%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP003^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:03:57 AM UTC 2026
% Result : Theorem 0.19s 0.33s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 75 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 864 ( 76 ~; 65 |; 43 &; 664 @)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 9 con; 0-3 aty)
% Number of variables : 112 ( 0 ^; 109 !; 3 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
d: $tType ).
thf(decl_sort2,type,
u: $tType ).
thf(decl_sort3,type,
du: $tType ).
thf(decl_sort4,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(decl_23,type,
tyop_2Emin_2Ebool: d ).
thf(decl_25,type,
tyop_2Enum_2Enum: d ).
thf(decl_26,type,
s: d > u > du ).
thf(decl_53,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(decl_79,type,
mono_2Ec_2Earithmetic_2E_2A: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_80,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_82,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(decl_83,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(decl_85,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_86,type,
mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_88,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_89,type,
mono_2Ec_2Earithmetic_2EEVEN: mono_2Etyop_2Enum_2Enum > $o ).
thf(decl_90,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(decl_91,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_92,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_93,type,
mono_2Ec_2Earithmetic_2EODD: mono_2Etyop_2Enum_2Enum > $o ).
thf(decl_94,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_95,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(decl_96,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(decl_99,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(decl_108,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(decl_118,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(decl_119,type,
esk1_0: mono_2Etyop_2Enum_2Enum ).
thf(decl_120,type,
esk2_1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(decl_121,type,
esk3_1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(thm_2Earithmetic_2EMOD__UNIQUE,axiom,
! [X56: mono_2Etyop_2Enum_2Enum,X58: mono_2Etyop_2Enum_2Enum,X59: mono_2Etyop_2Enum_2Enum] :
( ? [X60: mono_2Etyop_2Enum_2Enum] :
( ( X58
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ X60 @ X56 ) @ X59 ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ X59 @ X56 ) )
=> ( ( mono_2Ec_2Earithmetic_2EMOD @ X58 @ X56 )
= X59 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EMOD__UNIQUE) ).
thf(thm_2Earithmetic_2EADD1,axiom,
! [X54: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ X54 )
= ( mono_2Ec_2Earithmetic_2E_2B @ X54 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EADD1) ).
thf(thm_2Earithmetic_2EMOD__2,conjecture,
! [X56: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ X56 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ X56 ) @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EMOD__2) ).
thf(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X1: d,X64: u,X65: u] :
( ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X1 @ X64 ) @ ( s @ X1 @ X65 ) ) )
= ( s @ X1 @ X64 ) )
& ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X64 ) @ ( s @ X1 @ X65 ) ) )
= ( s @ X1 @ X65 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(thm_2Ebool_2EAND__CLAUSES,axiom,
! [X61: $o] :
( ( ( mono_2Ec_2Ebool_2ET
& X61 )
<=> X61 )
& ( ( X61
& mono_2Ec_2Ebool_2ET )
<=> X61 )
& ( ( mono_2Ec_2Ebool_2EF
& X61 )
<=> mono_2Ec_2Ebool_2EF )
& ( ( X61
& mono_2Ec_2Ebool_2EF )
<=> mono_2Ec_2Ebool_2EF )
& ( ( X61
& X61 )
<=> X61 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(thm_2Earithmetic_2EONE,axiom,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) )
= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EONE) ).
thf(thm_2Earithmetic_2EODD__EXISTS,axiom,
! [X56: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ X56 )
<=> ? [X57: mono_2Etyop_2Enum_2Enum] :
( X56
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X57 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EODD__EXISTS) ).
thf(thm_2Earithmetic_2EMULT__COMM,axiom,
! [X54: mono_2Etyop_2Enum_2Enum,X55: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ X54 @ X55 )
= ( mono_2Ec_2Earithmetic_2E_2A @ X55 @ X54 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EMULT__COMM) ).
thf(thm_2Earithmetic_2EADD__0,axiom,
! [X54: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ X54 @ mono_2Ec_2Enum_2E0 )
= X54 ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EADD__0) ).
thf(thm_2Earithmetic_2EEVEN__EXISTS,axiom,
! [X56: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ X56 )
<=> ? [X57: mono_2Etyop_2Enum_2Enum] :
( X56
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X57 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EEVEN__EXISTS) ).
thf(thm_2Eprim__rec_2ELESS__0,axiom,
! [X56: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ X56 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Eprim__rec_2ELESS__0) ).
thf(thm_2Earithmetic_2ETWO,axiom,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2ETWO) ).
thf(thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
! [X54: mono_2Etyop_2Enum_2Enum,X55: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ X54 ) @ ( mono_2Ec_2Enum_2ESUC @ X55 ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ X54 @ X55 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2ELESS__MONO__EQ) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [X61: $o] :
( mono_2Ec_2Ebool_2EF
=> X61 ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Ebool_2EFALSITY) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X9: $o,X40: mono_2Etyop_2Enum_2Enum,X41: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ X9 @ X40 @ X41 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X9 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X40 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X41 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) ).
thf(thm_2Earithmetic_2EEVEN__ODD,axiom,
! [X56: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ X56 )
<=> ~ ( mono_2Ec_2Earithmetic_2EODD @ X56 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',thm_2Earithmetic_2EEVEN__ODD) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X22 ) ) )
= X22 ),
file('/export/starexec/sandbox2/tmp/tmp.VOmq8sh4vQ/E---3.1_512153.p',ji_2Emono_2Etyop_2Enum_2Enum) ).
thf(c_0_17,plain,
! [X272: mono_2Etyop_2Enum_2Enum,X273: mono_2Etyop_2Enum_2Enum,X274: mono_2Etyop_2Enum_2Enum,X275: mono_2Etyop_2Enum_2Enum] :
( ( X273
!= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ X275 @ X272 ) @ X274 ) )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X274 @ X272 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ X273 @ X272 )
= X274 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EMOD__UNIQUE])])])]) ).
thf(c_0_18,plain,
! [X259: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ X259 )
= ( mono_2Ec_2Earithmetic_2E_2B @ X259 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD1]) ).
thf(c_0_19,negated_conjecture,
~ ! [X56: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD @ X56 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EEVEN @ X56 ) @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
inference(assume_negation,[status(cth)],[thm_2Earithmetic_2EMOD__2]) ).
thf(c_0_20,axiom,
! [X1: d,X64: u,X65: u] :
( ( ~ mono_2Ec_2Ebool_2ET
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X64 ) @ ( s @ X1 @ X65 ) ) )
= ( s @ X1 @ X64 ) ) )
& ( mono_2Ec_2Ebool_2ET
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X64 ) @ ( s @ X1 @ X65 ) ) )
= ( s @ X1 @ X64 ) ) )
& ( ~ mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X64 ) @ ( s @ X1 @ X65 ) ) )
= ( s @ X1 @ X65 ) ) )
& ( mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X64 ) @ ( s @ X1 @ X65 ) ) )
= ( s @ X1 @ X65 ) ) ) ),
inference(fool_unroll,[status(thm)],[thm_2Ebool_2ECOND__CLAUSES]) ).
thf(c_0_21,plain,
! [X61: $o] :
( ( ( mono_2Ec_2Ebool_2ET
& X61 )
<=> X61 )
& ( ( X61
& mono_2Ec_2Ebool_2ET )
<=> X61 )
& ( ( mono_2Ec_2Ebool_2EF
& X61 )
<=> mono_2Ec_2Ebool_2EF )
& ( ( X61
& mono_2Ec_2Ebool_2EF )
<=> mono_2Ec_2Ebool_2EF ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EAND__CLAUSES]) ).
thf(c_0_22,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum,X36: mono_2Etyop_2Enum_2Enum,X34: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ X22 @ X34 )
= X36 )
| ( X22
!= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ X32 @ X34 ) @ X36 ) )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X36 @ X34 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Enum_2ESUC @ X22 )
= ( mono_2Ec_2Earithmetic_2E_2B @ X22 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) )
= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EONE]) ).
thf(c_0_25,plain,
! [X264: mono_2Etyop_2Enum_2Enum,X266: mono_2Etyop_2Enum_2Enum,X267: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Earithmetic_2EODD @ X264 )
| ( X264
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( esk3_1 @ X264 ) ) ) ) )
& ( ( X266
!= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X267 ) ) )
| ( mono_2Ec_2Earithmetic_2EODD @ X266 ) ) ),
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)],[thm_2Earithmetic_2EODD__EXISTS])])])])])]) ).
thf(c_0_26,plain,
! [X333: mono_2Etyop_2Enum_2Enum,X334: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ X333 @ X334 )
= ( mono_2Ec_2Earithmetic_2E_2A @ X334 @ X333 ) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMULT__COMM]) ).
thf(c_0_27,negated_conjecture,
~ ! [X56: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Earithmetic_2EEVEN @ X56 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ X56 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( ( mono_2Ec_2Earithmetic_2EEVEN @ X56 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ X56 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
! [X268: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ X268 @ mono_2Ec_2Enum_2E0 )
= X268 ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD__0]) ).
thf(c_0_29,plain,
! [X260: mono_2Etyop_2Enum_2Enum,X262: mono_2Etyop_2Enum_2Enum,X263: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Earithmetic_2EEVEN @ X260 )
| ( X260
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( esk2_1 @ X260 ) ) ) )
& ( ( X262
!= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ X263 ) )
| ( mono_2Ec_2Earithmetic_2EEVEN @ X262 ) ) ),
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)],[thm_2Earithmetic_2EEVEN__EXISTS])])])])])]) ).
thf(c_0_30,plain,
! [X269: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ X269 ) ),
inference(variable_rename,[status(thm)],[thm_2Eprim__rec_2ELESS__0]) ).
thf(c_0_31,plain,
( ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) )
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2ETWO]) ).
thf(c_0_32,plain,
! [X304: d,X305: u,X306: u] :
( ( ~ mono_2Ec_2Ebool_2ET
| ( ( s @ X304 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X304 @ X305 ) @ ( s @ X304 @ X306 ) ) )
= ( s @ X304 @ X305 ) ) )
& ( mono_2Ec_2Ebool_2ET
| ( ( s @ X304 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X304 @ X305 ) @ ( s @ X304 @ X306 ) ) )
= ( s @ X304 @ X305 ) ) )
& ( ~ mono_2Ec_2Ebool_2EF
| ( ( s @ X304 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X304 @ X305 ) @ ( s @ X304 @ X306 ) ) )
= ( s @ X304 @ X306 ) ) )
& ( mono_2Ec_2Ebool_2EF
| ( ( s @ X304 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X304 @ X305 ) @ ( s @ X304 @ X306 ) ) )
= ( s @ X304 @ X306 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])]) ).
thf(c_0_33,plain,
! [X444: $o] :
( ( ~ mono_2Ec_2Ebool_2ET
| ~ X444
| X444 )
& ( mono_2Ec_2Ebool_2ET
| ~ X444 )
& ( X444
| ~ X444 )
& ( ~ X444
| ~ mono_2Ec_2Ebool_2ET
| X444 )
& ( X444
| ~ X444 )
& ( mono_2Ec_2Ebool_2ET
| ~ X444 )
& ( ~ mono_2Ec_2Ebool_2EF
| ~ X444
| mono_2Ec_2Ebool_2EF )
& ( mono_2Ec_2Ebool_2EF
| ~ mono_2Ec_2Ebool_2EF )
& ( X444
| ~ mono_2Ec_2Ebool_2EF )
& ( ~ X444
| ~ mono_2Ec_2Ebool_2EF
| mono_2Ec_2Ebool_2EF )
& ( X444
| ~ mono_2Ec_2Ebool_2EF )
& ( mono_2Ec_2Ebool_2EF
| ~ mono_2Ec_2Ebool_2EF ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_34,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X34: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ X22 @ X32 ) @ X34 ) @ X32 )
= X34 )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X34 @ X32 ) ),
inference(er,[status(thm)],[c_0_22]) ).
thf(c_0_35,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ X22 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Enum_2ESUC @ X22 ) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_36,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( X22
= ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( esk3_1 @ X22 ) ) ) )
| ~ ( mono_2Ec_2Earithmetic_2EODD @ X22 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_37,plain,
! [X32: mono_2Etyop_2Enum_2Enum,X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A @ X22 @ X32 )
= ( mono_2Ec_2Earithmetic_2E_2A @ X32 @ X22 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_38,plain,
! [X331: mono_2Etyop_2Enum_2Enum,X332: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ X331 ) @ ( mono_2Ec_2Enum_2ESUC @ X332 ) )
| ( mono_2Ec_2Eprim__rec_2E_3C @ X331 @ X332 ) )
& ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X331 @ X332 )
| ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ X331 ) @ ( mono_2Ec_2Enum_2ESUC @ X332 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2ELESS__MONO__EQ])])]) ).
thf(c_0_39,plain,
! [X441: $o] :
( ~ mono_2Ec_2Ebool_2EF
| X441 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).
thf(c_0_40,negated_conjecture,
( ( ~ ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 )
| ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 ) )
& ( ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
| ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 ) )
& ( ~ ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])]) ).
thf(c_0_41,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B @ X22 @ mono_2Ec_2Enum_2E0 )
= X22 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_42,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( X22
= ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( esk2_1 @ X22 ) ) )
| ~ ( mono_2Ec_2Earithmetic_2EEVEN @ X22 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_43,plain,
! [X22: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ X22 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_44,plain,
( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ),
inference(rw,[status(thm)],[c_0_31,c_0_24]) ).
thf(c_0_45,plain,
! [X1: d,X4: u,X3: u] :
( ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
= ( s @ X1 @ X3 ) )
| ~ mono_2Ec_2Ebool_2ET ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_46,plain,
mono_2Ec_2Ebool_2ET,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_33])])]) ).
thf(c_0_47,plain,
! [X256: $o,X257: mono_2Etyop_2Enum_2Enum,X258: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ X256 @ X257 @ X258 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X256 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X257 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X258 ) ) ) ) ),
inference(variable_rename,[status(thm)],[monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum]) ).
thf(c_0_48,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ X22 @ X32 ) ) @ X32 )
= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) @ X32 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_49,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2A @ ( esk3_1 @ X22 ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= X22 )
| ~ ( mono_2Ec_2Earithmetic_2EODD @ X22 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_50,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ X22 ) @ ( mono_2Ec_2Enum_2ESUC @ X32 ) )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X22 @ X32 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_51,plain,
! [X56: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN @ X56 )
<=> ~ ( mono_2Ec_2Earithmetic_2EODD @ X56 ) ),
inference(fof_simplification,[status(thm)],[thm_2Earithmetic_2EEVEN__ODD]) ).
thf(c_0_52,plain,
! [X1: d,X3: u,X4: u] :
( mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
= ( s @ X1 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_53,plain,
~ mono_2Ec_2Ebool_2EF,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_39])])]) ).
thf(c_0_54,negated_conjecture,
( ~ ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_55,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2E_2A @ X22 @ X32 ) @ X32 )
= mono_2Ec_2Enum_2E0 )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ X32 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
thf(c_0_56,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A @ ( esk2_1 @ X22 ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= X22 )
| ~ ( mono_2Ec_2Earithmetic_2EEVEN @ X22 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
thf(c_0_57,plain,
mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_58,plain,
! [X320: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X320 ) ) )
= X320 ),
inference(variable_rename,[status(thm)],[ji_2Emono_2Etyop_2Enum_2Enum]) ).
thf(c_0_59,plain,
! [X1: d,X4: u,X3: u] :
( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
= ( s @ X1 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
thf(c_0_60,plain,
! [X9: $o,X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ X9 @ X22 @ X32 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X9 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X22 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X32 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_61,negated_conjecture,
( ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ~ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_62,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ X22 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
| ~ ( mono_2Ec_2Earithmetic_2EODD @ X22 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_63,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Enum_2ESUC @ X22 ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
| ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X22 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ),
inference(spm,[status(thm)],[c_0_50,c_0_44]) ).
thf(c_0_64,plain,
! [X270: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Earithmetic_2EEVEN @ X270 )
| ~ ( mono_2Ec_2Earithmetic_2EODD @ X270 ) )
& ( ( mono_2Ec_2Earithmetic_2EODD @ X270 )
| ( mono_2Ec_2Earithmetic_2EEVEN @ X270 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
thf(c_0_65,plain,
! [X1: d,X3: u,X4: u] :
( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
= ( s @ X1 @ X4 ) ),
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_66,negated_conjecture,
( ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) )
| ~ ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 ) ),
inference(rw,[status(thm)],[c_0_54,c_0_24]) ).
thf(c_0_67,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ X22 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= mono_2Ec_2Enum_2E0 )
| ~ ( mono_2Ec_2Earithmetic_2EEVEN @ X22 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
thf(c_0_68,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X22 ) ) )
= X22 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_69,plain,
! [X32: mono_2Etyop_2Enum_2Enum,X22: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ X22 @ X32 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X22 ) ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_70,negated_conjecture,
( ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 )
| ( ( mono_2Ec_2Earithmetic_2EMOD @ esk1_0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
!= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ~ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ),
inference(rw,[status(thm)],[c_0_61,c_0_24]) ).
thf(c_0_71,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EMOD @ X22 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
| ~ ( mono_2Ec_2Earithmetic_2EODD @ X22 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_43])]) ).
thf(c_0_72,plain,
! [X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD @ X22 )
| ( mono_2Ec_2Earithmetic_2EEVEN @ X22 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_73,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ~ $true @ X22 @ X32 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X32 ) ) ),
inference(spm,[status(thm)],[c_0_65,c_0_60]) ).
thf(c_0_74,negated_conjecture,
( ( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
!= mono_2Ec_2Enum_2E0 )
| ~ ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_75,plain,
! [X32: mono_2Etyop_2Enum_2Enum,X22: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ X22 @ X32 )
= X22 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_68]) ).
thf(c_0_76,negated_conjecture,
( ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 )
| ( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ~ $true @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) )
!= ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
thf(c_0_77,plain,
! [X22: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ~ $true @ X22 @ X32 )
= X32 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_73]),c_0_68]) ).
thf(c_0_78,negated_conjecture,
~ ( mono_2Ec_2Earithmetic_2EEVEN @ esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
thf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]),c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP003^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:22:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.19/0.27 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.VOmq8sh4vQ/E---3.1_512153.p
% 0.19/0.33 % Version: 3.5.1-ho
% 0.19/0.33 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.19/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.33 % Starting additional_ho_4 with 1500s (5) cores
% 0.19/0.33 % Starting pre_casc_8 with 300s (1) cores
% 0.19/0.33 % Starting pre_casc_5 with 300s (1) cores
% 0.19/0.33 % Starting pre_casc_6 with 300s (1) cores
% 0.19/0.33 % pre_casc_8 with pid 512167 completed with status 0
% 0.19/0.33 % Result found by pre_casc_8
% 0.19/0.33 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.19/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.33 % Starting additional_ho_4 with 1500s (5) cores
% 0.19/0.33 % Starting pre_casc_8 with 300s (1) cores
% 0.19/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,5,,5,20000,3.0,true))
% 0.19/0.33 % SinE strategy is GSinE(CountTerms,hypos,5,,5,20000,3.0,true)
% 0.19/0.33 % Search class: HGHSM-FFLM32-DSFFFFBN
% 0.19/0.33 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.33 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.33 % SubtermCWHack with pid 512170 completed with status 0
% 0.19/0.33 % Result found by SubtermCWHack
% 0.19/0.33 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.19/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.33 % Starting additional_ho_4 with 1500s (5) cores
% 0.19/0.33 % Starting pre_casc_8 with 300s (1) cores
% 0.19/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,5,,5,20000,3.0,true))
% 0.19/0.33 % SinE strategy is GSinE(CountTerms,hypos,5,,5,20000,3.0,true)
% 0.19/0.33 % Search class: HGHSM-FFLM32-DSFFFFBN
% 0.19/0.33 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.33 % Starting SubtermCWHack with 31s (1) cores
% 0.19/0.33 % Preprocessing time : 0.003 s
% 0.19/0.33
% 0.19/0.33 % Proof found!
% 0.19/0.33 % SZS status Theorem
% 0.19/0.33 % SZS output start CNFRefutation
% See solution above
% 0.19/0.33 % Parsed axioms : 215
% 0.19/0.33 % Removed by relevancy pruning/SinE : 137
% 0.19/0.33 % Initial clauses : 196
% 0.19/0.33 % Removed in clause preprocessing : 71
% 0.19/0.33 % Initial clauses in saturation : 125
% 0.19/0.33 % Processed clauses : 377
% 0.19/0.33 % ...of these trivial : 27
% 0.19/0.33 % ...subsumed : 171
% 0.19/0.33 % ...remaining for further processing : 179
% 0.19/0.33 % Other redundant clauses eliminated : 3
% 0.19/0.33 % Clauses deleted for lack of memory : 0
% 0.19/0.33 % Backward-subsumed : 3
% 0.19/0.33 % Backward-rewritten : 5
% 0.19/0.33 % Generated clauses : 790
% 0.19/0.33 % ...of the previous two non-redundant : 562
% 0.19/0.33 % ...aggressively subsumed : 0
% 0.19/0.33 % Contextual simplify-reflections : 1
% 0.19/0.33 % Paramodulations : 736
% 0.19/0.33 % Factorizations : 5
% 0.19/0.33 % NegExts : 0
% 0.19/0.33 % Equation resolutions : 3
% 0.19/0.33 % Disequality decompositions : 0
% 0.19/0.33 % Total rewrite steps : 278
% 0.19/0.33 % ...of those cached : 148
% 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 : 162
% 0.19/0.33 % Positive orientable unit clauses : 56
% 0.19/0.33 % Positive unorientable unit clauses: 1
% 0.19/0.33 % Negative unit clauses : 7
% 0.19/0.33 % Non-unit-clauses : 98
% 0.19/0.33 % Current number of unprocessed clauses: 310
% 0.19/0.33 % ...number of literals in the above : 1026
% 0.19/0.33 % Current number of archived formulas : 0
% 0.19/0.33 % Current number of archived clauses : 14
% 0.19/0.33 % Clause-clause subsumption calls (NU) : 1751
% 0.19/0.33 % Rec. Clause-clause subsumption calls : 1440
% 0.19/0.33 % Non-unit clause-clause subsumptions : 152
% 0.19/0.33 % Unit Clause-clause subsumption calls : 114
% 0.19/0.33 % Rewrite failures with RHS unbound : 0
% 0.19/0.33 % BW rewrite match attempts : 22
% 0.19/0.33 % BW rewrite match successes : 2
% 0.19/0.33 % Condensation attempts : 0
% 0.19/0.33 % Condensation successes : 0
% 0.19/0.33 % Termbank termtop insertions : 31678
% 0.19/0.33 % Search garbage collected termcells : 3311
% 0.19/0.33
% 0.19/0.33 % -------------------------------------------------
% 0.19/0.33 % User time : 0.029 s
% 0.19/0.33 % System time : 0.009 s
% 0.19/0.33 % Total time : 0.039 s
% 0.19/0.33 % Maximum resident set size: 4376 pages
% 0.19/0.33
% 0.19/0.33 % -------------------------------------------------
% 0.19/0.33 % User time : 0.036 s
% 0.19/0.33 % System time : 0.014 s
% 0.19/0.33 % Total time : 0.051 s
% 0.19/0.33 % Maximum resident set size: 5120 pages
% 0.19/0.33 % E exiting
%------------------------------------------------------------------------------