TSTP Solution File: SEU516^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU516^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 03:27:53 EDT 2024
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 97
% Syntax : Number of formulae : 122 ( 17 unt; 62 typ; 0 def)
% Number of atoms : 444 ( 75 equ; 0 cnn)
% Maximal formula atoms : 120 ( 7 avg)
% Number of connectives : 1515 ( 111 ~; 113 |; 105 &; 941 @)
% ( 54 <=>; 191 =>; 0 <=; 0 <~>)
% Maximal formula depth : 132 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 62 usr; 40 con; 0-3 aty)
% Number of variables : 355 ( 39 ^ 270 !; 46 ?; 355 :)
% 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,
epred1_0: $o ).
thf(decl_66,type,
esk1_2: $i > $i > $i ).
thf(decl_67,type,
esk2_2: $i > $i > $i ).
thf(decl_68,type,
esk3_1: $i > $i ).
thf(decl_69,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_70,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_71,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_72,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_73,type,
esk8_1: $i > $i ).
thf(decl_74,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_75,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_76,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_77,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_78,type,
esk13_2: $i > $i > $i ).
thf(decl_79,type,
esk14_2: $i > $i > $i ).
thf(decl_80,type,
esk15_1: $i > $i ).
thf(decl_81,type,
esk16_1: $i > $i ).
thf(decl_82,type,
esk17_1: $i > $i ).
thf(decl_83,type,
esk18_0: $i ).
thf(decl_84,type,
esk19_0: $i ).
thf(decl_85,type,
esk20_0: $i ).
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(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(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(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
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(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(setadjoinOr,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
=> ! [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(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(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
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(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(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
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(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(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(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(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_34,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_35,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_36,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_37,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_38,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_39,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_40,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_41,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X111: $i] :
( ( X1 @ X111 )
& ! [X112: $i] :
( ( X1 @ X112 )
=> ( X111 = X112 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_42,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_43,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_36]) ).
thf(c_0_44,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_37,c_0_36]) ).
thf(c_0_45,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_36]) ).
thf(c_0_46,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X107: $i] :
( ( X6 @ X2 @ X107 )
& ! [X108: $i] :
( ( X6 @ X2 @ X108 )
=> ( X107 = X108 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_38,c_0_35]) ).
thf(c_0_47,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_48,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_49,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_50,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X109: $i] :
( ( X1 @ X109 )
& ! [X110: $i] :
( ( X1 @ X110 )
=> ( X109 = X110 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_39,c_0_35]) ).
thf(c_0_51,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_40]) ).
thf(c_0_52,plain,
( epred1_0
<=> ! [X139: $i] :
? [X140: $i] :
( ! [X141: $i] :
( ( in @ X141 @ X140 )
=> ! [X142: $i] :
( ( in @ X142 @ X141 )
=> ( in @ X142 @ X139 ) ) )
& ! [X143: $i,X144: $i] :
( ( ( in @ X143 @ X139 )
& ( in @ X144 @ X139 ) )
=> ( ! [X145: $i] :
( ( in @ X145 @ X140 )
=> ( ( in @ X143 @ X145 )
<=> ( in @ X144 @ X145 ) ) )
=> ( X143 = X144 ) ) )
& ! [X146: $i,X147: $i] :
( ( ( in @ X146 @ X140 )
& ( in @ X147 @ X140 ) )
=> ( ! [X148: $i] :
( ( in @ X148 @ X146 )
=> ( in @ X148 @ X147 ) )
| ! [X149: $i] :
( ( in @ X149 @ X147 )
=> ( in @ X149 @ X146 ) ) ) )
& ! [X150: $i] :
( ( ! [X151: $i] :
( ( in @ X151 @ X150 )
=> ( in @ X151 @ X139 ) )
& ? [X152: $i] : ( in @ X152 @ X150 ) )
=> ? [X153: $i,X154: $i] :
( ( in @ X153 @ X140 )
& ( in @ X154 @ X150 )
& ~ ? [X155: $i] :
( ( in @ X155 @ X153 )
& ( in @ X155 @ X150 ) )
& ! [X156: $i] :
( ( in @ X156 @ X140 )
=> ( ! [X157: $i] :
( ( in @ X157 @ X156 )
=> ( in @ X157 @ X153 ) )
| ( in @ X154 @ X156 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_53,negated_conjecture,
~ ( ! [X113: $i,X114: $i] :
( ! [X115: $i] :
( ( in @ X115 @ X113 )
<=> ( in @ X115 @ X114 ) )
=> ( X113 = X114 ) )
=> ( ! [X116: $i] :
~ ( in @ X116 @ emptyset )
=> ( ! [X117: $i,X118: $i,X119: $i] :
( ( in @ X119 @ ( setadjoin @ X117 @ X118 ) )
<=> ( ( X119 = X117 )
| ( in @ X119 @ X118 ) ) )
=> ( ! [X120: $i,X121: $i] :
( ( in @ X121 @ ( powerset @ X120 ) )
<=> ! [X122: $i] :
( ( in @ X122 @ X121 )
=> ( in @ X122 @ X120 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X123: $i] :
( ( in @ X123 @ omega )
=> ( in @ ( setadjoin @ X123 @ X123 ) @ omega ) )
=> ( ! [X124: $i] :
( ( ( in @ emptyset @ X124 )
& ! [X125: $i] :
( ( ( in @ X125 @ omega )
& ( in @ X125 @ X124 ) )
=> ( in @ ( setadjoin @ X125 @ X125 ) @ X124 ) ) )
=> ! [X126: $i] :
( ( in @ X126 @ omega )
=> ( in @ X126 @ X124 ) ) )
=> ( ! [X127: $i > $i > $o,X128: $i] :
( ! [X129: $i] :
( ( in @ X129 @ X128 )
=> ? [X130: $i] :
( ( X127 @ X129 @ X130 )
& ! [X131: $i] :
( ( X127 @ X129 @ X131 )
=> ( X130 = X131 ) ) ) )
=> ? [X132: $i] :
! [X133: $i] :
( ( in @ X133 @ X132 )
<=> ? [X134: $i] :
( ( in @ X134 @ X128 )
& ( X127 @ X134 @ X133 ) ) ) )
=> ( ! [X135: $i] :
( ? [X136: $i] : ( in @ X136 @ X135 )
=> ? [X137: $i] :
( ( in @ X137 @ X135 )
& ~ ? [X138: $i] :
( ( in @ X138 @ X137 )
& ( in @ X138 @ X135 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X158: $i,X159: $i > $o,X160: $i] :
( ( in @ X160 @ X158 )
=> ( ( X159 @ X160 )
=> ( in @ X160
@ ( dsetconstr @ X158
@ ^ [Z0: $i] : ( X159 @ Z0 ) ) ) ) )
=> ( ! [X161: $i,X162: $i > $o,X163: $i] :
( ( in @ X163
@ ( dsetconstr @ X161
@ ^ [Z0: $i] : ( X162 @ Z0 ) ) )
=> ( in @ X163 @ X161 ) )
=> ( ! [X164: $i,X165: $i > $o,X166: $i] :
( ( in @ X166
@ ( dsetconstr @ X164
@ ^ [Z0: $i] : ( X165 @ Z0 ) ) )
=> ( X165 @ X166 ) )
=> ( ! [X167: $i > $o] :
( ? [X168: $i] :
( ( X167 @ X168 )
& ! [X169: $i] :
( ( X167 @ X169 )
=> ( X168 = X169 ) ) )
=> ? [X170: $i] :
( ( X167 @ X170 )
& ! [X171: $i] :
( ( X167 @ X171 )
=> ( X170 = X171 ) ) ) )
=> ( ! [X172: $o,X173: $i] :
( ( in @ X173
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X172 ) )
=> X172 )
=> ( ! [X174: $i] :
( ( in @ X174 @ emptyset )
=> ! [X175: $o] : X175 )
=> ( ! [X176: $i] :
~ ( in @ X176 @ emptyset )
=> ( ! [X177: $i] :
~ ( in @ X177 @ emptyset )
=> ( ! [X178: $i > $o] :
( ? [X179: $i] :
( ( X178 @ X179 )
& ! [X180: $i] :
( ( X178 @ X180 )
=> ( X179 = X180 ) ) )
=> ? [X181: $i] : ( X178 @ X181 ) )
=> ( ! [X182: $i,X183: $i] :
( ! [X184: $i] :
( ( in @ X184 @ X182 )
=> ( in @ X184 @ X183 ) )
=> ( ! [X185: $i] :
( ( in @ X185 @ X183 )
=> ( in @ X185 @ X182 ) )
=> ( X182 = X183 ) ) )
=> ( ! [X186: $i] :
( ! [X187: $i] :
~ ( in @ X187 @ X186 )
=> ( X186 = emptyset ) )
=> ( ! [X188: $i] :
( ! [X189: $i] :
~ ( in @ X189 @ X188 )
=> ( X188 = emptyset ) )
=> ( ! [X190: $i,X191: $i > $o,X192: $i] :
( ( in @ X192 @ X190 )
=> ( ( in @ X192
@ ( dsetconstr @ X190
@ ^ [Z0: $i] : ( X191 @ Z0 ) ) )
<=> ( X191 @ X192 ) ) )
=> ( ! [X193: $i] :
( ( X193 != emptyset )
=> ? [X194: $i] : ( in @ X194 @ X193 ) )
=> ( ! [X195: $i,X196: $i > $o,X197: $i] :
( ( in @ X197 @ X195 )
=> ( ( X196 @ X197 )
=> ( ( dsetconstr @ X195
@ ^ [Z0: $i] : ( X196 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X198: $i] :
( ? [X199: $i] : ( in @ X199 @ X198 )
=> ( X198 != emptyset ) )
=> ( ! [X200: $i,X201: $i] : ( in @ X200 @ ( setadjoin @ X200 @ X201 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X202: $i,X203: $i,X204: $i] :
( ( in @ X204 @ X203 )
=> ( in @ X204 @ ( setadjoin @ X202 @ X203 ) ) )
=> ( ! [X205: $i,X206: $i,X207: $i] :
( ( in @ X207 @ ( setadjoin @ X205 @ X206 ) )
=> ! [X208: $o] :
( ( ( X207 = X205 )
=> X208 )
=> ( ( ( in @ X207 @ X206 )
=> X208 )
=> X208 ) ) )
=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ 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(assume_negation,[status(cth)],[setadjoinOr]),setadjoinE]),notinemptyset]),powersetAx]),c_0_41]),setext]),emptyI]),omega0Ax]),noeltsimpempty]),c_0_42]),omegaSAx]),c_0_43]),c_0_44]),omegaIndAx]),c_0_45]),setadjoinIL]),c_0_46]),emptyinunitempty]),setadjoinIR]),foundationAx]),wellorderingAx]),c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),emptysetE]),emptysetimpfalse]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_52]) ).
thf(c_0_54,negated_conjecture,
! [X209: $i,X210: $i,X212: $i,X213: $i,X214: $i,X215: $i,X216: $i,X217: $i,X218: $i,X219: $i,X220: $i,X222: $i,X223: $i,X225: $i,X226: $i > $i > $o,X227: $i,X229: $i,X232: $i,X234: $i,X235: $i,X236: $i,X237: $i,X239: $i,X240: $i,X241: $i > $o,X242: $i,X243: $i,X244: $i > $o,X245: $i,X246: $i,X247: $i > $o,X248: $i,X249: $i > $o,X250: $i,X253: $i,X254: $o,X255: $i,X256: $i,X257: $o,X258: $i,X259: $i,X260: $i > $o,X261: $i,X264: $i,X265: $i,X268: $i,X270: $i,X272: $i,X273: $i > $o,X274: $i,X275: $i,X277: $i,X278: $i > $o,X279: $i,X280: $i,X281: $i,X282: $i,X283: $i,X284: $i,X285: $i,X286: $i,X287: $i,X288: $i,X289: $i,X290: $o] :
( ( ~ ( in @ ( esk1_2 @ X209 @ X210 ) @ X209 )
| ~ ( in @ ( esk1_2 @ X209 @ X210 ) @ X210 )
| ( X209 = X210 ) )
& ( ( in @ ( esk1_2 @ X209 @ X210 ) @ X209 )
| ( in @ ( esk1_2 @ X209 @ X210 ) @ X210 )
| ( X209 = X210 ) )
& ~ ( in @ X212 @ emptyset )
& ( ~ ( in @ X215 @ ( setadjoin @ X213 @ X214 ) )
| ( X215 = X213 )
| ( in @ X215 @ X214 ) )
& ( ( X215 != X213 )
| ( in @ X215 @ ( setadjoin @ X213 @ X214 ) ) )
& ( ~ ( in @ X215 @ X214 )
| ( in @ X215 @ ( setadjoin @ X213 @ X214 ) ) )
& ( ~ ( in @ X217 @ ( powerset @ X216 ) )
| ~ ( in @ X218 @ X217 )
| ( in @ X218 @ X216 ) )
& ( ( in @ ( esk2_2 @ X219 @ X220 ) @ X220 )
| ( in @ X220 @ ( powerset @ X219 ) ) )
& ( ~ ( in @ ( esk2_2 @ X219 @ X220 ) @ X219 )
| ( in @ X220 @ ( powerset @ X219 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X222 @ omega )
| ( in @ ( setadjoin @ X222 @ X222 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X223 ) @ omega )
| ~ ( in @ emptyset @ X223 )
| ~ ( in @ X225 @ omega )
| ( in @ X225 @ X223 ) )
& ( ( in @ ( esk3_1 @ X223 ) @ X223 )
| ~ ( in @ emptyset @ X223 )
| ~ ( in @ X225 @ omega )
| ( in @ X225 @ X223 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X223 ) @ ( esk3_1 @ X223 ) ) @ X223 )
| ~ ( in @ emptyset @ X223 )
| ~ ( in @ X225 @ omega )
| ( in @ X225 @ X223 ) )
& ( ( in @ ( esk7_3 @ X226 @ X227 @ X232 ) @ X227 )
| ~ ( in @ X232 @ ( esk6_2 @ X226 @ X227 ) )
| ( in @ ( esk4_2 @ X226 @ X227 ) @ X227 ) )
& ( ( X226 @ ( esk7_3 @ X226 @ X227 @ X232 ) @ X232 )
| ~ ( in @ X232 @ ( esk6_2 @ X226 @ X227 ) )
| ( in @ ( esk4_2 @ X226 @ X227 ) @ X227 ) )
& ( ~ ( in @ X235 @ X227 )
| ~ ( X226 @ X235 @ X234 )
| ( in @ X234 @ ( esk6_2 @ X226 @ X227 ) )
| ( in @ ( esk4_2 @ X226 @ X227 ) @ X227 ) )
& ( ( in @ ( esk7_3 @ X226 @ X227 @ X232 ) @ X227 )
| ~ ( in @ X232 @ ( esk6_2 @ X226 @ X227 ) )
| ( X226 @ ( esk4_2 @ X226 @ X227 ) @ ( esk5_3 @ X226 @ X227 @ X229 ) )
| ~ ( X226 @ ( esk4_2 @ X226 @ X227 ) @ X229 ) )
& ( ( X226 @ ( esk7_3 @ X226 @ X227 @ X232 ) @ X232 )
| ~ ( in @ X232 @ ( esk6_2 @ X226 @ X227 ) )
| ( X226 @ ( esk4_2 @ X226 @ X227 ) @ ( esk5_3 @ X226 @ X227 @ X229 ) )
| ~ ( X226 @ ( esk4_2 @ X226 @ X227 ) @ X229 ) )
& ( ~ ( in @ X235 @ X227 )
| ~ ( X226 @ X235 @ X234 )
| ( in @ X234 @ ( esk6_2 @ X226 @ X227 ) )
| ( X226 @ ( esk4_2 @ X226 @ X227 ) @ ( esk5_3 @ X226 @ X227 @ X229 ) )
| ~ ( X226 @ ( esk4_2 @ X226 @ X227 ) @ X229 ) )
& ( ( in @ ( esk7_3 @ X226 @ X227 @ X232 ) @ X227 )
| ~ ( in @ X232 @ ( esk6_2 @ X226 @ X227 ) )
| ( X229
!= ( esk5_3 @ X226 @ X227 @ X229 ) )
| ~ ( X226 @ ( esk4_2 @ X226 @ X227 ) @ X229 ) )
& ( ( X226 @ ( esk7_3 @ X226 @ X227 @ X232 ) @ X232 )
| ~ ( in @ X232 @ ( esk6_2 @ X226 @ X227 ) )
| ( X229
!= ( esk5_3 @ X226 @ X227 @ X229 ) )
| ~ ( X226 @ ( esk4_2 @ X226 @ X227 ) @ X229 ) )
& ( ~ ( in @ X235 @ X227 )
| ~ ( X226 @ X235 @ X234 )
| ( in @ X234 @ ( esk6_2 @ X226 @ X227 ) )
| ( X229
!= ( esk5_3 @ X226 @ X227 @ X229 ) )
| ~ ( X226 @ ( esk4_2 @ X226 @ X227 ) @ X229 ) )
& ( ( in @ ( esk8_1 @ X236 ) @ X236 )
| ~ ( in @ X237 @ X236 ) )
& ( ~ ( in @ X239 @ ( esk8_1 @ X236 ) )
| ~ ( in @ X239 @ X236 )
| ~ ( in @ X237 @ X236 ) )
& epred1_0
& descrp
& ( ~ ( in @ X242 @ X240 )
| ~ ( X241 @ X242 )
| ( in @ X242
@ ( dsetconstr @ X240
@ ^ [Z0: $i] : ( X241 @ Z0 ) ) ) )
& ( ~ ( in @ X245
@ ( dsetconstr @ X243
@ ^ [Z0: $i] : ( X244 @ Z0 ) ) )
| ( in @ X245 @ X243 ) )
& ( ~ ( in @ X248
@ ( dsetconstr @ X246
@ ^ [Z0: $i] : ( X247 @ Z0 ) ) )
| ( X247 @ X248 ) )
& ( ( X249 @ ( esk10_1 @ X249 ) )
| ( X249 @ ( esk9_2 @ X249 @ X250 ) )
| ~ ( X249 @ X250 ) )
& ( ~ ( X249 @ X253 )
| ( ( esk10_1 @ X249 )
= X253 )
| ( X249 @ ( esk9_2 @ X249 @ X250 ) )
| ~ ( X249 @ X250 ) )
& ( ( X249 @ ( esk10_1 @ X249 ) )
| ( X250
!= ( esk9_2 @ X249 @ X250 ) )
| ~ ( X249 @ X250 ) )
& ( ~ ( X249 @ X253 )
| ( ( esk10_1 @ X249 )
= X253 )
| ( X250
!= ( esk9_2 @ X249 @ X250 ) )
| ~ ( X249 @ X250 ) )
& ( ~ ( in @ X255
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X254 ) )
| X254 )
& ( ~ ( in @ X256 @ emptyset )
| X257 )
& ~ ( in @ X258 @ emptyset )
& ~ ( in @ X259 @ emptyset )
& ( ( X260 @ ( esk11_2 @ X260 @ X261 ) )
| ~ ( X260 @ X261 )
| ( X260 @ ( esk12_1 @ X260 ) ) )
& ( ( X261
!= ( esk11_2 @ X260 @ X261 ) )
| ~ ( X260 @ X261 )
| ( X260 @ ( esk12_1 @ X260 ) ) )
& ( ( in @ ( esk14_2 @ X264 @ X265 ) @ X265 )
| ( X264 = X265 )
| ( in @ ( esk13_2 @ X264 @ X265 ) @ X264 ) )
& ( ~ ( in @ ( esk14_2 @ X264 @ X265 ) @ X264 )
| ( X264 = X265 )
| ( in @ ( esk13_2 @ X264 @ X265 ) @ X264 ) )
& ( ( in @ ( esk14_2 @ X264 @ X265 ) @ X265 )
| ( X264 = X265 )
| ~ ( in @ ( esk13_2 @ X264 @ X265 ) @ X265 ) )
& ( ~ ( in @ ( esk14_2 @ X264 @ X265 ) @ X264 )
| ( X264 = X265 )
| ~ ( in @ ( esk13_2 @ X264 @ X265 ) @ X265 ) )
& ( ( in @ ( esk15_1 @ X268 ) @ X268 )
| ( X268 = emptyset ) )
& ( ( in @ ( esk16_1 @ X270 ) @ X270 )
| ( X270 = emptyset ) )
& ( ~ ( in @ X274
@ ( dsetconstr @ X272
@ ^ [Z0: $i] : ( X273 @ Z0 ) ) )
| ( X273 @ X274 )
| ~ ( in @ X274 @ X272 ) )
& ( ~ ( X273 @ X274 )
| ( in @ X274
@ ( dsetconstr @ X272
@ ^ [Z0: $i] : ( X273 @ Z0 ) ) )
| ~ ( in @ X274 @ X272 ) )
& ( ( X275 = emptyset )
| ( in @ ( esk17_1 @ X275 ) @ X275 ) )
& ( ~ ( in @ X279 @ X277 )
| ~ ( X278 @ X279 )
| ( ( dsetconstr @ X277
@ ^ [Z0: $i] : ( X278 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X281 @ X280 )
| ( X280 != emptyset ) )
& ( in @ X282 @ ( setadjoin @ X282 @ X283 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X286 @ X285 )
| ( in @ X286 @ ( setadjoin @ X284 @ X285 ) ) )
& ( ( in @ X289 @ X288 )
| X290
| ( X289 = X287 )
| ~ ( in @ X289 @ ( setadjoin @ X287 @ X288 ) ) )
& ( ~ X290
| X290
| ( X289 = X287 )
| ~ ( in @ X289 @ ( setadjoin @ X287 @ X288 ) ) )
& ( ( in @ X289 @ X288 )
| X290
| ~ X290
| ~ ( in @ X289 @ ( setadjoin @ X287 @ X288 ) ) )
& ( ~ X290
| X290
| ~ X290
| ~ ( in @ X289 @ ( setadjoin @ X287 @ X288 ) ) )
& ( in @ esk20_0 @ ( setadjoin @ esk18_0 @ esk19_0 ) )
& ( esk20_0 != esk18_0 )
& ~ ( in @ esk20_0 @ 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_53])])])])])]) ).
thf(c_0_55,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ X3 )
| ( X2 = X4 )
| ~ ( in @ X2 @ ( setadjoin @ X4 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_54])])]) ).
thf(c_0_56,negated_conjecture,
in @ esk20_0 @ ( setadjoin @ esk18_0 @ esk19_0 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_57,negated_conjecture,
esk20_0 != esk18_0,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_58,negated_conjecture,
~ ( in @ esk20_0 @ esk19_0 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU516^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun May 19 15:48:08 EDT 2024
% 0.17/0.33 % CPUTime :
% 0.17/0.44 Running higher-order theorem proving
% 0.17/0.44 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
% 0.17/0.47 # Version: 3.1.0-ho
% 0.17/0.47 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.17/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.47 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.47 # Starting sh5l with 300s (1) cores
% 0.17/0.47 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.47 # Starting new_bool_2 with 300s (1) cores
% 0.17/0.47 # new_bool_2 with pid 19338 completed with status 0
% 0.17/0.47 # Result found by new_bool_2
% 0.17/0.47 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.17/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.47 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.47 # Starting sh5l with 300s (1) cores
% 0.17/0.47 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.47 # Starting new_bool_2 with 300s (1) cores
% 0.17/0.47 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.47 # Search class: HGHSF-FFMM31-SHFSMSBN
% 0.17/0.47 # partial match(2): HGHSM-FFMS31-SHFSMSBN
% 0.17/0.47 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.47 # Starting new_ho_10 with 181s (1) cores
% 0.17/0.47 # new_ho_10 with pid 19339 completed with status 0
% 0.17/0.47 # Result found by new_ho_10
% 0.17/0.47 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.17/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.47 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.47 # Starting sh5l with 300s (1) cores
% 0.17/0.47 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.47 # Starting new_bool_2 with 300s (1) cores
% 0.17/0.47 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.47 # Search class: HGHSF-FFMM31-SHFSMSBN
% 0.17/0.47 # partial match(2): HGHSM-FFMS31-SHFSMSBN
% 0.17/0.47 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.47 # Starting new_ho_10 with 181s (1) cores
% 0.17/0.47 # Preprocessing time : 0.002 s
% 0.17/0.47 # Presaturation interreduction done
% 0.17/0.47
% 0.17/0.47 # Proof found!
% 0.17/0.47 # SZS status Theorem
% 0.17/0.47 # SZS output start CNFRefutation
% See solution above
% 0.17/0.47 # Parsed axioms : 79
% 0.17/0.47 # Removed by relevancy pruning/SinE : 45
% 0.17/0.47 # Initial clauses : 75
% 0.17/0.47 # Removed in clause preprocessing : 3
% 0.17/0.47 # Initial clauses in saturation : 72
% 0.17/0.47 # Processed clauses : 111
% 0.17/0.47 # ...of these trivial : 1
% 0.17/0.47 # ...subsumed : 10
% 0.17/0.47 # ...remaining for further processing : 100
% 0.17/0.47 # Other redundant clauses eliminated : 2
% 0.17/0.47 # Clauses deleted for lack of memory : 0
% 0.17/0.47 # Backward-subsumed : 0
% 0.17/0.47 # Backward-rewritten : 2
% 0.17/0.47 # Generated clauses : 62
% 0.17/0.47 # ...of the previous two non-redundant : 51
% 0.17/0.47 # ...aggressively subsumed : 0
% 0.17/0.47 # Contextual simplify-reflections : 0
% 0.17/0.47 # Paramodulations : 60
% 0.17/0.47 # Factorizations : 0
% 0.17/0.47 # NegExts : 0
% 0.17/0.47 # Equation resolutions : 2
% 0.17/0.47 # Disequality decompositions : 0
% 0.17/0.47 # Total rewrite steps : 19
% 0.17/0.47 # ...of those cached : 13
% 0.17/0.47 # Propositional unsat checks : 0
% 0.17/0.47 # Propositional check models : 0
% 0.17/0.47 # Propositional check unsatisfiable : 0
% 0.17/0.47 # Propositional clauses : 0
% 0.17/0.47 # Propositional clauses after purity: 0
% 0.17/0.47 # Propositional unsat core size : 0
% 0.17/0.47 # Propositional preprocessing time : 0.000
% 0.17/0.47 # Propositional encoding time : 0.000
% 0.17/0.47 # Propositional solver time : 0.000
% 0.17/0.47 # Success case prop preproc time : 0.000
% 0.17/0.47 # Success case prop encoding time : 0.000
% 0.17/0.47 # Success case prop solver time : 0.000
% 0.17/0.47 # Current number of processed clauses : 34
% 0.17/0.47 # Positive orientable unit clauses : 11
% 0.17/0.47 # Positive unorientable unit clauses: 0
% 0.17/0.47 # Negative unit clauses : 3
% 0.17/0.47 # Non-unit-clauses : 20
% 0.17/0.47 # Current number of unprocessed clauses: 72
% 0.17/0.47 # ...number of literals in the above : 221
% 0.17/0.47 # Current number of archived formulas : 0
% 0.17/0.47 # Current number of archived clauses : 64
% 0.17/0.47 # Clause-clause subsumption calls (NU) : 1165
% 0.17/0.47 # Rec. Clause-clause subsumption calls : 451
% 0.17/0.47 # Non-unit clause-clause subsumptions : 7
% 0.17/0.47 # Unit Clause-clause subsumption calls : 15
% 0.17/0.47 # Rewrite failures with RHS unbound : 0
% 0.17/0.47 # BW rewrite match attempts : 7
% 0.17/0.47 # BW rewrite match successes : 2
% 0.17/0.47 # Condensation attempts : 111
% 0.17/0.47 # Condensation successes : 3
% 0.17/0.47 # Termbank termtop insertions : 10274
% 0.17/0.47 # Search garbage collected termcells : 2913
% 0.17/0.47
% 0.17/0.47 # -------------------------------------------------
% 0.17/0.47 # User time : 0.016 s
% 0.17/0.47 # System time : 0.002 s
% 0.17/0.47 # Total time : 0.018 s
% 0.17/0.47 # Maximum resident set size: 2544 pages
% 0.17/0.47
% 0.17/0.47 # -------------------------------------------------
% 0.17/0.47 # User time : 0.018 s
% 0.17/0.47 # System time : 0.005 s
% 0.17/0.47 # Total time : 0.022 s
% 0.17/0.47 # Maximum resident set size: 1804 pages
% 0.17/0.47 % E---3.1 exiting
% 0.17/0.47 % E exiting
%------------------------------------------------------------------------------