TSTP Solution File: SEU520^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU520^1 : 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 03:27:55 EDT 2024
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 104
% Syntax : Number of formulae : 128 ( 16 unt; 65 typ; 0 def)
% Number of atoms : 473 ( 77 equ; 0 cnn)
% Maximal formula atoms : 127 ( 7 avg)
% Number of connectives : 1584 ( 110 ~; 115 |; 108 &; 989 @)
% ( 59 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 142 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 65 usr; 42 con; 0-3 aty)
% Number of variables : 377 ( 43 ^ 288 !; 46 ?; 377 :)
% 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_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,
epred1_0: $o ).
thf(decl_70,type,
esk1_2: $i > $i > $i ).
thf(decl_71,type,
esk2_2: $i > $i > $i ).
thf(decl_72,type,
esk3_1: $i > $i ).
thf(decl_73,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_74,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_75,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_76,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_77,type,
esk8_1: $i > $i ).
thf(decl_78,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_79,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_80,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_81,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_82,type,
esk13_2: $i > $i > $i ).
thf(decl_83,type,
esk14_2: $i > $i > $i ).
thf(decl_84,type,
esk15_1: $i > $i ).
thf(decl_85,type,
esk16_1: $i > $i ).
thf(decl_86,type,
esk17_1: $i > $i ).
thf(decl_87,type,
esk18_2: $i > $i > $i ).
thf(decl_88,type,
esk19_0: $i ).
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(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(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
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(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
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(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(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(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(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(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(emptyInPowerset,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
=> ! [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(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
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(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(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X13: $o] :
( ( ( X3 = X2 )
=> X13 )
=> ( ( ( in @ X3 @ X4 )
=> X13 )
=> X13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(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(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(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(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
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_38,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_39,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_40,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_41,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_42,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_43,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_44,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_45,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X115: $i] :
( ( X1 @ X115 )
& ! [X116: $i] :
( ( X1 @ X116 )
=> ( X115 = X116 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_46,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_47,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_40]) ).
thf(c_0_48,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_41,c_0_40]) ).
thf(c_0_49,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_40]) ).
thf(c_0_50,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X113: $i] :
( ( X6 @ X2 @ X113 )
& ! [X114: $i] :
( ( X6 @ X2 @ X114 )
=> ( X113 = X114 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_42,c_0_39]) ).
thf(c_0_51,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_52,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_53,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_54,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_55,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_43]) ).
thf(c_0_56,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X117: $i] :
( ( X1 @ X117 )
& ! [X118: $i] :
( ( X1 @ X118 )
=> ( X117 = X118 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_44,c_0_39]) ).
thf(c_0_57,plain,
( epred1_0
<=> ! [X145: $i] :
? [X146: $i] :
( ! [X147: $i] :
( ( in @ X147 @ X146 )
=> ! [X148: $i] :
( ( in @ X148 @ X147 )
=> ( in @ X148 @ X145 ) ) )
& ! [X149: $i,X150: $i] :
( ( ( in @ X149 @ X145 )
& ( in @ X150 @ X145 ) )
=> ( ! [X151: $i] :
( ( in @ X151 @ X146 )
=> ( ( in @ X149 @ X151 )
<=> ( in @ X150 @ X151 ) ) )
=> ( X149 = X150 ) ) )
& ! [X152: $i,X153: $i] :
( ( ( in @ X152 @ X146 )
& ( in @ X153 @ X146 ) )
=> ( ! [X154: $i] :
( ( in @ X154 @ X152 )
=> ( in @ X154 @ X153 ) )
| ! [X155: $i] :
( ( in @ X155 @ X153 )
=> ( in @ X155 @ X152 ) ) ) )
& ! [X156: $i] :
( ( ! [X157: $i] :
( ( in @ X157 @ X156 )
=> ( in @ X157 @ X145 ) )
& ? [X158: $i] : ( in @ X158 @ X156 ) )
=> ? [X159: $i,X160: $i] :
( ( in @ X159 @ X146 )
& ( in @ X160 @ X156 )
& ~ ? [X161: $i] :
( ( in @ X161 @ X159 )
& ( in @ X161 @ X156 ) )
& ! [X162: $i] :
( ( in @ X162 @ X146 )
=> ( ! [X163: $i] :
( ( in @ X163 @ X162 )
=> ( in @ X163 @ X159 ) )
| ( in @ X160 @ X162 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_58,negated_conjecture,
~ ( ! [X119: $i,X120: $i] :
( ! [X121: $i] :
( ( in @ X121 @ X119 )
<=> ( in @ X121 @ X120 ) )
=> ( X119 = X120 ) )
=> ( ! [X122: $i] :
~ ( in @ X122 @ emptyset )
=> ( ! [X123: $i,X124: $i,X125: $i] :
( ( in @ X125 @ ( setadjoin @ X123 @ X124 ) )
<=> ( ( X125 = X123 )
| ( in @ X125 @ X124 ) ) )
=> ( ! [X126: $i,X127: $i] :
( ( in @ X127 @ ( powerset @ X126 ) )
<=> ! [X128: $i] :
( ( in @ X128 @ X127 )
=> ( in @ X128 @ X126 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X129: $i] :
( ( in @ X129 @ omega )
=> ( in @ ( setadjoin @ X129 @ X129 ) @ omega ) )
=> ( ! [X130: $i] :
( ( ( in @ emptyset @ X130 )
& ! [X131: $i] :
( ( ( in @ X131 @ omega )
& ( in @ X131 @ X130 ) )
=> ( in @ ( setadjoin @ X131 @ X131 ) @ X130 ) ) )
=> ! [X132: $i] :
( ( in @ X132 @ omega )
=> ( in @ X132 @ X130 ) ) )
=> ( ! [X133: $i > $i > $o,X134: $i] :
( ! [X135: $i] :
( ( in @ X135 @ X134 )
=> ? [X136: $i] :
( ( X133 @ X135 @ X136 )
& ! [X137: $i] :
( ( X133 @ X135 @ X137 )
=> ( X136 = X137 ) ) ) )
=> ? [X138: $i] :
! [X139: $i] :
( ( in @ X139 @ X138 )
<=> ? [X140: $i] :
( ( in @ X140 @ X134 )
& ( X133 @ X140 @ X139 ) ) ) )
=> ( ! [X141: $i] :
( ? [X142: $i] : ( in @ X142 @ X141 )
=> ? [X143: $i] :
( ( in @ X143 @ X141 )
& ~ ? [X144: $i] :
( ( in @ X144 @ X143 )
& ( in @ X144 @ X141 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X164: $i,X165: $i > $o,X166: $i] :
( ( in @ X166 @ X164 )
=> ( ( X165 @ X166 )
=> ( in @ X166
@ ( dsetconstr @ X164
@ ^ [Z0: $i] : ( X165 @ Z0 ) ) ) ) )
=> ( ! [X167: $i,X168: $i > $o,X169: $i] :
( ( in @ X169
@ ( dsetconstr @ X167
@ ^ [Z0: $i] : ( X168 @ Z0 ) ) )
=> ( in @ X169 @ X167 ) )
=> ( ! [X170: $i,X171: $i > $o,X172: $i] :
( ( in @ X172
@ ( dsetconstr @ X170
@ ^ [Z0: $i] : ( X171 @ Z0 ) ) )
=> ( X171 @ X172 ) )
=> ( ! [X173: $i > $o] :
( ? [X174: $i] :
( ( X173 @ X174 )
& ! [X175: $i] :
( ( X173 @ X175 )
=> ( X174 = X175 ) ) )
=> ? [X176: $i] :
( ( X173 @ X176 )
& ! [X177: $i] :
( ( X173 @ X177 )
=> ( X176 = X177 ) ) ) )
=> ( ! [X178: $o,X179: $i] :
( ( in @ X179
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X178 ) )
=> X178 )
=> ( ! [X180: $i] :
( ( in @ X180 @ emptyset )
=> ! [X181: $o] : X181 )
=> ( ! [X182: $i] :
~ ( in @ X182 @ emptyset )
=> ( ! [X183: $i] :
~ ( in @ X183 @ emptyset )
=> ( ! [X184: $i > $o] :
( ? [X185: $i] :
( ( X184 @ X185 )
& ! [X186: $i] :
( ( X184 @ X186 )
=> ( X185 = X186 ) ) )
=> ? [X187: $i] : ( X184 @ X187 ) )
=> ( ! [X188: $i,X189: $i] :
( ! [X190: $i] :
( ( in @ X190 @ X188 )
=> ( in @ X190 @ X189 ) )
=> ( ! [X191: $i] :
( ( in @ X191 @ X189 )
=> ( in @ X191 @ X188 ) )
=> ( X188 = X189 ) ) )
=> ( ! [X192: $i] :
( ! [X193: $i] :
~ ( in @ X193 @ X192 )
=> ( X192 = emptyset ) )
=> ( ! [X194: $i] :
( ! [X195: $i] :
~ ( in @ X195 @ X194 )
=> ( X194 = emptyset ) )
=> ( ! [X196: $i,X197: $i > $o,X198: $i] :
( ( in @ X198 @ X196 )
=> ( ( in @ X198
@ ( dsetconstr @ X196
@ ^ [Z0: $i] : ( X197 @ Z0 ) ) )
<=> ( X197 @ X198 ) ) )
=> ( ! [X199: $i] :
( ( X199 != emptyset )
=> ? [X200: $i] : ( in @ X200 @ X199 ) )
=> ( ! [X201: $i,X202: $i > $o,X203: $i] :
( ( in @ X203 @ X201 )
=> ( ( X202 @ X203 )
=> ( ( dsetconstr @ X201
@ ^ [Z0: $i] : ( X202 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X204: $i] :
( ? [X205: $i] : ( in @ X205 @ X204 )
=> ( X204 != emptyset ) )
=> ( ! [X206: $i,X207: $i] : ( in @ X206 @ ( setadjoin @ X206 @ X207 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X208: $i,X209: $i,X210: $i] :
( ( in @ X210 @ X209 )
=> ( in @ X210 @ ( setadjoin @ X208 @ X209 ) ) )
=> ( ! [X211: $i,X212: $i,X213: $i] :
( ( in @ X213 @ ( setadjoin @ X211 @ X212 ) )
=> ! [X214: $o] :
( ( ( X213 = X211 )
=> X214 )
=> ( ( ( in @ X213 @ X212 )
=> X214 )
=> X214 ) ) )
=> ( ! [X215: $i,X216: $i,X217: $i] :
( ( in @ X217 @ ( setadjoin @ X215 @ X216 ) )
=> ( ( X217 = X215 )
| ( in @ X217 @ X216 ) ) )
=> ( ! [X218: $i] :
( ( dsetconstr @ X218
@ ^ [Z0: $i] : $true )
= X218 )
=> ( ! [X219: $i,X220: $i] :
( ! [X221: $i] :
( ( in @ X221 @ X220 )
=> ( in @ X221 @ X219 ) )
=> ( in @ X220 @ ( powerset @ X219 ) ) )
=> ( ! [X222: $i] : ( in @ emptyset @ ( powerset @ X222 ) )
=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[emptyInPowerset]),c_0_45]),emptyinPowerset]),noeltsimpempty]),c_0_46]),c_0_47]),omega0Ax]),c_0_48]),c_0_49]),omegaSAx]),setadjoinIL]),emptyinunitempty]),omegaIndAx]),setadjoinIR]),setadjoinE]),c_0_50]),setadjoinOr]),c_0_51]),foundationAx]),powersetI]),wellorderingAx]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_56]),setext]),emptyI]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_57]) ).
thf(c_0_59,negated_conjecture,
! [X223: $i,X224: $i,X226: $i,X227: $i,X228: $i,X229: $i,X230: $i,X231: $i,X232: $i,X233: $i,X234: $i,X236: $i,X237: $i,X239: $i,X240: $i > $i > $o,X241: $i,X243: $i,X246: $i,X248: $i,X249: $i,X250: $i,X251: $i,X253: $i,X254: $i,X255: $i > $o,X256: $i,X257: $i,X258: $i > $o,X259: $i,X260: $i,X261: $i > $o,X262: $i,X263: $i > $o,X264: $i,X267: $i,X268: $o,X269: $i,X270: $i,X271: $o,X272: $i,X273: $i,X274: $i > $o,X275: $i,X278: $i,X279: $i,X282: $i,X284: $i,X286: $i,X287: $i > $o,X288: $i,X289: $i,X291: $i,X292: $i > $o,X293: $i,X294: $i,X295: $i,X296: $i,X297: $i,X298: $i,X299: $i,X300: $i,X301: $i,X302: $i,X303: $i,X304: $o,X305: $i,X306: $i,X307: $i,X308: $i,X309: $i,X310: $i,X312: $i] :
( ( ~ ( in @ ( esk1_2 @ X223 @ X224 ) @ X223 )
| ~ ( in @ ( esk1_2 @ X223 @ X224 ) @ X224 )
| ( X223 = X224 ) )
& ( ( in @ ( esk1_2 @ X223 @ X224 ) @ X223 )
| ( in @ ( esk1_2 @ X223 @ X224 ) @ X224 )
| ( X223 = X224 ) )
& ~ ( in @ X226 @ emptyset )
& ( ~ ( in @ X229 @ ( setadjoin @ X227 @ X228 ) )
| ( X229 = X227 )
| ( in @ X229 @ X228 ) )
& ( ( X229 != X227 )
| ( in @ X229 @ ( setadjoin @ X227 @ X228 ) ) )
& ( ~ ( in @ X229 @ X228 )
| ( in @ X229 @ ( setadjoin @ X227 @ X228 ) ) )
& ( ~ ( in @ X231 @ ( powerset @ X230 ) )
| ~ ( in @ X232 @ X231 )
| ( in @ X232 @ X230 ) )
& ( ( in @ ( esk2_2 @ X233 @ X234 ) @ X234 )
| ( in @ X234 @ ( powerset @ X233 ) ) )
& ( ~ ( in @ ( esk2_2 @ X233 @ X234 ) @ X233 )
| ( in @ X234 @ ( powerset @ X233 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X236 @ omega )
| ( in @ ( setadjoin @ X236 @ X236 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X237 ) @ omega )
| ~ ( in @ emptyset @ X237 )
| ~ ( in @ X239 @ omega )
| ( in @ X239 @ X237 ) )
& ( ( in @ ( esk3_1 @ X237 ) @ X237 )
| ~ ( in @ emptyset @ X237 )
| ~ ( in @ X239 @ omega )
| ( in @ X239 @ X237 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X237 ) @ ( esk3_1 @ X237 ) ) @ X237 )
| ~ ( in @ emptyset @ X237 )
| ~ ( in @ X239 @ omega )
| ( in @ X239 @ X237 ) )
& ( ( in @ ( esk7_3 @ X240 @ X241 @ X246 ) @ X241 )
| ~ ( in @ X246 @ ( esk6_2 @ X240 @ X241 ) )
| ( in @ ( esk4_2 @ X240 @ X241 ) @ X241 ) )
& ( ( X240 @ ( esk7_3 @ X240 @ X241 @ X246 ) @ X246 )
| ~ ( in @ X246 @ ( esk6_2 @ X240 @ X241 ) )
| ( in @ ( esk4_2 @ X240 @ X241 ) @ X241 ) )
& ( ~ ( in @ X249 @ X241 )
| ~ ( X240 @ X249 @ X248 )
| ( in @ X248 @ ( esk6_2 @ X240 @ X241 ) )
| ( in @ ( esk4_2 @ X240 @ X241 ) @ X241 ) )
& ( ( in @ ( esk7_3 @ X240 @ X241 @ X246 ) @ X241 )
| ~ ( in @ X246 @ ( esk6_2 @ X240 @ X241 ) )
| ( X240 @ ( esk4_2 @ X240 @ X241 ) @ ( esk5_3 @ X240 @ X241 @ X243 ) )
| ~ ( X240 @ ( esk4_2 @ X240 @ X241 ) @ X243 ) )
& ( ( X240 @ ( esk7_3 @ X240 @ X241 @ X246 ) @ X246 )
| ~ ( in @ X246 @ ( esk6_2 @ X240 @ X241 ) )
| ( X240 @ ( esk4_2 @ X240 @ X241 ) @ ( esk5_3 @ X240 @ X241 @ X243 ) )
| ~ ( X240 @ ( esk4_2 @ X240 @ X241 ) @ X243 ) )
& ( ~ ( in @ X249 @ X241 )
| ~ ( X240 @ X249 @ X248 )
| ( in @ X248 @ ( esk6_2 @ X240 @ X241 ) )
| ( X240 @ ( esk4_2 @ X240 @ X241 ) @ ( esk5_3 @ X240 @ X241 @ X243 ) )
| ~ ( X240 @ ( esk4_2 @ X240 @ X241 ) @ X243 ) )
& ( ( in @ ( esk7_3 @ X240 @ X241 @ X246 ) @ X241 )
| ~ ( in @ X246 @ ( esk6_2 @ X240 @ X241 ) )
| ( X243
!= ( esk5_3 @ X240 @ X241 @ X243 ) )
| ~ ( X240 @ ( esk4_2 @ X240 @ X241 ) @ X243 ) )
& ( ( X240 @ ( esk7_3 @ X240 @ X241 @ X246 ) @ X246 )
| ~ ( in @ X246 @ ( esk6_2 @ X240 @ X241 ) )
| ( X243
!= ( esk5_3 @ X240 @ X241 @ X243 ) )
| ~ ( X240 @ ( esk4_2 @ X240 @ X241 ) @ X243 ) )
& ( ~ ( in @ X249 @ X241 )
| ~ ( X240 @ X249 @ X248 )
| ( in @ X248 @ ( esk6_2 @ X240 @ X241 ) )
| ( X243
!= ( esk5_3 @ X240 @ X241 @ X243 ) )
| ~ ( X240 @ ( esk4_2 @ X240 @ X241 ) @ X243 ) )
& ( ( in @ ( esk8_1 @ X250 ) @ X250 )
| ~ ( in @ X251 @ X250 ) )
& ( ~ ( in @ X253 @ ( esk8_1 @ X250 ) )
| ~ ( in @ X253 @ X250 )
| ~ ( in @ X251 @ X250 ) )
& epred1_0
& descrp
& ( ~ ( in @ X256 @ X254 )
| ~ ( X255 @ X256 )
| ( in @ X256
@ ( dsetconstr @ X254
@ ^ [Z0: $i] : ( X255 @ Z0 ) ) ) )
& ( ~ ( in @ X259
@ ( dsetconstr @ X257
@ ^ [Z0: $i] : ( X258 @ Z0 ) ) )
| ( in @ X259 @ X257 ) )
& ( ~ ( in @ X262
@ ( dsetconstr @ X260
@ ^ [Z0: $i] : ( X261 @ Z0 ) ) )
| ( X261 @ X262 ) )
& ( ( X263 @ ( esk10_1 @ X263 ) )
| ( X263 @ ( esk9_2 @ X263 @ X264 ) )
| ~ ( X263 @ X264 ) )
& ( ~ ( X263 @ X267 )
| ( ( esk10_1 @ X263 )
= X267 )
| ( X263 @ ( esk9_2 @ X263 @ X264 ) )
| ~ ( X263 @ X264 ) )
& ( ( X263 @ ( esk10_1 @ X263 ) )
| ( X264
!= ( esk9_2 @ X263 @ X264 ) )
| ~ ( X263 @ X264 ) )
& ( ~ ( X263 @ X267 )
| ( ( esk10_1 @ X263 )
= X267 )
| ( X264
!= ( esk9_2 @ X263 @ X264 ) )
| ~ ( X263 @ X264 ) )
& ( ~ ( in @ X269
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X268 ) )
| X268 )
& ( ~ ( in @ X270 @ emptyset )
| X271 )
& ~ ( in @ X272 @ emptyset )
& ~ ( in @ X273 @ emptyset )
& ( ( X274 @ ( esk11_2 @ X274 @ X275 ) )
| ~ ( X274 @ X275 )
| ( X274 @ ( esk12_1 @ X274 ) ) )
& ( ( X275
!= ( esk11_2 @ X274 @ X275 ) )
| ~ ( X274 @ X275 )
| ( X274 @ ( esk12_1 @ X274 ) ) )
& ( ( in @ ( esk14_2 @ X278 @ X279 ) @ X279 )
| ( X278 = X279 )
| ( in @ ( esk13_2 @ X278 @ X279 ) @ X278 ) )
& ( ~ ( in @ ( esk14_2 @ X278 @ X279 ) @ X278 )
| ( X278 = X279 )
| ( in @ ( esk13_2 @ X278 @ X279 ) @ X278 ) )
& ( ( in @ ( esk14_2 @ X278 @ X279 ) @ X279 )
| ( X278 = X279 )
| ~ ( in @ ( esk13_2 @ X278 @ X279 ) @ X279 ) )
& ( ~ ( in @ ( esk14_2 @ X278 @ X279 ) @ X278 )
| ( X278 = X279 )
| ~ ( in @ ( esk13_2 @ X278 @ X279 ) @ X279 ) )
& ( ( in @ ( esk15_1 @ X282 ) @ X282 )
| ( X282 = emptyset ) )
& ( ( in @ ( esk16_1 @ X284 ) @ X284 )
| ( X284 = emptyset ) )
& ( ~ ( in @ X288
@ ( dsetconstr @ X286
@ ^ [Z0: $i] : ( X287 @ Z0 ) ) )
| ( X287 @ X288 )
| ~ ( in @ X288 @ X286 ) )
& ( ~ ( X287 @ X288 )
| ( in @ X288
@ ( dsetconstr @ X286
@ ^ [Z0: $i] : ( X287 @ Z0 ) ) )
| ~ ( in @ X288 @ X286 ) )
& ( ( X289 = emptyset )
| ( in @ ( esk17_1 @ X289 ) @ X289 ) )
& ( ~ ( in @ X293 @ X291 )
| ~ ( X292 @ X293 )
| ( ( dsetconstr @ X291
@ ^ [Z0: $i] : ( X292 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X295 @ X294 )
| ( X294 != emptyset ) )
& ( in @ X296 @ ( setadjoin @ X296 @ X297 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X300 @ X299 )
| ( in @ X300 @ ( setadjoin @ X298 @ X299 ) ) )
& ( ( in @ X303 @ X302 )
| X304
| ( X303 = X301 )
| ~ ( in @ X303 @ ( setadjoin @ X301 @ X302 ) ) )
& ( ~ X304
| X304
| ( X303 = X301 )
| ~ ( in @ X303 @ ( setadjoin @ X301 @ X302 ) ) )
& ( ( in @ X303 @ X302 )
| X304
| ~ X304
| ~ ( in @ X303 @ ( setadjoin @ X301 @ X302 ) ) )
& ( ~ X304
| X304
| ~ X304
| ~ ( in @ X303 @ ( setadjoin @ X301 @ X302 ) ) )
& ( ~ ( in @ X307 @ ( setadjoin @ X305 @ X306 ) )
| ( X307 = X305 )
| ( in @ X307 @ X306 ) )
& ( ( dsetconstr @ X308
@ ^ [Z0: $i] : $true )
= X308 )
& ( ( in @ ( esk18_2 @ X309 @ X310 ) @ X310 )
| ( in @ X310 @ ( powerset @ X309 ) ) )
& ( ~ ( in @ ( esk18_2 @ X309 @ X310 ) @ X309 )
| ( in @ X310 @ ( powerset @ X309 ) ) )
& ( in @ emptyset @ ( powerset @ X312 ) )
& ~ ( in @ emptyset @ ( powerset @ esk19_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_58])])])])])]) ).
thf(c_0_60,negated_conjecture,
~ ( in @ emptyset @ ( powerset @ esk19_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_61,negated_conjecture,
! [X2: $i] : ( in @ emptyset @ ( powerset @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU520^1 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 15:57:08 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.43 Running higher-order theorem proving
% 0.16/0.43 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
% 0.16/0.46 # Version: 3.1.0-ho
% 0.16/0.46 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.16/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.46 # Starting sh5l with 300s (1) cores
% 0.16/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.16/0.46 # new_bool_2 with pid 32445 completed with status 0
% 0.16/0.46 # Result found by new_bool_2
% 0.16/0.46 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.16/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.46 # Starting sh5l with 300s (1) cores
% 0.16/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.16/0.46 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.46 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.16/0.46 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.46 # Starting new_ho_10 with 181s (1) cores
% 0.16/0.46 # new_ho_10 with pid 32446 completed with status 0
% 0.16/0.46 # Result found by new_ho_10
% 0.16/0.46 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.16/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.46 # Starting sh5l with 300s (1) cores
% 0.16/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.16/0.46 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.46 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.16/0.46 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.46 # Starting new_ho_10 with 181s (1) cores
% 0.16/0.46 # Preprocessing time : 0.004 s
% 0.16/0.46 # Presaturation interreduction done
% 0.16/0.46
% 0.16/0.46 # Proof found!
% 0.16/0.46 # SZS status Theorem
% 0.16/0.46 # SZS output start CNFRefutation
% See solution above
% 0.16/0.46 # Parsed axioms : 87
% 0.16/0.46 # Removed by relevancy pruning/SinE : 49
% 0.16/0.46 # Initial clauses : 78
% 0.16/0.46 # Removed in clause preprocessing : 3
% 0.16/0.46 # Initial clauses in saturation : 75
% 0.16/0.46 # Processed clauses : 9
% 0.16/0.46 # ...of these trivial : 0
% 0.16/0.46 # ...subsumed : 1
% 0.16/0.46 # ...remaining for further processing : 8
% 0.16/0.46 # Other redundant clauses eliminated : 0
% 0.16/0.46 # Clauses deleted for lack of memory : 0
% 0.16/0.46 # Backward-subsumed : 0
% 0.16/0.46 # Backward-rewritten : 1
% 0.16/0.46 # Generated clauses : 0
% 0.16/0.46 # ...of the previous two non-redundant : 0
% 0.16/0.46 # ...aggressively subsumed : 0
% 0.16/0.46 # Contextual simplify-reflections : 0
% 0.16/0.46 # Paramodulations : 0
% 0.16/0.46 # Factorizations : 0
% 0.16/0.46 # NegExts : 0
% 0.16/0.46 # Equation resolutions : 0
% 0.16/0.46 # Disequality decompositions : 0
% 0.16/0.46 # Total rewrite steps : 1
% 0.16/0.46 # ...of those cached : 0
% 0.16/0.46 # Propositional unsat checks : 0
% 0.16/0.46 # Propositional check models : 0
% 0.16/0.46 # Propositional check unsatisfiable : 0
% 0.16/0.46 # Propositional clauses : 0
% 0.16/0.46 # Propositional clauses after purity: 0
% 0.16/0.46 # Propositional unsat core size : 0
% 0.16/0.46 # Propositional preprocessing time : 0.000
% 0.16/0.46 # Propositional encoding time : 0.000
% 0.16/0.46 # Propositional solver time : 0.000
% 0.16/0.46 # Success case prop preproc time : 0.000
% 0.16/0.46 # Success case prop encoding time : 0.000
% 0.16/0.46 # Success case prop solver time : 0.000
% 0.16/0.46 # Current number of processed clauses : 7
% 0.16/0.46 # Positive orientable unit clauses : 6
% 0.16/0.46 # Positive unorientable unit clauses: 0
% 0.16/0.46 # Negative unit clauses : 1
% 0.16/0.46 # Non-unit-clauses : 0
% 0.16/0.46 # Current number of unprocessed clauses: 66
% 0.16/0.46 # ...number of literals in the above : 216
% 0.16/0.46 # Current number of archived formulas : 0
% 0.16/0.46 # Current number of archived clauses : 1
% 0.16/0.46 # Clause-clause subsumption calls (NU) : 0
% 0.16/0.46 # Rec. Clause-clause subsumption calls : 0
% 0.16/0.46 # Non-unit clause-clause subsumptions : 0
% 0.16/0.46 # Unit Clause-clause subsumption calls : 1
% 0.16/0.46 # Rewrite failures with RHS unbound : 0
% 0.16/0.46 # BW rewrite match attempts : 1
% 0.16/0.46 # BW rewrite match successes : 1
% 0.16/0.46 # Condensation attempts : 9
% 0.16/0.46 # Condensation successes : 0
% 0.16/0.46 # Termbank termtop insertions : 8236
% 0.16/0.46 # Search garbage collected termcells : 3080
% 0.16/0.46
% 0.16/0.46 # -------------------------------------------------
% 0.16/0.46 # User time : 0.012 s
% 0.16/0.46 # System time : 0.001 s
% 0.16/0.46 # Total time : 0.013 s
% 0.16/0.46 # Maximum resident set size: 2748 pages
% 0.16/0.46
% 0.16/0.46 # -------------------------------------------------
% 0.16/0.46 # User time : 0.015 s
% 0.16/0.46 # System time : 0.002 s
% 0.16/0.46 # Total time : 0.017 s
% 0.16/0.46 # Maximum resident set size: 1812 pages
% 0.16/0.46 % E---3.1 exiting
% 0.16/0.46 % E exiting
%------------------------------------------------------------------------------