TSTP Solution File: SEU503^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU503^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 03:27:47 EDT 2024
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 60
% Syntax : Number of formulae : 75 ( 10 unt; 39 typ; 0 def)
% Number of atoms : 287 ( 34 equ; 0 cnn)
% Maximal formula atoms : 78 ( 7 avg)
% Number of connectives : 1039 ( 69 ~; 74 |; 80 &; 665 @)
% ( 35 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 83 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 25 con; 0-3 aty)
% Number of variables : 229 ( 25 ^ 170 !; 34 ?; 229 :)
% 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,
epred1_0: $o ).
thf(decl_52,type,
esk1_2: $i > $i > $i ).
thf(decl_53,type,
esk2_2: $i > $i > $i ).
thf(decl_54,type,
esk3_1: $i > $i ).
thf(decl_55,type,
esk4_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_56,type,
esk5_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_57,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_58,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_59,type,
esk8_1: $i > $i ).
thf(decl_60,type,
esk9_2: ( $i > $o ) > $i > $i ).
thf(decl_61,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_62,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/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(notinemptyset,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(c_0_20,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_21,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
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,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_24,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X74: $i] :
( ( X6 @ X2 @ X74 )
& ! [X75: $i] :
( ( X6 @ X2 @ X75 )
=> ( X74 = X75 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
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] :
( ? [X76: $i] :
( ( X1 @ X76 )
& ! [X77: $i] :
( ( X1 @ X77 )
=> ( X76 = X77 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_21]) ).
thf(c_0_29,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_23]) ).
thf(c_0_30,plain,
( epred1_0
<=> ! [X104: $i] :
? [X105: $i] :
( ! [X106: $i] :
( ( in @ X106 @ X105 )
=> ! [X107: $i] :
( ( in @ X107 @ X106 )
=> ( in @ X107 @ X104 ) ) )
& ! [X108: $i,X109: $i] :
( ( ( in @ X108 @ X104 )
& ( in @ X109 @ X104 ) )
=> ( ! [X110: $i] :
( ( in @ X110 @ X105 )
=> ( ( in @ X108 @ X110 )
<=> ( in @ X109 @ X110 ) ) )
=> ( X108 = X109 ) ) )
& ! [X111: $i,X112: $i] :
( ( ( in @ X111 @ X105 )
& ( in @ X112 @ X105 ) )
=> ( ! [X113: $i] :
( ( in @ X113 @ X111 )
=> ( in @ X113 @ X112 ) )
| ! [X114: $i] :
( ( in @ X114 @ X112 )
=> ( in @ X114 @ X111 ) ) ) )
& ! [X115: $i] :
( ( ! [X116: $i] :
( ( in @ X116 @ X115 )
=> ( in @ X116 @ X104 ) )
& ? [X117: $i] : ( in @ X117 @ X115 ) )
=> ? [X118: $i,X119: $i] :
( ( in @ X118 @ X105 )
& ( in @ X119 @ X115 )
& ~ ? [X120: $i] :
( ( in @ X120 @ X118 )
& ( in @ X120 @ X115 ) )
& ! [X121: $i] :
( ( in @ X121 @ X105 )
=> ( ! [X122: $i] :
( ( in @ X122 @ X121 )
=> ( in @ X122 @ X118 ) )
| ( in @ X119 @ X121 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_31,negated_conjecture,
~ ( ! [X78: $i,X79: $i] :
( ! [X80: $i] :
( ( in @ X80 @ X78 )
<=> ( in @ X80 @ X79 ) )
=> ( X78 = X79 ) )
=> ( ! [X81: $i] :
~ ( in @ X81 @ emptyset )
=> ( ! [X82: $i,X83: $i,X84: $i] :
( ( in @ X84 @ ( setadjoin @ X82 @ X83 ) )
<=> ( ( X84 = X82 )
| ( in @ X84 @ X83 ) ) )
=> ( ! [X85: $i,X86: $i] :
( ( in @ X86 @ ( powerset @ X85 ) )
<=> ! [X87: $i] :
( ( in @ X87 @ X86 )
=> ( in @ X87 @ X85 ) ) )
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( ! [X88: $i] :
( ( in @ X88 @ omega )
=> ( in @ ( setadjoin @ X88 @ X88 ) @ omega ) )
=> ( ! [X89: $i] :
( ( ( in @ emptyset @ X89 )
& ! [X90: $i] :
( ( ( in @ X90 @ omega )
& ( in @ X90 @ X89 ) )
=> ( in @ ( setadjoin @ X90 @ X90 ) @ X89 ) ) )
=> ! [X91: $i] :
( ( in @ X91 @ omega )
=> ( in @ X91 @ X89 ) ) )
=> ( ! [X92: $i > $i > $o,X93: $i] :
( ! [X94: $i] :
( ( in @ X94 @ X93 )
=> ? [X95: $i] :
( ( X92 @ X94 @ X95 )
& ! [X96: $i] :
( ( X92 @ X94 @ X96 )
=> ( X95 = X96 ) ) ) )
=> ? [X97: $i] :
! [X98: $i] :
( ( in @ X98 @ X97 )
<=> ? [X99: $i] :
( ( in @ X99 @ X93 )
& ( X92 @ X99 @ X98 ) ) ) )
=> ( ! [X100: $i] :
( ? [X101: $i] : ( in @ X101 @ X100 )
=> ? [X102: $i] :
( ( in @ X102 @ X100 )
& ~ ? [X103: $i] :
( ( in @ X103 @ X102 )
& ( in @ X103 @ X100 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X123: $i,X124: $i > $o,X125: $i] :
( ( in @ X125 @ X123 )
=> ( ( X124 @ X125 )
=> ( in @ X125
@ ( dsetconstr @ X123
@ ^ [Z0: $i] : ( X124 @ Z0 ) ) ) ) )
=> ( ! [X126: $i,X127: $i > $o,X128: $i] :
( ( in @ X128
@ ( dsetconstr @ X126
@ ^ [Z0: $i] : ( X127 @ Z0 ) ) )
=> ( in @ X128 @ X126 ) )
=> ( ! [X129: $i,X130: $i > $o,X131: $i] :
( ( in @ X131
@ ( dsetconstr @ X129
@ ^ [Z0: $i] : ( X130 @ Z0 ) ) )
=> ( X130 @ X131 ) )
=> ( ! [X132: $i > $o] :
( ? [X133: $i] :
( ( X132 @ X133 )
& ! [X134: $i] :
( ( X132 @ X134 )
=> ( X133 = X134 ) ) )
=> ? [X135: $i] :
( ( X132 @ X135 )
& ! [X136: $i] :
( ( X132 @ X136 )
=> ( X135 = X136 ) ) ) )
=> ( ! [X137: $o,X138: $i] :
( ( in @ X138
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X137 ) )
=> X137 )
=> ( ! [X139: $i] :
( ( in @ X139 @ emptyset )
=> ! [X140: $o] : X140 )
=> ( ! [X141: $i] :
~ ( in @ X141 @ emptyset )
=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[notinemptyset]),emptysetimpfalse]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_24]),foundationAx]),wellorderingAx]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),emptysetE]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx])]),c_0_30]) ).
thf(c_0_32,negated_conjecture,
! [X142: $i,X143: $i,X145: $i,X146: $i,X147: $i,X148: $i,X149: $i,X150: $i,X151: $i,X152: $i,X153: $i,X155: $i,X156: $i,X158: $i,X159: $i > $i > $o,X160: $i,X162: $i,X165: $i,X167: $i,X168: $i,X169: $i,X170: $i,X172: $i,X173: $i,X174: $i > $o,X175: $i,X176: $i,X177: $i > $o,X178: $i,X179: $i,X180: $i > $o,X181: $i,X182: $i > $o,X183: $i,X186: $i,X187: $o,X188: $i,X189: $i,X190: $o,X191: $i] :
( ( ~ ( in @ ( esk1_2 @ X142 @ X143 ) @ X142 )
| ~ ( in @ ( esk1_2 @ X142 @ X143 ) @ X143 )
| ( X142 = X143 ) )
& ( ( in @ ( esk1_2 @ X142 @ X143 ) @ X142 )
| ( in @ ( esk1_2 @ X142 @ X143 ) @ X143 )
| ( X142 = X143 ) )
& ~ ( in @ X145 @ emptyset )
& ( ~ ( in @ X148 @ ( setadjoin @ X146 @ X147 ) )
| ( X148 = X146 )
| ( in @ X148 @ X147 ) )
& ( ( X148 != X146 )
| ( in @ X148 @ ( setadjoin @ X146 @ X147 ) ) )
& ( ~ ( in @ X148 @ X147 )
| ( in @ X148 @ ( setadjoin @ X146 @ X147 ) ) )
& ( ~ ( in @ X150 @ ( powerset @ X149 ) )
| ~ ( in @ X151 @ X150 )
| ( in @ X151 @ X149 ) )
& ( ( in @ ( esk2_2 @ X152 @ X153 ) @ X153 )
| ( in @ X153 @ ( powerset @ X152 ) ) )
& ( ~ ( in @ ( esk2_2 @ X152 @ X153 ) @ X152 )
| ( in @ X153 @ ( powerset @ X152 ) ) )
& setunionAx
& ( in @ emptyset @ omega )
& ( ~ ( in @ X155 @ omega )
| ( in @ ( setadjoin @ X155 @ X155 ) @ omega ) )
& ( ( in @ ( esk3_1 @ X156 ) @ omega )
| ~ ( in @ emptyset @ X156 )
| ~ ( in @ X158 @ omega )
| ( in @ X158 @ X156 ) )
& ( ( in @ ( esk3_1 @ X156 ) @ X156 )
| ~ ( in @ emptyset @ X156 )
| ~ ( in @ X158 @ omega )
| ( in @ X158 @ X156 ) )
& ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X156 ) @ ( esk3_1 @ X156 ) ) @ X156 )
| ~ ( in @ emptyset @ X156 )
| ~ ( in @ X158 @ omega )
| ( in @ X158 @ X156 ) )
& ( ( in @ ( esk7_3 @ X159 @ X160 @ X165 ) @ X160 )
| ~ ( in @ X165 @ ( esk6_2 @ X159 @ X160 ) )
| ( in @ ( esk4_2 @ X159 @ X160 ) @ X160 ) )
& ( ( X159 @ ( esk7_3 @ X159 @ X160 @ X165 ) @ X165 )
| ~ ( in @ X165 @ ( esk6_2 @ X159 @ X160 ) )
| ( in @ ( esk4_2 @ X159 @ X160 ) @ X160 ) )
& ( ~ ( in @ X168 @ X160 )
| ~ ( X159 @ X168 @ X167 )
| ( in @ X167 @ ( esk6_2 @ X159 @ X160 ) )
| ( in @ ( esk4_2 @ X159 @ X160 ) @ X160 ) )
& ( ( in @ ( esk7_3 @ X159 @ X160 @ X165 ) @ X160 )
| ~ ( in @ X165 @ ( esk6_2 @ X159 @ X160 ) )
| ( X159 @ ( esk4_2 @ X159 @ X160 ) @ ( esk5_3 @ X159 @ X160 @ X162 ) )
| ~ ( X159 @ ( esk4_2 @ X159 @ X160 ) @ X162 ) )
& ( ( X159 @ ( esk7_3 @ X159 @ X160 @ X165 ) @ X165 )
| ~ ( in @ X165 @ ( esk6_2 @ X159 @ X160 ) )
| ( X159 @ ( esk4_2 @ X159 @ X160 ) @ ( esk5_3 @ X159 @ X160 @ X162 ) )
| ~ ( X159 @ ( esk4_2 @ X159 @ X160 ) @ X162 ) )
& ( ~ ( in @ X168 @ X160 )
| ~ ( X159 @ X168 @ X167 )
| ( in @ X167 @ ( esk6_2 @ X159 @ X160 ) )
| ( X159 @ ( esk4_2 @ X159 @ X160 ) @ ( esk5_3 @ X159 @ X160 @ X162 ) )
| ~ ( X159 @ ( esk4_2 @ X159 @ X160 ) @ X162 ) )
& ( ( in @ ( esk7_3 @ X159 @ X160 @ X165 ) @ X160 )
| ~ ( in @ X165 @ ( esk6_2 @ X159 @ X160 ) )
| ( X162
!= ( esk5_3 @ X159 @ X160 @ X162 ) )
| ~ ( X159 @ ( esk4_2 @ X159 @ X160 ) @ X162 ) )
& ( ( X159 @ ( esk7_3 @ X159 @ X160 @ X165 ) @ X165 )
| ~ ( in @ X165 @ ( esk6_2 @ X159 @ X160 ) )
| ( X162
!= ( esk5_3 @ X159 @ X160 @ X162 ) )
| ~ ( X159 @ ( esk4_2 @ X159 @ X160 ) @ X162 ) )
& ( ~ ( in @ X168 @ X160 )
| ~ ( X159 @ X168 @ X167 )
| ( in @ X167 @ ( esk6_2 @ X159 @ X160 ) )
| ( X162
!= ( esk5_3 @ X159 @ X160 @ X162 ) )
| ~ ( X159 @ ( esk4_2 @ X159 @ X160 ) @ X162 ) )
& ( ( in @ ( esk8_1 @ X169 ) @ X169 )
| ~ ( in @ X170 @ X169 ) )
& ( ~ ( in @ X172 @ ( esk8_1 @ X169 ) )
| ~ ( in @ X172 @ X169 )
| ~ ( in @ X170 @ X169 ) )
& epred1_0
& descrp
& ( ~ ( in @ X175 @ X173 )
| ~ ( X174 @ X175 )
| ( in @ X175
@ ( dsetconstr @ X173
@ ^ [Z0: $i] : ( X174 @ Z0 ) ) ) )
& ( ~ ( in @ X178
@ ( dsetconstr @ X176
@ ^ [Z0: $i] : ( X177 @ Z0 ) ) )
| ( in @ X178 @ X176 ) )
& ( ~ ( in @ X181
@ ( dsetconstr @ X179
@ ^ [Z0: $i] : ( X180 @ Z0 ) ) )
| ( X180 @ X181 ) )
& ( ( X182 @ ( esk10_1 @ X182 ) )
| ( X182 @ ( esk9_2 @ X182 @ X183 ) )
| ~ ( X182 @ X183 ) )
& ( ~ ( X182 @ X186 )
| ( ( esk10_1 @ X182 )
= X186 )
| ( X182 @ ( esk9_2 @ X182 @ X183 ) )
| ~ ( X182 @ X183 ) )
& ( ( X182 @ ( esk10_1 @ X182 ) )
| ( X183
!= ( esk9_2 @ X182 @ X183 ) )
| ~ ( X182 @ X183 ) )
& ( ~ ( X182 @ X186 )
| ( ( esk10_1 @ X182 )
= X186 )
| ( X183
!= ( esk9_2 @ X182 @ X183 ) )
| ~ ( X182 @ X183 ) )
& ( ~ ( in @ X188
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X187 ) )
| X187 )
& ( ~ ( in @ X189 @ emptyset )
| X190 )
& ~ ( in @ X191 @ emptyset )
& ( in @ esk11_0 @ emptyset ) ),
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_31])])])])])]) ).
thf(c_0_33,negated_conjecture,
in @ esk11_0 @ emptyset,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_34,negated_conjecture,
! [X2: $i] :
~ ( in @ X2 @ emptyset ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_33,c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU503^1 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:31:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.49 Running higher-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.52 # Version: 3.1.0-ho
% 0.20/0.52 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.52 # Starting sh5l with 300s (1) cores
% 0.20/0.52 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.52 # new_bool_2 with pid 25444 completed with status 0
% 0.20/0.52 # Result found by new_bool_2
% 0.20/0.52 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.52 # Starting sh5l with 300s (1) cores
% 0.20/0.52 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.52 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 # Search class: HGHSF-FFMS31-SHFSMSBN
% 0.20/0.52 # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.52 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 # Starting new_ho_10 with 181s (1) cores
% 0.20/0.52 # new_ho_10 with pid 25445 completed with status 0
% 0.20/0.52 # Result found by new_ho_10
% 0.20/0.52 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.52 # Starting sh5l with 300s (1) cores
% 0.20/0.52 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.52 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 # Search class: HGHSF-FFMS31-SHFSMSBN
% 0.20/0.52 # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.52 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 # Starting new_ho_10 with 181s (1) cores
% 0.20/0.52 # Preprocessing time : 0.004 s
% 0.20/0.52 # Presaturation interreduction done
% 0.20/0.52
% 0.20/0.52 # Proof found!
% 0.20/0.52 # SZS status Theorem
% 0.20/0.52 # SZS output start CNFRefutation
% See solution above
% 0.20/0.52 # Parsed axioms : 51
% 0.20/0.52 # Removed by relevancy pruning/SinE : 31
% 0.20/0.52 # Initial clauses : 52
% 0.20/0.52 # Removed in clause preprocessing : 0
% 0.20/0.52 # Initial clauses in saturation : 52
% 0.20/0.52 # Processed clauses : 6
% 0.20/0.52 # ...of these trivial : 0
% 0.20/0.52 # ...subsumed : 0
% 0.20/0.52 # ...remaining for further processing : 6
% 0.20/0.52 # Other redundant clauses eliminated : 0
% 0.20/0.52 # Clauses deleted for lack of memory : 0
% 0.20/0.52 # Backward-subsumed : 0
% 0.20/0.52 # Backward-rewritten : 0
% 0.20/0.52 # Generated clauses : 1
% 0.20/0.52 # ...of the previous two non-redundant : 0
% 0.20/0.52 # ...aggressively subsumed : 0
% 0.20/0.52 # Contextual simplify-reflections : 0
% 0.20/0.52 # Paramodulations : 0
% 0.20/0.52 # Factorizations : 0
% 0.20/0.52 # NegExts : 0
% 0.20/0.52 # Equation resolutions : 0
% 0.20/0.52 # Disequality decompositions : 0
% 0.20/0.52 # Total rewrite steps : 0
% 0.20/0.52 # ...of those cached : 0
% 0.20/0.52 # Propositional unsat checks : 0
% 0.20/0.52 # Propositional check models : 0
% 0.20/0.52 # Propositional check unsatisfiable : 0
% 0.20/0.52 # Propositional clauses : 0
% 0.20/0.52 # Propositional clauses after purity: 0
% 0.20/0.52 # Propositional unsat core size : 0
% 0.20/0.52 # Propositional preprocessing time : 0.000
% 0.20/0.52 # Propositional encoding time : 0.000
% 0.20/0.52 # Propositional solver time : 0.000
% 0.20/0.52 # Success case prop preproc time : 0.000
% 0.20/0.52 # Success case prop encoding time : 0.000
% 0.20/0.52 # Success case prop solver time : 0.000
% 0.20/0.52 # Current number of processed clauses : 5
% 0.20/0.52 # Positive orientable unit clauses : 4
% 0.20/0.52 # Positive unorientable unit clauses: 0
% 0.20/0.52 # Negative unit clauses : 1
% 0.20/0.52 # Non-unit-clauses : 0
% 0.20/0.52 # Current number of unprocessed clauses: 46
% 0.20/0.52 # ...number of literals in the above : 167
% 0.20/0.52 # Current number of archived formulas : 0
% 0.20/0.52 # Current number of archived clauses : 1
% 0.20/0.52 # Clause-clause subsumption calls (NU) : 0
% 0.20/0.52 # Rec. Clause-clause subsumption calls : 0
% 0.20/0.52 # Non-unit clause-clause subsumptions : 0
% 0.20/0.52 # Unit Clause-clause subsumption calls : 0
% 0.20/0.52 # Rewrite failures with RHS unbound : 0
% 0.20/0.52 # BW rewrite match attempts : 0
% 0.20/0.52 # BW rewrite match successes : 0
% 0.20/0.52 # Condensation attempts : 6
% 0.20/0.52 # Condensation successes : 0
% 0.20/0.52 # Termbank termtop insertions : 5356
% 0.20/0.52 # Search garbage collected termcells : 1940
% 0.20/0.52
% 0.20/0.52 # -------------------------------------------------
% 0.20/0.52 # User time : 0.009 s
% 0.20/0.52 # System time : 0.004 s
% 0.20/0.52 # Total time : 0.012 s
% 0.20/0.52 # Maximum resident set size: 2324 pages
% 0.20/0.52
% 0.20/0.52 # -------------------------------------------------
% 0.20/0.52 # User time : 0.012 s
% 0.20/0.52 # System time : 0.004 s
% 0.20/0.52 # Total time : 0.017 s
% 0.20/0.52 # Maximum resident set size: 1780 pages
% 0.20/0.52 % E---3.1 exiting
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------