%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX175^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:40:27 AM UTC 2026
% Result : Theorem 10.06s 2.02s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of formulae : 85 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 435 ( 39 equ; 0 cnn)
% Maximal formula atoms : 138 ( 5 avg)
% Number of connectives : 1852 ( 264 ~; 293 |; 129 &;1146 @)
% ( 17 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 167 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 4 con; 0-5 aty)
% Number of variables : 378 ( 43 ^; 333 !; 2 ?; 378 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
d_unsorted: $tType ).
thf(decl_23,type,
irel: $i > $i > $o ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_29,type,
iatom: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
inot: ( $i > $o ) > $i > $o ).
thf(decl_31,type,
itrue: $i > $o ).
thf(decl_32,type,
ifalse: $i > $o ).
thf(decl_33,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_35,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_36,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_40,type,
isatisfiable: ( $i > $o ) > $o ).
thf(decl_41,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(decl_42,type,
iinvalid: ( $i > $o ) > $o ).
thf(decl_43,type,
d2unsorted: d_unsorted > $i ).
thf(decl_44,type,
d_unsorted_0: d_unsorted ).
thf(decl_45,type,
esk1_1: $i > d_unsorted ).
thf(decl_46,type,
esk2_2: ( $i > $o ) > $i > $i ).
thf(decl_47,type,
esk3_2: ( $i > $o ) > $i > $i ).
thf(decl_48,type,
esk4_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_49,type,
esk5_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_50,type,
esk6_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_51,type,
esk7_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_52,type,
esk8_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_53,type,
esk9_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_54,type,
esk10_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_55,type,
esk11_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_56,type,
esk12_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_57,type,
esk13_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_58,type,
esk14_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_59,type,
esk15_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_60,type,
esk16_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_61,type,
esk17_5: ( $i > $o ) > ( $i > $o ) > $i > $i > $i > $i ).
thf(decl_62,type,
esk18_5: ( $i > $o ) > ( $i > $o ) > $i > $i > $i > $i ).
thf(decl_63,type,
esk19_1: ( $i > $o ) > $i ).
thf(decl_64,type,
esk20_1: ( $i > $o ) > $i ).
thf(decl_65,type,
esk21_1: ( $i > $o ) > $i ).
thf(decl_66,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_67,type,
epred1_0: $i > $o ).
thf(decl_68,type,
epred2_0: $i > $o ).
thf(decl_69,type,
esk23_0: $i ).
thf(decl_70,type,
esk3_0: $i ).
thf(lcl695_1,axiom,
( ! [X1: $i] :
? [X2: d_unsorted] :
( X1
= ( d2unsorted @ X2 ) )
& ! [X2: d_unsorted] : ( X2 = d_unsorted_0 )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( mnot
= ( ^ [X5: $i > $o,X1: $i] :
~ ( X5 @ X1 ) ) )
& ( mor
= ( ^ [X5: $i > $o,X6: $i > $o,X1: $i] :
( ( X5 @ X1 )
| ( X6 @ X1 ) ) ) )
& ( mand
= ( ^ [X5: $i > $o,X6: $i > $o,X1: $i] :
( ( X5 @ X1 )
& ( X6 @ X1 ) ) ) )
& ( mimplies
= ( ^ [X7: $i > $o,X8: $i > $o,X9: $i] :
( ~ ( X7 @ X9 )
| ( X8 @ X9 ) ) ) )
& ( mbox_s4
= ( ^ [X10: $i > $o,X11: $i] :
! [X12: $i] :
( ~ ( irel @ X11 @ X12 )
| ( X10 @ X12 ) ) ) )
& ( iatom
= ( ^ [X10: $i > $o,X9: $i] : ( X10 @ X9 ) ) )
& ( inot
= ( ^ [X10: $i > $o,X9: $i] :
~ ! [X13: $i] :
( ~ ( irel @ X9 @ X13 )
| ( X10 @ X13 ) ) ) )
& ( iand
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ( X10 @ X9 )
& ( X14 @ X9 ) ) ) )
& ( ior
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ! [X15: $i] :
( ~ ( irel @ X9 @ X15 )
| ( X10 @ X15 ) )
| ! [X16: $i] :
( ~ ( irel @ X9 @ X16 )
| ( X14 @ X16 ) ) ) ) )
& ( iimplies
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ~ ! [X17: $i] :
( ~ ( irel @ X9 @ X17 )
| ( X10 @ X17 ) )
| ! [X18: $i] :
( ~ ( irel @ X9 @ X18 )
| ( X14 @ X18 ) ) ) ) )
& ( iimplied
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ~ ! [X19: $i] :
( ~ ( irel @ X9 @ X19 )
| ( X14 @ X19 ) )
| ! [X20: $i] :
( ~ ( irel @ X9 @ X20 )
| ( X10 @ X20 ) ) ) ) )
& ( iequiv
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ( ~ ! [X21: $i] :
( ~ ( irel @ X9 @ X21 )
| ( X10 @ X21 ) )
| ! [X22: $i] :
( ~ ( irel @ X9 @ X22 )
| ( X14 @ X22 ) ) )
& ( ~ ! [X23: $i] :
( ~ ( irel @ X9 @ X23 )
| ( X14 @ X23 ) )
| ! [X24: $i] :
( ~ ( irel @ X9 @ X24 )
| ( X10 @ X24 ) ) ) ) ) )
& ( ixor
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
~ ! [X25: $i,X26: $i,X27: $i] :
( ~ ( irel @ X9 @ X25 )
| ( ( ~ ! [X28: $i] :
( ~ ( irel @ X25 @ X28 )
| ( X10 @ X28 ) )
| ~ ( irel @ X25 @ X26 )
| ( X14 @ X26 ) )
& ( ~ ! [X29: $i] :
( ~ ( irel @ X25 @ X29 )
| ( X14 @ X29 ) )
| ~ ( irel @ X25 @ X27 )
| ( X10 @ X27 ) ) ) ) ) )
& ( ivalid
= ( ^ [X30: $i > $o] :
! [X31: $i] : ( X30 @ X31 ) ) )
& ( isatisfiable
= ( ^ [X30: $i > $o] :
~ ! [X31: $i] :
~ ( X30 @ X31 ) ) )
& ( icountersatisfiable
= ( ^ [X30: $i > $o] :
~ ! [X31: $i] : ( X30 @ X31 ) ) )
& ( iinvalid
= ( ^ [X30: $i > $o] :
! [X31: $i] :
~ ( X30 @ X31 ) ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.euFEaaZfkR/E---3.1_980329.p',lcl695_1) ).
thf(ixor,conjecture,
( ixor
= ( ^ [X10: $i > $o,X14: $i > $o] : ( inot @ ( iequiv @ X10 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.euFEaaZfkR/E---3.1_980329.p',ixor) ).
thf(c_0_2,plain,
( ! [X1: $i] :
? [X2: d_unsorted] :
( X1
= ( d2unsorted @ X2 ) )
& ! [X2: d_unsorted] : ( X2 = d_unsorted_0 )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ! [X37: $i > $o,X38: $i] :
( ( mnot @ X37 @ X38 )
<=> ~ ( X37 @ X38 ) )
& ! [X39: $i > $o,X40: $i > $o,X41: $i] :
( ( mor @ X39 @ X40 @ X41 )
<=> ( ( X39 @ X41 )
| ( X40 @ X41 ) ) )
& ! [X42: $i > $o,X43: $i > $o,X44: $i] :
( ( mand @ X42 @ X43 @ X44 )
<=> ( ( X42 @ X44 )
& ( X43 @ X44 ) ) )
& ! [X45: $i > $o,X46: $i > $o,X47: $i] :
( ( mimplies @ X45 @ X46 @ X47 )
<=> ( ~ ( X45 @ X47 )
| ( X46 @ X47 ) ) )
& ! [X48: $i > $o,X49: $i] :
( ( mbox_s4 @ X48 @ X49 )
<=> ! [X12: $i] :
( ~ ( irel @ X49 @ X12 )
| ( X48 @ X12 ) ) )
& ! [X50: $i > $o,X51: $i] :
( ( iatom @ X50 @ X51 )
<=> ( X50 @ X51 ) )
& ! [X52: $i > $o,X53: $i] :
( ( inot @ X52 @ X53 )
<=> ~ ! [X13: $i] :
( ~ ( irel @ X53 @ X13 )
| ( X52 @ X13 ) ) )
& ! [X54: $i > $o,X55: $i > $o,X56: $i] :
( ( iand @ X54 @ X55 @ X56 )
<=> ( ( X54 @ X56 )
& ( X55 @ X56 ) ) )
& ! [X57: $i > $o,X58: $i > $o,X59: $i] :
( ( ior @ X57 @ X58 @ X59 )
<=> ( ! [X15: $i] :
( ~ ( irel @ X59 @ X15 )
| ( X57 @ X15 ) )
| ! [X16: $i] :
( ~ ( irel @ X59 @ X16 )
| ( X58 @ X16 ) ) ) )
& ! [X60: $i > $o,X61: $i > $o,X62: $i] :
( ( iimplies @ X60 @ X61 @ X62 )
<=> ( ~ ! [X17: $i] :
( ~ ( irel @ X62 @ X17 )
| ( X60 @ X17 ) )
| ! [X18: $i] :
( ~ ( irel @ X62 @ X18 )
| ( X61 @ X18 ) ) ) )
& ! [X63: $i > $o,X64: $i > $o,X65: $i] :
( ( iimplied @ X63 @ X64 @ X65 )
<=> ( ~ ! [X19: $i] :
( ~ ( irel @ X65 @ X19 )
| ( X64 @ X19 ) )
| ! [X20: $i] :
( ~ ( irel @ X65 @ X20 )
| ( X63 @ X20 ) ) ) )
& ! [X66: $i > $o,X67: $i > $o,X68: $i] :
( ( iequiv @ X66 @ X67 @ X68 )
<=> ( ( ~ ! [X21: $i] :
( ~ ( irel @ X68 @ X21 )
| ( X66 @ X21 ) )
| ! [X22: $i] :
( ~ ( irel @ X68 @ X22 )
| ( X67 @ X22 ) ) )
& ( ~ ! [X23: $i] :
( ~ ( irel @ X68 @ X23 )
| ( X67 @ X23 ) )
| ! [X24: $i] :
( ~ ( irel @ X68 @ X24 )
| ( X66 @ X24 ) ) ) ) )
& ! [X69: $i > $o,X70: $i > $o,X71: $i] :
( ( ixor @ X69 @ X70 @ X71 )
<=> ~ ! [X25: $i,X26: $i,X27: $i] :
( ~ ( irel @ X71 @ X25 )
| ( ( ~ ! [X28: $i] :
( ~ ( irel @ X25 @ X28 )
| ( X69 @ X28 ) )
| ~ ( irel @ X25 @ X26 )
| ( X70 @ X26 ) )
& ( ~ ! [X29: $i] :
( ~ ( irel @ X25 @ X29 )
| ( X70 @ X29 ) )
| ~ ( irel @ X25 @ X27 )
| ( X69 @ X27 ) ) ) ) )
& ! [X72: $i > $o] :
( ( ivalid @ X72 )
<=> ! [X31: $i] : ( X72 @ X31 ) )
& ! [X73: $i > $o] :
( ( isatisfiable @ X73 )
<=> ~ ! [X31: $i] :
~ ( X73 @ X31 ) )
& ! [X74: $i > $o] :
( ( icountersatisfiable @ X74 )
<=> ~ ! [X31: $i] : ( X74 @ X31 ) )
& ! [X75: $i > $o] :
( ( iinvalid @ X75 )
<=> ! [X31: $i] :
~ ( X75 @ X31 ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[lcl695_1])])]) ).
thf(c_0_3,plain,
! [X78: $i,X80: d_unsorted,X81: d_unsorted,X82: d_unsorted,X83: $i > $o,X84: $i,X85: $i > $o,X86: $i > $o,X87: $i,X88: $i > $o,X89: $i > $o,X90: $i,X91: $i > $o,X92: $i > $o,X93: $i,X94: $i > $o,X95: $i,X96: $i,X97: $i > $o,X98: $i,X100: $i > $o,X101: $i,X102: $i > $o,X103: $i,X105: $i > $o,X106: $i,X107: $i,X108: $i > $o,X109: $i > $o,X110: $i,X111: $i > $o,X112: $i > $o,X113: $i,X114: $i,X115: $i,X116: $i > $o,X117: $i > $o,X118: $i,X121: $i > $o,X122: $i > $o,X123: $i,X125: $i,X126: $i > $o,X127: $i > $o,X128: $i,X129: $i,X131: $i > $o,X132: $i > $o,X133: $i,X135: $i,X136: $i > $o,X137: $i > $o,X138: $i,X139: $i,X141: $i > $o,X142: $i > $o,X143: $i,X145: $i,X147: $i,X148: $i > $o,X149: $i > $o,X150: $i,X151: $i,X153: $i,X155: $i > $o,X156: $i > $o,X157: $i,X160: $i,X162: $i,X163: $i > $o,X164: $i > $o,X165: $i,X166: $i,X167: $i,X169: $i,X171: $i > $o,X172: $i,X173: $i > $o,X175: $i > $o,X177: $i > $o,X178: $i,X179: $i > $o,X181: $i > $o,X182: $i,X183: $i > $o,X184: $i,X185: $i > $o] :
( ( X78
= ( d2unsorted @ ( esk1_1 @ X78 ) ) )
& ( X80 = d_unsorted_0 )
& ( ( ( d2unsorted @ X81 )
!= ( d2unsorted @ X82 ) )
| ( X81 = X82 ) )
& ( ~ ( mnot @ X83 @ X84 )
| ~ ( X83 @ X84 ) )
& ( ( X83 @ X84 )
| ( mnot @ X83 @ X84 ) )
& ( ~ ( mor @ X85 @ X86 @ X87 )
| ( X85 @ X87 )
| ( X86 @ X87 ) )
& ( ~ ( X85 @ X87 )
| ( mor @ X85 @ X86 @ X87 ) )
& ( ~ ( X86 @ X87 )
| ( mor @ X85 @ X86 @ X87 ) )
& ( ( X88 @ X90 )
| ~ ( mand @ X88 @ X89 @ X90 ) )
& ( ( X89 @ X90 )
| ~ ( mand @ X88 @ X89 @ X90 ) )
& ( ~ ( X88 @ X90 )
| ~ ( X89 @ X90 )
| ( mand @ X88 @ X89 @ X90 ) )
& ( ~ ( mimplies @ X91 @ X92 @ X93 )
| ~ ( X91 @ X93 )
| ( X92 @ X93 ) )
& ( ( X91 @ X93 )
| ( mimplies @ X91 @ X92 @ X93 ) )
& ( ~ ( X92 @ X93 )
| ( mimplies @ X91 @ X92 @ X93 ) )
& ( ~ ( mbox_s4 @ X94 @ X95 )
| ~ ( irel @ X95 @ X96 )
| ( X94 @ X96 ) )
& ( ( irel @ X98 @ ( esk2_2 @ X97 @ X98 ) )
| ( mbox_s4 @ X97 @ X98 ) )
& ( ~ ( X97 @ ( esk2_2 @ X97 @ X98 ) )
| ( mbox_s4 @ X97 @ X98 ) )
& ( ~ ( iatom @ X100 @ X101 )
| ( X100 @ X101 ) )
& ( ~ ( X100 @ X101 )
| ( iatom @ X100 @ X101 ) )
& ( ( irel @ X103 @ ( esk3_2 @ X102 @ X103 ) )
| ~ ( inot @ X102 @ X103 ) )
& ( ~ ( X102 @ ( esk3_2 @ X102 @ X103 ) )
| ~ ( inot @ X102 @ X103 ) )
& ( ~ ( irel @ X106 @ X107 )
| ( X105 @ X107 )
| ( inot @ X105 @ X106 ) )
& ( ( X108 @ X110 )
| ~ ( iand @ X108 @ X109 @ X110 ) )
& ( ( X109 @ X110 )
| ~ ( iand @ X108 @ X109 @ X110 ) )
& ( ~ ( X108 @ X110 )
| ~ ( X109 @ X110 )
| ( iand @ X108 @ X109 @ X110 ) )
& ( ~ ( ior @ X111 @ X112 @ X113 )
| ~ ( irel @ X113 @ X114 )
| ( X111 @ X114 )
| ~ ( irel @ X113 @ X115 )
| ( X112 @ X115 ) )
& ( ( irel @ X118 @ ( esk4_3 @ X116 @ X117 @ X118 ) )
| ( ior @ X116 @ X117 @ X118 ) )
& ( ~ ( X116 @ ( esk4_3 @ X116 @ X117 @ X118 ) )
| ( ior @ X116 @ X117 @ X118 ) )
& ( ( irel @ X118 @ ( esk5_3 @ X116 @ X117 @ X118 ) )
| ( ior @ X116 @ X117 @ X118 ) )
& ( ~ ( X117 @ ( esk5_3 @ X116 @ X117 @ X118 ) )
| ( ior @ X116 @ X117 @ X118 ) )
& ( ( irel @ X123 @ ( esk6_3 @ X121 @ X122 @ X123 ) )
| ~ ( irel @ X123 @ X125 )
| ( X122 @ X125 )
| ~ ( iimplies @ X121 @ X122 @ X123 ) )
& ( ~ ( X121 @ ( esk6_3 @ X121 @ X122 @ X123 ) )
| ~ ( irel @ X123 @ X125 )
| ( X122 @ X125 )
| ~ ( iimplies @ X121 @ X122 @ X123 ) )
& ( ~ ( irel @ X128 @ X129 )
| ( X126 @ X129 )
| ( iimplies @ X126 @ X127 @ X128 ) )
& ( ( irel @ X128 @ ( esk7_3 @ X126 @ X127 @ X128 ) )
| ( iimplies @ X126 @ X127 @ X128 ) )
& ( ~ ( X127 @ ( esk7_3 @ X126 @ X127 @ X128 ) )
| ( iimplies @ X126 @ X127 @ X128 ) )
& ( ( irel @ X133 @ ( esk8_3 @ X131 @ X132 @ X133 ) )
| ~ ( irel @ X133 @ X135 )
| ( X131 @ X135 )
| ~ ( iimplied @ X131 @ X132 @ X133 ) )
& ( ~ ( X132 @ ( esk8_3 @ X131 @ X132 @ X133 ) )
| ~ ( irel @ X133 @ X135 )
| ( X131 @ X135 )
| ~ ( iimplied @ X131 @ X132 @ X133 ) )
& ( ~ ( irel @ X138 @ X139 )
| ( X137 @ X139 )
| ( iimplied @ X136 @ X137 @ X138 ) )
& ( ( irel @ X138 @ ( esk9_3 @ X136 @ X137 @ X138 ) )
| ( iimplied @ X136 @ X137 @ X138 ) )
& ( ~ ( X136 @ ( esk9_3 @ X136 @ X137 @ X138 ) )
| ( iimplied @ X136 @ X137 @ X138 ) )
& ( ( irel @ X143 @ ( esk10_3 @ X141 @ X142 @ X143 ) )
| ~ ( irel @ X143 @ X145 )
| ( X142 @ X145 )
| ~ ( iequiv @ X141 @ X142 @ X143 ) )
& ( ~ ( X141 @ ( esk10_3 @ X141 @ X142 @ X143 ) )
| ~ ( irel @ X143 @ X145 )
| ( X142 @ X145 )
| ~ ( iequiv @ X141 @ X142 @ X143 ) )
& ( ( irel @ X143 @ ( esk11_3 @ X141 @ X142 @ X143 ) )
| ~ ( irel @ X143 @ X147 )
| ( X141 @ X147 )
| ~ ( iequiv @ X141 @ X142 @ X143 ) )
& ( ~ ( X142 @ ( esk11_3 @ X141 @ X142 @ X143 ) )
| ~ ( irel @ X143 @ X147 )
| ( X141 @ X147 )
| ~ ( iequiv @ X141 @ X142 @ X143 ) )
& ( ~ ( irel @ X150 @ X153 )
| ( X149 @ X153 )
| ~ ( irel @ X150 @ X151 )
| ( X148 @ X151 )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ( irel @ X150 @ ( esk13_3 @ X148 @ X149 @ X150 ) )
| ~ ( irel @ X150 @ X151 )
| ( X148 @ X151 )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ~ ( X148 @ ( esk13_3 @ X148 @ X149 @ X150 ) )
| ~ ( irel @ X150 @ X151 )
| ( X148 @ X151 )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ~ ( irel @ X150 @ X153 )
| ( X149 @ X153 )
| ( irel @ X150 @ ( esk12_3 @ X148 @ X149 @ X150 ) )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ( irel @ X150 @ ( esk13_3 @ X148 @ X149 @ X150 ) )
| ( irel @ X150 @ ( esk12_3 @ X148 @ X149 @ X150 ) )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ~ ( X148 @ ( esk13_3 @ X148 @ X149 @ X150 ) )
| ( irel @ X150 @ ( esk12_3 @ X148 @ X149 @ X150 ) )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ~ ( irel @ X150 @ X153 )
| ( X149 @ X153 )
| ~ ( X149 @ ( esk12_3 @ X148 @ X149 @ X150 ) )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ( irel @ X150 @ ( esk13_3 @ X148 @ X149 @ X150 ) )
| ~ ( X149 @ ( esk12_3 @ X148 @ X149 @ X150 ) )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ~ ( X148 @ ( esk13_3 @ X148 @ X149 @ X150 ) )
| ~ ( X149 @ ( esk12_3 @ X148 @ X149 @ X150 ) )
| ( iequiv @ X148 @ X149 @ X150 ) )
& ( ( irel @ X157 @ ( esk14_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ~ ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ X162 )
| ( X156 @ X162 )
| ~ ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ X160 )
| ( X155 @ X160 )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ ( esk16_3 @ X155 @ X156 @ X157 ) )
| ~ ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ X160 )
| ( X155 @ X160 )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ~ ( X155 @ ( esk16_3 @ X155 @ X156 @ X157 ) )
| ~ ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ X160 )
| ( X155 @ X160 )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ~ ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ X162 )
| ( X156 @ X162 )
| ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ ( esk15_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ ( esk16_3 @ X155 @ X156 @ X157 ) )
| ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ ( esk15_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ~ ( X155 @ ( esk16_3 @ X155 @ X156 @ X157 ) )
| ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ ( esk15_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ~ ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ X162 )
| ( X156 @ X162 )
| ~ ( X156 @ ( esk15_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ( irel @ ( esk14_3 @ X155 @ X156 @ X157 ) @ ( esk16_3 @ X155 @ X156 @ X157 ) )
| ~ ( X156 @ ( esk15_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ~ ( X155 @ ( esk16_3 @ X155 @ X156 @ X157 ) )
| ~ ( X156 @ ( esk15_3 @ X155 @ X156 @ X157 ) )
| ~ ( ixor @ X155 @ X156 @ X157 ) )
& ( ( irel @ X166 @ ( esk17_5 @ X163 @ X164 @ X165 @ X166 @ X167 ) )
| ~ ( irel @ X166 @ X167 )
| ( X164 @ X167 )
| ~ ( irel @ X165 @ X166 )
| ( ixor @ X163 @ X164 @ X165 ) )
& ( ~ ( X163 @ ( esk17_5 @ X163 @ X164 @ X165 @ X166 @ X167 ) )
| ~ ( irel @ X166 @ X167 )
| ( X164 @ X167 )
| ~ ( irel @ X165 @ X166 )
| ( ixor @ X163 @ X164 @ X165 ) )
& ( ( irel @ X166 @ ( esk18_5 @ X163 @ X164 @ X165 @ X166 @ X169 ) )
| ~ ( irel @ X166 @ X169 )
| ( X163 @ X169 )
| ~ ( irel @ X165 @ X166 )
| ( ixor @ X163 @ X164 @ X165 ) )
& ( ~ ( X164 @ ( esk18_5 @ X163 @ X164 @ X165 @ X166 @ X169 ) )
| ~ ( irel @ X166 @ X169 )
| ( X163 @ X169 )
| ~ ( irel @ X165 @ X166 )
| ( ixor @ X163 @ X164 @ X165 ) )
& ( ~ ( ivalid @ X171 )
| ( X171 @ X172 ) )
& ( ~ ( X173 @ ( esk19_1 @ X173 ) )
| ( ivalid @ X173 ) )
& ( ~ ( isatisfiable @ X175 )
| ( X175 @ ( esk20_1 @ X175 ) ) )
& ( ~ ( X177 @ X178 )
| ( isatisfiable @ X177 ) )
& ( ~ ( icountersatisfiable @ X179 )
| ~ ( X179 @ ( esk21_1 @ X179 ) ) )
& ( ( X181 @ X182 )
| ( icountersatisfiable @ X181 ) )
& ( ~ ( iinvalid @ X183 )
| ~ ( X183 @ X184 ) )
& ( ( X185 @ ( esk22_1 @ X185 ) )
| ( iinvalid @ X185 ) )
& ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( itrue @ ( d2unsorted @ d_unsorted_0 ) )
& ~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])])]) ).
thf(c_0_4,negated_conjecture,
( ixor
!= ( ^ [X10: $i > $o,X14: $i > $o] : ( inot @ ( iequiv @ X10 @ X14 ) ) ) ),
inference(assume_negation,[status(cth)],[ixor]) ).
thf(c_0_5,plain,
! [X1: $i] :
( X1
= ( d2unsorted @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
! [X2: d_unsorted] : ( X2 = d_unsorted_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
~ ! [X76: $i > $o,X77: $i > $o] :
( ( ixor @ X76 @ X77 )
= ( inot @ ( iequiv @ X76 @ X77 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])]) ).
thf(c_0_8,plain,
! [X1: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X1 ),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,negated_conjecture,
( ( ixor @ epred1_0 @ epred2_0 )
!= ( inot @ ( iequiv @ epred1_0 @ epred2_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
thf(c_0_10,plain,
! [X5: $i > $o] :
( ( X5 @ ( esk22_1 @ X5 ) )
| ( iinvalid @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_11,plain,
irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_12,plain,
! [X1: $i] : ( esk23_0 = X1 ),
inference(rw,[status(thm)],[c_0_8,c_0_8]) ).
thf(c_0_13,negated_conjecture,
( ( ixor @ epred1_0 @ epred2_0 )
!= ( inot @ ( iequiv @ epred1_0 @ epred2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X5: $i > $o,X1: $i] :
( ~ ( iinvalid @ X5 )
| ~ ( X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,plain,
! [X5: $i > $o] :
( ( X5 @ esk23_0 )
| ( iinvalid @ X5 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_8]),c_0_8]) ).
thf(c_0_16,plain,
irel @ esk23_0 @ esk23_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_8]),c_0_8]) ).
thf(c_0_17,plain,
! [X1: $i,X9: $i] : ( X1 = X9 ),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
thf(c_0_18,plain,
! [X5: $i > $o,X1: $i] :
( ~ ( X5 @ ( esk3_2 @ X5 @ X1 ) )
| ~ ( inot @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_19,negated_conjecture,
( ( inot @ ( iequiv @ epred1_0 @ epred2_0 ) @ esk3_0 )
<~> ( ixor @ epred1_0 @ epred2_0 @ esk3_0 ) ),
inference(neg_ext,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X5: $i > $o,X1: $i] :
( ( X5 @ esk23_0 )
| ~ ( X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_21,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_22,plain,
! [X5: $i > $o] :
( ~ ( icountersatisfiable @ X5 )
| ~ ( X5 @ ( esk21_1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_23,plain,
! [X1: $i,X5: $i > $o] :
( ~ ( inot @ X5 @ X1 )
| ~ ( X5 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_8]),c_0_8]) ).
thf(c_0_24,negated_conjecture,
( ( inot @ ( iequiv @ epred1_0 @ epred2_0 ) @ esk3_0 )
| ( ixor @ epred1_0 @ epred2_0 @ esk3_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i,X11: $i,X9: $i] :
( ( X6 @ X11 )
| ( ixor @ X6 @ X5 @ X1 )
| ~ ( X5 @ ( esk18_5 @ X6 @ X5 @ X1 @ X9 @ X11 ) )
| ~ ( irel @ X9 @ X11 )
| ~ ( irel @ X1 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_26,plain,
! [X1: $i] : ( irel @ X1 @ esk23_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X5: $i > $o] :
( ~ ( icountersatisfiable @ X5 )
| ~ ( X5 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_8]),c_0_8]) ).
thf(c_0_28,plain,
! [X1: $i,X5: $i > $o] :
( ( X5 @ X1 )
| ( icountersatisfiable @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_29,negated_conjecture,
( ( ixor @ epred1_0 @ epred2_0 @ esk3_0 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_30,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i] :
( ( iequiv @ X5 @ X6 @ X1 )
| ~ ( X5 @ ( esk13_3 @ X5 @ X6 @ X1 ) )
| ~ ( X6 @ ( esk12_3 @ X5 @ X6 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_31,plain,
! [X5: $i > $o,X1: $i,X9: $i,X11: $i,X6: $i > $o] :
( ( ixor @ X5 @ X6 @ X1 )
| ( X5 @ X9 )
| ~ ( irel @ X11 @ X9 )
| ~ ( irel @ X1 @ X11 )
| ~ ( X6 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_8]),c_0_8]) ).
thf(c_0_32,plain,
! [X1: $i,X9: $i] : ( irel @ X1 @ X9 ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
thf(c_0_33,negated_conjecture,
( ~ ( inot @ ( iequiv @ epred1_0 @ epred2_0 ) @ esk3_0 )
| ~ ( ixor @ epred1_0 @ epred2_0 @ esk3_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_19]) ).
thf(c_0_34,plain,
! [X1: $i,X5: $i > $o,X9: $i] :
( ( X5 @ X9 )
| ( inot @ X5 @ X1 )
| ~ ( irel @ X1 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_35,plain,
! [X1: $i,X5: $i > $o] :
( ( X5 @ X1 )
| ~ ( X5 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
( ( ixor @ epred1_0 @ epred2_0 @ esk3_0 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
thf(c_0_37,plain,
! [X1: $i,X6: $i > $o,X5: $i > $o] :
( ( iequiv @ X5 @ X6 @ X1 )
| ~ ( X6 @ esk23_0 )
| ~ ( X5 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_8]),c_0_8]),c_0_8]),c_0_8]) ).
thf(c_0_38,plain,
! [X1: $i,X5: $i > $o,X9: $i,X6: $i > $o] :
( ( ixor @ X5 @ X6 @ X1 )
| ( X5 @ X9 )
| ~ ( X6 @ esk23_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32])]) ).
thf(c_0_39,plain,
! [X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X6 @ X9 )
| ~ ( X5 @ ( esk11_3 @ X6 @ X5 @ X1 ) )
| ~ ( irel @ X1 @ X9 )
| ~ ( iequiv @ X6 @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i] :
( ~ ( inot @ ( iequiv @ epred1_0 @ epred2_0 ) @ X1 )
| ~ ( ixor @ epred1_0 @ epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
thf(c_0_41,plain,
! [X1: $i,X5: $i > $o,X9: $i] :
( ( inot @ X5 @ X1 )
| ( X5 @ X9 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_32])]) ).
thf(c_0_42,plain,
! [X1: $i,X5: $i > $o,X9: $i] :
( ( X5 @ X1 )
| ~ ( X5 @ X9 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
thf(c_0_43,negated_conjecture,
( ( ixor @ epred1_0 @ epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ esk23_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
thf(c_0_44,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i] :
( ~ ( X5 @ ( esk16_3 @ X5 @ X6 @ X1 ) )
| ~ ( X6 @ ( esk15_3 @ X5 @ X6 @ X1 ) )
| ~ ( ixor @ X5 @ X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_45,plain,
! [X5: $i > $o,X1: $i,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X5 @ X6 @ X9 )
| ~ ( irel @ X9 @ X1 )
| ~ ( X6 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_8]),c_0_8]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i,X9: $i] :
( ( iequiv @ epred1_0 @ epred2_0 @ X1 )
| ~ ( ixor @ epred1_0 @ epred2_0 @ X9 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i] :
( ( ixor @ epred1_0 @ epred2_0 @ X1 )
| ~ ( epred2_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_48,plain,
! [X1: $i,X6: $i > $o,X5: $i > $o] :
( ~ ( ixor @ X5 @ X6 @ X1 )
| ~ ( X6 @ esk23_0 )
| ~ ( X5 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_8]),c_0_8]),c_0_8]),c_0_8]) ).
thf(c_0_49,plain,
! [X1: $i,X5: $i > $o,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X5 @ X6 @ X9 )
| ~ ( X6 @ esk23_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_32])]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( iequiv @ epred1_0 @ epred2_0 @ X1 )
| ~ ( epred2_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_51,negated_conjecture,
( ~ ( epred2_0 @ esk23_0 )
| ~ ( epred1_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( epred2_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ~ ( epred2_0 @ X1 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_17]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i,X9: $i] :
( ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X9 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_17]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( icountersatisfiable @ epred2_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_28]) ).
thf(c_0_56,plain,
! [X1: $i,X6: $i > $o,X9: $i,X5: $i > $o,X11: $i] :
( ( X5 @ X9 )
| ( X6 @ X11 )
| ( iequiv @ X6 @ X5 @ X1 )
| ~ ( irel @ X1 @ X9 )
| ~ ( irel @ X1 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_57,negated_conjecture,
icountersatisfiable @ epred2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_55]) ).
thf(c_0_58,plain,
! [X5: $i > $o,X1: $i] :
( ( isatisfiable @ X5 )
| ~ ( X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_59,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i,X11: $i] :
( ( iequiv @ X5 @ X6 @ X1 )
| ( X5 @ X9 )
| ( X6 @ X11 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_32]),c_0_32])]) ).
thf(c_0_60,negated_conjecture,
~ ( epred2_0 @ esk23_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_57]) ).
thf(c_0_61,plain,
! [X11: $i,X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X6 @ X9 )
| ( X5 @ X11 )
| ~ ( irel @ ( esk14_3 @ X5 @ X6 @ X1 ) @ X9 )
| ~ ( irel @ ( esk14_3 @ X5 @ X6 @ X1 ) @ X11 )
| ~ ( ixor @ X5 @ X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_62,plain,
! [X5: $i > $o] :
( ( X5 @ ( esk20_1 @ X5 ) )
| ~ ( isatisfiable @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_63,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i] :
( ( iequiv @ X5 @ X6 @ X1 )
| ( isatisfiable @ X5 )
| ( X6 @ X9 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
thf(c_0_64,negated_conjecture,
! [X1: $i] :
~ ( epred2_0 @ X1 ),
inference(spm,[status(thm)],[c_0_60,c_0_17]) ).
thf(c_0_65,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i,X11: $i,X9: $i] :
( ( X5 @ X1 )
| ( X6 @ X9 )
| ~ ( ixor @ X5 @ X6 @ X11 )
| ~ ( irel @ esk23_0 @ X1 )
| ~ ( irel @ esk23_0 @ X9 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_8]),c_0_8]),c_0_8]),c_0_8]) ).
thf(c_0_66,plain,
! [X5: $i > $o] :
( ( X5 @ esk23_0 )
| ~ ( isatisfiable @ X5 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_8]),c_0_8]) ).
thf(c_0_67,negated_conjecture,
( ( ixor @ epred1_0 @ epred2_0 @ esk3_0 )
| ( isatisfiable @ epred1_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_63]),c_0_64]) ).
thf(c_0_68,plain,
! [X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X6 @ X9 )
| ~ ( X5 @ ( esk10_3 @ X5 @ X6 @ X1 ) )
| ~ ( irel @ X1 @ X9 )
| ~ ( iequiv @ X5 @ X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_69,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i,X11: $i] :
( ( X5 @ X1 )
| ( X6 @ X9 )
| ~ ( ixor @ X6 @ X5 @ X11 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_32]),c_0_32])]) ).
thf(c_0_70,negated_conjecture,
( ( ixor @ epred1_0 @ epred2_0 @ esk3_0 )
| ( epred1_0 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_71,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i,X11: $i,X9: $i] :
( ( X6 @ X11 )
| ( ixor @ X5 @ X6 @ X1 )
| ~ ( X5 @ ( esk17_5 @ X5 @ X6 @ X1 @ X9 @ X11 ) )
| ~ ( irel @ X9 @ X11 )
| ~ ( irel @ X1 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_72,plain,
! [X5: $i > $o,X1: $i,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X6 @ X5 @ X9 )
| ~ ( irel @ X9 @ X1 )
| ~ ( X6 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_8]),c_0_8]) ).
thf(c_0_73,negated_conjecture,
epred1_0 @ esk23_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_64]),c_0_42]) ).
thf(c_0_74,plain,
! [X1: $i,X9: $i,X11: $i,X6: $i > $o,X5: $i > $o] :
( ( ixor @ X5 @ X6 @ X1 )
| ( X6 @ X9 )
| ~ ( irel @ X11 @ X9 )
| ~ ( irel @ X1 @ X11 )
| ~ ( X5 @ esk23_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_8]),c_0_8]) ).
thf(c_0_75,plain,
! [X1: $i,X5: $i > $o,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X6 @ X5 @ X9 )
| ~ ( X6 @ esk23_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_32])]) ).
thf(c_0_76,negated_conjecture,
! [X1: $i] :
( ( icountersatisfiable @ ( ixor @ epred1_0 @ epred2_0 ) )
| ( iequiv @ epred1_0 @ epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_28]) ).
thf(c_0_77,negated_conjecture,
! [X1: $i] : ( epred1_0 @ X1 ),
inference(spm,[status(thm)],[c_0_42,c_0_73]) ).
thf(c_0_78,plain,
! [X1: $i,X9: $i,X6: $i > $o,X5: $i > $o] :
( ( ixor @ X5 @ X6 @ X1 )
| ( X6 @ X9 )
| ~ ( X5 @ esk23_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_32]),c_0_32])]) ).
thf(c_0_79,negated_conjecture,
icountersatisfiable @ ( ixor @ epred1_0 @ epred2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]),c_0_64]) ).
thf(c_0_80,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i,X11: $i] :
( ( ixor @ X5 @ X6 @ X1 )
| ( X6 @ X9 )
| ~ ( X5 @ X11 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_17]) ).
thf(c_0_81,negated_conjecture,
~ ( ixor @ epred1_0 @ epred2_0 @ esk23_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_79]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i,X5: $i > $o,X9: $i] :
( ( ixor @ epred1_0 @ X5 @ X1 )
| ( X5 @ X9 ) ),
inference(spm,[status(thm)],[c_0_80,c_0_77]) ).
thf(c_0_83,negated_conjecture,
! [X1: $i] :
~ ( ixor @ epred1_0 @ epred2_0 @ X1 ),
inference(spm,[status(thm)],[c_0_81,c_0_17]) ).
thf(c_0_84,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_82]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX175^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:10:03 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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/tmp/tmp.euFEaaZfkR/E---3.1_980329.p
% 10.06/2.02 % Version: 3.5.1-ho
% 10.06/2.02 % Preprocessing class: HSMSSMSSSSSNHHN.
% 10.06/2.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.06/2.02 % Starting new_ho_12 with 1200s (4) cores
% 10.06/2.02 % Starting sh3l with 600s (2) cores
% 10.06/2.02 % Starting ehoh_best5_lambda with 300s (1) cores
% 10.06/2.02 % Starting lpo9_lambda_fix with 300s (1) cores
% 10.06/2.02 % sh3l with pid 980357 completed with status 9
% 10.06/2.02 % new_ho_12 with pid 980356 completed with status 0
% 10.06/2.02 % Result found by new_ho_12
% 10.06/2.02 % Preprocessing class: HSMSSMSSSSSNHHN.
% 10.06/2.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.06/2.02 % Starting new_ho_12 with 1200s (4) cores
% 10.06/2.02 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.06/2.02 % No SInE strategy applied
% 10.06/2.02 % Search class: HGHSS-FFMF32-SHHFFMBN
% 10.06/2.02 % partial match(2): HGHNF-FFMF32-SHHFFMBN
% 10.06/2.02 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 10.06/2.02 % Starting SubtermCWHack with 109s (1) cores
% 10.06/2.02 % Starting new_ho_12 with 121s (1) cores
% 10.06/2.02 % Starting ehoh_best_sine_rwall with 181s (1) cores
% 10.06/2.02 % Starting lpo1_def_fix with 181s (1) cores
% 10.06/2.02 % new_ho_12 with pid 980372 completed with status 0
% 10.06/2.02 % Result found by new_ho_12
% 10.06/2.02 % Preprocessing class: HSMSSMSSSSSNHHN.
% 10.06/2.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.06/2.02 % Starting new_ho_12 with 1200s (4) cores
% 10.06/2.02 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.06/2.02 % No SInE strategy applied
% 10.06/2.02 % Search class: HGHSS-FFMF32-SHHFFMBN
% 10.06/2.02 % partial match(2): HGHNF-FFMF32-SHHFFMBN
% 10.06/2.02 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 10.06/2.02 % Starting SubtermCWHack with 109s (1) cores
% 10.06/2.02 % Starting new_ho_12 with 121s (1) cores
% 10.06/2.02 % Preprocessing time : 0.002 s
% 10.06/2.02 % Presaturation interreduction done
% 10.06/2.02
% 10.06/2.02 % Proof found!
% 10.06/2.02 % SZS status Theorem
% 10.06/2.02 % SZS output start CNFRefutation
% See solution above
% 10.06/2.02 % Parsed axioms : 26
% 10.06/2.02 % Removed by relevancy pruning/SinE : 0
% 10.06/2.02 % Initial clauses : 103
% 10.06/2.02 % Removed in clause preprocessing : 24
% 10.06/2.02 % Initial clauses in saturation : 79
% 10.06/2.02 % Processed clauses : 3057
% 10.06/2.02 % ...of these trivial : 316
% 10.06/2.02 % ...subsumed : 849
% 10.06/2.02 % ...remaining for further processing : 1892
% 10.06/2.02 % Other redundant clauses eliminated : 0
% 10.06/2.02 % Clauses deleted for lack of memory : 0
% 10.06/2.02 % Backward-subsumed : 298
% 10.06/2.02 % Backward-rewritten : 29
% 10.06/2.02 % Generated clauses : 236786
% 10.06/2.02 % ...of the previous two non-redundant : 233296
% 10.06/2.02 % ...aggressively subsumed : 0
% 10.06/2.02 % Contextual simplify-reflections : 4
% 10.06/2.02 % Paramodulations : 236648
% 10.06/2.02 % Factorizations : 130
% 10.06/2.02 % NegExts : 1
% 10.06/2.02 % Equation resolutions : 0
% 10.06/2.02 % Disequality decompositions : 0
% 10.06/2.02 % Total rewrite steps : 3316
% 10.06/2.02 % ...of those cached : 2208
% 10.06/2.02 % Propositional unsat checks : 0
% 10.06/2.02 % Propositional check models : 0
% 10.06/2.02 % Propositional check unsatisfiable : 0
% 10.06/2.02 % Propositional clauses : 0
% 10.06/2.02 % Propositional clauses after purity: 0
% 10.06/2.02 % Propositional unsat core size : 0
% 10.06/2.02 % Propositional preprocessing time : 0.000
% 10.06/2.02 % Propositional encoding time : 0.000
% 10.06/2.02 % Propositional solver time : 0.000
% 10.06/2.02 % Success case prop preproc time : 0.000
% 10.06/2.02 % Success case prop encoding time : 0.000
% 10.06/2.02 % Success case prop solver time : 0.000
% 10.06/2.02 % Current number of processed clauses : 1495
% 10.06/2.02 % Positive orientable unit clauses : 702
% 10.06/2.02 % Positive unorientable unit clauses: 2
% 10.06/2.02 % Negative unit clauses : 198
% 10.06/2.02 % Non-unit-clauses : 593
% 10.06/2.02 % Current number of unprocessed clauses: 229744
% 10.06/2.02 % ...number of literals in the above : 464728
% 10.06/2.02 % Current number of archived formulas : 0
% 10.06/2.02 % Current number of archived clauses : 397
% 10.06/2.02 % Clause-clause subsumption calls (NU) : 106011
% 10.06/2.02 % Rec. Clause-clause subsumption calls : 72625
% 10.06/2.02 % Non-unit clause-clause subsumptions : 362
% 10.06/2.02 % Unit Clause-clause subsumption calls : 91819
% 10.06/2.02 % Rewrite failures with RHS unbound : 0
% 10.06/2.02 % BW rewrite match attempts : 3119
% 10.06/2.02 % BW rewrite match successes : 31
% 10.06/2.02 % Condensation attempts : 0
% 10.06/2.02 % Condensation successes : 0
% 10.06/2.02 % Termbank termtop insertions : 2444609
% 10.06/2.02 % Search garbage collected termcells : 2348
% 10.06/2.02
% 10.06/2.02 % -------------------------------------------------
% 10.06/2.02 % User time : 1.618 s
% 10.06/2.02 % System time : 0.104 s
% 10.06/2.02 % Total time : 1.722 s
% 10.06/2.02 % Maximum resident set size: 4200 pages
% 10.06/2.02
% 10.06/2.02 % -------------------------------------------------
% 10.06/2.02 % User time : 6.594 s
% 10.06/2.02 % System time : 0.365 s
% 10.06/2.02 % Total time : 6.959 s
% 10.06/2.02 % Maximum resident set size: 4864 pages
% 10.06/2.02 % E exiting
%------------------------------------------------------------------------------