TSTP Solution File: SEU518^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU518^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 03:27:54 EDT 2024
% Result : Theorem 0.60s 0.58s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 100
% Syntax : Number of formulae : 127 ( 15 unt; 63 typ; 0 def)
% Number of atoms : 469 ( 77 equ; 0 cnn)
% Maximal formula atoms : 124 ( 7 avg)
% Number of connectives : 1578 ( 112 ~; 118 |; 106 &; 986 @)
% ( 57 <=>; 199 =>; 0 <=; 0 <~>)
% Maximal formula depth : 137 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 41 con; 0-3 aty)
% Number of variables : 376 ( 43 ^ 287 !; 46 ?; 376 :)
% 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,
epred1_0: $o ).
thf(decl_68,type,
esk1_2: $i > $i > $i ).
thf(decl_69,type,
esk2_2: $i > $i > $i ).
thf(decl_70,type,
esk3_1: $i > $i ).
thf(decl_71,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_72,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_73,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_74,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_75,type,
esk8_1: $i > $i ).
thf(decl_76,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_77,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_78,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_79,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_80,type,
esk13_2: $i > $i > $i ).
thf(decl_81,type,
esk14_2: $i > $i > $i ).
thf(decl_82,type,
esk15_1: $i > $i ).
thf(decl_83,type,
esk16_1: $i > $i ).
thf(decl_84,type,
esk17_1: $i > $i ).
thf(decl_85,type,
esk18_0: $i ).
thf(decl_86,type,
esk19_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
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(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(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(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(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
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(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(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(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
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(powersetI,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
=> ! [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(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
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(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
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(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(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(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(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
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(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(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_36,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_37,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_38,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_39,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_40,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_41,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_42,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_43,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_44,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_36]) ).
thf(c_0_45,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X111: $i] :
( ( X6 @ X2 @ X111 )
& ! [X112: $i] :
( ( X6 @ X2 @ X112 )
=> ( X111 = X112 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_46,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_39,c_0_36]) ).
thf(c_0_47,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_36]) ).
thf(c_0_48,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_49,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_50,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_51,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_52,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X113: $i] :
( ( X1 @ X113 )
& ! [X114: $i] :
( ( X1 @ X114 )
=> ( X113 = X114 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_40,c_0_38]) ).
thf(c_0_53,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_41]) ).
thf(c_0_54,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X115: $i] :
( ( X1 @ X115 )
& ! [X116: $i] :
( ( X1 @ X116 )
=> ( X115 = X116 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_42,c_0_38]) ).
thf(c_0_55,plain,
( epred1_0
<=> ! [X143: $i] :
? [X144: $i] :
( ! [X145: $i] :
( ( in @ X145 @ X144 )
=> ! [X146: $i] :
( ( in @ X146 @ X145 )
=> ( in @ X146 @ X143 ) ) )
& ! [X147: $i,X148: $i] :
( ( ( in @ X147 @ X143 )
& ( in @ X148 @ X143 ) )
=> ( ! [X149: $i] :
( ( in @ X149 @ X144 )
=> ( ( in @ X147 @ X149 )
<=> ( in @ X148 @ X149 ) ) )
=> ( X147 = X148 ) ) )
& ! [X150: $i,X151: $i] :
( ( ( in @ X150 @ X144 )
& ( in @ X151 @ X144 ) )
=> ( ! [X152: $i] :
( ( in @ X152 @ X150 )
=> ( in @ X152 @ X151 ) )
| ! [X153: $i] :
( ( in @ X153 @ X151 )
=> ( in @ X153 @ X150 ) ) ) )
& ! [X154: $i] :
( ( ! [X155: $i] :
( ( in @ X155 @ X154 )
=> ( in @ X155 @ X143 ) )
& ? [X156: $i] : ( in @ X156 @ X154 ) )
=> ? [X157: $i,X158: $i] :
( ( in @ X157 @ X144 )
& ( in @ X158 @ X154 )
& ~ ? [X159: $i] :
( ( in @ X159 @ X157 )
& ( in @ X159 @ X154 ) )
& ! [X160: $i] :
( ( in @ X160 @ X144 )
=> ( ! [X161: $i] :
( ( in @ X161 @ X160 )
=> ( in @ X161 @ X157 ) )
| ( in @ X158 @ X160 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_56,negated_conjecture,
~ ( ! [X117: $i,X118: $i] :
( ! [X119: $i] :
( ( in @ X119 @ X117 )
<=> ( in @ X119 @ X118 ) )
=> ( X117 = X118 ) )
=> ( ! [X120: $i] :
~ ( in @ X120 @ emptyset )
=> ( ! [X121: $i,X122: $i,X123: $i] :
( ( in @ X123 @ ( setadjoin @ X121 @ X122 ) )
<=> ( ( X123 = X121 )
| ( in @ X123 @ X122 ) ) )
=> ( ! [X124: $i,X125: $i] :
( ( in @ X125 @ ( powerset @ X124 ) )
<=> ! [X126: $i] :
( ( in @ X126 @ X125 )
=> ( in @ X126 @ X124 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X127: $i] :
( ( in @ X127 @ omega )
=> ( in @ ( setadjoin @ X127 @ X127 ) @ omega ) )
=> ( ! [X128: $i] :
( ( ( in @ emptyset @ X128 )
& ! [X129: $i] :
( ( ( in @ X129 @ omega )
& ( in @ X129 @ X128 ) )
=> ( in @ ( setadjoin @ X129 @ X129 ) @ X128 ) ) )
=> ! [X130: $i] :
( ( in @ X130 @ omega )
=> ( in @ X130 @ X128 ) ) )
=> ( ! [X131: $i > $i > $o,X132: $i] :
( ! [X133: $i] :
( ( in @ X133 @ X132 )
=> ? [X134: $i] :
( ( X131 @ X133 @ X134 )
& ! [X135: $i] :
( ( X131 @ X133 @ X135 )
=> ( X134 = X135 ) ) ) )
=> ? [X136: $i] :
! [X137: $i] :
( ( in @ X137 @ X136 )
<=> ? [X138: $i] :
( ( in @ X138 @ X132 )
& ( X131 @ X138 @ X137 ) ) ) )
=> ( ! [X139: $i] :
( ? [X140: $i] : ( in @ X140 @ X139 )
=> ? [X141: $i] :
( ( in @ X141 @ X139 )
& ~ ? [X142: $i] :
( ( in @ X142 @ X141 )
& ( in @ X142 @ X139 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X162: $i,X163: $i > $o,X164: $i] :
( ( in @ X164 @ X162 )
=> ( ( X163 @ X164 )
=> ( in @ X164
@ ( dsetconstr @ X162
@ ^ [Z0: $i] : ( X163 @ Z0 ) ) ) ) )
=> ( ! [X165: $i,X166: $i > $o,X167: $i] :
( ( in @ X167
@ ( dsetconstr @ X165
@ ^ [Z0: $i] : ( X166 @ Z0 ) ) )
=> ( in @ X167 @ X165 ) )
=> ( ! [X168: $i,X169: $i > $o,X170: $i] :
( ( in @ X170
@ ( dsetconstr @ X168
@ ^ [Z0: $i] : ( X169 @ Z0 ) ) )
=> ( X169 @ X170 ) )
=> ( ! [X171: $i > $o] :
( ? [X172: $i] :
( ( X171 @ X172 )
& ! [X173: $i] :
( ( X171 @ X173 )
=> ( X172 = X173 ) ) )
=> ? [X174: $i] :
( ( X171 @ X174 )
& ! [X175: $i] :
( ( X171 @ X175 )
=> ( X174 = X175 ) ) ) )
=> ( ! [X176: $o,X177: $i] :
( ( in @ X177
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X176 ) )
=> X176 )
=> ( ! [X178: $i] :
( ( in @ X178 @ emptyset )
=> ! [X179: $o] : X179 )
=> ( ! [X180: $i] :
~ ( in @ X180 @ emptyset )
=> ( ! [X181: $i] :
~ ( in @ X181 @ emptyset )
=> ( ! [X182: $i > $o] :
( ? [X183: $i] :
( ( X182 @ X183 )
& ! [X184: $i] :
( ( X182 @ X184 )
=> ( X183 = X184 ) ) )
=> ? [X185: $i] : ( X182 @ X185 ) )
=> ( ! [X186: $i,X187: $i] :
( ! [X188: $i] :
( ( in @ X188 @ X186 )
=> ( in @ X188 @ X187 ) )
=> ( ! [X189: $i] :
( ( in @ X189 @ X187 )
=> ( in @ X189 @ X186 ) )
=> ( X186 = X187 ) ) )
=> ( ! [X190: $i] :
( ! [X191: $i] :
~ ( in @ X191 @ X190 )
=> ( X190 = emptyset ) )
=> ( ! [X192: $i] :
( ! [X193: $i] :
~ ( in @ X193 @ X192 )
=> ( X192 = emptyset ) )
=> ( ! [X194: $i,X195: $i > $o,X196: $i] :
( ( in @ X196 @ X194 )
=> ( ( in @ X196
@ ( dsetconstr @ X194
@ ^ [Z0: $i] : ( X195 @ Z0 ) ) )
<=> ( X195 @ X196 ) ) )
=> ( ! [X197: $i] :
( ( X197 != emptyset )
=> ? [X198: $i] : ( in @ X198 @ X197 ) )
=> ( ! [X199: $i,X200: $i > $o,X201: $i] :
( ( in @ X201 @ X199 )
=> ( ( X200 @ X201 )
=> ( ( dsetconstr @ X199
@ ^ [Z0: $i] : ( X200 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X202: $i] :
( ? [X203: $i] : ( in @ X203 @ X202 )
=> ( X202 != emptyset ) )
=> ( ! [X204: $i,X205: $i] : ( in @ X204 @ ( setadjoin @ X204 @ X205 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X206: $i,X207: $i,X208: $i] :
( ( in @ X208 @ X207 )
=> ( in @ X208 @ ( setadjoin @ X206 @ X207 ) ) )
=> ( ! [X209: $i,X210: $i,X211: $i] :
( ( in @ X211 @ ( setadjoin @ X209 @ X210 ) )
=> ! [X212: $o] :
( ( ( X211 = X209 )
=> X212 )
=> ( ( ( in @ X211 @ X210 )
=> X212 )
=> X212 ) ) )
=> ( ! [X213: $i,X214: $i,X215: $i] :
( ( in @ X215 @ ( setadjoin @ X213 @ X214 ) )
=> ( ( X215 = X213 )
| ( in @ X215 @ X214 ) ) )
=> ( ! [X216: $i] :
( ( dsetconstr @ X216
@ ^ [Z0: $i] : $true )
= X216 )
=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( 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(assume_negation,[status(cth)],[powersetI]),emptysetimpfalse]),powersetAx]),noeltsimpempty]),c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]),foundationAx]),setadjoinIL]),emptyinunitempty]),wellorderingAx]),setadjoinIR]),setadjoinE]),c_0_48]),setadjoinOr]),c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53]),emptysetE]),notinemptyset]),c_0_54]),setext]),emptyI]),omegaIndAx]),omegaSAx]),omega0Ax]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_55]) ).
thf(c_0_57,negated_conjecture,
! [X217: $i,X218: $i,X220: $i,X221: $i,X222: $i,X223: $i,X224: $i,X225: $i,X226: $i,X227: $i,X228: $i,X230: $i,X231: $i,X233: $i,X234: $i > $i > $o,X235: $i,X237: $i,X240: $i,X242: $i,X243: $i,X244: $i,X245: $i,X247: $i,X248: $i,X249: $i > $o,X250: $i,X251: $i,X252: $i > $o,X253: $i,X254: $i,X255: $i > $o,X256: $i,X257: $i > $o,X258: $i,X261: $i,X262: $o,X263: $i,X264: $i,X265: $o,X266: $i,X267: $i,X268: $i > $o,X269: $i,X272: $i,X273: $i,X276: $i,X278: $i,X280: $i,X281: $i > $o,X282: $i,X283: $i,X285: $i,X286: $i > $o,X287: $i,X288: $i,X289: $i,X290: $i,X291: $i,X292: $i,X293: $i,X294: $i,X295: $i,X296: $i,X297: $i,X298: $o,X299: $i,X300: $i,X301: $i,X302: $i,X305: $i] :
( ( ~ ( in @ ( esk1_2 @ X217 @ X218 ) @ X217 )
| ~ ( in @ ( esk1_2 @ X217 @ X218 ) @ X218 )
| ( X217 = X218 ) )
& ( ( in @ ( esk1_2 @ X217 @ X218 ) @ X217 )
| ( in @ ( esk1_2 @ X217 @ X218 ) @ X218 )
| ( X217 = X218 ) )
& ~ ( in @ X220 @ emptyset )
& ( ~ ( in @ X223 @ ( setadjoin @ X221 @ X222 ) )
| ( X223 = X221 )
| ( in @ X223 @ X222 ) )
& ( ( X223 != X221 )
| ( in @ X223 @ ( setadjoin @ X221 @ X222 ) ) )
& ( ~ ( in @ X223 @ X222 )
| ( in @ X223 @ ( setadjoin @ X221 @ X222 ) ) )
& ( ~ ( in @ X225 @ ( powerset @ X224 ) )
| ~ ( in @ X226 @ X225 )
| ( in @ X226 @ X224 ) )
& ( ( in @ ( esk2_2 @ X227 @ X228 ) @ X228 )
| ( in @ X228 @ ( powerset @ X227 ) ) )
& ( ~ ( in @ ( esk2_2 @ X227 @ X228 ) @ X227 )
| ( in @ X228 @ ( powerset @ X227 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X230 @ omega )
| ( in @ ( setadjoin @ X230 @ X230 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X231 ) @ omega )
| ~ ( in @ emptyset @ X231 )
| ~ ( in @ X233 @ omega )
| ( in @ X233 @ X231 ) )
& ( ( in @ ( esk3_1 @ X231 ) @ X231 )
| ~ ( in @ emptyset @ X231 )
| ~ ( in @ X233 @ omega )
| ( in @ X233 @ X231 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X231 ) @ ( esk3_1 @ X231 ) ) @ X231 )
| ~ ( in @ emptyset @ X231 )
| ~ ( in @ X233 @ omega )
| ( in @ X233 @ X231 ) )
& ( ( in @ ( esk7_3 @ X234 @ X235 @ X240 ) @ X235 )
| ~ ( in @ X240 @ ( esk6_2 @ X234 @ X235 ) )
| ( in @ ( esk4_2 @ X234 @ X235 ) @ X235 ) )
& ( ( X234 @ ( esk7_3 @ X234 @ X235 @ X240 ) @ X240 )
| ~ ( in @ X240 @ ( esk6_2 @ X234 @ X235 ) )
| ( in @ ( esk4_2 @ X234 @ X235 ) @ X235 ) )
& ( ~ ( in @ X243 @ X235 )
| ~ ( X234 @ X243 @ X242 )
| ( in @ X242 @ ( esk6_2 @ X234 @ X235 ) )
| ( in @ ( esk4_2 @ X234 @ X235 ) @ X235 ) )
& ( ( in @ ( esk7_3 @ X234 @ X235 @ X240 ) @ X235 )
| ~ ( in @ X240 @ ( esk6_2 @ X234 @ X235 ) )
| ( X234 @ ( esk4_2 @ X234 @ X235 ) @ ( esk5_3 @ X234 @ X235 @ X237 ) )
| ~ ( X234 @ ( esk4_2 @ X234 @ X235 ) @ X237 ) )
& ( ( X234 @ ( esk7_3 @ X234 @ X235 @ X240 ) @ X240 )
| ~ ( in @ X240 @ ( esk6_2 @ X234 @ X235 ) )
| ( X234 @ ( esk4_2 @ X234 @ X235 ) @ ( esk5_3 @ X234 @ X235 @ X237 ) )
| ~ ( X234 @ ( esk4_2 @ X234 @ X235 ) @ X237 ) )
& ( ~ ( in @ X243 @ X235 )
| ~ ( X234 @ X243 @ X242 )
| ( in @ X242 @ ( esk6_2 @ X234 @ X235 ) )
| ( X234 @ ( esk4_2 @ X234 @ X235 ) @ ( esk5_3 @ X234 @ X235 @ X237 ) )
| ~ ( X234 @ ( esk4_2 @ X234 @ X235 ) @ X237 ) )
& ( ( in @ ( esk7_3 @ X234 @ X235 @ X240 ) @ X235 )
| ~ ( in @ X240 @ ( esk6_2 @ X234 @ X235 ) )
| ( X237
!= ( esk5_3 @ X234 @ X235 @ X237 ) )
| ~ ( X234 @ ( esk4_2 @ X234 @ X235 ) @ X237 ) )
& ( ( X234 @ ( esk7_3 @ X234 @ X235 @ X240 ) @ X240 )
| ~ ( in @ X240 @ ( esk6_2 @ X234 @ X235 ) )
| ( X237
!= ( esk5_3 @ X234 @ X235 @ X237 ) )
| ~ ( X234 @ ( esk4_2 @ X234 @ X235 ) @ X237 ) )
& ( ~ ( in @ X243 @ X235 )
| ~ ( X234 @ X243 @ X242 )
| ( in @ X242 @ ( esk6_2 @ X234 @ X235 ) )
| ( X237
!= ( esk5_3 @ X234 @ X235 @ X237 ) )
| ~ ( X234 @ ( esk4_2 @ X234 @ X235 ) @ X237 ) )
& ( ( in @ ( esk8_1 @ X244 ) @ X244 )
| ~ ( in @ X245 @ X244 ) )
& ( ~ ( in @ X247 @ ( esk8_1 @ X244 ) )
| ~ ( in @ X247 @ X244 )
| ~ ( in @ X245 @ X244 ) )
& epred1_0
& descrp
& ( ~ ( in @ X250 @ X248 )
| ~ ( X249 @ X250 )
| ( in @ X250
@ ( dsetconstr @ X248
@ ^ [Z0: $i] : ( X249 @ Z0 ) ) ) )
& ( ~ ( in @ X253
@ ( dsetconstr @ X251
@ ^ [Z0: $i] : ( X252 @ Z0 ) ) )
| ( in @ X253 @ X251 ) )
& ( ~ ( in @ X256
@ ( dsetconstr @ X254
@ ^ [Z0: $i] : ( X255 @ Z0 ) ) )
| ( X255 @ X256 ) )
& ( ( X257 @ ( esk10_1 @ X257 ) )
| ( X257 @ ( esk9_2 @ X257 @ X258 ) )
| ~ ( X257 @ X258 ) )
& ( ~ ( X257 @ X261 )
| ( ( esk10_1 @ X257 )
= X261 )
| ( X257 @ ( esk9_2 @ X257 @ X258 ) )
| ~ ( X257 @ X258 ) )
& ( ( X257 @ ( esk10_1 @ X257 ) )
| ( X258
!= ( esk9_2 @ X257 @ X258 ) )
| ~ ( X257 @ X258 ) )
& ( ~ ( X257 @ X261 )
| ( ( esk10_1 @ X257 )
= X261 )
| ( X258
!= ( esk9_2 @ X257 @ X258 ) )
| ~ ( X257 @ X258 ) )
& ( ~ ( in @ X263
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X262 ) )
| X262 )
& ( ~ ( in @ X264 @ emptyset )
| X265 )
& ~ ( in @ X266 @ emptyset )
& ~ ( in @ X267 @ emptyset )
& ( ( X268 @ ( esk11_2 @ X268 @ X269 ) )
| ~ ( X268 @ X269 )
| ( X268 @ ( esk12_1 @ X268 ) ) )
& ( ( X269
!= ( esk11_2 @ X268 @ X269 ) )
| ~ ( X268 @ X269 )
| ( X268 @ ( esk12_1 @ X268 ) ) )
& ( ( in @ ( esk14_2 @ X272 @ X273 ) @ X273 )
| ( X272 = X273 )
| ( in @ ( esk13_2 @ X272 @ X273 ) @ X272 ) )
& ( ~ ( in @ ( esk14_2 @ X272 @ X273 ) @ X272 )
| ( X272 = X273 )
| ( in @ ( esk13_2 @ X272 @ X273 ) @ X272 ) )
& ( ( in @ ( esk14_2 @ X272 @ X273 ) @ X273 )
| ( X272 = X273 )
| ~ ( in @ ( esk13_2 @ X272 @ X273 ) @ X273 ) )
& ( ~ ( in @ ( esk14_2 @ X272 @ X273 ) @ X272 )
| ( X272 = X273 )
| ~ ( in @ ( esk13_2 @ X272 @ X273 ) @ X273 ) )
& ( ( in @ ( esk15_1 @ X276 ) @ X276 )
| ( X276 = emptyset ) )
& ( ( in @ ( esk16_1 @ X278 ) @ X278 )
| ( X278 = emptyset ) )
& ( ~ ( in @ X282
@ ( dsetconstr @ X280
@ ^ [Z0: $i] : ( X281 @ Z0 ) ) )
| ( X281 @ X282 )
| ~ ( in @ X282 @ X280 ) )
& ( ~ ( X281 @ X282 )
| ( in @ X282
@ ( dsetconstr @ X280
@ ^ [Z0: $i] : ( X281 @ Z0 ) ) )
| ~ ( in @ X282 @ X280 ) )
& ( ( X283 = emptyset )
| ( in @ ( esk17_1 @ X283 ) @ X283 ) )
& ( ~ ( in @ X287 @ X285 )
| ~ ( X286 @ X287 )
| ( ( dsetconstr @ X285
@ ^ [Z0: $i] : ( X286 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X289 @ X288 )
| ( X288 != emptyset ) )
& ( in @ X290 @ ( setadjoin @ X290 @ X291 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X294 @ X293 )
| ( in @ X294 @ ( setadjoin @ X292 @ X293 ) ) )
& ( ( in @ X297 @ X296 )
| X298
| ( X297 = X295 )
| ~ ( in @ X297 @ ( setadjoin @ X295 @ X296 ) ) )
& ( ~ X298
| X298
| ( X297 = X295 )
| ~ ( in @ X297 @ ( setadjoin @ X295 @ X296 ) ) )
& ( ( in @ X297 @ X296 )
| X298
| ~ X298
| ~ ( in @ X297 @ ( setadjoin @ X295 @ X296 ) ) )
& ( ~ X298
| X298
| ~ X298
| ~ ( in @ X297 @ ( setadjoin @ X295 @ X296 ) ) )
& ( ~ ( in @ X301 @ ( setadjoin @ X299 @ X300 ) )
| ( X301 = X299 )
| ( in @ X301 @ X300 ) )
& ( ( dsetconstr @ X302
@ ^ [Z0: $i] : $true )
= X302 )
& ( ~ ( in @ X305 @ esk19_0 )
| ( in @ X305 @ esk18_0 ) )
& ~ ( in @ esk19_0 @ ( powerset @ esk18_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_56])])])])])]) ).
thf(c_0_58,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk18_0 )
| ~ ( in @ X2 @ esk19_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_59,negated_conjecture,
! [X3: $i,X2: $i] :
( ( in @ ( esk2_2 @ X2 @ X3 ) @ X3 )
| ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i,X2: $i] :
( ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ ( esk2_2 @ X2 @ X3 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_61,negated_conjecture,
! [X2: $i] :
( ( in @ ( esk2_2 @ X2 @ esk19_0 ) @ esk18_0 )
| ( in @ esk19_0 @ ( powerset @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_62,negated_conjecture,
~ ( in @ esk19_0 @ ( powerset @ esk18_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
thf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU518^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:04:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.49 Running higher-order theorem proving
% 0.22/0.49 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
% 0.60/0.58 # Version: 3.1.0-ho
% 0.60/0.58 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.60/0.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.58 # Starting new_ho_10 with 1500s (5) cores
% 0.60/0.58 # Starting sh5l with 300s (1) cores
% 0.60/0.58 # Starting new_bool_1 with 300s (1) cores
% 0.60/0.58 # Starting new_bool_2 with 300s (1) cores
% 0.60/0.58 # new_bool_2 with pid 17750 completed with status 0
% 0.60/0.58 # Result found by new_bool_2
% 0.60/0.58 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.60/0.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.58 # Starting new_ho_10 with 1500s (5) cores
% 0.60/0.58 # Starting sh5l with 300s (1) cores
% 0.60/0.58 # Starting new_bool_1 with 300s (1) cores
% 0.60/0.58 # Starting new_bool_2 with 300s (1) cores
% 0.60/0.58 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.60/0.58 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.60/0.58 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.60/0.58 # Starting new_ho_10 with 181s (1) cores
% 0.60/0.58 # new_ho_10 with pid 17755 completed with status 0
% 0.60/0.58 # Result found by new_ho_10
% 0.60/0.58 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.60/0.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.58 # Starting new_ho_10 with 1500s (5) cores
% 0.60/0.58 # Starting sh5l with 300s (1) cores
% 0.60/0.58 # Starting new_bool_1 with 300s (1) cores
% 0.60/0.58 # Starting new_bool_2 with 300s (1) cores
% 0.60/0.58 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.60/0.58 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.60/0.58 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.60/0.58 # Starting new_ho_10 with 181s (1) cores
% 0.60/0.58 # Preprocessing time : 0.007 s
% 0.60/0.58 # Presaturation interreduction done
% 0.60/0.58
% 0.60/0.58 # Proof found!
% 0.60/0.58 # SZS status Theorem
% 0.60/0.58 # SZS output start CNFRefutation
% See solution above
% 0.60/0.58 # Parsed axioms : 83
% 0.60/0.58 # Removed by relevancy pruning/SinE : 47
% 0.60/0.58 # Initial clauses : 76
% 0.60/0.58 # Removed in clause preprocessing : 3
% 0.60/0.58 # Initial clauses in saturation : 73
% 0.60/0.58 # Processed clauses : 173
% 0.60/0.58 # ...of these trivial : 5
% 0.60/0.58 # ...subsumed : 23
% 0.60/0.58 # ...remaining for further processing : 145
% 0.60/0.58 # Other redundant clauses eliminated : 3
% 0.60/0.58 # Clauses deleted for lack of memory : 0
% 0.60/0.58 # Backward-subsumed : 0
% 0.60/0.58 # Backward-rewritten : 3
% 0.60/0.58 # Generated clauses : 511
% 0.60/0.58 # ...of the previous two non-redundant : 497
% 0.60/0.58 # ...aggressively subsumed : 0
% 0.60/0.58 # Contextual simplify-reflections : 0
% 0.60/0.58 # Paramodulations : 506
% 0.60/0.58 # Factorizations : 2
% 0.60/0.58 # NegExts : 0
% 0.60/0.58 # Equation resolutions : 3
% 0.60/0.58 # Disequality decompositions : 0
% 0.60/0.58 # Total rewrite steps : 32
% 0.60/0.58 # ...of those cached : 23
% 0.60/0.58 # Propositional unsat checks : 0
% 0.60/0.58 # Propositional check models : 0
% 0.60/0.58 # Propositional check unsatisfiable : 0
% 0.60/0.58 # Propositional clauses : 0
% 0.60/0.58 # Propositional clauses after purity: 0
% 0.60/0.58 # Propositional unsat core size : 0
% 0.60/0.58 # Propositional preprocessing time : 0.000
% 0.60/0.58 # Propositional encoding time : 0.000
% 0.60/0.58 # Propositional solver time : 0.000
% 0.60/0.58 # Success case prop preproc time : 0.000
% 0.60/0.58 # Success case prop encoding time : 0.000
% 0.60/0.58 # Success case prop solver time : 0.000
% 0.60/0.58 # Current number of processed clauses : 78
% 0.60/0.58 # Positive orientable unit clauses : 11
% 0.60/0.58 # Positive unorientable unit clauses: 0
% 0.60/0.58 # Negative unit clauses : 3
% 0.60/0.58 # Non-unit-clauses : 64
% 0.60/0.58 # Current number of unprocessed clauses: 445
% 0.60/0.58 # ...number of literals in the above : 1756
% 0.60/0.58 # Current number of archived formulas : 0
% 0.60/0.58 # Current number of archived clauses : 65
% 0.60/0.58 # Clause-clause subsumption calls (NU) : 2171
% 0.60/0.58 # Rec. Clause-clause subsumption calls : 923
% 0.60/0.58 # Non-unit clause-clause subsumptions : 14
% 0.60/0.58 # Unit Clause-clause subsumption calls : 32
% 0.60/0.58 # Rewrite failures with RHS unbound : 0
% 0.60/0.58 # BW rewrite match attempts : 7
% 0.60/0.58 # BW rewrite match successes : 3
% 0.60/0.58 # Condensation attempts : 173
% 0.60/0.58 # Condensation successes : 3
% 0.60/0.58 # Termbank termtop insertions : 18133
% 0.60/0.58 # Search garbage collected termcells : 3017
% 0.60/0.58
% 0.60/0.58 # -------------------------------------------------
% 0.60/0.58 # User time : 0.053 s
% 0.60/0.58 # System time : 0.009 s
% 0.60/0.58 # Total time : 0.062 s
% 0.60/0.58 # Maximum resident set size: 2748 pages
% 0.60/0.58
% 0.60/0.58 # -------------------------------------------------
% 0.60/0.58 # User time : 0.056 s
% 0.60/0.58 # System time : 0.014 s
% 0.60/0.58 # Total time : 0.069 s
% 0.60/0.58 # Maximum resident set size: 1812 pages
% 0.60/0.58 % E---3.1 exiting
% 0.60/0.58 % E exiting
%------------------------------------------------------------------------------