%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV292^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:35:20 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 93 equ; 0 cnn)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 798 ( 186 ~; 57 |; 178 &; 364 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 165 ( 165 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 268 ( 105 ^; 31 !; 132 ?; 268 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cP: ( ( $i > $o ) > $o ) > $o ).
thf(decl_24,type,
cONE: ( $i > $o ) > $o ).
thf(decl_25,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
cZERO: ( $i > $o ) > $o ).
thf(decl_27,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(decl_28,type,
epred1_1: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(decl_29,type,
epred2_1: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(c_less__eq__def,axiom,
( c_less__eq_
= ( ^ [X5: ( $i > $o ) > $o,X6: ( $i > $o ) > $o] :
! [X7: ( ( $i > $o ) > $o ) > $o] :
( ( ( X7 @ X5 )
& ! [X8: ( $i > $o ) > $o] :
( ( X7 @ X8 )
=> ( X7 @ ( cSUCC @ X8 ) ) ) )
=> ( X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.inuJvFOYDB/E---3.1_2644409.p',c_less__eq__def) ).
thf(cSUCC_def,axiom,
( cSUCC
= ( ^ [X3: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X3
@ ^ [X4: $i] :
( ( X4 != X2 )
& ( X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.inuJvFOYDB/E---3.1_2644409.p',cSUCC_def) ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X1: $i > $o] :
~ ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.inuJvFOYDB/E---3.1_2644409.p',cZERO_def) ).
thf(cBLEDSOE7A,conjecture,
( ( cP @ cONE )
=> ? [X9: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ X9 )
& ( c_less__eq_ @ X9 @ ( cSUCC @ cONE ) )
& ( cP @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.inuJvFOYDB/E---3.1_2644409.p',cBLEDSOE7A) ).
thf(cONE_def,axiom,
( cONE
= ( ^ [Z0: $i > $o] :
? [X12: $i] :
( ( Z0 @ X12 )
& ~ ? [X11: $i] :
( ( X11 != X12 )
& ( Z0 @ X11 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.inuJvFOYDB/E---3.1_2644409.p',cONE_def) ).
thf(c_0_5,plain,
( c_less__eq_
= ( ^ [Z0: ( $i > $o ) > $o,Z1: ( $i > $o ) > $o] :
! [X7: ( ( $i > $o ) > $o ) > $o] :
( ( ( X7 @ Z0 )
& ! [X8: ( $i > $o ) > $o] :
( ( X7 @ X8 )
=> ( X7
@ ^ [Z2: $i > $o] :
? [X13: $i] :
( ( Z2 @ X13 )
& ( X8
@ ^ [Z3: $i] :
( ( Z3 != X13 )
& ( Z2 @ Z3 ) ) ) ) ) ) )
=> ( X7 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_less__eq__def]) ).
thf(c_0_6,plain,
( cSUCC
= ( ^ [Z0: ( $i > $o ) > $o,Z1: $i > $o] :
? [X2: $i] :
( ( Z1 @ X2 )
& ( Z0
@ ^ [Z2: $i] :
( ( Z2 != X2 )
& ( Z1 @ Z2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cSUCC_def]) ).
thf(c_0_7,plain,
( cZERO
= ( ^ [Z0: $i > $o] :
~ ? [X2: $i] : ( Z0 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[cZERO_def]) ).
thf(c_0_8,negated_conjecture,
~ ( ( cP @ cONE )
=> ? [X9: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ X9 )
& ( c_less__eq_ @ X9 @ ( cSUCC @ cONE ) )
& ( cP @ X9 ) ) ),
inference(assume_negation,[status(cth)],[cBLEDSOE7A]) ).
thf(c_0_9,plain,
( c_less__eq_
= ( ^ [Z0: ( $i > $o ) > $o,Z1: ( $i > $o ) > $o] :
! [X7: ( ( $i > $o ) > $o ) > $o] :
( ( ( X7 @ Z0 )
& ! [X8: ( $i > $o ) > $o] :
( ( X7 @ X8 )
=> ( X7
@ ^ [Z2: $i > $o] :
? [X13: $i] :
( ( Z2 @ X13 )
& ( X8
@ ^ [Z3: $i] :
( ( Z3 != X13 )
& ( Z2 @ Z3 ) ) ) ) ) ) )
=> ( X7 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,axiom,
( cONE
= ( ^ [Z0: $i > $o] :
? [X12: $i] :
( ( Z0 @ X12 )
& ~ ? [X11: $i] :
( ( X11 != X12 )
& ( Z0 @ X11 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[cONE_def,c_0_7]),c_0_6]) ).
thf(c_0_11,negated_conjecture,
~ ( ( cP
@ ^ [Z0: $i > $o] :
? [X14: $i] :
( ( Z0 @ X14 )
& ~ ? [X15: $i] :
( ( X15 != X14 )
& ( Z0 @ X15 ) ) ) )
=> ? [X9: ( $i > $o ) > $o] :
( ! [X17: ( ( $i > $o ) > $o ) > $o] :
( ( ( X17
@ ^ [Z0: $i > $o] :
~ ? [X16: $i] : ( Z0 @ X16 ) )
& ! [X18: ( $i > $o ) > $o] :
( ( X17 @ X18 )
=> ( X17
@ ^ [Z0: $i > $o] :
? [X19: $i] :
( ( Z0 @ X19 )
& ( X18
@ ^ [Z1: $i] :
( ( Z1 != X19 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ( X17 @ X9 ) )
& ! [X23: ( ( $i > $o ) > $o ) > $o] :
( ( ( X23 @ X9 )
& ! [X24: ( $i > $o ) > $o] :
( ( X23 @ X24 )
=> ( X23
@ ^ [Z0: $i > $o] :
? [X25: $i] :
( ( Z0 @ X25 )
& ( X24
@ ^ [Z1: $i] :
( ( Z1 != X25 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ( X23
@ ^ [Z0: $i > $o] :
? [X22: $i] :
( ( Z0 @ X22 )
& ? [X20: $i] :
( ( X20 != X22 )
& ( Z0 @ X20 )
& ~ ? [X21: $i] :
( ( X21 != X20 )
& ( X21 != X22 )
& ( Z0 @ X21 ) ) ) ) ) )
& ( cP @ X9 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_7]),c_0_10]),c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X26: ( $i > $o ) > $o,X28: ( $i > $o ) > $o,X30: ( $i > $o ) > $o] :
( ( cP
@ ^ [Z0: $i > $o] :
? [X14: $i] :
( ( Z0 @ X14 )
& ~ ? [X15: $i] :
( ( X15 != X14 )
& ( Z0 @ X15 ) ) ) )
& ( ( epred2_1 @ X26 @ X26 )
| ( epred1_1 @ X26
@ ^ [Z0: $i > $o] :
~ ? [X16: $i] : ( Z0 @ X16 ) )
| ~ ( cP @ X26 ) )
& ( ~ ( epred2_1 @ X26 @ X30 )
| ( epred2_1 @ X26
@ ^ [Z0: $i > $o] :
? [X25: $i] :
( ( Z0 @ X25 )
& ( X30
@ ^ [Z1: $i] :
( ( Z1 != X25 )
& ( Z0 @ Z1 ) ) ) ) )
| ( epred1_1 @ X26
@ ^ [Z0: $i > $o] :
~ ? [X16: $i] : ( Z0 @ X16 ) )
| ~ ( cP @ X26 ) )
& ( ~ ( epred2_1 @ X26
@ ^ [Z0: $i > $o] :
? [X22: $i] :
( ( Z0 @ X22 )
& ? [X20: $i] :
( ( X20 != X22 )
& ( Z0 @ X20 )
& ~ ? [X21: $i] :
( ( X21 != X20 )
& ( X21 != X22 )
& ( Z0 @ X21 ) ) ) ) )
| ( epred1_1 @ X26
@ ^ [Z0: $i > $o] :
~ ? [X16: $i] : ( Z0 @ X16 ) )
| ~ ( cP @ X26 ) )
& ( ( epred2_1 @ X26 @ X26 )
| ~ ( epred1_1 @ X26 @ X28 )
| ( epred1_1 @ X26
@ ^ [Z0: $i > $o] :
? [X19: $i] :
( ( Z0 @ X19 )
& ( X28
@ ^ [Z1: $i] :
( ( Z1 != X19 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( cP @ X26 ) )
& ( ~ ( epred2_1 @ X26 @ X30 )
| ( epred2_1 @ X26
@ ^ [Z0: $i > $o] :
? [X25: $i] :
( ( Z0 @ X25 )
& ( X30
@ ^ [Z1: $i] :
( ( Z1 != X25 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred1_1 @ X26 @ X28 )
| ( epred1_1 @ X26
@ ^ [Z0: $i > $o] :
? [X19: $i] :
( ( Z0 @ X19 )
& ( X28
@ ^ [Z1: $i] :
( ( Z1 != X19 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( cP @ X26 ) )
& ( ~ ( epred2_1 @ X26
@ ^ [Z0: $i > $o] :
? [X22: $i] :
( ( Z0 @ X22 )
& ? [X20: $i] :
( ( X20 != X22 )
& ( Z0 @ X20 )
& ~ ? [X21: $i] :
( ( X21 != X20 )
& ( X21 != X22 )
& ( Z0 @ X21 ) ) ) ) )
| ~ ( epred1_1 @ X26 @ X28 )
| ( epred1_1 @ X26
@ ^ [Z0: $i > $o] :
? [X19: $i] :
( ( Z0 @ X19 )
& ( X28
@ ^ [Z1: $i] :
( ( Z1 != X19 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( cP @ X26 ) )
& ( ( epred2_1 @ X26 @ X26 )
| ~ ( epred1_1 @ X26 @ X26 )
| ~ ( cP @ X26 ) )
& ( ~ ( epred2_1 @ X26 @ X30 )
| ( epred2_1 @ X26
@ ^ [Z0: $i > $o] :
? [X25: $i] :
( ( Z0 @ X25 )
& ( X30
@ ^ [Z1: $i] :
( ( Z1 != X25 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred1_1 @ X26 @ X26 )
| ~ ( cP @ X26 ) )
& ( ~ ( epred2_1 @ X26
@ ^ [Z0: $i > $o] :
? [X22: $i] :
( ( Z0 @ X22 )
& ? [X20: $i] :
( ( X20 != X22 )
& ( Z0 @ X20 )
& ~ ? [X21: $i] :
( ( X21 != X20 )
& ( X21 != X22 )
& ( Z0 @ X21 ) ) ) ) )
| ~ ( epred1_1 @ X26 @ X26 )
| ~ ( cP @ X26 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred2_1 @ X3 @ X3 )
| ( epred1_1 @ X3
@ ^ [Z0: $i > $o] :
~ ? [X117: $i] : ( Z0 @ X117 ) )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
( cP
@ ^ [Z0: $i > $o] :
? [X118: $i] :
( ( Z0 @ X118 )
& ~ ? [X119: $i] :
( ( X119 != X118 )
& ( Z0 @ X119 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X5: ( $i > $o ) > $o,X3: ( $i > $o ) > $o] :
( ( epred2_1 @ X3
@ ^ [Z0: $i > $o] :
? [X120: $i] :
( ( Z0 @ X120 )
& ( X5
@ ^ [Z1: $i] :
( ( Z1 != X120 )
& ( Z0 @ Z1 ) ) ) ) )
| ( epred1_1 @ X3
@ ^ [Z0: $i > $o] :
~ ? [X121: $i] : ( Z0 @ X121 ) )
| ~ ( epred2_1 @ X3 @ X5 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
( ( epred2_1
@ ^ [Z0: $i > $o] :
? [X122: $i] :
( ( Z0 @ X122 )
& ~ ? [X123: $i] :
( ( X123 != X122 )
& ( Z0 @ X123 ) ) )
@ ^ [Z0: $i > $o] :
? [X124: $i] :
( ( Z0 @ X124 )
& ~ ? [X125: $i] :
( ( X125 != X124 )
& ( Z0 @ X125 ) ) ) )
| ( epred1_1
@ ^ [Z0: $i > $o] :
? [X126: $i] :
( ( Z0 @ X126 )
& ~ ? [X127: $i] :
( ( X127 != X126 )
& ( Z0 @ X127 ) ) )
@ ^ [Z0: $i > $o] :
~ ? [X128: $i] : ( Z0 @ X128 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred1_1 @ X3
@ ^ [Z0: $i > $o] :
~ ? [X129: $i] : ( Z0 @ X129 ) )
| ~ ( epred2_1 @ X3
@ ^ [Z0: $i > $o] :
? [X130: $i] :
( ( Z0 @ X130 )
& ? [X131: $i] :
( ( X131 != X130 )
& ( Z0 @ X131 )
& ~ ? [X132: $i] :
( ( X132 != X131 )
& ( X132 != X130 )
& ( Z0 @ X132 ) ) ) ) )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,negated_conjecture,
( ( epred2_1
@ ^ [Z0: $i > $o] :
? [X133: $i] :
( ( Z0 @ X133 )
& ~ ? [X134: $i] :
( ( X134 != X133 )
& ( Z0 @ X134 ) ) )
@ ^ [Z0: $i > $o] :
? [X135: $i] :
( ( Z0 @ X135 )
& ? [X136: $i] :
( ( X136 != X135 )
& ( Z0 @ X136 )
& ~ ? [X137: $i] :
( ( X137 != X136 )
& ( X137 != X135 )
& ( Z0 @ X137 ) ) ) ) )
| ( epred1_1
@ ^ [Z0: $i > $o] :
? [X138: $i] :
( ( Z0 @ X138 )
& ~ ? [X139: $i] :
( ( X139 != X138 )
& ( Z0 @ X139 ) ) )
@ ^ [Z0: $i > $o] :
~ ? [X140: $i] : ( Z0 @ X140 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14])]) ).
thf(c_0_19,negated_conjecture,
! [X5: ( $i > $o ) > $o,X3: ( $i > $o ) > $o] :
( ( epred2_1 @ X3 @ X3 )
| ( epred1_1 @ X3
@ ^ [Z0: $i > $o] :
? [X141: $i] :
( ( Z0 @ X141 )
& ( X5
@ ^ [Z1: $i] :
( ( Z1 != X141 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred1_1 @ X3 @ X5 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_20,negated_conjecture,
( epred1_1
@ ^ [Z0: $i > $o] :
? [X142: $i] :
( ( Z0 @ X142 )
& ~ ? [X143: $i] :
( ( X143 != X142 )
& ( Z0 @ X143 ) ) )
@ ^ [Z0: $i > $o] :
~ ? [X144: $i] : ( Z0 @ X144 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14])]) ).
thf(c_0_21,negated_conjecture,
! [X6: ( $i > $o ) > $o,X5: ( $i > $o ) > $o,X3: ( $i > $o ) > $o] :
( ( epred2_1 @ X3
@ ^ [Z0: $i > $o] :
? [X145: $i] :
( ( Z0 @ X145 )
& ( X5
@ ^ [Z1: $i] :
( ( Z1 != X145 )
& ( Z0 @ Z1 ) ) ) ) )
| ( epred1_1 @ X3
@ ^ [Z0: $i > $o] :
? [X146: $i] :
( ( Z0 @ X146 )
& ( X6
@ ^ [Z1: $i] :
( ( Z1 != X146 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred2_1 @ X3 @ X5 )
| ~ ( epred1_1 @ X3 @ X6 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred2_1 @ X3 @ X3 )
| ~ ( epred1_1 @ X3 @ X3 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_23,negated_conjecture,
( ( epred2_1
@ ^ [Z0: $i > $o] :
? [X147: $i] :
( ( Z0 @ X147 )
& ~ ? [X148: $i] :
( ( X148 != X147 )
& ( Z0 @ X148 ) ) )
@ ^ [Z0: $i > $o] :
? [X149: $i] :
( ( Z0 @ X149 )
& ~ ? [X150: $i] :
( ( X150 != X149 )
& ( Z0 @ X150 ) ) ) )
| ( epred1_1
@ ^ [Z0: $i > $o] :
? [X151: $i] :
( ( Z0 @ X151 )
& ~ ? [X152: $i] :
( ( X152 != X151 )
& ( Z0 @ X152 ) ) )
@ ^ [Z0: $i > $o] :
? [X153: $i] :
( ( Z0 @ X153 )
& ~ ? [X154: $i] :
( ( X154 != X153 )
& ( Z0 @ X154 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14])]) ).
thf(c_0_24,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred1_1
@ ^ [Z0: $i > $o] :
? [X155: $i] :
( ( Z0 @ X155 )
& ~ ? [X156: $i] :
( ( X156 != X155 )
& ( Z0 @ X156 ) ) )
@ ^ [Z0: $i > $o] :
? [X157: $i] :
( ( Z0 @ X157 )
& ~ ? [X158: $i] :
( ( X158 != X157 )
& ( Z0 @ X158 ) ) ) )
| ( epred2_1
@ ^ [Z0: $i > $o] :
? [X159: $i] :
( ( Z0 @ X159 )
& ~ ? [X160: $i] :
( ( X160 != X159 )
& ( Z0 @ X160 ) ) )
@ ^ [Z0: $i > $o] :
? [X161: $i] :
( ( Z0 @ X161 )
& ( X3
@ ^ [Z1: $i] :
( ( Z1 != X161 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred2_1
@ ^ [Z0: $i > $o] :
? [X162: $i] :
( ( Z0 @ X162 )
& ~ ? [X163: $i] :
( ( X163 != X162 )
& ( Z0 @ X163 ) ) )
@ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_14])]) ).
thf(c_0_25,negated_conjecture,
( epred2_1
@ ^ [Z0: $i > $o] :
? [X164: $i] :
( ( Z0 @ X164 )
& ~ ? [X165: $i] :
( ( X165 != X164 )
& ( Z0 @ X165 ) ) )
@ ^ [Z0: $i > $o] :
? [X166: $i] :
( ( Z0 @ X166 )
& ~ ? [X167: $i] :
( ( X167 != X166 )
& ( Z0 @ X167 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14])]) ).
thf(c_0_26,negated_conjecture,
! [X5: ( $i > $o ) > $o,X3: ( $i > $o ) > $o] :
( ( epred1_1 @ X3
@ ^ [Z0: $i > $o] :
? [X168: $i] :
( ( Z0 @ X168 )
& ( X5
@ ^ [Z1: $i] :
( ( Z1 != X168 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred2_1 @ X3
@ ^ [Z0: $i > $o] :
? [X169: $i] :
( ( Z0 @ X169 )
& ? [X170: $i] :
( ( X170 != X169 )
& ( Z0 @ X170 )
& ~ ? [X171: $i] :
( ( X171 != X170 )
& ( X171 != X169 )
& ( Z0 @ X171 ) ) ) ) )
| ~ ( epred1_1 @ X3 @ X5 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_27,negated_conjecture,
( ( epred2_1
@ ^ [Z0: $i > $o] :
? [X172: $i] :
( ( Z0 @ X172 )
& ~ ? [X173: $i] :
( ( X173 != X172 )
& ( Z0 @ X173 ) ) )
@ ^ [Z0: $i > $o] :
? [X174: $i] :
( ( Z0 @ X174 )
& ? [X175: $i] :
( ( X175 != X174 )
& ( Z0 @ X175 )
& ~ ? [X176: $i] :
( ( X176 != X175 )
& ( X176 != X174 )
& ( Z0 @ X176 ) ) ) ) )
| ( epred1_1
@ ^ [Z0: $i > $o] :
? [X177: $i] :
( ( Z0 @ X177 )
& ~ ? [X178: $i] :
( ( X178 != X177 )
& ( Z0 @ X178 ) ) )
@ ^ [Z0: $i > $o] :
? [X179: $i] :
( ( Z0 @ X179 )
& ~ ? [X180: $i] :
( ( X180 != X179 )
& ( Z0 @ X180 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred1_1
@ ^ [Z0: $i > $o] :
? [X181: $i] :
( ( Z0 @ X181 )
& ~ ? [X182: $i] :
( ( X182 != X181 )
& ( Z0 @ X182 ) ) )
@ ^ [Z0: $i > $o] :
? [X183: $i] :
( ( Z0 @ X183 )
& ~ ? [X184: $i] :
( ( X184 != X183 )
& ( Z0 @ X184 ) ) ) )
| ( epred1_1
@ ^ [Z0: $i > $o] :
? [X185: $i] :
( ( Z0 @ X185 )
& ~ ? [X186: $i] :
( ( X186 != X185 )
& ( Z0 @ X186 ) ) )
@ ^ [Z0: $i > $o] :
? [X187: $i] :
( ( Z0 @ X187 )
& ( X3
@ ^ [Z1: $i] :
( ( Z1 != X187 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred1_1
@ ^ [Z0: $i > $o] :
? [X188: $i] :
( ( Z0 @ X188 )
& ~ ? [X189: $i] :
( ( X189 != X188 )
& ( Z0 @ X189 ) ) )
@ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14])]) ).
thf(c_0_29,negated_conjecture,
! [X5: ( $i > $o ) > $o,X3: ( $i > $o ) > $o] :
( ( epred2_1 @ X3
@ ^ [Z0: $i > $o] :
? [X190: $i] :
( ( Z0 @ X190 )
& ( X5
@ ^ [Z1: $i] :
( ( Z1 != X190 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred2_1 @ X3 @ X5 )
| ~ ( epred1_1 @ X3 @ X3 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_30,negated_conjecture,
( epred1_1
@ ^ [Z0: $i > $o] :
? [X191: $i] :
( ( Z0 @ X191 )
& ~ ? [X192: $i] :
( ( X192 != X191 )
& ( Z0 @ X192 ) ) )
@ ^ [Z0: $i > $o] :
? [X193: $i] :
( ( Z0 @ X193 )
& ~ ? [X194: $i] :
( ( X194 != X193 )
& ( Z0 @ X194 ) ) ) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
thf(c_0_31,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ( epred2_1
@ ^ [Z0: $i > $o] :
? [X195: $i] :
( ( Z0 @ X195 )
& ~ ? [X196: $i] :
( ( X196 != X195 )
& ( Z0 @ X196 ) ) )
@ ^ [Z0: $i > $o] :
? [X197: $i] :
( ( Z0 @ X197 )
& ( X3
@ ^ [Z1: $i] :
( ( Z1 != X197 )
& ( Z0 @ Z1 ) ) ) ) )
| ~ ( epred2_1
@ ^ [Z0: $i > $o] :
? [X198: $i] :
( ( Z0 @ X198 )
& ~ ? [X199: $i] :
( ( X199 != X198 )
& ( Z0 @ X199 ) ) )
@ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14])]) ).
thf(c_0_32,negated_conjecture,
! [X3: ( $i > $o ) > $o] :
( ~ ( epred2_1 @ X3
@ ^ [Z0: $i > $o] :
? [X200: $i] :
( ( Z0 @ X200 )
& ? [X201: $i] :
( ( X201 != X200 )
& ( Z0 @ X201 )
& ~ ? [X202: $i] :
( ( X202 != X201 )
& ( X202 != X200 )
& ( Z0 @ X202 ) ) ) ) )
| ~ ( epred1_1 @ X3 @ X3 )
| ~ ( cP @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_33,negated_conjecture,
( epred2_1
@ ^ [Z0: $i > $o] :
? [X203: $i] :
( ( Z0 @ X203 )
& ~ ? [X204: $i] :
( ( X204 != X203 )
& ( Z0 @ X204 ) ) )
@ ^ [Z0: $i > $o] :
? [X205: $i] :
( ( Z0 @ X205 )
& ? [X206: $i] :
( ( X206 != X205 )
& ( Z0 @ X206 )
& ~ ? [X207: $i] :
( ( X207 != X206 )
& ( X207 != X205 )
& ( Z0 @ X207 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV292^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:33:28 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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/tmp/tmp.inuJvFOYDB/E---3.1_2644409.p
% 0.20/0.29 % Version: 3.5.1-ho
% 0.20/0.29 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.20/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.29 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.20/0.29 % Starting sh5l with 300s (1) cores
% 0.20/0.29 % Starting full_lambda_10 with 300s (1) cores
% 0.20/0.29 % Starting full_lambda_6 with 300s (1) cores
% 0.20/0.29 % full_lambda_6 with pid 2644425 completed with status 0
% 0.20/0.29 % Result found by full_lambda_6
% 0.20/0.29 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.20/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.29 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.20/0.29 % Starting sh5l with 300s (1) cores
% 0.20/0.29 % Starting full_lambda_10 with 300s (1) cores
% 0.20/0.29 % Starting full_lambda_6 with 300s (1) cores
% 0.20/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.20/0.29 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.20/0.29 % Search class: HGHNF-FFMF00-DHHFMFBN
% 0.20/0.29 % partial match(3): HGHNF-FFMF00-SHHFFSBN
% 0.20/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.30 % SubtermCWHack with pid 2644426 completed with status 10
% 0.20/0.30 % Starting full_lambda_6 with 31s (1) cores
% 0.20/0.30 % full_lambda_6 with pid 2644434 completed with status 0
% 0.20/0.30 % Result found by full_lambda_6
% 0.20/0.30 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.20/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.30 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.20/0.30 % Starting sh5l with 300s (1) cores
% 0.20/0.30 % Starting full_lambda_10 with 300s (1) cores
% 0.20/0.30 % Starting full_lambda_6 with 300s (1) cores
% 0.20/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.20/0.30 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.20/0.30 % Search class: HGHNF-FFMF00-DHHFMFBN
% 0.20/0.30 % partial match(3): HGHNF-FFMF00-SHHFFSBN
% 0.20/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.30 % SubtermCWHack with pid 2644426 completed with status 10
% 0.20/0.30 % Starting full_lambda_6 with 31s (1) cores
% 0.20/0.30 % Preprocessing time : 0.002 s
% 0.20/0.30 % Presaturation interreduction done
% 0.20/0.30
% 0.20/0.30 % Proof found!
% 0.20/0.30 % SZS status Theorem
% 0.20/0.30 % SZS output start CNFRefutation
% See solution above
% 0.20/0.30 % Parsed axioms : 10
% 0.20/0.30 % Removed by relevancy pruning/SinE : 5
% 0.20/0.30 % Initial clauses : 10
% 0.20/0.30 % Removed in clause preprocessing : 0
% 0.20/0.30 % Initial clauses in saturation : 10
% 0.20/0.30 % Processed clauses : 112
% 0.20/0.30 % ...of these trivial : 2
% 0.20/0.30 % ...subsumed : 10
% 0.20/0.30 % ...remaining for further processing : 100
% 0.20/0.30 % Other redundant clauses eliminated : 12
% 0.20/0.30 % Clauses deleted for lack of memory : 0
% 0.20/0.30 % Backward-subsumed : 7
% 0.20/0.30 % Backward-rewritten : 20
% 0.20/0.30 % Generated clauses : 230
% 0.20/0.30 % ...of the previous two non-redundant : 181
% 0.20/0.30 % ...aggressively subsumed : 0
% 0.20/0.30 % Contextual simplify-reflections : 0
% 0.20/0.30 % Paramodulations : 146
% 0.20/0.30 % Factorizations : 0
% 0.20/0.30 % NegExts : 4
% 0.20/0.30 % Equation resolutions : 12
% 0.20/0.30 % Disequality decompositions : 0
% 0.20/0.30 % Total rewrite steps : 170
% 0.20/0.30 % ...of those cached : 166
% 0.20/0.30 % Propositional unsat checks : 0
% 0.20/0.30 % Propositional check models : 0
% 0.20/0.30 % Propositional check unsatisfiable : 0
% 0.20/0.30 % Propositional clauses : 0
% 0.20/0.30 % Propositional clauses after purity: 0
% 0.20/0.30 % Propositional unsat core size : 0
% 0.20/0.30 % Propositional preprocessing time : 0.000
% 0.20/0.30 % Propositional encoding time : 0.000
% 0.20/0.30 % Propositional solver time : 0.000
% 0.20/0.30 % Success case prop preproc time : 0.000
% 0.20/0.30 % Success case prop encoding time : 0.000
% 0.20/0.30 % Success case prop solver time : 0.000
% 0.20/0.30 % Current number of processed clauses : 56
% 0.20/0.30 % Positive orientable unit clauses : 5
% 0.20/0.30 % Positive unorientable unit clauses: 0
% 0.20/0.30 % Negative unit clauses : 0
% 0.20/0.30 % Non-unit-clauses : 51
% 0.20/0.30 % Current number of unprocessed clauses: 33
% 0.20/0.30 % ...number of literals in the above : 160
% 0.20/0.30 % Current number of archived formulas : 0
% 0.20/0.30 % Current number of archived clauses : 44
% 0.20/0.30 % Clause-clause subsumption calls (NU) : 2468
% 0.20/0.30 % Rec. Clause-clause subsumption calls : 62
% 0.20/0.30 % Non-unit clause-clause subsumptions : 13
% 0.20/0.30 % Unit Clause-clause subsumption calls : 6
% 0.20/0.30 % Rewrite failures with RHS unbound : 0
% 0.20/0.30 % BW rewrite match attempts : 7
% 0.20/0.30 % BW rewrite match successes : 3
% 0.20/0.30 % Condensation attempts : 0
% 0.20/0.30 % Condensation successes : 0
% 0.20/0.30 % Termbank termtop insertions : 51789
% 0.20/0.30 % Search garbage collected termcells : 536
% 0.20/0.30
% 0.20/0.30 % -------------------------------------------------
% 0.20/0.30 % User time : 0.037 s
% 0.20/0.30 % System time : 0.007 s
% 0.20/0.30 % Total time : 0.044 s
% 0.20/0.30 % Maximum resident set size: 3644 pages
% 0.20/0.30
% 0.20/0.30 % -------------------------------------------------
% 0.20/0.30 % User time : 0.037 s
% 0.20/0.30 % System time : 0.013 s
% 0.20/0.30 % Total time : 0.050 s
% 0.20/0.30 % Maximum resident set size: 4864 pages
% 0.20/0.30 % E exiting
%------------------------------------------------------------------------------