TSTP Solution File: SEU505^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU505^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.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 03:27:48 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 67
% Syntax : Number of formulae : 90 ( 12 unt; 44 typ; 0 def)
% Number of atoms : 330 ( 45 equ; 0 cnn)
% Maximal formula atoms : 85 ( 7 avg)
% Number of connectives : 1173 ( 82 ~; 89 |; 87 &; 742 @)
% ( 38 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 93 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 44 usr; 28 con; 0-3 aty)
% Number of variables : 256 ( 21 ^ 195 !; 40 ?; 256 :)
% 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,
epred1_0: $o ).
thf(decl_54,type,
esk1_2: $i > $i > $i ).
thf(decl_55,type,
esk2_2: $i > $i > $i ).
thf(decl_56,type,
esk3_1: $i > $i ).
thf(decl_57,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_58,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_59,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_60,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_61,type,
esk8_1: $i > $i ).
thf(decl_62,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_63,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_64,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_65,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_66,type,
esk13_0: $i ).
thf(decl_67,type,
esk14_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(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(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(setext,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ! [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(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(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(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(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
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(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(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(c_0_22,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_23,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_24,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_25,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_26,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_27,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X84: $i] :
( ( X1 @ X84 )
& ! [X85: $i] :
( ( X1 @ X85 )
=> ( X84 = X85 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X80: $i] :
( ( X6 @ X2 @ X80 )
& ! [X81: $i] :
( ( X6 @ X2 @ X81 )
=> ( X80 = X81 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_23]) ).
thf(c_0_29,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_30,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_31,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_32,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X82: $i] :
( ( X1 @ X82 )
& ! [X83: $i] :
( ( X1 @ X83 )
=> ( X82 = X83 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_23]) ).
thf(c_0_33,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_26]) ).
thf(c_0_34,plain,
( epred1_0
<=> ! [X112: $i] :
? [X113: $i] :
( ! [X114: $i] :
( ( in @ X114 @ X113 )
=> ! [X115: $i] :
( ( in @ X115 @ X114 )
=> ( in @ X115 @ X112 ) ) )
& ! [X116: $i,X117: $i] :
( ( ( in @ X116 @ X112 )
& ( in @ X117 @ X112 ) )
=> ( ! [X118: $i] :
( ( in @ X118 @ X113 )
=> ( ( in @ X116 @ X118 )
<=> ( in @ X117 @ X118 ) ) )
=> ( X116 = X117 ) ) )
& ! [X119: $i,X120: $i] :
( ( ( in @ X119 @ X113 )
& ( in @ X120 @ X113 ) )
=> ( ! [X121: $i] :
( ( in @ X121 @ X119 )
=> ( in @ X121 @ X120 ) )
| ! [X122: $i] :
( ( in @ X122 @ X120 )
=> ( in @ X122 @ X119 ) ) ) )
& ! [X123: $i] :
( ( ! [X124: $i] :
( ( in @ X124 @ X123 )
=> ( in @ X124 @ X112 ) )
& ? [X125: $i] : ( in @ X125 @ X123 ) )
=> ? [X126: $i,X127: $i] :
( ( in @ X126 @ X113 )
& ( in @ X127 @ X123 )
& ~ ? [X128: $i] :
( ( in @ X128 @ X126 )
& ( in @ X128 @ X123 ) )
& ! [X129: $i] :
( ( in @ X129 @ X113 )
=> ( ! [X130: $i] :
( ( in @ X130 @ X129 )
=> ( in @ X130 @ X126 ) )
| ( in @ X127 @ X129 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_35,negated_conjecture,
~ ( ! [X86: $i,X87: $i] :
( ! [X88: $i] :
( ( in @ X88 @ X86 )
<=> ( in @ X88 @ X87 ) )
=> ( X86 = X87 ) )
=> ( ! [X89: $i] :
~ ( in @ X89 @ emptyset )
=> ( ! [X90: $i,X91: $i,X92: $i] :
( ( in @ X92 @ ( setadjoin @ X90 @ X91 ) )
<=> ( ( X92 = X90 )
| ( in @ X92 @ X91 ) ) )
=> ( ! [X93: $i,X94: $i] :
( ( in @ X94 @ ( powerset @ X93 ) )
<=> ! [X95: $i] :
( ( in @ X95 @ X94 )
=> ( in @ X95 @ X93 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X96: $i] :
( ( in @ X96 @ omega )
=> ( in @ ( setadjoin @ X96 @ X96 ) @ omega ) )
=> ( ! [X97: $i] :
( ( ( in @ emptyset @ X97 )
& ! [X98: $i] :
( ( ( in @ X98 @ omega )
& ( in @ X98 @ X97 ) )
=> ( in @ ( setadjoin @ X98 @ X98 ) @ X97 ) ) )
=> ! [X99: $i] :
( ( in @ X99 @ omega )
=> ( in @ X99 @ X97 ) ) )
=> ( ! [X100: $i > $i > $o,X101: $i] :
( ! [X102: $i] :
( ( in @ X102 @ X101 )
=> ? [X103: $i] :
( ( X100 @ X102 @ X103 )
& ! [X104: $i] :
( ( X100 @ X102 @ X104 )
=> ( X103 = X104 ) ) ) )
=> ? [X105: $i] :
! [X106: $i] :
( ( in @ X106 @ X105 )
<=> ? [X107: $i] :
( ( in @ X107 @ X101 )
& ( X100 @ X107 @ X106 ) ) ) )
=> ( ! [X108: $i] :
( ? [X109: $i] : ( in @ X109 @ X108 )
=> ? [X110: $i] :
( ( in @ X110 @ X108 )
& ~ ? [X111: $i] :
( ( in @ X111 @ X110 )
& ( in @ X111 @ X108 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X131: $i,X132: $i > $o,X133: $i] :
( ( in @ X133 @ X131 )
=> ( ( X132 @ X133 )
=> ( in @ X133 @ ( dsetconstr @ X131 @ X132 ) ) ) )
=> ( ! [X134: $i,X135: $i > $o,X136: $i] :
( ( in @ X136 @ ( dsetconstr @ X134 @ X135 ) )
=> ( in @ X136 @ X134 ) )
=> ( ! [X137: $i,X138: $i > $o,X139: $i] :
( ( in @ X139 @ ( dsetconstr @ X137 @ X138 ) )
=> ( X138 @ X139 ) )
=> ( ! [X140: $i > $o] :
( ? [X141: $i] :
( ( X140 @ X141 )
& ! [X142: $i] :
( ( X140 @ X142 )
=> ( X141 = X142 ) ) )
=> ? [X143: $i] :
( ( X140 @ X143 )
& ! [X144: $i] :
( ( X140 @ X144 )
=> ( X143 = X144 ) ) ) )
=> ( ! [X145: $o,X146: $i] :
( ( in @ X146
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X145 ) )
=> X145 )
=> ( ! [X147: $i] :
( ( in @ X147 @ emptyset )
=> ! [X148: $o] : X148 )
=> ( ! [X149: $i] :
( ( in @ X149 @ emptyset )
=> ~ $true )
=> ( ! [X150: $i] :
~ ( in @ X150 @ emptyset )
=> ( ! [X151: $i > $o] :
( ? [X152: $i] :
( ( X151 @ X152 )
& ! [X153: $i] :
( ( X151 @ X153 )
=> ( X152 = X153 ) ) )
=> ? [X154: $i] : ( X151 @ X154 ) )
=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[setext]),omegaSAx]),c_0_27]),omegaIndAx]),c_0_28]),foundationAx]),wellorderingAx]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),emptysetE]),emptysetimpfalse]),setextAx]),notinemptyset]),emptysetAx]),setadjoinAx]),powersetAx]),omega0Ax])])]),c_0_34]) ).
thf(c_0_36,negated_conjecture,
! [X155: $i,X156: $i,X158: $i,X159: $i,X160: $i,X161: $i,X162: $i,X163: $i,X164: $i,X165: $i,X166: $i,X168: $i,X169: $i,X171: $i,X172: $i > $i > $o,X173: $i,X175: $i,X178: $i,X180: $i,X181: $i,X182: $i,X183: $i,X185: $i,X186: $i,X187: $i > $o,X188: $i,X189: $i,X190: $i > $o,X191: $i,X192: $i,X193: $i > $o,X194: $i,X195: $i > $o,X196: $i,X199: $i,X200: $o,X201: $i,X202: $i,X203: $o,X204: $i,X205: $i,X206: $i > $o,X207: $i,X212: $i,X213: $i] :
( ( ~ ( in @ ( esk1_2 @ X155 @ X156 ) @ X155 )
| ~ ( in @ ( esk1_2 @ X155 @ X156 ) @ X156 )
| ( X155 = X156 ) )
& ( ( in @ ( esk1_2 @ X155 @ X156 ) @ X155 )
| ( in @ ( esk1_2 @ X155 @ X156 ) @ X156 )
| ( X155 = X156 ) )
& ~ ( in @ X158 @ emptyset )
& ( ~ ( in @ X161 @ ( setadjoin @ X159 @ X160 ) )
| ( X161 = X159 )
| ( in @ X161 @ X160 ) )
& ( ( X161 != X159 )
| ( in @ X161 @ ( setadjoin @ X159 @ X160 ) ) )
& ( ~ ( in @ X161 @ X160 )
| ( in @ X161 @ ( setadjoin @ X159 @ X160 ) ) )
& ( ~ ( in @ X163 @ ( powerset @ X162 ) )
| ~ ( in @ X164 @ X163 )
| ( in @ X164 @ X162 ) )
& ( ( in @ ( esk2_2 @ X165 @ X166 ) @ X166 )
| ( in @ X166 @ ( powerset @ X165 ) ) )
& ( ~ ( in @ ( esk2_2 @ X165 @ X166 ) @ X165 )
| ( in @ X166 @ ( powerset @ X165 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X168 @ omega )
| ( in @ ( setadjoin @ X168 @ X168 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X169 ) @ omega )
| ~ ( in @ emptyset @ X169 )
| ~ ( in @ X171 @ omega )
| ( in @ X171 @ X169 ) )
& ( ( in @ ( esk3_1 @ X169 ) @ X169 )
| ~ ( in @ emptyset @ X169 )
| ~ ( in @ X171 @ omega )
| ( in @ X171 @ X169 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X169 ) @ ( esk3_1 @ X169 ) ) @ X169 )
| ~ ( in @ emptyset @ X169 )
| ~ ( in @ X171 @ omega )
| ( in @ X171 @ X169 ) )
& ( ( in @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X173 )
| ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
| ( in @ ( esk4_2 @ X172 @ X173 ) @ X173 ) )
& ( ( X172 @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X178 )
| ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
| ( in @ ( esk4_2 @ X172 @ X173 ) @ X173 ) )
& ( ~ ( in @ X181 @ X173 )
| ~ ( X172 @ X181 @ X180 )
| ( in @ X180 @ ( esk6_2 @ X172 @ X173 ) )
| ( in @ ( esk4_2 @ X172 @ X173 ) @ X173 ) )
& ( ( in @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X173 )
| ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
| ( X172 @ ( esk4_2 @ X172 @ X173 ) @ ( esk5_3 @ X172 @ X173 @ X175 ) )
| ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
& ( ( X172 @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X178 )
| ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
| ( X172 @ ( esk4_2 @ X172 @ X173 ) @ ( esk5_3 @ X172 @ X173 @ X175 ) )
| ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
& ( ~ ( in @ X181 @ X173 )
| ~ ( X172 @ X181 @ X180 )
| ( in @ X180 @ ( esk6_2 @ X172 @ X173 ) )
| ( X172 @ ( esk4_2 @ X172 @ X173 ) @ ( esk5_3 @ X172 @ X173 @ X175 ) )
| ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
& ( ( in @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X173 )
| ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
| ( X175
!= ( esk5_3 @ X172 @ X173 @ X175 ) )
| ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
& ( ( X172 @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X178 )
| ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
| ( X175
!= ( esk5_3 @ X172 @ X173 @ X175 ) )
| ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
& ( ~ ( in @ X181 @ X173 )
| ~ ( X172 @ X181 @ X180 )
| ( in @ X180 @ ( esk6_2 @ X172 @ X173 ) )
| ( X175
!= ( esk5_3 @ X172 @ X173 @ X175 ) )
| ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
& ( ( in @ ( esk8_1 @ X182 ) @ X182 )
| ~ ( in @ X183 @ X182 ) )
& ( ~ ( in @ X185 @ ( esk8_1 @ X182 ) )
| ~ ( in @ X185 @ X182 )
| ~ ( in @ X183 @ X182 ) )
& epred1_0
& descrp
& ( ~ ( in @ X188 @ X186 )
| ~ ( X187 @ X188 )
| ( in @ X188 @ ( dsetconstr @ X186 @ X187 ) ) )
& ( ~ ( in @ X191 @ ( dsetconstr @ X189 @ X190 ) )
| ( in @ X191 @ X189 ) )
& ( ~ ( in @ X194 @ ( dsetconstr @ X192 @ X193 ) )
| ( X193 @ X194 ) )
& ( ( X195 @ ( esk10_1 @ X195 ) )
| ( X195 @ ( esk9_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ~ ( X195 @ X199 )
| ( ( esk10_1 @ X195 )
= X199 )
| ( X195 @ ( esk9_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ( X195 @ ( esk10_1 @ X195 ) )
| ( X196
!= ( esk9_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ~ ( X195 @ X199 )
| ( ( esk10_1 @ X195 )
= X199 )
| ( X196
!= ( esk9_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ~ ( in @ X201
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X200 ) )
| X200 )
& ( ~ ( in @ X202 @ emptyset )
| X203 )
& ( ~ ( in @ X204 @ emptyset )
| ~ $true )
& ~ ( in @ X205 @ emptyset )
& ( ( X206 @ ( esk11_2 @ X206 @ X207 ) )
| ~ ( X206 @ X207 )
| ( X206 @ ( esk12_1 @ X206 ) ) )
& ( ( X207
!= ( esk11_2 @ X206 @ X207 ) )
| ~ ( X206 @ X207 )
| ( X206 @ ( esk12_1 @ X206 ) ) )
& ( ~ ( in @ X212 @ esk13_0 )
| ( in @ X212 @ esk14_0 ) )
& ( ~ ( in @ X213 @ esk14_0 )
| ( in @ X213 @ esk13_0 ) )
& ( esk13_0 != esk14_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_35])])])])])])]) ).
thf(c_0_37,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk13_0 )
| ~ ( in @ X2 @ esk14_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk1_2 @ X2 @ X3 ) @ X2 )
| ( in @ ( esk1_2 @ X2 @ X3 ) @ X3 )
| ( X2 = X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X2: $i] :
( ( esk14_0 = X2 )
| ( in @ ( esk1_2 @ esk14_0 @ X2 ) @ esk13_0 )
| ( in @ ( esk1_2 @ esk14_0 @ X2 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_40,negated_conjecture,
esk13_0 != esk14_0,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ ( in @ ( esk1_2 @ X2 @ X3 ) @ X2 )
| ~ ( in @ ( esk1_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_42,negated_conjecture,
in @ ( esk1_2 @ esk14_0 @ esk13_0 ) @ esk13_0,
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_39]),c_0_40]) ).
thf(c_0_43,negated_conjecture,
~ ( in @ ( esk1_2 @ esk14_0 @ esk13_0 ) @ esk14_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]) ).
thf(c_0_44,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk14_0 )
| ~ ( in @ X2 @ esk13_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU505^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 17:22:52 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.20/0.54 # Version: 3.1.0-ho
% 0.20/0.54 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.54 # Starting sh5l with 300s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.54 # new_bool_1 with pid 30206 completed with status 0
% 0.20/0.54 # Result found by new_bool_1
% 0.20/0.54 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.54 # Starting sh5l with 300s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.54 # Search class: HGHSF-FFMS31-SHFSMSBN
% 0.20/0.54 # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.54 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54 # Starting new_ho_10 with 181s (1) cores
% 0.20/0.54 # new_ho_10 with pid 30209 completed with status 0
% 0.20/0.54 # Result found by new_ho_10
% 0.20/0.54 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.54 # Starting sh5l with 300s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.54 # Search class: HGHSF-FFMS31-SHFSMSBN
% 0.20/0.54 # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.54 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54 # Starting new_ho_10 with 181s (1) cores
% 0.20/0.54 # Preprocessing time : 0.003 s
% 0.20/0.54 # Presaturation interreduction done
% 0.20/0.54
% 0.20/0.54 # Proof found!
% 0.20/0.54 # SZS status Theorem
% 0.20/0.54 # SZS output start CNFRefutation
% See solution above
% 0.20/0.54 # Parsed axioms : 55
% 0.20/0.54 # Removed by relevancy pruning/SinE : 33
% 0.20/0.54 # Initial clauses : 57
% 0.20/0.54 # Removed in clause preprocessing : 0
% 0.20/0.54 # Initial clauses in saturation : 57
% 0.20/0.54 # Processed clauses : 179
% 0.20/0.54 # ...of these trivial : 3
% 0.20/0.54 # ...subsumed : 16
% 0.20/0.54 # ...remaining for further processing : 160
% 0.20/0.54 # Other redundant clauses eliminated : 1
% 0.20/0.54 # Clauses deleted for lack of memory : 0
% 0.20/0.54 # Backward-subsumed : 0
% 0.20/0.54 # Backward-rewritten : 2
% 0.20/0.54 # Generated clauses : 835
% 0.20/0.54 # ...of the previous two non-redundant : 808
% 0.20/0.54 # ...aggressively subsumed : 0
% 0.20/0.54 # Contextual simplify-reflections : 0
% 0.20/0.54 # Paramodulations : 828
% 0.20/0.54 # Factorizations : 6
% 0.20/0.54 # NegExts : 0
% 0.20/0.54 # Equation resolutions : 1
% 0.20/0.54 # Disequality decompositions : 0
% 0.20/0.54 # Total rewrite steps : 57
% 0.20/0.54 # ...of those cached : 42
% 0.20/0.54 # Propositional unsat checks : 0
% 0.20/0.54 # Propositional check models : 0
% 0.20/0.54 # Propositional check unsatisfiable : 0
% 0.20/0.54 # Propositional clauses : 0
% 0.20/0.54 # Propositional clauses after purity: 0
% 0.20/0.54 # Propositional unsat core size : 0
% 0.20/0.54 # Propositional preprocessing time : 0.000
% 0.20/0.54 # Propositional encoding time : 0.000
% 0.20/0.54 # Propositional solver time : 0.000
% 0.20/0.54 # Success case prop preproc time : 0.000
% 0.20/0.54 # Success case prop encoding time : 0.000
% 0.20/0.54 # Success case prop solver time : 0.000
% 0.20/0.54 # Current number of processed clauses : 103
% 0.20/0.54 # Positive orientable unit clauses : 15
% 0.20/0.54 # Positive unorientable unit clauses: 0
% 0.20/0.54 # Negative unit clauses : 12
% 0.20/0.54 # Non-unit-clauses : 76
% 0.20/0.54 # Current number of unprocessed clauses: 740
% 0.20/0.54 # ...number of literals in the above : 2700
% 0.20/0.54 # Current number of archived formulas : 0
% 0.20/0.54 # Current number of archived clauses : 56
% 0.20/0.54 # Clause-clause subsumption calls (NU) : 3325
% 0.20/0.54 # Rec. Clause-clause subsumption calls : 1698
% 0.20/0.54 # Non-unit clause-clause subsumptions : 12
% 0.20/0.54 # Unit Clause-clause subsumption calls : 122
% 0.20/0.54 # Rewrite failures with RHS unbound : 0
% 0.20/0.54 # BW rewrite match attempts : 5
% 0.20/0.54 # BW rewrite match successes : 1
% 0.20/0.54 # Condensation attempts : 179
% 0.20/0.54 # Condensation successes : 3
% 0.20/0.54 # Termbank termtop insertions : 29042
% 0.20/0.54 # Search garbage collected termcells : 2620
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.042 s
% 0.20/0.54 # System time : 0.006 s
% 0.20/0.54 # Total time : 0.048 s
% 0.20/0.54 # Maximum resident set size: 2312 pages
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.044 s
% 0.20/0.54 # System time : 0.009 s
% 0.20/0.54 # Total time : 0.053 s
% 0.20/0.54 # Maximum resident set size: 1788 pages
% 0.20/0.54 % E---3.1 exiting
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------