%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX178^1 : 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 : n026.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 0.19s 0.32s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 70 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 502 ( 39 equ; 0 cnn)
% Maximal formula atoms : 193 ( 7 avg)
% Number of connectives : 2277 ( 294 ~; 334 |; 146 &;1483 @)
% ( 17 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 193 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 54 usr; 4 con; 0-6 aty)
% Number of variables : 380 ( 43 ^; 335 !; 2 ?; 380 :)
% 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_5: ( $i > $o ) > ( $i > $o ) > $i > $i > $i > $i ).
thf(decl_57,type,
esk13_5: ( $i > $o ) > ( $i > $o ) > $i > $i > $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_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_62,type,
esk18_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_63,type,
esk19_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_64,type,
esk20_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_65,type,
esk21_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_66,type,
esk22_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_67,type,
esk23_6: ( $i > $o ) > ( $i > $o ) > $i > $i > $i > $i > $i ).
thf(decl_68,type,
esk24_6: ( $i > $o ) > ( $i > $o ) > $i > $i > $i > $i > $i ).
thf(decl_69,type,
esk25_1: ( $i > $o ) > $i ).
thf(decl_70,type,
esk26_1: ( $i > $o ) > $i ).
thf(decl_71,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_72,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_73,type,
epred1_0: $i > $o ).
thf(decl_74,type,
epred2_0: $i > $o ).
thf(decl_75,type,
esk29_0: $i ).
thf(decl_76,type,
esk3_0: $i ).
thf(lcl696_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] :
( ! [X15: $i] :
( ~ ( irel @ X9 @ X15 )
| ( X10 @ X15 ) )
& ! [X16: $i] :
( ~ ( irel @ X9 @ X16 )
| ( X14 @ X16 ) ) ) ) )
& ( ior
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ! [X17: $i] :
( ~ ( irel @ X9 @ X17 )
| ( X10 @ X17 ) )
| ! [X18: $i] :
( ~ ( irel @ X9 @ X18 )
| ( X14 @ X18 ) ) ) ) )
& ( iimplies
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ~ ! [X19: $i] :
( ~ ( irel @ X9 @ X19 )
| ( X10 @ X19 ) )
| ! [X20: $i] :
( ~ ( irel @ X9 @ X20 )
| ( X14 @ X20 ) ) ) ) )
& ( iimplied
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ~ ! [X21: $i] :
( ~ ( irel @ X9 @ X21 )
| ( X14 @ X21 ) )
| ! [X22: $i] :
( ~ ( irel @ X9 @ X22 )
| ( X10 @ X22 ) ) ) ) )
& ( iequiv
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
( ! [X23: $i,X24: $i] :
( ~ ( irel @ X9 @ X23 )
| ~ ! [X25: $i] :
( ~ ( irel @ X23 @ X25 )
| ( X10 @ X25 ) )
| ~ ( irel @ X23 @ X24 )
| ( X14 @ X24 ) )
& ! [X26: $i,X27: $i] :
( ~ ( irel @ X9 @ X26 )
| ~ ! [X28: $i] :
( ~ ( irel @ X26 @ X28 )
| ( X14 @ X28 ) )
| ~ ( irel @ X26 @ X27 )
| ( X10 @ X27 ) ) ) ) )
& ( ixor
= ( ^ [X10: $i > $o,X14: $i > $o,X9: $i] :
~ ! [X29: $i,X30: $i,X31: $i,X32: $i,X33: $i] :
( ~ ( irel @ X9 @ X29 )
| ( ( ~ ( irel @ X29 @ X30 )
| ~ ! [X25: $i] :
( ~ ( irel @ X30 @ X25 )
| ( X10 @ X25 ) )
| ~ ( irel @ X30 @ X31 )
| ( X14 @ X31 ) )
& ( ~ ( irel @ X29 @ X32 )
| ~ ! [X28: $i] :
( ~ ( irel @ X32 @ X28 )
| ( X14 @ X28 ) )
| ~ ( irel @ X32 @ X33 )
| ( X10 @ X33 ) ) ) ) ) )
& ( ivalid
= ( ^ [X34: $i > $o] :
! [X35: $i] : ( X34 @ X35 ) ) )
& ( isatisfiable
= ( ^ [X34: $i > $o] :
~ ! [X35: $i] :
~ ( X34 @ X35 ) ) )
& ( icountersatisfiable
= ( ^ [X34: $i > $o] :
~ ! [X35: $i] : ( X34 @ X35 ) ) )
& ( iinvalid
= ( ^ [X34: $i > $o] :
! [X35: $i] :
~ ( X34 @ X35 ) ) )
& ( 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.nz7ml2WIjL/E---3.1_797521.p',lcl696_1) ).
thf(iequiv,conjecture,
( iequiv
= ( ^ [X10: $i > $o,X14: $i > $o] : ( iand @ ( iimplies @ X10 @ X14 ) @ ( iimplies @ X14 @ X10 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nz7ml2WIjL/E---3.1_797521.p',iequiv) ).
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 ) )
& ! [X41: $i > $o,X42: $i] :
( ( mnot @ X41 @ X42 )
<=> ~ ( X41 @ X42 ) )
& ! [X43: $i > $o,X44: $i > $o,X45: $i] :
( ( mor @ X43 @ X44 @ X45 )
<=> ( ( X43 @ X45 )
| ( X44 @ X45 ) ) )
& ! [X46: $i > $o,X47: $i > $o,X48: $i] :
( ( mand @ X46 @ X47 @ X48 )
<=> ( ( X46 @ X48 )
& ( X47 @ X48 ) ) )
& ! [X49: $i > $o,X50: $i > $o,X51: $i] :
( ( mimplies @ X49 @ X50 @ X51 )
<=> ( ~ ( X49 @ X51 )
| ( X50 @ X51 ) ) )
& ! [X52: $i > $o,X53: $i] :
( ( mbox_s4 @ X52 @ X53 )
<=> ! [X12: $i] :
( ~ ( irel @ X53 @ X12 )
| ( X52 @ X12 ) ) )
& ! [X54: $i > $o,X55: $i] :
( ( iatom @ X54 @ X55 )
<=> ( X54 @ X55 ) )
& ! [X56: $i > $o,X57: $i] :
( ( inot @ X56 @ X57 )
<=> ~ ! [X13: $i] :
( ~ ( irel @ X57 @ X13 )
| ( X56 @ X13 ) ) )
& ! [X58: $i > $o,X59: $i > $o,X60: $i] :
( ( iand @ X58 @ X59 @ X60 )
<=> ( ! [X15: $i] :
( ~ ( irel @ X60 @ X15 )
| ( X58 @ X15 ) )
& ! [X16: $i] :
( ~ ( irel @ X60 @ X16 )
| ( X59 @ X16 ) ) ) )
& ! [X61: $i > $o,X62: $i > $o,X63: $i] :
( ( ior @ X61 @ X62 @ X63 )
<=> ( ! [X17: $i] :
( ~ ( irel @ X63 @ X17 )
| ( X61 @ X17 ) )
| ! [X18: $i] :
( ~ ( irel @ X63 @ X18 )
| ( X62 @ X18 ) ) ) )
& ! [X64: $i > $o,X65: $i > $o,X66: $i] :
( ( iimplies @ X64 @ X65 @ X66 )
<=> ( ~ ! [X19: $i] :
( ~ ( irel @ X66 @ X19 )
| ( X64 @ X19 ) )
| ! [X20: $i] :
( ~ ( irel @ X66 @ X20 )
| ( X65 @ X20 ) ) ) )
& ! [X67: $i > $o,X68: $i > $o,X69: $i] :
( ( iimplied @ X67 @ X68 @ X69 )
<=> ( ~ ! [X21: $i] :
( ~ ( irel @ X69 @ X21 )
| ( X68 @ X21 ) )
| ! [X22: $i] :
( ~ ( irel @ X69 @ X22 )
| ( X67 @ X22 ) ) ) )
& ! [X70: $i > $o,X71: $i > $o,X72: $i] :
( ( iequiv @ X70 @ X71 @ X72 )
<=> ( ! [X23: $i,X24: $i] :
( ~ ( irel @ X72 @ X23 )
| ~ ! [X25: $i] :
( ~ ( irel @ X23 @ X25 )
| ( X70 @ X25 ) )
| ~ ( irel @ X23 @ X24 )
| ( X71 @ X24 ) )
& ! [X26: $i,X27: $i] :
( ~ ( irel @ X72 @ X26 )
| ~ ! [X28: $i] :
( ~ ( irel @ X26 @ X28 )
| ( X71 @ X28 ) )
| ~ ( irel @ X26 @ X27 )
| ( X70 @ X27 ) ) ) )
& ! [X73: $i > $o,X74: $i > $o,X75: $i] :
( ( ixor @ X73 @ X74 @ X75 )
<=> ~ ! [X29: $i,X30: $i,X31: $i,X32: $i,X33: $i] :
( ~ ( irel @ X75 @ X29 )
| ( ( ~ ( irel @ X29 @ X30 )
| ~ ! [X25: $i] :
( ~ ( irel @ X30 @ X25 )
| ( X73 @ X25 ) )
| ~ ( irel @ X30 @ X31 )
| ( X74 @ X31 ) )
& ( ~ ( irel @ X29 @ X32 )
| ~ ! [X28: $i] :
( ~ ( irel @ X32 @ X28 )
| ( X74 @ X28 ) )
| ~ ( irel @ X32 @ X33 )
| ( X73 @ X33 ) ) ) ) )
& ! [X76: $i > $o] :
( ( ivalid @ X76 )
<=> ! [X35: $i] : ( X76 @ X35 ) )
& ! [X77: $i > $o] :
( ( isatisfiable @ X77 )
<=> ~ ! [X35: $i] :
~ ( X77 @ X35 ) )
& ! [X78: $i > $o] :
( ( icountersatisfiable @ X78 )
<=> ~ ! [X35: $i] : ( X78 @ X35 ) )
& ! [X79: $i > $o] :
( ( iinvalid @ X79 )
<=> ! [X35: $i] :
~ ( X79 @ X35 ) )
& ( 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)],[lcl696_1])])]) ).
thf(c_0_3,negated_conjecture,
( iequiv
!= ( ^ [X10: $i > $o,X14: $i > $o] : ( iand @ ( iimplies @ X10 @ X14 ) @ ( iimplies @ X14 @ X10 ) ) ) ),
inference(assume_negation,[status(cth)],[iequiv]) ).
thf(c_0_4,plain,
! [X82: $i,X84: d_unsorted,X85: d_unsorted,X86: d_unsorted,X87: $i > $o,X88: $i,X89: $i > $o,X90: $i > $o,X91: $i,X92: $i > $o,X93: $i > $o,X94: $i,X95: $i > $o,X96: $i > $o,X97: $i,X98: $i > $o,X99: $i,X100: $i,X101: $i > $o,X102: $i,X104: $i > $o,X105: $i,X106: $i > $o,X107: $i,X109: $i > $o,X110: $i,X111: $i,X112: $i > $o,X113: $i > $o,X114: $i,X115: $i,X116: $i,X117: $i > $o,X118: $i > $o,X119: $i,X122: $i > $o,X123: $i > $o,X124: $i,X125: $i,X126: $i,X127: $i > $o,X128: $i > $o,X129: $i,X132: $i > $o,X133: $i > $o,X134: $i,X136: $i,X137: $i > $o,X138: $i > $o,X139: $i,X140: $i,X142: $i > $o,X143: $i > $o,X144: $i,X146: $i,X147: $i > $o,X148: $i > $o,X149: $i,X150: $i,X152: $i > $o,X153: $i > $o,X154: $i,X155: $i,X156: $i,X158: $i,X159: $i,X161: $i > $o,X162: $i > $o,X163: $i,X166: $i,X169: $i,X170: $i > $o,X171: $i > $o,X172: $i,X176: $i,X179: $i,X180: $i > $o,X181: $i > $o,X182: $i,X183: $i,X184: $i,X185: $i,X187: $i,X188: $i,X190: $i > $o,X191: $i,X192: $i > $o,X194: $i > $o,X196: $i > $o,X197: $i,X198: $i > $o,X200: $i > $o,X201: $i,X202: $i > $o,X203: $i,X204: $i > $o] :
( ( X82
= ( d2unsorted @ ( esk1_1 @ X82 ) ) )
& ( X84 = d_unsorted_0 )
& ( ( ( d2unsorted @ X85 )
!= ( d2unsorted @ X86 ) )
| ( X85 = X86 ) )
& ( ~ ( mnot @ X87 @ X88 )
| ~ ( X87 @ X88 ) )
& ( ( X87 @ X88 )
| ( mnot @ X87 @ X88 ) )
& ( ~ ( mor @ X89 @ X90 @ X91 )
| ( X89 @ X91 )
| ( X90 @ X91 ) )
& ( ~ ( X89 @ X91 )
| ( mor @ X89 @ X90 @ X91 ) )
& ( ~ ( X90 @ X91 )
| ( mor @ X89 @ X90 @ X91 ) )
& ( ( X92 @ X94 )
| ~ ( mand @ X92 @ X93 @ X94 ) )
& ( ( X93 @ X94 )
| ~ ( mand @ X92 @ X93 @ X94 ) )
& ( ~ ( X92 @ X94 )
| ~ ( X93 @ X94 )
| ( mand @ X92 @ X93 @ X94 ) )
& ( ~ ( mimplies @ X95 @ X96 @ X97 )
| ~ ( X95 @ X97 )
| ( X96 @ X97 ) )
& ( ( X95 @ X97 )
| ( mimplies @ X95 @ X96 @ X97 ) )
& ( ~ ( X96 @ X97 )
| ( mimplies @ X95 @ X96 @ X97 ) )
& ( ~ ( mbox_s4 @ X98 @ X99 )
| ~ ( irel @ X99 @ X100 )
| ( X98 @ X100 ) )
& ( ( irel @ X102 @ ( esk2_2 @ X101 @ X102 ) )
| ( mbox_s4 @ X101 @ X102 ) )
& ( ~ ( X101 @ ( esk2_2 @ X101 @ X102 ) )
| ( mbox_s4 @ X101 @ X102 ) )
& ( ~ ( iatom @ X104 @ X105 )
| ( X104 @ X105 ) )
& ( ~ ( X104 @ X105 )
| ( iatom @ X104 @ X105 ) )
& ( ( irel @ X107 @ ( esk3_2 @ X106 @ X107 ) )
| ~ ( inot @ X106 @ X107 ) )
& ( ~ ( X106 @ ( esk3_2 @ X106 @ X107 ) )
| ~ ( inot @ X106 @ X107 ) )
& ( ~ ( irel @ X110 @ X111 )
| ( X109 @ X111 )
| ( inot @ X109 @ X110 ) )
& ( ~ ( irel @ X114 @ X115 )
| ( X112 @ X115 )
| ~ ( iand @ X112 @ X113 @ X114 ) )
& ( ~ ( irel @ X114 @ X116 )
| ( X113 @ X116 )
| ~ ( iand @ X112 @ X113 @ X114 ) )
& ( ( irel @ X119 @ ( esk5_3 @ X117 @ X118 @ X119 ) )
| ( irel @ X119 @ ( esk4_3 @ X117 @ X118 @ X119 ) )
| ( iand @ X117 @ X118 @ X119 ) )
& ( ~ ( X118 @ ( esk5_3 @ X117 @ X118 @ X119 ) )
| ( irel @ X119 @ ( esk4_3 @ X117 @ X118 @ X119 ) )
| ( iand @ X117 @ X118 @ X119 ) )
& ( ( irel @ X119 @ ( esk5_3 @ X117 @ X118 @ X119 ) )
| ~ ( X117 @ ( esk4_3 @ X117 @ X118 @ X119 ) )
| ( iand @ X117 @ X118 @ X119 ) )
& ( ~ ( X118 @ ( esk5_3 @ X117 @ X118 @ X119 ) )
| ~ ( X117 @ ( esk4_3 @ X117 @ X118 @ X119 ) )
| ( iand @ X117 @ X118 @ X119 ) )
& ( ~ ( ior @ X122 @ X123 @ X124 )
| ~ ( irel @ X124 @ X125 )
| ( X122 @ X125 )
| ~ ( irel @ X124 @ X126 )
| ( X123 @ X126 ) )
& ( ( irel @ X129 @ ( esk6_3 @ X127 @ X128 @ X129 ) )
| ( ior @ X127 @ X128 @ X129 ) )
& ( ~ ( X127 @ ( esk6_3 @ X127 @ X128 @ X129 ) )
| ( ior @ X127 @ X128 @ X129 ) )
& ( ( irel @ X129 @ ( esk7_3 @ X127 @ X128 @ X129 ) )
| ( ior @ X127 @ X128 @ X129 ) )
& ( ~ ( X128 @ ( esk7_3 @ X127 @ X128 @ X129 ) )
| ( ior @ X127 @ X128 @ X129 ) )
& ( ( irel @ X134 @ ( esk8_3 @ X132 @ X133 @ X134 ) )
| ~ ( irel @ X134 @ X136 )
| ( X133 @ X136 )
| ~ ( iimplies @ X132 @ X133 @ X134 ) )
& ( ~ ( X132 @ ( esk8_3 @ X132 @ X133 @ X134 ) )
| ~ ( irel @ X134 @ X136 )
| ( X133 @ X136 )
| ~ ( iimplies @ X132 @ X133 @ X134 ) )
& ( ~ ( irel @ X139 @ X140 )
| ( X137 @ X140 )
| ( iimplies @ X137 @ X138 @ X139 ) )
& ( ( irel @ X139 @ ( esk9_3 @ X137 @ X138 @ X139 ) )
| ( iimplies @ X137 @ X138 @ X139 ) )
& ( ~ ( X138 @ ( esk9_3 @ X137 @ X138 @ X139 ) )
| ( iimplies @ X137 @ X138 @ X139 ) )
& ( ( irel @ X144 @ ( esk10_3 @ X142 @ X143 @ X144 ) )
| ~ ( irel @ X144 @ X146 )
| ( X142 @ X146 )
| ~ ( iimplied @ X142 @ X143 @ X144 ) )
& ( ~ ( X143 @ ( esk10_3 @ X142 @ X143 @ X144 ) )
| ~ ( irel @ X144 @ X146 )
| ( X142 @ X146 )
| ~ ( iimplied @ X142 @ X143 @ X144 ) )
& ( ~ ( irel @ X149 @ X150 )
| ( X148 @ X150 )
| ( iimplied @ X147 @ X148 @ X149 ) )
& ( ( irel @ X149 @ ( esk11_3 @ X147 @ X148 @ X149 ) )
| ( iimplied @ X147 @ X148 @ X149 ) )
& ( ~ ( X147 @ ( esk11_3 @ X147 @ X148 @ X149 ) )
| ( iimplied @ X147 @ X148 @ X149 ) )
& ( ( irel @ X155 @ ( esk12_5 @ X152 @ X153 @ X154 @ X155 @ X156 ) )
| ~ ( irel @ X154 @ X155 )
| ~ ( irel @ X155 @ X156 )
| ( X153 @ X156 )
| ~ ( iequiv @ X152 @ X153 @ X154 ) )
& ( ~ ( X152 @ ( esk12_5 @ X152 @ X153 @ X154 @ X155 @ X156 ) )
| ~ ( irel @ X154 @ X155 )
| ~ ( irel @ X155 @ X156 )
| ( X153 @ X156 )
| ~ ( iequiv @ X152 @ X153 @ X154 ) )
& ( ( irel @ X158 @ ( esk13_5 @ X152 @ X153 @ X154 @ X158 @ X159 ) )
| ~ ( irel @ X154 @ X158 )
| ~ ( irel @ X158 @ X159 )
| ( X152 @ X159 )
| ~ ( iequiv @ X152 @ X153 @ X154 ) )
& ( ~ ( X153 @ ( esk13_5 @ X152 @ X153 @ X154 @ X158 @ X159 ) )
| ~ ( irel @ X154 @ X158 )
| ~ ( irel @ X158 @ X159 )
| ( X152 @ X159 )
| ~ ( iequiv @ X152 @ X153 @ X154 ) )
& ( ( irel @ X163 @ ( esk16_3 @ X161 @ X162 @ X163 ) )
| ( irel @ X163 @ ( esk14_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ X169 )
| ( X162 @ X169 )
| ( irel @ X163 @ ( esk14_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ( irel @ X163 @ ( esk14_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( X161 @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ( irel @ X163 @ ( esk14_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ X163 @ ( esk16_3 @ X161 @ X162 @ X163 ) )
| ~ ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ X166 )
| ( X161 @ X166 )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ X169 )
| ( X162 @ X169 )
| ~ ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ X166 )
| ( X161 @ X166 )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ~ ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ X166 )
| ( X161 @ X166 )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( X161 @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ~ ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ X166 )
| ( X161 @ X166 )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ X163 @ ( esk16_3 @ X161 @ X162 @ X163 ) )
| ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ X169 )
| ( X162 @ X169 )
| ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( X161 @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ( irel @ ( esk14_3 @ X161 @ X162 @ X163 ) @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ X163 @ ( esk16_3 @ X161 @ X162 @ X163 ) )
| ~ ( X162 @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ X169 )
| ( X162 @ X169 )
| ~ ( X162 @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ ( esk16_3 @ X161 @ X162 @ X163 ) @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ~ ( X162 @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ~ ( X161 @ ( esk17_3 @ X161 @ X162 @ X163 ) )
| ~ ( X162 @ ( esk15_3 @ X161 @ X162 @ X163 ) )
| ( iequiv @ X161 @ X162 @ X163 ) )
& ( ( irel @ X172 @ ( esk18_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk21_3 @ X170 @ X171 @ X172 ) )
| ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk19_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ X179 )
| ( X171 @ X179 )
| ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk19_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk19_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( X170 @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk19_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk21_3 @ X170 @ X171 @ X172 ) )
| ~ ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ X176 )
| ( X170 @ X176 )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ X179 )
| ( X171 @ X179 )
| ~ ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ X176 )
| ( X170 @ X176 )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ~ ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ X176 )
| ( X170 @ X176 )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( X170 @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ~ ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ X176 )
| ( X170 @ X176 )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk21_3 @ X170 @ X171 @ X172 ) )
| ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ X179 )
| ( X171 @ X179 )
| ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( X170 @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ( irel @ ( esk19_3 @ X170 @ X171 @ X172 ) @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk18_3 @ X170 @ X171 @ X172 ) @ ( esk21_3 @ X170 @ X171 @ X172 ) )
| ~ ( X171 @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ X179 )
| ( X171 @ X179 )
| ~ ( X171 @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ ( esk21_3 @ X170 @ X171 @ X172 ) @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ~ ( X171 @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ~ ( X170 @ ( esk22_3 @ X170 @ X171 @ X172 ) )
| ~ ( X171 @ ( esk20_3 @ X170 @ X171 @ X172 ) )
| ~ ( ixor @ X170 @ X171 @ X172 ) )
& ( ( irel @ X184 @ ( esk23_6 @ X180 @ X181 @ X182 @ X183 @ X184 @ X185 ) )
| ~ ( irel @ X183 @ X184 )
| ~ ( irel @ X184 @ X185 )
| ( X181 @ X185 )
| ~ ( irel @ X182 @ X183 )
| ( ixor @ X180 @ X181 @ X182 ) )
& ( ~ ( X180 @ ( esk23_6 @ X180 @ X181 @ X182 @ X183 @ X184 @ X185 ) )
| ~ ( irel @ X183 @ X184 )
| ~ ( irel @ X184 @ X185 )
| ( X181 @ X185 )
| ~ ( irel @ X182 @ X183 )
| ( ixor @ X180 @ X181 @ X182 ) )
& ( ( irel @ X187 @ ( esk24_6 @ X180 @ X181 @ X182 @ X183 @ X187 @ X188 ) )
| ~ ( irel @ X183 @ X187 )
| ~ ( irel @ X187 @ X188 )
| ( X180 @ X188 )
| ~ ( irel @ X182 @ X183 )
| ( ixor @ X180 @ X181 @ X182 ) )
& ( ~ ( X181 @ ( esk24_6 @ X180 @ X181 @ X182 @ X183 @ X187 @ X188 ) )
| ~ ( irel @ X183 @ X187 )
| ~ ( irel @ X187 @ X188 )
| ( X180 @ X188 )
| ~ ( irel @ X182 @ X183 )
| ( ixor @ X180 @ X181 @ X182 ) )
& ( ~ ( ivalid @ X190 )
| ( X190 @ X191 ) )
& ( ~ ( X192 @ ( esk25_1 @ X192 ) )
| ( ivalid @ X192 ) )
& ( ~ ( isatisfiable @ X194 )
| ( X194 @ ( esk26_1 @ X194 ) ) )
& ( ~ ( X196 @ X197 )
| ( isatisfiable @ X196 ) )
& ( ~ ( icountersatisfiable @ X198 )
| ~ ( X198 @ ( esk27_1 @ X198 ) ) )
& ( ( X200 @ X201 )
| ( icountersatisfiable @ X200 ) )
& ( ~ ( iinvalid @ X202 )
| ~ ( X202 @ X203 ) )
& ( ( X204 @ ( esk28_1 @ X204 ) )
| ( iinvalid @ X204 ) )
& ( 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_5,negated_conjecture,
~ ! [X80: $i > $o,X81: $i > $o] :
( ( iequiv @ X80 @ X81 )
= ( iand @ ( iimplies @ X80 @ X81 ) @ ( iimplies @ X81 @ X80 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3])]) ).
thf(c_0_6,plain,
! [X1: $i] :
( X1
= ( d2unsorted @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X2: d_unsorted] : ( X2 = d_unsorted_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,negated_conjecture,
( ( iequiv @ epred1_0 @ epred2_0 )
!= ( iand @ ( iimplies @ epred1_0 @ epred2_0 ) @ ( iimplies @ epred2_0 @ epred1_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_9,plain,
! [X1: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X1 ),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ( iequiv @ epred1_0 @ epred2_0 )
!= ( iand @ ( iimplies @ epred1_0 @ epred2_0 ) @ ( iimplies @ epred2_0 @ epred1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X5: $i > $o] :
( ( X5 @ ( esk28_1 @ X5 ) )
| ( iinvalid @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_12,plain,
irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_13,plain,
! [X1: $i] : ( esk29_0 = X1 ),
inference(rw,[status(thm)],[c_0_9,c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( iand @ ( iimplies @ epred1_0 @ epred2_0 ) @ ( iimplies @ epred2_0 @ epred1_0 ) @ esk3_0 )
<~> ( iequiv @ epred1_0 @ epred2_0 @ esk3_0 ) ),
inference(neg_ext,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X5: $i > $o,X1: $i] :
( ~ ( iinvalid @ X5 )
| ~ ( X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_16,plain,
! [X5: $i > $o] :
( ( X5 @ esk29_0 )
| ( iinvalid @ X5 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_9]),c_0_9]) ).
thf(c_0_17,plain,
irel @ esk29_0 @ esk29_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_9]),c_0_9]) ).
thf(c_0_18,plain,
! [X1: $i,X9: $i] : ( X1 = X9 ),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
thf(c_0_19,negated_conjecture,
( ~ ( iand @ ( iimplies @ epred1_0 @ epred2_0 ) @ ( iimplies @ epred2_0 @ epred1_0 ) @ esk3_0 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ esk3_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i] :
( ( iand @ X6 @ X5 @ X1 )
| ~ ( X5 @ ( esk5_3 @ X6 @ X5 @ X1 ) )
| ~ ( X6 @ ( esk4_3 @ X6 @ X5 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_21,plain,
! [X5: $i > $o,X1: $i] :
( ( X5 @ esk29_0 )
| ~ ( X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_22,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i] :
( ~ ( iand @ ( iimplies @ epred1_0 @ epred2_0 ) @ ( iimplies @ epred2_0 @ epred1_0 ) @ X1 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
thf(c_0_24,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o] :
( ( iand @ X5 @ X6 @ X1 )
| ~ ( X5 @ esk29_0 )
| ~ ( X6 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_9]),c_0_9]),c_0_9]),c_0_9]) ).
thf(c_0_25,plain,
! [X1: $i] : ( irel @ X1 @ esk29_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ~ ( iimplies @ epred1_0 @ epred2_0 @ esk29_0 )
| ~ ( iimplies @ epred2_0 @ epred1_0 @ esk29_0 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_27,plain,
! [X1: $i,X6: $i > $o,X5: $i > $o,X9: $i] :
( ( X5 @ X9 )
| ( iimplies @ X5 @ X6 @ X1 )
| ~ ( irel @ X1 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_28,plain,
! [X1: $i,X9: $i] : ( irel @ X1 @ X9 ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
thf(c_0_29,plain,
! [X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X6 @ X9 )
| ~ ( X5 @ ( esk8_3 @ X5 @ X6 @ X1 ) )
| ~ ( irel @ X1 @ X9 )
| ~ ( iimplies @ X5 @ X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_30,plain,
! [X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X5 @ X9 )
| ~ ( irel @ X1 @ X9 )
| ~ ( iand @ X6 @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X9: $i] :
( ~ ( iimplies @ epred1_0 @ epred2_0 @ X1 )
| ~ ( iimplies @ epred2_0 @ epred1_0 @ X1 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ X9 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
thf(c_0_32,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i] :
( ( iimplies @ X5 @ X6 @ X1 )
| ( X5 @ X9 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_33,plain,
! [X1: $i,X6: $i > $o,X9: $i,X5: $i > $o,X11: $i] :
( ( X6 @ X9 )
| ( X5 @ X11 )
| ( iequiv @ X5 @ X6 @ X1 )
| ~ ( irel @ ( esk16_3 @ X5 @ X6 @ X1 ) @ X9 )
| ~ ( irel @ ( esk14_3 @ X5 @ X6 @ X1 ) @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_34,plain,
! [X5: $i > $o] :
( ~ ( icountersatisfiable @ X5 )
| ~ ( X5 @ ( esk27_1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_35,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i] :
( ( iimplies @ X6 @ X5 @ X1 )
| ~ ( X5 @ ( esk9_3 @ X6 @ X5 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_36,plain,
! [X11: $i,X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X6 @ X11 )
| ~ ( X5 @ ( esk12_5 @ X5 @ X6 @ X1 @ X9 @ X11 ) )
| ~ ( irel @ X1 @ X9 )
| ~ ( irel @ X9 @ X11 )
| ~ ( iequiv @ X5 @ X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_37,plain,
! [X11: $i,X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X6 @ X11 )
| ~ ( X5 @ ( esk13_5 @ X6 @ X5 @ X1 @ X9 @ X11 ) )
| ~ ( irel @ X1 @ X9 )
| ~ ( irel @ X9 @ X11 )
| ~ ( iequiv @ X6 @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_38,plain,
! [X5: $i > $o,X1: $i,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iimplies @ X6 @ X5 @ X9 )
| ~ ( irel @ X9 @ X1 )
| ~ ( X6 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_9]),c_0_9]) ).
thf(c_0_39,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i] :
( ( X5 @ X1 )
| ~ ( iand @ X6 @ X5 @ X9 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28])]) ).
thf(c_0_40,negated_conjecture,
( ( iand @ ( iimplies @ epred1_0 @ epred2_0 ) @ ( iimplies @ epred2_0 @ epred1_0 ) @ esk3_0 )
| ( iequiv @ epred1_0 @ epred2_0 @ esk3_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_14]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X9: $i,X11: $i] :
( ( epred2_0 @ X1 )
| ~ ( iimplies @ epred1_0 @ epred2_0 @ X9 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ X11 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_42,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i,X11: $i] :
( ( iequiv @ X5 @ X6 @ X1 )
| ( X6 @ X9 )
| ( X5 @ X11 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_18]),c_0_28]),c_0_18]),c_0_28])]) ).
thf(c_0_43,plain,
! [X5: $i > $o] :
( ~ ( icountersatisfiable @ X5 )
| ~ ( X5 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_9]),c_0_9]) ).
thf(c_0_44,plain,
! [X1: $i,X5: $i > $o] :
( ( X5 @ X1 )
| ( icountersatisfiable @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_45,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o] :
( ( iimplies @ X5 @ X6 @ X1 )
| ~ ( X6 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_9]),c_0_9]) ).
thf(c_0_46,plain,
! [X1: $i,X5: $i > $o,X11: $i,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X6 @ X5 @ X9 )
| ~ ( irel @ X11 @ X1 )
| ~ ( irel @ X9 @ X11 )
| ~ ( X6 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_9]),c_0_9]) ).
thf(c_0_47,plain,
! [X1: $i,X5: $i > $o,X11: $i,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X5 @ X6 @ X9 )
| ~ ( irel @ X11 @ X1 )
| ~ ( irel @ X9 @ X11 )
| ~ ( X6 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_9]),c_0_9]) ).
thf(c_0_48,plain,
! [X1: $i,X5: $i > $o,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iimplies @ X6 @ X5 @ X9 )
| ~ ( X6 @ esk29_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_28])]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i] :
( ( iequiv @ epred1_0 @ epred2_0 @ esk3_0 )
| ( iimplies @ epred2_0 @ epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X9: $i] :
( ( epred1_0 @ X1 )
| ( epred2_0 @ X9 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_32]),c_0_42]) ).
thf(c_0_51,plain,
! [X1: $i,X5: $i > $o] :
( ( X5 @ X1 )
| ~ ( X5 @ esk29_0 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i] :
( ~ ( iimplies @ epred1_0 @ epred2_0 @ esk29_0 )
| ~ ( iequiv @ epred1_0 @ epred2_0 @ X1 )
| ~ ( epred1_0 @ esk29_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
thf(c_0_53,plain,
! [X1: $i,X5: $i > $o,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X6 @ X5 @ X9 )
| ~ ( X6 @ esk29_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_28]),c_0_28])]) ).
thf(c_0_54,plain,
! [X6: $i > $o,X5: $i > $o,X1: $i] :
( ( iequiv @ X5 @ X6 @ X1 )
| ~ ( X5 @ ( esk17_3 @ X5 @ X6 @ X1 ) )
| ~ ( X6 @ ( esk15_3 @ X5 @ X6 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_55,plain,
! [X9: $i,X6: $i > $o,X5: $i > $o,X1: $i] :
( ( X5 @ X9 )
| ~ ( irel @ X1 @ X9 )
| ~ ( iand @ X5 @ X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_56,plain,
! [X1: $i,X5: $i > $o,X9: $i,X6: $i > $o] :
( ( X5 @ X1 )
| ~ ( iequiv @ X5 @ X6 @ X9 )
| ~ ( X6 @ esk29_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_28]),c_0_28])]) ).
thf(c_0_57,negated_conjecture,
! [X1: $i] :
( ( iequiv @ epred1_0 @ epred2_0 @ esk3_0 )
| ( epred1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
thf(c_0_58,plain,
! [X1: $i,X5: $i > $o,X9: $i] :
( ( X5 @ X1 )
| ~ ( X5 @ X9 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
thf(c_0_59,negated_conjecture,
! [X1: $i] :
( ~ ( iequiv @ epred1_0 @ epred2_0 @ X1 )
| ~ ( epred1_0 @ esk29_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_45]),c_0_53]) ).
thf(c_0_60,plain,
! [X1: $i,X6: $i > $o,X5: $i > $o] :
( ( iequiv @ X5 @ X6 @ X1 )
| ~ ( X6 @ esk29_0 )
| ~ ( X5 @ esk29_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_9]),c_0_9]),c_0_9]),c_0_9]) ).
thf(c_0_61,plain,
! [X1: $i,X5: $i > $o,X6: $i > $o,X9: $i] :
( ( X5 @ X1 )
| ~ ( iand @ X5 @ X6 @ X9 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_28])]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i] : ( epred1_0 @ X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_50]),c_0_58]) ).
thf(c_0_63,negated_conjecture,
( ~ ( epred1_0 @ esk29_0 )
| ~ ( epred2_0 @ esk29_0 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_64,negated_conjecture,
! [X1: $i] :
( ( iequiv @ epred1_0 @ epred2_0 @ esk3_0 )
| ( iimplies @ epred1_0 @ epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_40]) ).
thf(c_0_65,negated_conjecture,
! [X1: $i] :
~ ( iequiv @ epred1_0 @ epred2_0 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_62])]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_18]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i] : ( iimplies @ epred1_0 @ epred2_0 @ X1 ),
inference(sr,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i] :
~ ( epred2_0 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_62])]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_67]),c_0_62])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX178^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n026.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:12:57 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.nz7ml2WIjL/E---3.1_797521.p
% 0.19/0.32 % Version: 3.5.1-ho
% 0.19/0.32 % Preprocessing class: HSMSSMSSSSSNHHN.
% 0.19/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.32 % Starting new_ho_12 with 1200s (4) cores
% 0.19/0.32 % Starting sh3l with 600s (2) cores
% 0.19/0.32 % Starting ehoh_best5_lambda with 300s (1) cores
% 0.19/0.32 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.19/0.32 % sh3l with pid 797555 completed with status 9
% 0.19/0.32 % new_ho_12 with pid 797554 completed with status 0
% 0.19/0.32 % Result found by new_ho_12
% 0.19/0.32 % Preprocessing class: HSMSSMSSSSSNHHN.
% 0.19/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.32 % Starting new_ho_12 with 1200s (4) cores
% 0.19/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.32 % No SInE strategy applied
% 0.19/0.32 % Search class: HGHSS-FFMF32-SHHFFMBN
% 0.19/0.32 % partial match(2): HGHNF-FFMF32-SHHFFMBN
% 0.19/0.32 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.19/0.32 % Starting SubtermCWHack with 109s (1) cores
% 0.19/0.32 % Starting new_ho_12 with 121s (1) cores
% 0.19/0.32 % Starting ehoh_best_sine_rwall with 181s (1) cores
% 0.19/0.32 % Starting lpo1_def_fix with 181s (1) cores
% 0.19/0.32 % new_ho_12 with pid 797569 completed with status 0
% 0.19/0.32 % Result found by new_ho_12
% 0.19/0.32 % Preprocessing class: HSMSSMSSSSSNHHN.
% 0.19/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.32 % Starting new_ho_12 with 1200s (4) cores
% 0.19/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.32 % No SInE strategy applied
% 0.19/0.32 % Search class: HGHSS-FFMF32-SHHFFMBN
% 0.19/0.32 % partial match(2): HGHNF-FFMF32-SHHFFMBN
% 0.19/0.32 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.19/0.32 % Starting SubtermCWHack with 109s (1) cores
% 0.19/0.32 % Starting new_ho_12 with 121s (1) cores
% 0.19/0.32 % Preprocessing time : 0.003 s
% 0.19/0.32 % Presaturation interreduction done
% 0.19/0.32
% 0.19/0.32 % Proof found!
% 0.19/0.32 % SZS status Theorem
% 0.19/0.32 % SZS output start CNFRefutation
% See solution above
% 0.19/0.33 % Parsed axioms : 26
% 0.19/0.33 % Removed by relevancy pruning/SinE : 0
% 0.19/0.33 % Initial clauses : 120
% 0.19/0.33 % Removed in clause preprocessing : 24
% 0.19/0.33 % Initial clauses in saturation : 96
% 0.19/0.33 % Processed clauses : 493
% 0.19/0.33 % ...of these trivial : 38
% 0.19/0.33 % ...subsumed : 112
% 0.19/0.33 % ...remaining for further processing : 343
% 0.19/0.33 % Other redundant clauses eliminated : 0
% 0.19/0.33 % Clauses deleted for lack of memory : 0
% 0.19/0.33 % Backward-subsumed : 49
% 0.19/0.33 % Backward-rewritten : 32
% 0.19/0.33 % Generated clauses : 2686
% 0.19/0.33 % ...of the previous two non-redundant : 2560
% 0.19/0.33 % ...aggressively subsumed : 0
% 0.19/0.33 % Contextual simplify-reflections : 6
% 0.19/0.33 % Paramodulations : 2675
% 0.19/0.33 % Factorizations : 2
% 0.19/0.33 % NegExts : 1
% 0.19/0.33 % Equation resolutions : 0
% 0.19/0.33 % Disequality decompositions : 0
% 0.19/0.33 % Total rewrite steps : 449
% 0.19/0.33 % ...of those cached : 311
% 0.19/0.33 % Propositional unsat checks : 0
% 0.19/0.33 % Propositional check models : 0
% 0.19/0.33 % Propositional check unsatisfiable : 0
% 0.19/0.33 % Propositional clauses : 0
% 0.19/0.33 % Propositional clauses after purity: 0
% 0.19/0.33 % Propositional unsat core size : 0
% 0.19/0.33 % Propositional preprocessing time : 0.000
% 0.19/0.33 % Propositional encoding time : 0.000
% 0.19/0.33 % Propositional solver time : 0.000
% 0.19/0.33 % Success case prop preproc time : 0.000
% 0.19/0.33 % Success case prop encoding time : 0.000
% 0.19/0.33 % Success case prop solver time : 0.000
% 0.19/0.33 % Current number of processed clauses : 167
% 0.19/0.33 % Positive orientable unit clauses : 59
% 0.19/0.33 % Positive unorientable unit clauses: 2
% 0.19/0.33 % Negative unit clauses : 14
% 0.19/0.33 % Non-unit-clauses : 92
% 0.19/0.33 % Current number of unprocessed clauses: 2163
% 0.19/0.33 % ...number of literals in the above : 4303
% 0.19/0.33 % Current number of archived formulas : 0
% 0.19/0.33 % Current number of archived clauses : 176
% 0.19/0.33 % Clause-clause subsumption calls (NU) : 10206
% 0.19/0.33 % Rec. Clause-clause subsumption calls : 7832
% 0.19/0.33 % Non-unit clause-clause subsumptions : 118
% 0.19/0.33 % Unit Clause-clause subsumption calls : 1032
% 0.19/0.33 % Rewrite failures with RHS unbound : 0
% 0.19/0.33 % BW rewrite match attempts : 134
% 0.19/0.33 % BW rewrite match successes : 26
% 0.19/0.33 % Condensation attempts : 0
% 0.19/0.33 % Condensation successes : 0
% 0.19/0.33 % Termbank termtop insertions : 35613
% 0.19/0.33 % Search garbage collected termcells : 2701
% 0.19/0.33
% 0.19/0.33 % -------------------------------------------------
% 0.19/0.33 % User time : 0.066 s
% 0.19/0.33 % System time : 0.010 s
% 0.19/0.33 % Total time : 0.076 s
% 0.19/0.33 % Maximum resident set size: 4208 pages
% 0.19/0.33
% 0.19/0.33 % -------------------------------------------------
% 0.19/0.33 % User time : 0.267 s
% 0.19/0.33 % System time : 0.050 s
% 0.19/0.33 % Total time : 0.317 s
% 0.19/0.33 % Maximum resident set size: 4864 pages
% 0.19/0.33 % E exiting
%------------------------------------------------------------------------------