TSTP Solution File: SEU504^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU504^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 63
% Syntax : Number of formulae : 78 ( 10 unt; 41 typ; 0 def)
% Number of atoms : 295 ( 36 equ; 0 cnn)
% Maximal formula atoms : 82 ( 7 avg)
% Number of connectives : 1060 ( 72 ~; 75 |; 84 &; 672 @)
% ( 36 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 88 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 26 con; 0-3 aty)
% Number of variables : 239 ( 26 ^ 176 !; 37 ?; 239 :)
% 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,
epred1_0: $o ).
thf(decl_53,type,
esk1_2: $i > $i > $i ).
thf(decl_54,type,
esk2_2: $i > $i > $i ).
thf(decl_55,type,
esk3_1: $i > $i ).
thf(decl_56,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_57,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_58,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_59,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_60,type,
esk8_1: $i > $i ).
thf(decl_61,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_62,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_63,type,
epred2_0: $i > $o ).
thf(decl_64,type,
esk11_0: $i ).
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(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(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(exuE3e,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
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(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(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(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(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(c_0_21,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_22,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_23,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_24,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_25,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X76: $i] :
( ( X6 @ X2 @ X76 )
& ! [X77: $i] :
( ( X6 @ X2 @ X77 )
=> ( X76 = X77 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,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_27,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_28,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_29,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X78: $i] :
( ( X1 @ X78 )
& ! [X79: $i] :
( ( X1 @ X79 )
=> ( X78 = X79 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_22]) ).
thf(c_0_30,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_24]) ).
thf(c_0_31,plain,
( epred1_0
<=> ! [X106: $i] :
? [X107: $i] :
( ! [X108: $i] :
( ( in @ X108 @ X107 )
=> ! [X109: $i] :
( ( in @ X109 @ X108 )
=> ( in @ X109 @ X106 ) ) )
& ! [X110: $i,X111: $i] :
( ( ( in @ X110 @ X106 )
& ( in @ X111 @ X106 ) )
=> ( ! [X112: $i] :
( ( in @ X112 @ X107 )
=> ( ( in @ X110 @ X112 )
<=> ( in @ X111 @ X112 ) ) )
=> ( X110 = X111 ) ) )
& ! [X113: $i,X114: $i] :
( ( ( in @ X113 @ X107 )
& ( in @ X114 @ X107 ) )
=> ( ! [X115: $i] :
( ( in @ X115 @ X113 )
=> ( in @ X115 @ X114 ) )
| ! [X116: $i] :
( ( in @ X116 @ X114 )
=> ( in @ X116 @ X113 ) ) ) )
& ! [X117: $i] :
( ( ! [X118: $i] :
( ( in @ X118 @ X117 )
=> ( in @ X118 @ X106 ) )
& ? [X119: $i] : ( in @ X119 @ X117 ) )
=> ? [X120: $i,X121: $i] :
( ( in @ X120 @ X107 )
& ( in @ X121 @ X117 )
& ~ ? [X122: $i] :
( ( in @ X122 @ X120 )
& ( in @ X122 @ X117 ) )
& ! [X123: $i] :
( ( in @ X123 @ X107 )
=> ( ! [X124: $i] :
( ( in @ X124 @ X123 )
=> ( in @ X124 @ X120 ) )
| ( in @ X121 @ X123 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_32,negated_conjecture,
~ ( ! [X80: $i,X81: $i] :
( ! [X82: $i] :
( ( in @ X82 @ X80 )
<=> ( in @ X82 @ X81 ) )
=> ( X80 = X81 ) )
=> ( ! [X83: $i] :
~ ( in @ X83 @ emptyset )
=> ( ! [X84: $i,X85: $i,X86: $i] :
( ( in @ X86 @ ( setadjoin @ X84 @ X85 ) )
<=> ( ( X86 = X84 )
| ( in @ X86 @ X85 ) ) )
=> ( ! [X87: $i,X88: $i] :
( ( in @ X88 @ ( powerset @ X87 ) )
<=> ! [X89: $i] :
( ( in @ X89 @ X88 )
=> ( in @ X89 @ X87 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X90: $i] :
( ( in @ X90 @ omega )
=> ( in @ ( setadjoin @ X90 @ X90 ) @ omega ) )
=> ( ! [X91: $i] :
( ( ( in @ emptyset @ X91 )
& ! [X92: $i] :
( ( ( in @ X92 @ omega )
& ( in @ X92 @ X91 ) )
=> ( in @ ( setadjoin @ X92 @ X92 ) @ X91 ) ) )
=> ! [X93: $i] :
( ( in @ X93 @ omega )
=> ( in @ X93 @ X91 ) ) )
=> ( ! [X94: $i > $i > $o,X95: $i] :
( ! [X96: $i] :
( ( in @ X96 @ X95 )
=> ? [X97: $i] :
( ( X94 @ X96 @ X97 )
& ! [X98: $i] :
( ( X94 @ X96 @ X98 )
=> ( X97 = X98 ) ) ) )
=> ? [X99: $i] :
! [X100: $i] :
( ( in @ X100 @ X99 )
<=> ? [X101: $i] :
( ( in @ X101 @ X95 )
& ( X94 @ X101 @ X100 ) ) ) )
=> ( ! [X102: $i] :
( ? [X103: $i] : ( in @ X103 @ X102 )
=> ? [X104: $i] :
( ( in @ X104 @ X102 )
& ~ ? [X105: $i] :
( ( in @ X105 @ X104 )
& ( in @ X105 @ X102 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X125: $i,X126: $i > $o,X127: $i] :
( ( in @ X127 @ X125 )
=> ( ( X126 @ X127 )
=> ( in @ X127
@ ( dsetconstr @ X125
@ ^ [Z0: $i] : ( X126 @ Z0 ) ) ) ) )
=> ( ! [X128: $i,X129: $i > $o,X130: $i] :
( ( in @ X130
@ ( dsetconstr @ X128
@ ^ [Z0: $i] : ( X129 @ Z0 ) ) )
=> ( in @ X130 @ X128 ) )
=> ( ! [X131: $i,X132: $i > $o,X133: $i] :
( ( in @ X133
@ ( dsetconstr @ X131
@ ^ [Z0: $i] : ( X132 @ Z0 ) ) )
=> ( X132 @ X133 ) )
=> ( ! [X134: $i > $o] :
( ? [X135: $i] :
( ( X134 @ X135 )
& ! [X136: $i] :
( ( X134 @ X136 )
=> ( X135 = X136 ) ) )
=> ? [X137: $i] :
( ( X134 @ X137 )
& ! [X138: $i] :
( ( X134 @ X138 )
=> ( X137 = X138 ) ) ) )
=> ( ! [X139: $o,X140: $i] :
( ( in @ X140
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X139 ) )
=> X139 )
=> ( ! [X141: $i] :
( ( in @ X141 @ emptyset )
=> ! [X142: $o] : X142 )
=> ( ! [X143: $i] :
~ ( in @ X143 @ emptyset )
=> ( ! [X144: $i] :
~ ( in @ X144 @ emptyset )
=> ! [X1: $i > $o] :
( ? [X145: $i] :
( ( X1 @ X145 )
& ! [X146: $i] :
( ( X1 @ X146 )
=> ( X145 = X146 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[exuE3e])]),c_0_22]),omegaIndAx]),c_0_25]),foundationAx]),wellorderingAx]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),emptysetE]),setextAx]),emptysetimpfalse]),notinemptyset]),emptysetAx]),setadjoinAx]),powersetAx]),omega0Ax]),omegaSAx])]),c_0_31]) ).
thf(c_0_33,negated_conjecture,
! [X147: $i,X148: $i,X150: $i,X151: $i,X152: $i,X153: $i,X154: $i,X155: $i,X156: $i,X157: $i,X158: $i,X160: $i,X161: $i,X163: $i,X164: $i > $i > $o,X165: $i,X167: $i,X170: $i,X172: $i,X173: $i,X174: $i,X175: $i,X177: $i,X178: $i,X179: $i > $o,X180: $i,X181: $i,X182: $i > $o,X183: $i,X184: $i,X185: $i > $o,X186: $i,X187: $i > $o,X188: $i,X191: $i,X192: $o,X193: $i,X194: $i,X195: $o,X196: $i,X197: $i,X200: $i,X201: $i] :
( ( ~ ( in @ ( esk1_2 @ X147 @ X148 ) @ X147 )
| ~ ( in @ ( esk1_2 @ X147 @ X148 ) @ X148 )
| ( X147 = X148 ) )
& ( ( in @ ( esk1_2 @ X147 @ X148 ) @ X147 )
| ( in @ ( esk1_2 @ X147 @ X148 ) @ X148 )
| ( X147 = X148 ) )
& ~ ( in @ X150 @ emptyset )
& ( ~ ( in @ X153 @ ( setadjoin @ X151 @ X152 ) )
| ( X153 = X151 )
| ( in @ X153 @ X152 ) )
& ( ( X153 != X151 )
| ( in @ X153 @ ( setadjoin @ X151 @ X152 ) ) )
& ( ~ ( in @ X153 @ X152 )
| ( in @ X153 @ ( setadjoin @ X151 @ X152 ) ) )
& ( ~ ( in @ X155 @ ( powerset @ X154 ) )
| ~ ( in @ X156 @ X155 )
| ( in @ X156 @ X154 ) )
& ( ( in @ ( esk2_2 @ X157 @ X158 ) @ X158 )
| ( in @ X158 @ ( powerset @ X157 ) ) )
& ( ~ ( in @ ( esk2_2 @ X157 @ X158 ) @ X157 )
| ( in @ X158 @ ( powerset @ X157 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X160 @ omega )
| ( in @ ( setadjoin @ X160 @ X160 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X161 ) @ omega )
| ~ ( in @ emptyset @ X161 )
| ~ ( in @ X163 @ omega )
| ( in @ X163 @ X161 ) )
& ( ( in @ ( esk3_1 @ X161 ) @ X161 )
| ~ ( in @ emptyset @ X161 )
| ~ ( in @ X163 @ omega )
| ( in @ X163 @ X161 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X161 ) @ ( esk3_1 @ X161 ) ) @ X161 )
| ~ ( in @ emptyset @ X161 )
| ~ ( in @ X163 @ omega )
| ( in @ X163 @ X161 ) )
& ( ( in @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X165 )
| ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
| ( in @ ( esk4_2 @ X164 @ X165 ) @ X165 ) )
& ( ( X164 @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X170 )
| ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
| ( in @ ( esk4_2 @ X164 @ X165 ) @ X165 ) )
& ( ~ ( in @ X173 @ X165 )
| ~ ( X164 @ X173 @ X172 )
| ( in @ X172 @ ( esk6_2 @ X164 @ X165 ) )
| ( in @ ( esk4_2 @ X164 @ X165 ) @ X165 ) )
& ( ( in @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X165 )
| ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
| ( X164 @ ( esk4_2 @ X164 @ X165 ) @ ( esk5_3 @ X164 @ X165 @ X167 ) )
| ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
& ( ( X164 @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X170 )
| ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
| ( X164 @ ( esk4_2 @ X164 @ X165 ) @ ( esk5_3 @ X164 @ X165 @ X167 ) )
| ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
& ( ~ ( in @ X173 @ X165 )
| ~ ( X164 @ X173 @ X172 )
| ( in @ X172 @ ( esk6_2 @ X164 @ X165 ) )
| ( X164 @ ( esk4_2 @ X164 @ X165 ) @ ( esk5_3 @ X164 @ X165 @ X167 ) )
| ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
& ( ( in @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X165 )
| ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
| ( X167
!= ( esk5_3 @ X164 @ X165 @ X167 ) )
| ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
& ( ( X164 @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X170 )
| ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
| ( X167
!= ( esk5_3 @ X164 @ X165 @ X167 ) )
| ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
& ( ~ ( in @ X173 @ X165 )
| ~ ( X164 @ X173 @ X172 )
| ( in @ X172 @ ( esk6_2 @ X164 @ X165 ) )
| ( X167
!= ( esk5_3 @ X164 @ X165 @ X167 ) )
| ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
& ( ( in @ ( esk8_1 @ X174 ) @ X174 )
| ~ ( in @ X175 @ X174 ) )
& ( ~ ( in @ X177 @ ( esk8_1 @ X174 ) )
| ~ ( in @ X177 @ X174 )
| ~ ( in @ X175 @ X174 ) )
& epred1_0
& descrp
& ( ~ ( in @ X180 @ X178 )
| ~ ( X179 @ X180 )
| ( in @ X180
@ ( dsetconstr @ X178
@ ^ [Z0: $i] : ( X179 @ Z0 ) ) ) )
& ( ~ ( in @ X183
@ ( dsetconstr @ X181
@ ^ [Z0: $i] : ( X182 @ Z0 ) ) )
| ( in @ X183 @ X181 ) )
& ( ~ ( in @ X186
@ ( dsetconstr @ X184
@ ^ [Z0: $i] : ( X185 @ Z0 ) ) )
| ( X185 @ X186 ) )
& ( ( X187 @ ( esk10_1 @ X187 ) )
| ( X187 @ ( esk9_2 @ X187 @ X188 ) )
| ~ ( X187 @ X188 ) )
& ( ~ ( X187 @ X191 )
| ( ( esk10_1 @ X187 )
= X191 )
| ( X187 @ ( esk9_2 @ X187 @ X188 ) )
| ~ ( X187 @ X188 ) )
& ( ( X187 @ ( esk10_1 @ X187 ) )
| ( X188
!= ( esk9_2 @ X187 @ X188 ) )
| ~ ( X187 @ X188 ) )
& ( ~ ( X187 @ X191 )
| ( ( esk10_1 @ X187 )
= X191 )
| ( X188
!= ( esk9_2 @ X187 @ X188 ) )
| ~ ( X187 @ X188 ) )
& ( ~ ( in @ X193
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X192 ) )
| X192 )
& ( ~ ( in @ X194 @ emptyset )
| X195 )
& ~ ( in @ X196 @ emptyset )
& ~ ( in @ X197 @ emptyset )
& ( epred2_0 @ esk11_0 )
& ( ~ ( epred2_0 @ X200 )
| ( esk11_0 = X200 ) )
& ~ ( epred2_0 @ X201 ) ),
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_32])])])])])]) ).
thf(c_0_34,negated_conjecture,
epred2_0 @ esk11_0,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_35,negated_conjecture,
! [X2: $i] :
~ ( epred2_0 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_34,c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU504^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n017.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 16:19:23 EDT 2024
% 0.11/0.32 % 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
% 0.17/0.46 # Version: 3.1.0-ho
% 0.17/0.46 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.17/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.46 # Starting sh5l with 300s (1) cores
% 0.17/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.17/0.46 # new_bool_2 with pid 20438 completed with status 0
% 0.17/0.46 # Result found by new_bool_2
% 0.17/0.46 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.17/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.46 # Starting sh5l with 300s (1) cores
% 0.17/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.17/0.46 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.46 # Search class: HGHSF-FFMS31-SHSSMSBN
% 0.17/0.46 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.46 # Starting sh2 with 163s (1) cores
% 0.17/0.46 # sh2 with pid 20439 completed with status 0
% 0.17/0.46 # Result found by sh2
% 0.17/0.46 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.17/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.46 # Starting sh5l with 300s (1) cores
% 0.17/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.17/0.46 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.46 # Search class: HGHSF-FFMS31-SHSSMSBN
% 0.17/0.46 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.46 # Starting sh2 with 163s (1) cores
% 0.17/0.46 # Preprocessing time : 0.002 s
% 0.17/0.46 # Presaturation interreduction done
% 0.17/0.46
% 0.17/0.46 # Proof found!
% 0.17/0.46 # SZS status Theorem
% 0.17/0.46 # SZS output start CNFRefutation
% See solution above
% 0.17/0.46 # Parsed axioms : 53
% 0.17/0.46 # Removed by relevancy pruning/SinE : 32
% 0.17/0.46 # Initial clauses : 55
% 0.17/0.46 # Removed in clause preprocessing : 0
% 0.17/0.46 # Initial clauses in saturation : 55
% 0.17/0.46 # Processed clauses : 6
% 0.17/0.46 # ...of these trivial : 0
% 0.17/0.46 # ...subsumed : 0
% 0.17/0.46 # ...remaining for further processing : 6
% 0.17/0.46 # Other redundant clauses eliminated : 0
% 0.17/0.46 # Clauses deleted for lack of memory : 0
% 0.17/0.46 # Backward-subsumed : 0
% 0.17/0.46 # Backward-rewritten : 0
% 0.17/0.46 # Generated clauses : 1
% 0.17/0.46 # ...of the previous two non-redundant : 0
% 0.17/0.46 # ...aggressively subsumed : 0
% 0.17/0.46 # Contextual simplify-reflections : 0
% 0.17/0.46 # Paramodulations : 0
% 0.17/0.46 # Factorizations : 0
% 0.17/0.46 # NegExts : 0
% 0.17/0.46 # Equation resolutions : 0
% 0.17/0.46 # Disequality decompositions : 0
% 0.17/0.46 # Total rewrite steps : 0
% 0.17/0.46 # ...of those cached : 0
% 0.17/0.46 # Propositional unsat checks : 0
% 0.17/0.46 # Propositional check models : 0
% 0.17/0.46 # Propositional check unsatisfiable : 0
% 0.17/0.46 # Propositional clauses : 0
% 0.17/0.46 # Propositional clauses after purity: 0
% 0.17/0.46 # Propositional unsat core size : 0
% 0.17/0.46 # Propositional preprocessing time : 0.000
% 0.17/0.46 # Propositional encoding time : 0.000
% 0.17/0.46 # Propositional solver time : 0.000
% 0.17/0.46 # Success case prop preproc time : 0.000
% 0.17/0.46 # Success case prop encoding time : 0.000
% 0.17/0.46 # Success case prop solver time : 0.000
% 0.17/0.46 # Current number of processed clauses : 5
% 0.17/0.46 # Positive orientable unit clauses : 4
% 0.17/0.46 # Positive unorientable unit clauses: 0
% 0.17/0.46 # Negative unit clauses : 1
% 0.17/0.46 # Non-unit-clauses : 0
% 0.17/0.46 # Current number of unprocessed clauses: 49
% 0.17/0.46 # ...number of literals in the above : 171
% 0.17/0.46 # Current number of archived formulas : 0
% 0.17/0.46 # Current number of archived clauses : 1
% 0.17/0.46 # Clause-clause subsumption calls (NU) : 0
% 0.17/0.46 # Rec. Clause-clause subsumption calls : 0
% 0.17/0.46 # Non-unit clause-clause subsumptions : 0
% 0.17/0.46 # Unit Clause-clause subsumption calls : 0
% 0.17/0.46 # Rewrite failures with RHS unbound : 0
% 0.17/0.46 # BW rewrite match attempts : 0
% 0.17/0.46 # BW rewrite match successes : 0
% 0.17/0.46 # Condensation attempts : 0
% 0.17/0.46 # Condensation successes : 0
% 0.17/0.46 # Termbank termtop insertions : 5611
% 0.17/0.46 # Search garbage collected termcells : 2091
% 0.17/0.46
% 0.17/0.46 # -------------------------------------------------
% 0.17/0.46 # User time : 0.007 s
% 0.17/0.46 # System time : 0.003 s
% 0.17/0.46 # Total time : 0.010 s
% 0.17/0.46 # Maximum resident set size: 2392 pages
% 0.17/0.46
% 0.17/0.46 # -------------------------------------------------
% 0.17/0.46 # User time : 0.008 s
% 0.17/0.46 # System time : 0.006 s
% 0.17/0.46 # Total time : 0.014 s
% 0.17/0.46 # Maximum resident set size: 1788 pages
% 0.17/0.46 % E---3.1 exiting
% 0.17/0.46 % E exiting
%------------------------------------------------------------------------------