TSTP Solution File: SEU519^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU519^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.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 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 102
% Syntax : Number of formulae : 128 ( 17 unt; 64 typ; 0 def)
% Number of atoms : 473 ( 77 equ; 0 cnn)
% Maximal formula atoms : 127 ( 7 avg)
% Number of connectives : 1574 ( 112 ~; 117 |; 107 &; 978 @)
% ( 58 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 141 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 41 con; 0-3 aty)
% Number of variables : 366 ( 32 ^ 288 !; 46 ?; 366 :)
% 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,
epred1_0: $o ).
thf(decl_69,type,
esk1_2: $i > $i > $i ).
thf(decl_70,type,
esk2_2: $i > $i > $i ).
thf(decl_71,type,
esk3_1: $i > $i ).
thf(decl_72,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_73,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_74,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_75,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_76,type,
esk8_1: $i > $i ).
thf(decl_77,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_78,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_79,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_80,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_81,type,
esk13_2: $i > $i > $i ).
thf(decl_82,type,
esk14_2: $i > $i > $i ).
thf(decl_83,type,
esk15_1: $i > $i ).
thf(decl_84,type,
esk16_1: $i > $i ).
thf(decl_85,type,
esk17_1: $i > $i ).
thf(decl_86,type,
esk18_2: $i > $i > $i ).
thf(decl_87,type,
esk19_0: $i ).
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(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(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(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(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(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(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox/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
=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
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(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(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(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
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(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(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(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(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(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(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_37,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_38,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_39,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_40,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_41,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_42,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_43,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_44,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_45,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_46,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_37]) ).
thf(c_0_47,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_38,c_0_37]) ).
thf(c_0_48,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_37]) ).
thf(c_0_49,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X112: $i] :
( ( X6 @ X2 @ X112 )
& ! [X113: $i] :
( ( X6 @ X2 @ X113 )
=> ( X112 = X113 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_50,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_51,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_52,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_53,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X114: $i] :
( ( X1 @ X114 )
& ! [X115: $i] :
( ( X1 @ X115 )
=> ( X114 = X115 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_41,c_0_40]) ).
thf(c_0_54,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_42]) ).
thf(c_0_55,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X116: $i] :
( ( X1 @ X116 )
& ! [X117: $i] :
( ( X1 @ X117 )
=> ( X116 = X117 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_43,c_0_40]) ).
thf(c_0_56,plain,
( epred1_0
<=> ! [X144: $i] :
? [X145: $i] :
( ! [X146: $i] :
( ( in @ X146 @ X145 )
=> ! [X147: $i] :
( ( in @ X147 @ X146 )
=> ( in @ X147 @ X144 ) ) )
& ! [X148: $i,X149: $i] :
( ( ( in @ X148 @ X144 )
& ( in @ X149 @ X144 ) )
=> ( ! [X150: $i] :
( ( in @ X150 @ X145 )
=> ( ( in @ X148 @ X150 )
<=> ( in @ X149 @ X150 ) ) )
=> ( X148 = X149 ) ) )
& ! [X151: $i,X152: $i] :
( ( ( in @ X151 @ X145 )
& ( in @ X152 @ X145 ) )
=> ( ! [X153: $i] :
( ( in @ X153 @ X151 )
=> ( in @ X153 @ X152 ) )
| ! [X154: $i] :
( ( in @ X154 @ X152 )
=> ( in @ X154 @ X151 ) ) ) )
& ! [X155: $i] :
( ( ! [X156: $i] :
( ( in @ X156 @ X155 )
=> ( in @ X156 @ X144 ) )
& ? [X157: $i] : ( in @ X157 @ X155 ) )
=> ? [X158: $i,X159: $i] :
( ( in @ X158 @ X145 )
& ( in @ X159 @ X155 )
& ~ ? [X160: $i] :
( ( in @ X160 @ X158 )
& ( in @ X160 @ X155 ) )
& ! [X161: $i] :
( ( in @ X161 @ X145 )
=> ( ! [X162: $i] :
( ( in @ X162 @ X161 )
=> ( in @ X162 @ X158 ) )
| ( in @ X159 @ X161 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_57,negated_conjecture,
~ ( ! [X118: $i,X119: $i] :
( ! [X120: $i] :
( ( in @ X120 @ X118 )
<=> ( in @ X120 @ X119 ) )
=> ( X118 = X119 ) )
=> ( ! [X121: $i] :
~ ( in @ X121 @ emptyset )
=> ( ! [X122: $i,X123: $i,X124: $i] :
( ( in @ X124 @ ( setadjoin @ X122 @ X123 ) )
<=> ( ( X124 = X122 )
| ( in @ X124 @ X123 ) ) )
=> ( ! [X125: $i,X126: $i] :
( ( in @ X126 @ ( powerset @ X125 ) )
<=> ! [X127: $i] :
( ( in @ X127 @ X126 )
=> ( in @ X127 @ X125 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X128: $i] :
( ( in @ X128 @ omega )
=> ( in @ ( setadjoin @ X128 @ X128 ) @ omega ) )
=> ( ! [X129: $i] :
( ( ( in @ emptyset @ X129 )
& ! [X130: $i] :
( ( ( in @ X130 @ omega )
& ( in @ X130 @ X129 ) )
=> ( in @ ( setadjoin @ X130 @ X130 ) @ X129 ) ) )
=> ! [X131: $i] :
( ( in @ X131 @ omega )
=> ( in @ X131 @ X129 ) ) )
=> ( ! [X132: $i > $i > $o,X133: $i] :
( ! [X134: $i] :
( ( in @ X134 @ X133 )
=> ? [X135: $i] :
( ( X132 @ X134 @ X135 )
& ! [X136: $i] :
( ( X132 @ X134 @ X136 )
=> ( X135 = X136 ) ) ) )
=> ? [X137: $i] :
! [X138: $i] :
( ( in @ X138 @ X137 )
<=> ? [X139: $i] :
( ( in @ X139 @ X133 )
& ( X132 @ X139 @ X138 ) ) ) )
=> ( ! [X140: $i] :
( ? [X141: $i] : ( in @ X141 @ X140 )
=> ? [X142: $i] :
( ( in @ X142 @ X140 )
& ~ ? [X143: $i] :
( ( in @ X143 @ X142 )
& ( in @ X143 @ X140 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X163: $i,X164: $i > $o,X165: $i] :
( ( in @ X165 @ X163 )
=> ( ( X164 @ X165 )
=> ( in @ X165 @ ( dsetconstr @ X163 @ X164 ) ) ) )
=> ( ! [X166: $i,X167: $i > $o,X168: $i] :
( ( in @ X168 @ ( dsetconstr @ X166 @ X167 ) )
=> ( in @ X168 @ X166 ) )
=> ( ! [X169: $i,X170: $i > $o,X171: $i] :
( ( in @ X171 @ ( dsetconstr @ X169 @ X170 ) )
=> ( X170 @ X171 ) )
=> ( ! [X172: $i > $o] :
( ? [X173: $i] :
( ( X172 @ X173 )
& ! [X174: $i] :
( ( X172 @ X174 )
=> ( X173 = X174 ) ) )
=> ? [X175: $i] :
( ( X172 @ X175 )
& ! [X176: $i] :
( ( X172 @ X176 )
=> ( X175 = X176 ) ) ) )
=> ( ! [X177: $o,X178: $i] :
( ( in @ X178
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X177 ) )
=> X177 )
=> ( ! [X179: $i] :
( ( in @ X179 @ emptyset )
=> ! [X180: $o] : X180 )
=> ( ! [X181: $i] :
( ( in @ X181 @ emptyset )
=> ~ $true )
=> ( ! [X182: $i] :
~ ( in @ X182 @ emptyset )
=> ( ! [X183: $i > $o] :
( ? [X184: $i] :
( ( X183 @ X184 )
& ! [X185: $i] :
( ( X183 @ X185 )
=> ( X184 = X185 ) ) )
=> ? [X186: $i] : ( X183 @ X186 ) )
=> ( ! [X187: $i,X188: $i] :
( ! [X189: $i] :
( ( in @ X189 @ X187 )
=> ( in @ X189 @ X188 ) )
=> ( ! [X190: $i] :
( ( in @ X190 @ X188 )
=> ( in @ X190 @ X187 ) )
=> ( X187 = X188 ) ) )
=> ( ! [X191: $i] :
( ! [X192: $i] :
~ ( in @ X192 @ X191 )
=> ( X191 = emptyset ) )
=> ( ! [X193: $i] :
( ! [X194: $i] :
~ ( in @ X194 @ X193 )
=> ( X193 = emptyset ) )
=> ( ! [X195: $i,X196: $i > $o,X197: $i] :
( ( in @ X197 @ X195 )
=> ( ( in @ X197 @ ( dsetconstr @ X195 @ X196 ) )
<=> ( X196 @ X197 ) ) )
=> ( ! [X198: $i] :
( ( X198 != emptyset )
=> ? [X199: $i] : ( in @ X199 @ X198 ) )
=> ( ! [X200: $i,X201: $i > $o,X202: $i] :
( ( in @ X202 @ X200 )
=> ( ( X201 @ X202 )
=> ( ( dsetconstr @ X200 @ X201 )
!= emptyset ) ) )
=> ( ! [X203: $i] :
( ? [X204: $i] : ( in @ X204 @ X203 )
=> ( X203 != emptyset ) )
=> ( ! [X205: $i,X206: $i] : ( in @ X205 @ ( setadjoin @ X205 @ X206 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X207: $i,X208: $i,X209: $i] :
( ( in @ X209 @ X208 )
=> ( in @ X209 @ ( setadjoin @ X207 @ X208 ) ) )
=> ( ! [X210: $i,X211: $i,X212: $i] :
( ( in @ X212 @ ( setadjoin @ X210 @ X211 ) )
=> ! [X213: $o] :
( ( ( X212 = X210 )
=> X213 )
=> ( ( ( in @ X212 @ X211 )
=> X213 )
=> X213 ) ) )
=> ( ! [X214: $i,X215: $i,X216: $i] :
( ( in @ X216 @ ( setadjoin @ X214 @ X215 ) )
=> ( ( X216 = X214 )
| ( in @ X216 @ X215 ) ) )
=> ( ! [X217: $i] :
( ( dsetconstr @ X217
@ ^ [Z0: $i] : $true )
= X217 )
=> ( ! [X218: $i,X219: $i] :
( ! [X220: $i] :
( ( in @ X220 @ X219 )
=> ( in @ X220 @ X218 ) )
=> ( in @ X219 @ ( powerset @ X218 ) ) )
=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[emptyinPowerset]),c_0_44]),powersetI]),emptyI]),noeltsimpempty]),c_0_45]),powersetAx]),c_0_46]),c_0_47]),omega0Ax]),c_0_48]),setadjoinIL]),omegaSAx]),emptyinunitempty]),setadjoinIR]),omegaIndAx]),setadjoinE]),setadjoinOr]),c_0_49]),c_0_50]),foundationAx]),wellorderingAx]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_55]),setext]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_56]) ).
thf(c_0_58,negated_conjecture,
! [X221: $i,X222: $i,X224: $i,X225: $i,X226: $i,X227: $i,X228: $i,X229: $i,X230: $i,X231: $i,X232: $i,X234: $i,X235: $i,X237: $i,X238: $i > $i > $o,X239: $i,X241: $i,X244: $i,X246: $i,X247: $i,X248: $i,X249: $i,X251: $i,X252: $i,X253: $i > $o,X254: $i,X255: $i,X256: $i > $o,X257: $i,X258: $i,X259: $i > $o,X260: $i,X261: $i > $o,X262: $i,X265: $i,X266: $o,X267: $i,X268: $i,X269: $o,X270: $i,X271: $i,X272: $i > $o,X273: $i,X276: $i,X277: $i,X280: $i,X282: $i,X284: $i,X285: $i > $o,X286: $i,X287: $i,X289: $i,X290: $i > $o,X291: $i,X292: $i,X293: $i,X294: $i,X295: $i,X296: $i,X297: $i,X298: $i,X299: $i,X300: $i,X301: $i,X302: $o,X303: $i,X304: $i,X305: $i,X306: $i,X307: $i,X308: $i] :
( ( ~ ( in @ ( esk1_2 @ X221 @ X222 ) @ X221 )
| ~ ( in @ ( esk1_2 @ X221 @ X222 ) @ X222 )
| ( X221 = X222 ) )
& ( ( in @ ( esk1_2 @ X221 @ X222 ) @ X221 )
| ( in @ ( esk1_2 @ X221 @ X222 ) @ X222 )
| ( X221 = X222 ) )
& ~ ( in @ X224 @ emptyset )
& ( ~ ( in @ X227 @ ( setadjoin @ X225 @ X226 ) )
| ( X227 = X225 )
| ( in @ X227 @ X226 ) )
& ( ( X227 != X225 )
| ( in @ X227 @ ( setadjoin @ X225 @ X226 ) ) )
& ( ~ ( in @ X227 @ X226 )
| ( in @ X227 @ ( setadjoin @ X225 @ X226 ) ) )
& ( ~ ( in @ X229 @ ( powerset @ X228 ) )
| ~ ( in @ X230 @ X229 )
| ( in @ X230 @ X228 ) )
& ( ( in @ ( esk2_2 @ X231 @ X232 ) @ X232 )
| ( in @ X232 @ ( powerset @ X231 ) ) )
& ( ~ ( in @ ( esk2_2 @ X231 @ X232 ) @ X231 )
| ( in @ X232 @ ( powerset @ X231 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X234 @ omega )
| ( in @ ( setadjoin @ X234 @ X234 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X235 ) @ omega )
| ~ ( in @ emptyset @ X235 )
| ~ ( in @ X237 @ omega )
| ( in @ X237 @ X235 ) )
& ( ( in @ ( esk3_1 @ X235 ) @ X235 )
| ~ ( in @ emptyset @ X235 )
| ~ ( in @ X237 @ omega )
| ( in @ X237 @ X235 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X235 ) @ ( esk3_1 @ X235 ) ) @ X235 )
| ~ ( in @ emptyset @ X235 )
| ~ ( in @ X237 @ omega )
| ( in @ X237 @ X235 ) )
& ( ( in @ ( esk7_3 @ X238 @ X239 @ X244 ) @ X239 )
| ~ ( in @ X244 @ ( esk6_2 @ X238 @ X239 ) )
| ( in @ ( esk4_2 @ X238 @ X239 ) @ X239 ) )
& ( ( X238 @ ( esk7_3 @ X238 @ X239 @ X244 ) @ X244 )
| ~ ( in @ X244 @ ( esk6_2 @ X238 @ X239 ) )
| ( in @ ( esk4_2 @ X238 @ X239 ) @ X239 ) )
& ( ~ ( in @ X247 @ X239 )
| ~ ( X238 @ X247 @ X246 )
| ( in @ X246 @ ( esk6_2 @ X238 @ X239 ) )
| ( in @ ( esk4_2 @ X238 @ X239 ) @ X239 ) )
& ( ( in @ ( esk7_3 @ X238 @ X239 @ X244 ) @ X239 )
| ~ ( in @ X244 @ ( esk6_2 @ X238 @ X239 ) )
| ( X238 @ ( esk4_2 @ X238 @ X239 ) @ ( esk5_3 @ X238 @ X239 @ X241 ) )
| ~ ( X238 @ ( esk4_2 @ X238 @ X239 ) @ X241 ) )
& ( ( X238 @ ( esk7_3 @ X238 @ X239 @ X244 ) @ X244 )
| ~ ( in @ X244 @ ( esk6_2 @ X238 @ X239 ) )
| ( X238 @ ( esk4_2 @ X238 @ X239 ) @ ( esk5_3 @ X238 @ X239 @ X241 ) )
| ~ ( X238 @ ( esk4_2 @ X238 @ X239 ) @ X241 ) )
& ( ~ ( in @ X247 @ X239 )
| ~ ( X238 @ X247 @ X246 )
| ( in @ X246 @ ( esk6_2 @ X238 @ X239 ) )
| ( X238 @ ( esk4_2 @ X238 @ X239 ) @ ( esk5_3 @ X238 @ X239 @ X241 ) )
| ~ ( X238 @ ( esk4_2 @ X238 @ X239 ) @ X241 ) )
& ( ( in @ ( esk7_3 @ X238 @ X239 @ X244 ) @ X239 )
| ~ ( in @ X244 @ ( esk6_2 @ X238 @ X239 ) )
| ( X241
!= ( esk5_3 @ X238 @ X239 @ X241 ) )
| ~ ( X238 @ ( esk4_2 @ X238 @ X239 ) @ X241 ) )
& ( ( X238 @ ( esk7_3 @ X238 @ X239 @ X244 ) @ X244 )
| ~ ( in @ X244 @ ( esk6_2 @ X238 @ X239 ) )
| ( X241
!= ( esk5_3 @ X238 @ X239 @ X241 ) )
| ~ ( X238 @ ( esk4_2 @ X238 @ X239 ) @ X241 ) )
& ( ~ ( in @ X247 @ X239 )
| ~ ( X238 @ X247 @ X246 )
| ( in @ X246 @ ( esk6_2 @ X238 @ X239 ) )
| ( X241
!= ( esk5_3 @ X238 @ X239 @ X241 ) )
| ~ ( X238 @ ( esk4_2 @ X238 @ X239 ) @ X241 ) )
& ( ( in @ ( esk8_1 @ X248 ) @ X248 )
| ~ ( in @ X249 @ X248 ) )
& ( ~ ( in @ X251 @ ( esk8_1 @ X248 ) )
| ~ ( in @ X251 @ X248 )
| ~ ( in @ X249 @ X248 ) )
& epred1_0
& descrp
& ( ~ ( in @ X254 @ X252 )
| ~ ( X253 @ X254 )
| ( in @ X254 @ ( dsetconstr @ X252 @ X253 ) ) )
& ( ~ ( in @ X257 @ ( dsetconstr @ X255 @ X256 ) )
| ( in @ X257 @ X255 ) )
& ( ~ ( in @ X260 @ ( dsetconstr @ X258 @ X259 ) )
| ( X259 @ X260 ) )
& ( ( X261 @ ( esk10_1 @ X261 ) )
| ( X261 @ ( esk9_2 @ X261 @ X262 ) )
| ~ ( X261 @ X262 ) )
& ( ~ ( X261 @ X265 )
| ( ( esk10_1 @ X261 )
= X265 )
| ( X261 @ ( esk9_2 @ X261 @ X262 ) )
| ~ ( X261 @ X262 ) )
& ( ( X261 @ ( esk10_1 @ X261 ) )
| ( X262
!= ( esk9_2 @ X261 @ X262 ) )
| ~ ( X261 @ X262 ) )
& ( ~ ( X261 @ X265 )
| ( ( esk10_1 @ X261 )
= X265 )
| ( X262
!= ( esk9_2 @ X261 @ X262 ) )
| ~ ( X261 @ X262 ) )
& ( ~ ( in @ X267
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X266 ) )
| X266 )
& ( ~ ( in @ X268 @ emptyset )
| X269 )
& ( ~ ( in @ X270 @ emptyset )
| ~ $true )
& ~ ( in @ X271 @ emptyset )
& ( ( X272 @ ( esk11_2 @ X272 @ X273 ) )
| ~ ( X272 @ X273 )
| ( X272 @ ( esk12_1 @ X272 ) ) )
& ( ( X273
!= ( esk11_2 @ X272 @ X273 ) )
| ~ ( X272 @ X273 )
| ( X272 @ ( esk12_1 @ X272 ) ) )
& ( ( in @ ( esk14_2 @ X276 @ X277 ) @ X277 )
| ( X276 = X277 )
| ( in @ ( esk13_2 @ X276 @ X277 ) @ X276 ) )
& ( ~ ( in @ ( esk14_2 @ X276 @ X277 ) @ X276 )
| ( X276 = X277 )
| ( in @ ( esk13_2 @ X276 @ X277 ) @ X276 ) )
& ( ( in @ ( esk14_2 @ X276 @ X277 ) @ X277 )
| ( X276 = X277 )
| ~ ( in @ ( esk13_2 @ X276 @ X277 ) @ X277 ) )
& ( ~ ( in @ ( esk14_2 @ X276 @ X277 ) @ X276 )
| ( X276 = X277 )
| ~ ( in @ ( esk13_2 @ X276 @ X277 ) @ X277 ) )
& ( ( in @ ( esk15_1 @ X280 ) @ X280 )
| ( X280 = emptyset ) )
& ( ( in @ ( esk16_1 @ X282 ) @ X282 )
| ( X282 = emptyset ) )
& ( ~ ( in @ X286 @ ( dsetconstr @ X284 @ X285 ) )
| ( X285 @ X286 )
| ~ ( in @ X286 @ X284 ) )
& ( ~ ( X285 @ X286 )
| ( in @ X286 @ ( dsetconstr @ X284 @ X285 ) )
| ~ ( in @ X286 @ X284 ) )
& ( ( X287 = emptyset )
| ( in @ ( esk17_1 @ X287 ) @ X287 ) )
& ( ~ ( in @ X291 @ X289 )
| ~ ( X290 @ X291 )
| ( ( dsetconstr @ X289 @ X290 )
!= emptyset ) )
& ( ~ ( in @ X293 @ X292 )
| ( X292 != emptyset ) )
& ( in @ X294 @ ( setadjoin @ X294 @ X295 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X298 @ X297 )
| ( in @ X298 @ ( setadjoin @ X296 @ X297 ) ) )
& ( ( in @ X301 @ X300 )
| X302
| ( X301 = X299 )
| ~ ( in @ X301 @ ( setadjoin @ X299 @ X300 ) ) )
& ( ~ X302
| X302
| ( X301 = X299 )
| ~ ( in @ X301 @ ( setadjoin @ X299 @ X300 ) ) )
& ( ( in @ X301 @ X300 )
| X302
| ~ X302
| ~ ( in @ X301 @ ( setadjoin @ X299 @ X300 ) ) )
& ( ~ X302
| X302
| ~ X302
| ~ ( in @ X301 @ ( setadjoin @ X299 @ X300 ) ) )
& ( ~ ( in @ X305 @ ( setadjoin @ X303 @ X304 ) )
| ( X305 = X303 )
| ( in @ X305 @ X304 ) )
& ( ( dsetconstr @ X306
@ ^ [Z0: $i] : $true )
= X306 )
& ( ( in @ ( esk18_2 @ X307 @ X308 ) @ X308 )
| ( in @ X308 @ ( powerset @ X307 ) ) )
& ( ~ ( in @ ( esk18_2 @ X307 @ X308 ) @ X307 )
| ( in @ X308 @ ( powerset @ X307 ) ) )
& ~ ( in @ emptyset @ ( powerset @ esk19_0 ) ) ),
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_57])])])])])])]) ).
thf(c_0_59,negated_conjecture,
! [X2: $i] :
~ ( in @ X2 @ emptyset ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i,X2: $i] :
( ( in @ ( esk2_2 @ X2 @ X3 ) @ X3 )
| ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_61,negated_conjecture,
~ ( in @ emptyset @ ( powerset @ esk19_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_62,negated_conjecture,
! [X2: $i] : ( in @ emptyset @ ( powerset @ X2 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU519^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 17:34:07 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 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
% 0.19/0.50 # Version: 3.1.0-ho
% 0.19/0.50 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50 # Starting sh5l with 300s (1) cores
% 0.19/0.50 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.50 # Starting new_bool_2 with 300s (1) cores
% 0.19/0.50 # new_bool_1 with pid 12118 completed with status 0
% 0.19/0.50 # Result found by new_bool_1
% 0.19/0.50 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50 # Starting sh5l with 300s (1) cores
% 0.19/0.50 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.50 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.50 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.19/0.50 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50 # Starting new_ho_10 with 181s (1) cores
% 0.19/0.50 # new_ho_10 with pid 12121 completed with status 0
% 0.19/0.50 # Result found by new_ho_10
% 0.19/0.50 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50 # Starting sh5l with 300s (1) cores
% 0.19/0.50 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.50 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.50 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.19/0.50 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50 # Starting new_ho_10 with 181s (1) cores
% 0.19/0.50 # Preprocessing time : 0.003 s
% 0.19/0.50 # Presaturation interreduction done
% 0.19/0.50
% 0.19/0.50 # Proof found!
% 0.19/0.50 # SZS status Theorem
% 0.19/0.50 # SZS output start CNFRefutation
% See solution above
% 0.19/0.50 # Parsed axioms : 85
% 0.19/0.50 # Removed by relevancy pruning/SinE : 48
% 0.19/0.50 # Initial clauses : 77
% 0.19/0.50 # Removed in clause preprocessing : 3
% 0.19/0.50 # Initial clauses in saturation : 74
% 0.19/0.50 # Processed clauses : 106
% 0.19/0.50 # ...of these trivial : 0
% 0.19/0.50 # ...subsumed : 11
% 0.19/0.50 # ...remaining for further processing : 95
% 0.19/0.50 # Other redundant clauses eliminated : 3
% 0.19/0.50 # Clauses deleted for lack of memory : 0
% 0.19/0.50 # Backward-subsumed : 0
% 0.19/0.50 # Backward-rewritten : 3
% 0.19/0.50 # Generated clauses : 43
% 0.19/0.50 # ...of the previous two non-redundant : 39
% 0.19/0.50 # ...aggressively subsumed : 0
% 0.19/0.50 # Contextual simplify-reflections : 0
% 0.19/0.50 # Paramodulations : 40
% 0.19/0.50 # Factorizations : 0
% 0.19/0.50 # NegExts : 0
% 0.19/0.50 # Equation resolutions : 3
% 0.19/0.50 # Disequality decompositions : 0
% 0.19/0.50 # Total rewrite steps : 18
% 0.19/0.50 # ...of those cached : 12
% 0.19/0.50 # Propositional unsat checks : 0
% 0.19/0.50 # Propositional check models : 0
% 0.19/0.50 # Propositional check unsatisfiable : 0
% 0.19/0.50 # Propositional clauses : 0
% 0.19/0.50 # Propositional clauses after purity: 0
% 0.19/0.50 # Propositional unsat core size : 0
% 0.19/0.50 # Propositional preprocessing time : 0.000
% 0.19/0.50 # Propositional encoding time : 0.000
% 0.19/0.50 # Propositional solver time : 0.000
% 0.19/0.50 # Success case prop preproc time : 0.000
% 0.19/0.50 # Success case prop encoding time : 0.000
% 0.19/0.50 # Success case prop solver time : 0.000
% 0.19/0.50 # Current number of processed clauses : 27
% 0.19/0.50 # Positive orientable unit clauses : 9
% 0.19/0.50 # Positive unorientable unit clauses: 0
% 0.19/0.50 # Negative unit clauses : 1
% 0.19/0.50 # Non-unit-clauses : 17
% 0.19/0.50 # Current number of unprocessed clauses: 68
% 0.19/0.50 # ...number of literals in the above : 197
% 0.19/0.50 # Current number of archived formulas : 0
% 0.19/0.50 # Current number of archived clauses : 66
% 0.19/0.50 # Clause-clause subsumption calls (NU) : 1028
% 0.19/0.50 # Rec. Clause-clause subsumption calls : 414
% 0.19/0.50 # Non-unit clause-clause subsumptions : 8
% 0.19/0.50 # Unit Clause-clause subsumption calls : 11
% 0.19/0.50 # Rewrite failures with RHS unbound : 0
% 0.19/0.50 # BW rewrite match attempts : 3
% 0.19/0.50 # BW rewrite match successes : 3
% 0.19/0.50 # Condensation attempts : 106
% 0.19/0.50 # Condensation successes : 3
% 0.19/0.50 # Termbank termtop insertions : 11134
% 0.19/0.50 # Search garbage collected termcells : 3657
% 0.19/0.50
% 0.19/0.50 # -------------------------------------------------
% 0.19/0.50 # User time : 0.019 s
% 0.19/0.50 # System time : 0.004 s
% 0.19/0.50 # Total time : 0.023 s
% 0.19/0.50 # Maximum resident set size: 2736 pages
% 0.19/0.50
% 0.19/0.50 # -------------------------------------------------
% 0.19/0.50 # User time : 0.022 s
% 0.19/0.50 # System time : 0.006 s
% 0.19/0.50 # Total time : 0.028 s
% 0.19/0.50 # Maximum resident set size: 1808 pages
% 0.19/0.50 % E---3.1 exiting
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------