TSTP Solution File: SEU500^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU500^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 03:27:46 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 64
% Syntax : Number of formulae : 86 ( 13 unt; 42 typ; 0 def)
% Number of atoms : 308 ( 39 equ; 0 cnn)
% Maximal formula atoms : 87 ( 7 avg)
% Number of connectives : 1134 ( 79 ~; 87 |; 87 &; 731 @)
% ( 38 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 86 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 23 con; 0-3 aty)
% Number of variables : 244 ( 22 ^ 184 !; 38 ?; 244 :)
% 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_31,type,
setunion: $i > $i ).
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_40,type,
descr: ( $i > $o ) > $i ).
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,
epred1_0: $o ).
thf(decl_49,type,
esk1_2: $i > $i > $i ).
thf(decl_50,type,
esk2_2: $i > $i > $i ).
thf(decl_51,type,
esk3_2: $i > $i > $i ).
thf(decl_52,type,
esk4_1: $i > $i ).
thf(decl_53,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_54,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_55,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_56,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_57,type,
esk9_1: $i > $i ).
thf(decl_58,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_59,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_60,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_61,type,
epred2_0: $o ).
thf(decl_62,type,
esk13_0: $i ).
thf(decl_68,type,
epred3_1: $o > $i > $o ).
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(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
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(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,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
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(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(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
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(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(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(c_0_19,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_20,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_21,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_22,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_23,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X73: $i] :
( ( X6 @ X2 @ X73 )
& ! [X74: $i] :
( ( X6 @ X2 @ X74 )
=> ( X73 = X74 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_24,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X75: $i] :
( ( X1 @ X75 )
& ! [X76: $i] :
( ( X1 @ X76 )
=> ( X75 = X76 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_20]) ).
thf(c_0_25,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_26,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_27,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_28,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X77: $i] :
( ( X1 @ X77 )
& ! [X78: $i] :
( ( X1 @ X78 )
=> ( X77 = X78 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_20]) ).
thf(c_0_29,plain,
( epred1_0
<=> ! [X108: $i] :
? [X109: $i] :
( ! [X110: $i] :
( ( in @ X110 @ X109 )
=> ! [X111: $i] :
( ( in @ X111 @ X110 )
=> ( in @ X111 @ X108 ) ) )
& ! [X112: $i,X113: $i] :
( ( ( in @ X112 @ X108 )
& ( in @ X113 @ X108 ) )
=> ( ! [X114: $i] :
( ( in @ X114 @ X109 )
=> ( ( in @ X112 @ X114 )
<=> ( in @ X113 @ X114 ) ) )
=> ( X112 = X113 ) ) )
& ! [X115: $i,X116: $i] :
( ( ( in @ X115 @ X109 )
& ( in @ X116 @ X109 ) )
=> ( ! [X117: $i] :
( ( in @ X117 @ X115 )
=> ( in @ X117 @ X116 ) )
| ! [X118: $i] :
( ( in @ X118 @ X116 )
=> ( in @ X118 @ X115 ) ) ) )
& ! [X119: $i] :
( ( ! [X120: $i] :
( ( in @ X120 @ X119 )
=> ( in @ X120 @ X108 ) )
& ? [X121: $i] : ( in @ X121 @ X119 ) )
=> ? [X122: $i,X123: $i] :
( ( in @ X122 @ X109 )
& ( in @ X123 @ X119 )
& ~ ? [X124: $i] :
( ( in @ X124 @ X122 )
& ( in @ X124 @ X119 ) )
& ! [X125: $i] :
( ( in @ X125 @ X109 )
=> ( ! [X126: $i] :
( ( in @ X126 @ X125 )
=> ( in @ X126 @ X122 ) )
| ( in @ X123 @ X125 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_30,negated_conjecture,
~ ( ! [X79: $i,X80: $i] :
( ! [X81: $i] :
( ( in @ X81 @ X79 )
<=> ( in @ X81 @ X80 ) )
=> ( X79 = X80 ) )
=> ( ! [X82: $i] :
~ ( in @ X82 @ emptyset )
=> ( ! [X83: $i,X84: $i,X85: $i] :
( ( in @ X85 @ ( setadjoin @ X83 @ X84 ) )
<=> ( ( X85 = X83 )
| ( in @ X85 @ X84 ) ) )
=> ( ! [X86: $i,X87: $i] :
( ( in @ X87 @ ( powerset @ X86 ) )
<=> ! [X88: $i] :
( ( in @ X88 @ X87 )
=> ( in @ X88 @ X86 ) ) )
=> ( ! [X89: $i,X90: $i] :
( ( in @ X90 @ ( setunion @ X89 ) )
<=> ? [X91: $i] :
( ( in @ X90 @ X91 )
& ( in @ X91 @ X89 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X92: $i] :
( ( in @ X92 @ omega )
=> ( in @ ( setadjoin @ X92 @ X92 ) @ omega ) )
=> ( ! [X93: $i] :
( ( ( in @ emptyset @ X93 )
& ! [X94: $i] :
( ( ( in @ X94 @ omega )
& ( in @ X94 @ X93 ) )
=> ( in @ ( setadjoin @ X94 @ X94 ) @ X93 ) ) )
=> ! [X95: $i] :
( ( in @ X95 @ omega )
=> ( in @ X95 @ X93 ) ) )
=> ( ! [X96: $i > $i > $o,X97: $i] :
( ! [X98: $i] :
( ( in @ X98 @ X97 )
=> ? [X99: $i] :
( ( X96 @ X98 @ X99 )
& ! [X100: $i] :
( ( X96 @ X98 @ X100 )
=> ( X99 = X100 ) ) ) )
=> ? [X101: $i] :
! [X102: $i] :
( ( in @ X102 @ X101 )
<=> ? [X103: $i] :
( ( in @ X103 @ X97 )
& ( X96 @ X103 @ X102 ) ) ) )
=> ( ! [X104: $i] :
( ? [X105: $i] : ( in @ X105 @ X104 )
=> ? [X106: $i] :
( ( in @ X106 @ X104 )
& ~ ? [X107: $i] :
( ( in @ X107 @ X106 )
& ( in @ X107 @ X104 ) ) ) )
=> ( epred1_0
=> ( ! [X127: $i > $o] :
( ? [X128: $i] :
( ( X127 @ X128 )
& ! [X129: $i] :
( ( X127 @ X129 )
=> ( X128 = X129 ) ) )
=> ( X127
@ ( descr
@ ^ [Z0: $i] : ( X127 @ Z0 ) ) ) )
=> ( ! [X130: $i,X131: $i > $o,X132: $i] :
( ( in @ X132 @ X130 )
=> ( ( X131 @ X132 )
=> ( in @ X132 @ ( dsetconstr @ X130 @ X131 ) ) ) )
=> ( ! [X133: $i,X134: $i > $o,X135: $i] :
( ( in @ X135 @ ( dsetconstr @ X133 @ X134 ) )
=> ( in @ X135 @ X133 ) )
=> ( ! [X136: $i,X137: $i > $o,X138: $i] :
( ( in @ X138 @ ( dsetconstr @ X136 @ X137 ) )
=> ( X137 @ X138 ) )
=> ( ! [X139: $i > $o] :
( ? [X140: $i] :
( ( X139 @ X140 )
& ! [X141: $i] :
( ( X139 @ X141 )
=> ( X140 = X141 ) ) )
=> ? [X142: $i] :
( ( X139 @ X142 )
& ! [X143: $i] :
( ( X139 @ X143 )
=> ( X142 = X143 ) ) ) )
=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[prop2setE]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_23]),foundationAx]),wellorderingAx]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28])])]),c_0_29]) ).
thf(c_0_31,plain,
! [X144: $o] :
( ( prop2set @ X144 )
= ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X144 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[prop2set])]) ).
thf(c_0_32,negated_conjecture,
! [X146: $i,X147: $i,X149: $i,X150: $i,X151: $i,X152: $i,X153: $i,X154: $i,X155: $i,X156: $i,X157: $i,X159: $i,X160: $i,X162: $i,X163: $i,X164: $i,X165: $i,X166: $i,X168: $i,X169: $i > $i > $o,X170: $i,X172: $i,X175: $i,X177: $i,X178: $i,X179: $i,X180: $i,X182: $i,X183: $i > $o,X184: $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] :
( ( ~ ( in @ ( esk1_2 @ X146 @ X147 ) @ X146 )
| ~ ( in @ ( esk1_2 @ X146 @ X147 ) @ X147 )
| ( X146 = X147 ) )
& ( ( in @ ( esk1_2 @ X146 @ X147 ) @ X146 )
| ( in @ ( esk1_2 @ X146 @ X147 ) @ X147 )
| ( X146 = X147 ) )
& ~ ( in @ X149 @ emptyset )
& ( ~ ( in @ X152 @ ( setadjoin @ X150 @ X151 ) )
| ( X152 = X150 )
| ( in @ X152 @ X151 ) )
& ( ( X152 != X150 )
| ( in @ X152 @ ( setadjoin @ X150 @ X151 ) ) )
& ( ~ ( in @ X152 @ X151 )
| ( in @ X152 @ ( setadjoin @ X150 @ X151 ) ) )
& ( ~ ( in @ X154 @ ( powerset @ X153 ) )
| ~ ( in @ X155 @ X154 )
| ( in @ X155 @ X153 ) )
& ( ( in @ ( esk2_2 @ X156 @ X157 ) @ X157 )
| ( in @ X157 @ ( powerset @ X156 ) ) )
& ( ~ ( in @ ( esk2_2 @ X156 @ X157 ) @ X156 )
| ( in @ X157 @ ( powerset @ X156 ) ) )
& ( ( in @ X160 @ ( esk3_2 @ X159 @ X160 ) )
| ~ ( in @ X160 @ ( setunion @ X159 ) ) )
& ( ( in @ ( esk3_2 @ X159 @ X160 ) @ X159 )
| ~ ( in @ X160 @ ( setunion @ X159 ) ) )
& ( ~ ( in @ X163 @ X164 )
| ~ ( in @ X164 @ X162 )
| ( in @ X163 @ ( setunion @ X162 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X165 @ omega )
| ( in @ ( setadjoin @ X165 @ X165 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X166 ) @ omega )
| ~ ( in @ emptyset @ X166 )
| ~ ( in @ X168 @ omega )
| ( in @ X168 @ X166 ) )
& ( ( in @ ( esk4_1 @ X166 ) @ X166 )
| ~ ( in @ emptyset @ X166 )
| ~ ( in @ X168 @ omega )
| ( in @ X168 @ X166 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X166 ) @ ( esk4_1 @ X166 ) ) @ X166 )
| ~ ( in @ emptyset @ X166 )
| ~ ( in @ X168 @ omega )
| ( in @ X168 @ X166 ) )
& ( ( in @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X170 )
| ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
| ( in @ ( esk5_2 @ X169 @ X170 ) @ X170 ) )
& ( ( X169 @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X175 )
| ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
| ( in @ ( esk5_2 @ X169 @ X170 ) @ X170 ) )
& ( ~ ( in @ X178 @ X170 )
| ~ ( X169 @ X178 @ X177 )
| ( in @ X177 @ ( esk7_2 @ X169 @ X170 ) )
| ( in @ ( esk5_2 @ X169 @ X170 ) @ X170 ) )
& ( ( in @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X170 )
| ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
| ( X169 @ ( esk5_2 @ X169 @ X170 ) @ ( esk6_3 @ X169 @ X170 @ X172 ) )
| ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
& ( ( X169 @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X175 )
| ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
| ( X169 @ ( esk5_2 @ X169 @ X170 ) @ ( esk6_3 @ X169 @ X170 @ X172 ) )
| ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
& ( ~ ( in @ X178 @ X170 )
| ~ ( X169 @ X178 @ X177 )
| ( in @ X177 @ ( esk7_2 @ X169 @ X170 ) )
| ( X169 @ ( esk5_2 @ X169 @ X170 ) @ ( esk6_3 @ X169 @ X170 @ X172 ) )
| ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
& ( ( in @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X170 )
| ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
| ( X172
!= ( esk6_3 @ X169 @ X170 @ X172 ) )
| ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
& ( ( X169 @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X175 )
| ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
| ( X172
!= ( esk6_3 @ X169 @ X170 @ X172 ) )
| ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
& ( ~ ( in @ X178 @ X170 )
| ~ ( X169 @ X178 @ X177 )
| ( in @ X177 @ ( esk7_2 @ X169 @ X170 ) )
| ( X172
!= ( esk6_3 @ X169 @ X170 @ X172 ) )
| ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
& ( ( in @ ( esk9_1 @ X179 ) @ X179 )
| ~ ( in @ X180 @ X179 ) )
& ( ~ ( in @ X182 @ ( esk9_1 @ X179 ) )
| ~ ( in @ X182 @ X179 )
| ~ ( in @ X180 @ X179 ) )
& epred1_0
& ( ( X183 @ ( esk10_2 @ X183 @ X184 ) )
| ~ ( X183 @ X184 )
| ( X183 @ ( descr @ X183 ) ) )
& ( ( X184
!= ( esk10_2 @ X183 @ X184 ) )
| ~ ( X183 @ X184 )
| ( X183 @ ( descr @ X183 ) ) )
& ( ~ ( 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 @ ( esk12_1 @ X195 ) )
| ( X195 @ ( esk11_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ~ ( X195 @ X199 )
| ( ( esk12_1 @ X195 )
= X199 )
| ( X195 @ ( esk11_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ( X195 @ ( esk12_1 @ X195 ) )
| ( X196
!= ( esk11_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ~ ( X195 @ X199 )
| ( ( esk12_1 @ X195 )
= X199 )
| ( X196
!= ( esk11_2 @ X195 @ X196 ) )
| ~ ( X195 @ X196 ) )
& ( ~ epred2_0
| ( in @ esk13_0 @ ( prop2set @ $true ) ) )
& ( epred2_0
| ( in @ esk13_0 @ ( prop2set @ $false ) ) )
& ~ epred2_0 ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[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_30])])])])])])])]) ).
thf(c_0_33,plain,
! [X145: $o] :
( ( prop2set @ X145 )
= ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X145 ) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
thf(c_0_34,plain,
! [X221: $i,X10: $o] :
( ( epred3_1 @ X10 @ X221 )
<=> X10 ),
introduced(definition) ).
thf(c_0_35,negated_conjecture,
! [X3: $i,X2: $i,X1: $i > $o] :
( ( X1 @ X2 )
| ~ ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_36,plain,
! [X10: $o] :
( ( prop2set @ X10 )
= ( dsetconstr @ ( powerset @ emptyset ) @ ( epred3_1 @ X10 ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_33]),c_0_34]) ).
thf(c_0_37,negated_conjecture,
( epred2_0
| ( in @ esk13_0 @ ( prop2set @ ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,negated_conjecture,
~ epred2_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,plain,
! [X222: $i,X223: $o] :
( ( ~ ( epred3_1 @ X223 @ X222 )
| X223 )
& ( ~ X223
| ( epred3_1 @ X223 @ X222 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_40,negated_conjecture,
! [X2: $i,X10: $o] :
( ( epred3_1 @ X10 @ X2 )
| ~ ( in @ X2 @ ( prop2set @ X10 ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_41,negated_conjecture,
in @ esk13_0 @ ( prop2set @ ~ $true ),
inference(sr,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_42,plain,
! [X2: $i] :
~ ( epred3_1 @ ~ $true @ X2 ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_39])])]) ).
thf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU500^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n004.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun May 19 15:20:23 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.20/0.51 Running higher-order theorem proving
% 0.20/0.51 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_ho_10 with pid 19488 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 # No SInE strategy applied
% 0.20/0.54 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.20/0.54 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.54 # Starting new_ho_10 with 901s (1) cores
% 0.20/0.54 # Starting sh5l with 151s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 151s (1) cores
% 0.20/0.54 # Starting new_bool_2 with 151s (1) cores
% 0.20/0.54 # Starting new_bool_9 with 146s (1) cores
% 0.20/0.54 # new_ho_10 with pid 19492 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 # No SInE strategy applied
% 0.20/0.54 # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.20/0.54 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.54 # Starting new_ho_10 with 901s (1) cores
% 0.20/0.54 # Preprocessing time : 0.005 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 : 45
% 0.20/0.54 # Removed by relevancy pruning/SinE : 0
% 0.20/0.54 # Initial clauses : 83
% 0.20/0.54 # Removed in clause preprocessing : 26
% 0.20/0.54 # Initial clauses in saturation : 57
% 0.20/0.54 # Processed clauses : 72
% 0.20/0.54 # ...of these trivial : 0
% 0.20/0.54 # ...subsumed : 1
% 0.20/0.54 # ...remaining for further processing : 71
% 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 : 0
% 0.20/0.54 # Generated clauses : 3
% 0.20/0.54 # ...of the previous two non-redundant : 2
% 0.20/0.54 # ...aggressively subsumed : 0
% 0.20/0.54 # Contextual simplify-reflections : 0
% 0.20/0.54 # Paramodulations : 2
% 0.20/0.54 # Factorizations : 0
% 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 : 13
% 0.20/0.54 # ...of those cached : 12
% 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 : 14
% 0.20/0.54 # Positive orientable unit clauses : 6
% 0.20/0.54 # Positive unorientable unit clauses: 0
% 0.20/0.54 # Negative unit clauses : 3
% 0.20/0.54 # Non-unit-clauses : 5
% 0.20/0.54 # Current number of unprocessed clauses: 43
% 0.20/0.54 # ...number of literals in the above : 150
% 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) : 1033
% 0.20/0.54 # Rec. Clause-clause subsumption calls : 435
% 0.20/0.54 # Non-unit clause-clause subsumptions : 3
% 0.20/0.54 # Unit Clause-clause subsumption calls : 2
% 0.20/0.54 # Rewrite failures with RHS unbound : 0
% 0.20/0.54 # BW rewrite match attempts : 0
% 0.20/0.54 # BW rewrite match successes : 0
% 0.20/0.54 # Condensation attempts : 72
% 0.20/0.54 # Condensation successes : 3
% 0.20/0.54 # Termbank termtop insertions : 8351
% 0.20/0.54 # Search garbage collected termcells : 2581
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.010 s
% 0.20/0.54 # System time : 0.008 s
% 0.20/0.54 # Total time : 0.019 s
% 0.20/0.54 # Maximum resident set size: 2356 pages
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.031 s
% 0.20/0.54 # System time : 0.046 s
% 0.20/0.54 # Total time : 0.076 s
% 0.20/0.54 # Maximum resident set size: 1776 pages
% 0.20/0.54 % E---3.1 exiting
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------