X313: $i > $o,X314: $i,X315: $i > $o,X316: $i,X319: $i,X320: $o,X321: $i,X322: $i,X323: $o,X324: $i,X325: $i,X326: $i > $o,X327: $i,X330: $i,X331: $i,X334: $i,X336: $i,X338: $i,X339: $i > $o,X340: $i,X341: $i,X343: $i,X344: $i > $o,X345: $i,X346: $i,X347: $i,X348: $i,X349: $i,X350: $i,X351: $i,X352: $i,X353: $i,X354: $i,X355: $i,X356: $o,X357: $i,X358: $i,X359: $i,X360: $i,X361: $i,X362: $i,X364: $i,X365: $i,X366: $i,X367: $i,X368: $i,X369: $i,X370: $i,X371: $i,X372: $i,X373: $i,X374: $o,X376: $i,X377: $i,X380: $i,X381: $i] :
( ( ~ ( in @ ( esk1_2 @ X266 @ X267 ) @ X266 )
| ~ ( in @ ( esk1_2 @ X266 @ X267 ) @ X267 )
| ( X266 = X267 ) )
& ( ( in @ ( esk1_2 @ X266 @ X267 ) @ X266 )
| ( in @ ( esk1_2 @ X266 @ X267 ) @ X267 )
| ( X266 = X267 ) )
& ~ ( in @ X269 @ emptyset )
& ( ~ ( in @ X272 @ ( setadjoin @ X270 @ X271 ) )
| ( X272 = X270 )
| ( in @ X272 @ X271 ) )
& ( ( X272 != X270 )
| ( in @ X272 @ ( setadjoin @ X270 @ X271 ) ) )
& ( ~ ( in @ X272 @ X271 )
| ( in @ X272 @ ( setadjoin @ X270 @ X271 ) ) )
& ( ~ ( in @ X274 @ ( powerset @ X273 ) )
| ~ ( in @ X275 @ X274 )
| ( in @ X275 @ X273 ) )
& ( ( in @ ( esk2_2 @ X276 @ X277 ) @ X277 )
| ( in @ X277 @ ( powerset @ X276 ) ) )
& ( ~ ( in @ ( esk2_2 @ X276 @ X277 ) @ X276 )
| ( in @ X277 @ ( powerset @ X276 ) ) )
& ( ( in @ X280 @ ( esk3_2 @ X279 @ X280 ) )
| ~ ( in @ X280 @ ( setunion @ X279 ) ) )
& ( ( in @ ( esk3_2 @ X279 @ X280 ) @ X279 )
| ~ ( in @ X280 @ ( setunion @ X279 ) ) )
& ( ~ ( in @ X283 @ X284 )
| ~ ( in @ X284 @ X282 )
| ( in @ X283 @ ( setunion @ X282 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X285 @ omega )
| ( in @ ( setadjoin @ X285 @ X285 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X286 ) @ omega )
| ~ ( in @ emptyset @ X286 )
| ~ ( in @ X288 @ omega )
| ( in @ X288 @ X286 ) )
& ( ( in @ ( esk4_1 @ X286 ) @ X286 )
| ~ ( in @ emptyset @ X286 )
| ~ ( in @ X288 @ omega )
| ( in @ X288 @ X286 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X286 ) @ ( esk4_1 @ X286 ) ) @ X286 )
| ~ ( in @ emptyset @ X286 )
| ~ ( in @ X288 @ omega )
| ( in @ X288 @ X286 ) )
& ( ( in @ ( esk8_3 @ X289 @ X290 @ X295 ) @ X290 )
| ~ ( in @ X295 @ ( esk7_2 @ X289 @ X290 ) )
| ( in @ ( esk5_2 @ X289 @ X290 ) @ X290 ) )
& ( ( X289 @ ( esk8_3 @ X289 @ X290 @ X295 ) @ X295 )
| ~ ( in @ X295 @ ( esk7_2 @ X289 @ X290 ) )
| ( in @ ( esk5_2 @ X289 @ X290 ) @ X290 ) )
& ( ~ ( in @ X298 @ X290 )
| ~ ( X289 @ X298 @ X297 )
| ( in @ X297 @ ( esk7_2 @ X289 @ X290 ) )
| ( in @ ( esk5_2 @ X289 @ X290 ) @ X290 ) )
& ( ( in @ ( esk8_3 @ X289 @ X290 @ X295 ) @ X290 )
| ~ ( in @ X295 @ ( esk7_2 @ X289 @ X290 ) )
| ( X289 @ ( esk5_2 @ X289 @ X290 ) @ ( esk6_3 @ X289 @ X290 @ X292 ) )
| ~ ( X289 @ ( esk5_2 @ X289 @ X290 ) @ X292 ) )
& ( ( X289 @ ( esk8_3 @ X289 @ X290 @ X295 ) @ X295 )
| ~ ( in @ X295 @ ( esk7_2 @ X289 @ X290 ) )
| ( X289 @ ( esk5_2 @ X289 @ X290 ) @ ( esk6_3 @ X289 @ X290 @ X292 ) )
| ~ ( X289 @ ( esk5_2 @ X289 @ X290 ) @ X292 ) )
& ( ~ ( in @ X298 @ X290 )
| ~ ( X289 @ X298 @ X297 )
| ( in @ X297 @ ( esk7_2 @ X289 @ X290 ) )
| ( X289 @ ( esk5_2 @ X289 @ X290 ) @ ( esk6_3 @ X289 @ X290 @ X292 ) )
| ~ ( X289 @ ( esk5_2 @ X289 @ X290 ) @ X292 ) )
& ( ( in @ ( esk8_3 @ X289 @ X290 @ X295 ) @ X290 )
| ~ ( in @ X295 @ ( esk7_2 @ X289 @ X290 ) )
| ( X292
!= ( esk6_3 @ X289 @ X290 @ X292 ) )
| ~ ( X289 @ ( esk5_2 @ X289 @ X290 ) @ X292 ) )
& ( ( X289 @ ( esk8_3 @ X289 @ X290 @ X295 ) @ X295 )
| ~ ( in @ X295 @ ( esk7_2 @ X289 @ X290 ) )
| ( X292
!= ( esk6_3 @ X289 @ X290 @ X292 ) )
| ~ ( X289 @ ( esk5_2 @ X289 @ X290 ) @ X292 ) )
& ( ~ ( in @ X298 @ X290 )
| ~ ( X289 @ X298 @ X297 )
| ( in @ X297 @ ( esk7_2 @ X289 @ X290 ) )
| ( X292
!= ( esk6_3 @ X289 @ X290 @ X292 ) )
| ~ ( X289 @ ( esk5_2 @ X289 @ X290 ) @ X292 ) )
& ( ( in @ ( esk9_1 @ X299 ) @ X299 )
| ~ ( in @ X300 @ X299 ) )
& ( ~ ( in @ X302 @ ( esk9_1 @ X299 ) )
| ~ ( in @ X302 @ X299 )
| ~ ( in @ X300 @ X299 ) )
& epred1_0
& ( ( X303 @ ( esk10_2 @ X303 @ X304 ) )
| ~ ( X303 @ X304 )
| ( X303 @ ( descr @ X303 ) ) )
& ( ( X304
!= ( esk10_2 @ X303 @ X304 ) )
| ~ ( X303 @ X304 )
| ( X303 @ ( descr @ X303 ) ) )
& ( ~ ( in @ X308 @ X306 )
| ~ ( X307 @ X308 )
| ( in @ X308 @ ( dsetconstr @ X306 @ X307 ) ) )
& ( ~ ( in @ X311 @ ( dsetconstr @ X309 @ X310 ) )
| ( in @ X311 @ X309 ) )
& ( ~ ( in @ X314 @ ( dsetconstr @ X312 @ X313 ) )
| ( X313 @ X314 ) )
& ( ( X315 @ ( esk12_1 @ X315 ) )
| ( X315 @ ( esk11_2 @ X315 @ X316 ) )
| ~ ( X315 @ X316 ) )
& ( ~ ( X315 @ X319 )
| ( ( esk12_1 @ X315 )
= X319 )
| ( X315 @ ( esk11_2 @ X315 @ X316 ) )
| ~ ( X315 @ X316 ) )
& ( ( X315 @ ( esk12_1 @ X315 ) )
| ( X316
!= ( esk11_2 @ X315 @ X316 ) )
| ~ ( X315 @ X316 ) )
& ( ~ ( X315 @ X319 )
| ( ( esk12_1 @ X315 )
= X319 )
| ( X316
!= ( esk11_2 @ X315 @ X316 ) )
| ~ ( X315 @ X316 ) )
& ( ~ ( in @ X321
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X320 ) )
| X320 )
& ( ~ ( in @ X322 @ emptyset )
| X323 )
& ( ~ ( in @ X324 @ emptyset )
| ~ $true )
& ~ ( in @ X325 @ emptyset )
& ( ( X326 @ ( esk13_2 @ X326 @ X327 ) )
| ~ ( X326 @ X327 )
| ( X326 @ ( esk14_1 @ X326 ) ) )
& ( ( X327
!= ( esk13_2 @ X326 @ X327 ) )
| ~ ( X326 @ X327 )
| ( X326 @ ( esk14_1 @ X326 ) ) )
& ( ( in @ ( esk16_2 @ X330 @ X331 ) @ X331 )
| ( X330 = X331 )
| ( in @ ( esk15_2 @ X330 @ X331 ) @ X330 ) )
& ( ~ ( in @ ( esk16_2 @ X330 @ X331 ) @ X330 )
| ( X330 = X331 )
| ( in @ ( esk15_2 @ X330 @ X331 ) @ X330 ) )
& ( ( in @ ( esk16_2 @ X330 @ X331 ) @ X331 )
| ( X330 = X331 )
| ~ ( in @ ( esk15_2 @ X330 @ X331 ) @ X331 ) )
& ( ~ ( in @ ( esk16_2 @ X330 @ X331 ) @ X330 )
| ( X330 = X331 )
| ~ ( in @ ( esk15_2 @ X330 @ X331 ) @ X331 ) )
& ( ( in @ ( esk17_1 @ X334 ) @ X334 )
| ( X334 = emptyset ) )
& ( ( in @ ( esk18_1 @ X336 ) @ X336 )
| ( X336 = emptyset ) )
& ( ~ ( in @ X340 @ ( dsetconstr @ X338 @ X339 ) )
| ( X339 @ X340 )
| ~ ( in @ X340 @ X338 ) )
& ( ~ ( X339 @ X340 )
| ( in @ X340 @ ( dsetconstr @ X338 @ X339 ) )
| ~ ( in @ X340 @ X338 ) )
& ( ( X341 = emptyset )
| ( in @ ( esk19_1 @ X341 ) @ X341 ) )
& ( ~ ( in @ X345 @ X343 )
| ~ ( X344 @ X345 )
| ( ( dsetconstr @ X343 @ X344 )
!= emptyset ) )
& ( ~ ( in @ X347 @ X346 )
| ( X346 != emptyset ) )
& ( in @ X348 @ ( setadjoin @ X348 @ X349 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X352 @ X351 )
| ( in @ X352 @ ( setadjoin @ X350 @ X351 ) ) )
& ( ( in @ X355 @ X354 )
| X356
| ( X355 = X353 )
| ~ ( in @ X355 @ ( setadjoin @ X353 @ X354 ) ) )
& ( ~ X356
| X356
| ( X355 = X353 )
| ~ ( in @ X355 @ ( setadjoin @ X353 @ X354 ) ) )
& ( ( in @ X355 @ X354 )
| X356
| ~ X356
| ~ ( in @ X355 @ ( setadjoin @ X353 @ X354 ) ) )
& ( ~ X356
| X356
| ~ X356
| ~ ( in @ X355 @ ( setadjoin @ X353 @ X354 ) ) )
& ( ~ ( in @ X359 @ ( setadjoin @ X357 @ X358 ) )
| ( X359 = X357 )
| ( in @ X359 @ X358 ) )
& ( ( dsetconstr @ X360
@ ^ [Z0: $i] : $true )
= X360 )
& ( ( in @ ( esk20_2 @ X361 @ X362 ) @ X362 )
| ( in @ X362 @ ( powerset @ X361 ) ) )
& ( ~ ( in @ ( esk20_2 @ X361 @ X362 ) @ X361 )
| ( in @ X362 @ ( powerset @ X361 ) ) )
& ( in @ emptyset @ ( powerset @ X364 ) )
& ( in @ emptyset @ ( powerset @ X365 ) )
& ( ~ ( in @ X367 @ ( powerset @ X366 ) )
| ~ ( in @ X368 @ X367 )
| ( in @ X368 @ X366 ) )
& ( ~ ( in @ X370 @ X371 )
| ~ ( in @ X371 @ X369 )
| ( in @ X370 @ ( setunion @ X369 ) ) )
& ( ( in @ X373 @ ( esk21_3 @ X372 @ X373 @ X374 ) )
| X374
| ~ ( in @ X373 @ ( setunion @ X372 ) ) )
& ( ( in @ ( esk21_3 @ X372 @ X373 @ X374 ) @ X372 )
| X374
| ~ ( in @ X373 @ ( setunion @ X372 ) ) )
& ( ~ X374
| X374
| ~ ( in @ X373 @ ( setunion @ X372 ) ) )
& ( ~ ( in @ X377 @ X376 )
| ( in @ X377 @ ( powerset @ ( setunion @ X376 ) ) ) )
& ( epred2_0 @ esk22_0 )
& ( ~ ( epred2_0 @ X380 )
| ( esk22_0 = X380 ) )
& ( ~ ( epred2_0 @ ( esk23_1 @ X381 ) )
| ( ( esk23_1 @ X381 )
!= X381 ) )
& ( ( epred2_0 @ ( esk23_1 @ X381 ) )
| ( ( esk23_1 @ X381 )
= X381 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])])])])]) ).
thf(c_0_69,negated_conjecture,
! [X2: $i] :
( ( esk22_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ ( esk23_1 @ X2 ) )
| ( ( esk23_1 @ X2 )
= X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_71,negated_conjecture,
! [X2: $i] :
( ( ( esk23_1 @ X2 )
= esk22_0 )
| ( ( esk23_1 @ X2 )
= X2 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_72,negated_conjecture,
! [X2: $i] :
( ~ ( epred2_0 @ ( esk23_1 @ X2 ) )
| ( ( esk23_1 @ X2 )
!= X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_73,negated_conjecture,
( ( esk23_1 @ esk22_0 )
= esk22_0 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_71])]) ).
thf(c_0_74,negated_conjecture,
epred2_0 @ esk22_0,
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU525^1 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun May 19 17:41:22 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.46 Running higher-order theorem proving
% 0.16/0.46 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 # Version: 3.1.0-ho
% 0.16/0.48 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.16/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.48 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.48 # Starting sh5l with 300s (1) cores
% 0.16/0.48 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.48 # Starting new_bool_2 with 300s (1) cores
% 0.16/0.48 # sh5l with pid 15990 completed with status 0
% 0.16/0.48 # Result found by sh5l
% 0.16/0.48 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.16/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.48 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.48 # Starting sh5l with 300s (1) cores
% 0.16/0.48 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.16/0.48 # Search class: HGHSM-FFMS31-SHSSMSBN
% 0.16/0.48 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.48 # Starting new_ho_10 with 181s (1) cores
% 0.16/0.48 # new_ho_10 with pid 15999 completed with status 0
% 0.16/0.48 # Result found by new_ho_10
% 0.16/0.48 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.16/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.48 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.48 # Starting sh5l with 300s (1) cores
% 0.16/0.48 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.16/0.48 # Search class: HGHSM-FFMS31-SHSSMSBN
% 0.16/0.48 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.48 # Starting new_ho_10 with 181s (1) cores
% 0.16/0.48 # Preprocessing time : 0.002 s
% 0.16/0.48 # Presaturation interreduction done
% 0.16/0.48
% 0.16/0.48 # Proof found!
% 0.16/0.48 # SZS status Theorem
% 0.16/0.48 # SZS output start CNFRefutation
% See solution above
% 0.16/0.48 # Parsed axioms : 97
% 0.16/0.48 # Removed by relevancy pruning/SinE : 52
% 0.16/0.48 # Initial clauses : 91
% 0.16/0.48 # Removed in clause preprocessing : 4
% 0.16/0.48 # Initial clauses in saturation : 87
% 0.16/0.48 # Processed clauses : 106
% 0.16/0.48 # ...of these trivial : 1
% 0.16/0.48 # ...subsumed : 11
% 0.16/0.48 # ...remaining for further processing : 94
% 0.16/0.48 # Other redundant clauses eliminated : 5
% 0.16/0.48 # Clauses deleted for lack of memory : 0
% 0.16/0.48 # Backward-subsumed : 0
% 0.16/0.48 # Backward-rewritten : 1
% 0.16/0.48 # Generated clauses : 19
% 0.16/0.48 # ...of the previous two non-redundant : 12
% 0.16/0.48 # ...aggressively subsumed : 0
% 0.16/0.48 # Contextual simplify-reflections : 0
% 0.16/0.48 # Paramodulations : 12
% 0.16/0.48 # Factorizations : 2
% 0.16/0.48 # NegExts : 0
% 0.16/0.48 # Equation resolutions : 5
% 0.16/0.48 # Disequality decompositions : 0
% 0.16/0.48 # Total rewrite steps : 19
% 0.16/0.48 # ...of those cached : 14
% 0.16/0.48 # Propositional unsat checks : 0
% 0.16/0.48 # Propositional check models : 0
% 0.16/0.48 # Propositional check unsatisfiable : 0
% 0.16/0.48 # Propositional clauses : 0
% 0.16/0.48 # Propositional clauses after purity: 0
% 0.16/0.48 # Propositional unsat core size : 0
% 0.16/0.48 # Propositional preprocessing time : 0.000
% 0.16/0.48 # Propositional encoding time : 0.000
% 0.16/0.49 # Propositional solver time : 0.000
% 0.16/0.49 # Success case prop preproc time : 0.000
% 0.16/0.49 # Success case prop encoding time : 0.000
% 0.16/0.49 # Success case prop solver time : 0.000
% 0.16/0.49 # Current number of processed clauses : 18
% 0.16/0.49 # Positive orientable unit clauses : 7
% 0.16/0.49 # Positive unorientable unit clauses: 0
% 0.16/0.49 # Negative unit clauses : 2
% 0.16/0.49 # Non-unit-clauses : 9
% 0.16/0.49 # Current number of unprocessed clauses: 66
% 0.16/0.49 # ...number of literals in the above : 199
% 0.16/0.49 # Current number of archived formulas : 0
% 0.16/0.49 # Current number of archived clauses : 74
% 0.16/0.49 # Clause-clause subsumption calls (NU) : 1945
% 0.16/0.49 # Rec. Clause-clause subsumption calls : 806
% 0.16/0.49 # Non-unit clause-clause subsumptions : 10
% 0.16/0.49 # Unit Clause-clause subsumption calls : 11
% 0.16/0.49 # Rewrite failures with RHS unbound : 0
% 0.16/0.49 # BW rewrite match attempts : 3
% 0.16/0.49 # BW rewrite match successes : 1
% 0.16/0.49 # Condensation attempts : 106
% 0.16/0.49 # Condensation successes : 3
% 0.16/0.49 # Termbank termtop insertions : 13161
% 0.16/0.49 # Search garbage collected termcells : 4539
% 0.16/0.49
% 0.16/0.49 # -------------------------------------------------
% 0.16/0.49 # User time : 0.013 s
% 0.16/0.49 # System time : 0.002 s
% 0.16/0.49 # Total time : 0.015 s
% 0.16/0.49 # Maximum resident set size: 3020 pages
% 0.16/0.49
% 0.16/0.49 # -------------------------------------------------
% 0.16/0.49 # User time : 0.014 s
% 0.16/0.49 # System time : 0.007 s
% 0.16/0.49 # Total time : 0.021 s
% 0.16/0.49 # Maximum resident set size: 1828 pages
% 0.16/0.49 % E---3.1 exiting
% 0.16/0.49 % E exiting
%------------------------------------------------------------------------------