%------------------------------------------------------------------------------
% 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 : n007.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 : Thu Sep 24 12:53:25 PM UTC 2026
% Result : Theorem 0.20s 16.71s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 98 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 105 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 200 ( 65 ~; 62 |; 40 &)
% ( 22 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 8 con; 0-3 aty)
% Number of variables : 131 ( 0 sgn 128 !; 3 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
d: $tType ).
tff(decl_sort2,type,
u: $tType ).
tff(decl_sort3,type,
du: $tType ).
tff(decl_sort4,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(decl_sort5,type,
mono_2Etyop_2Enum_2Enum: $tType ).
tff(decl_sort6,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
tff(decl_23,type,
tyop_2Emin_2Ebool: d ).
tff(decl_25,type,
tyop_2Enum_2Enum: d ).
tff(decl_26,type,
s: ( u * d ) > du ).
tff(decl_28,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(decl_54,type,
c_2Ebool_2ECOND_2E3: ( du * ( du * du ) ) > u ).
tff(decl_79,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_81,type,
mono_2Ec_2Earithmetic_2E_2A_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_83,type,
mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_86,type,
mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).
tff(decl_88,type,
mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_91,type,
mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
tff(decl_92,type,
mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_94,type,
mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_98,type,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Ebool ) ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_100,type,
mono_2Ec_2Earithmetic_2EEVEN_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).
tff(decl_101,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_103,type,
mono_2Ec_2Earithmetic_2EMOD_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_105,type,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_107,type,
mono_2Ec_2Earithmetic_2EODD_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).
tff(decl_109,type,
mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_110,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(decl_111,type,
mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).
tff(decl_116,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(decl_125,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
tff(decl_135,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
tff(decl_137,type,
esk1_0: mono_2Etyop_2Enum_2Enum ).
tff(decl_138,type,
esk2_1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_139,type,
esk3_1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(thm_2Earithmetic_2EEVEN__ODD,axiom,
! [X83: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X83))
<=> ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X83)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__ODD) ).
tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ p(X8) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X8 )
<=> ~ p(X8) )
& ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
<=> p(X8) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X8 )
<=> p(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(thm_2Earithmetic_2EEVEN__EXISTS,axiom,
! [X83: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X83))
<=> ? [X84: mono_2Etyop_2Enum_2Enum] : ( X83 = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X84) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS) ).
tff(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X1: d,X90: u,X91: u] :
( ( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X1,X90),s(X1,X91))) = s(X1,X91) )
& ( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X1,X90),s(X1,X91))) = s(X1,X90) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X6: mono_2Etyop_2Emin_2Ebool,X79: mono_2Etyop_2Enum_2Enum,X80: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X6,X79,X80))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X6)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X79)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X80)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) ).
tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(X8)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ~ p(X8) )
& ( ( p(X8)
=> p(X8) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2EF_2E0)
=> p(X8) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(X8)
=> p(mono_2Ec_2Ebool_2ET_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2ET_2E0)
=> p(X8) )
<=> p(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X33: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X33))) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Enum_2Enum) ).
tff(reserved_2Eho_2Eboolext,axiom,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( p(X6)
<=> p(X7) )
=> ( X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X44: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X44) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) ).
tff(thm_2Earithmetic_2EMOD__2,conjecture,
! [X83: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMOD_2E2(X83,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(X83),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__2) ).
tff(reserved_2Eho_2Enotfalse,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
tff(thm_2Earithmetic_2EMOD__UNIQUE,axiom,
! [X83: mono_2Etyop_2Enum_2Enum,X85: mono_2Etyop_2Enum_2Enum,X86: mono_2Etyop_2Enum_2Enum] :
( ? [X87: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X86,X83))
& ( X85 = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X87,X83),X86) ) )
=> ( mono_2Ec_2Earithmetic_2EMOD_2E2(X85,X83) = X86 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__UNIQUE) ).
tff(thm_2Eprim__rec_2ELESS__0,axiom,
! [X83: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(X83))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0) ).
tff(thm_2Earithmetic_2EONE,axiom,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE) ).
tff(thm_2Earithmetic_2EADD__0,axiom,
! [X81: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X81,mono_2Ec_2Enum_2E0_2E0) = X81 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__0) ).
tff(thm_2Earithmetic_2EMULT__COMM,axiom,
! [X81: mono_2Etyop_2Enum_2Enum,X82: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2A_2E2(X81,X82) = mono_2Ec_2Earithmetic_2E_2A_2E2(X82,X81) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).
tff(thm_2Earithmetic_2ETWO,axiom,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO) ).
tff(thm_2Earithmetic_2EADD1,axiom,
! [X81: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X81) = mono_2Ec_2Earithmetic_2E_2B_2E2(X81,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1) ).
tff(thm_2Earithmetic_2EODD__EXISTS,axiom,
! [X83: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EODD_2E1(X83))
<=> ? [X84: mono_2Etyop_2Enum_2Enum] : ( X83 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X84)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS) ).
tff(thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
! [X81: mono_2Etyop_2Enum_2Enum,X82: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2ESUC_2E1(X81),mono_2Ec_2Enum_2ESUC_2E1(X82)) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X81,X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__EQ) ).
tff(c_0_20,plain,
! [X83: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X83))
<=> ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X83)) ),
inference(fof_simplification,[status(thm)],[thm_2Earithmetic_2EEVEN__ODD]) ).
tff(c_0_21,plain,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ p(X8) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X8 )
<=> ~ p(X8) )
& ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
<=> p(X8) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X8 )
<=> p(X8) ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EEQ__CLAUSES]) ).
tff(c_0_22,plain,
! [X131: mono_2Etyop_2Enum_2Enum,X133: mono_2Etyop_2Enum_2Enum,X134: mono_2Etyop_2Enum_2Enum] :
( ( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X133))
| ( X133 != mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X134) ) )
& ( ( X131 = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk2_1(X131)) )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X131)) ) ),
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])])])])])]) ).
tff(c_0_23,plain,
! [X284: d,X285: u,X286: u] :
( ( s(X284,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X284,X285),s(X284,X286))) = s(X284,X286) )
& ( s(X284,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X284,X285),s(X284,X286))) = s(X284,X285) ) ),
inference(variable_rename,[status(thm)],[thm_2Ebool_2ECOND__CLAUSES]) ).
tff(c_0_24,plain,
! [X127: mono_2Etyop_2Emin_2Ebool,X128: mono_2Etyop_2Enum_2Enum,X129: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X127,X128,X129))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X127)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X128)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X129)))) ),
inference(variable_rename,[status(thm)],[monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum]) ).
tff(c_0_25,plain,
! [X143: mono_2Etyop_2Enum_2Enum] :
( ( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X143))
| p(mono_2Ec_2Earithmetic_2EODD_2E1(X143)) )
& ( ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X143))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X143)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
tff(c_0_26,plain,
! [X373: mono_2Etyop_2Emin_2Ebool] :
( ( ( X373 = mono_2Ec_2Ebool_2EF_2E0 )
| p(X373) )
& ( ~ p(X373)
| ( X373 != mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = X373 )
| p(X373) )
& ( ~ p(X373)
| ( mono_2Ec_2Ebool_2EF_2E0 != X373 ) )
& ( ( X373 = mono_2Ec_2Ebool_2ET_2E0 )
| ~ p(X373) )
& ( p(X373)
| ( X373 != mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = X373 )
| ~ p(X373) )
& ( p(X373)
| ( mono_2Ec_2Ebool_2ET_2E0 != X373 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
tcf(c_0_27,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] :
( ( X33 != mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X35) )
| p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tff(c_0_28,plain,
! [X8: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(X8)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ~ p(X8) )
& p(mono_2Ec_2Ebool_2ET_2E0)
& ( ( p(mono_2Ec_2Ebool_2EF_2E0)
=> p(X8) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(X8)
=> p(mono_2Ec_2Ebool_2ET_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2ET_2E0)
=> p(X8) )
<=> p(X8) ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EIMP__CLAUSES]) ).
tff(c_0_29,plain,
! [X300: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X300))) = X300 ),
inference(variable_rename,[status(thm)],[ji_2Emono_2Etyop_2Enum_2Enum]) ).
tcf(c_0_30,plain,
! [X1: d,X4: u,X3: u] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X1,X3),s(X1,X4))) = s(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tcf(c_0_31,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] : s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X6,X33,X35))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X6)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X33)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X35)))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tff(c_0_32,plain,
! [X313: mono_2Etyop_2Emin_2Ebool,X314: mono_2Etyop_2Emin_2Ebool] :
( ( ( X313 = X314 )
| p(X314)
| p(X313) )
& ( ( X313 = X314 )
| ~ p(X314)
| ~ p(X313) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).
tff(c_0_33,plain,
! [X139: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X139) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X139) ),
inference(variable_rename,[status(thm)],[arityeq1_2Ec_2Earithmetic_2EBIT1_2E1]) ).
tff(c_0_34,negated_conjecture,
~ ! [X83: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMOD_2E2(X83,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(X83),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
inference(assume_negation,[status(cth)],[thm_2Earithmetic_2EMOD__2]) ).
tcf(c_0_35,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X33))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_36,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = mono_2Ec_2Ebool_2EF_2E0 )
| p(X6) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
tcf(c_0_37,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X6)
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
tcf(c_0_38,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X33))),
inference(er,[status(thm)],[c_0_27]) ).
tff(c_0_39,plain,
! [X372: mono_2Etyop_2Emin_2Ebool] :
( ( p(mono_2Ec_2Ebool_2EF_2E0)
| ~ p(X372)
| p(X372) )
& ( ~ p(X372)
| ~ p(mono_2Ec_2Ebool_2EF_2E0) )
& ( ~ p(X372)
| p(X372) )
& p(mono_2Ec_2Ebool_2ET_2E0)
& ( p(X372)
| ~ p(mono_2Ec_2Ebool_2EF_2E0)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X372) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| p(mono_2Ec_2Ebool_2EF_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X372)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(mono_2Ec_2Ebool_2ET_2E0) )
& ( p(mono_2Ec_2Ebool_2ET_2E0)
| p(X372) )
& ( p(X372)
| ~ p(mono_2Ec_2Ebool_2ET_2E0)
| ~ p(X372) )
& ( p(X372)
| ~ p(X372) )
& ( p(X372)
| p(mono_2Ec_2Ebool_2ET_2E0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
tcf(c_0_40,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X33))) = X33,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_41,plain,
! [X35: mono_2Etyop_2Enum_2Enum,X33: mono_2Etyop_2Enum_2Enum] : s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ET_2E0,X33,X35))) = s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X33)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
tcf(c_0_42,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = X7 )
| p(X7)
| p(X6) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tff(c_0_43,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
tff(c_0_44,plain,
! [X147: mono_2Etyop_2Enum_2Enum,X148: mono_2Etyop_2Enum_2Enum,X149: mono_2Etyop_2Enum_2Enum,X150: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD_2E2(X148,X147) = X149 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X149,X147))
| ( X148 != mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X150,X147),X149) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EMOD__UNIQUE])])])]) ).
tff(c_0_45,plain,
! [X141: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(X141))),
inference(variable_rename,[status(thm)],[thm_2Eprim__rec_2ELESS__0]) ).
tcf(c_0_46,plain,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EONE]) ).
tcf(c_0_47,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EBIT1_2E1(X33) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X33),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
tff(c_0_48,negated_conjecture,
mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) != mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
tcf(c_0_49,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33))
| ( mono_2Ec_2Earithmetic_2EODD_2E1(X33) = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
tcf(c_0_50,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X33)) = mono_2Ec_2Ebool_2ET_2E0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
tcf(c_0_51,plain,
p(mono_2Ec_2Ebool_2ET_2E0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
tcf(c_0_52,plain,
! [X35: mono_2Etyop_2Enum_2Enum,X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ET_2E0,X33,X35) = X33,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_40]) ).
tcf(c_0_53,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( p(X7)
| ( X7 = X6 )
| ( X6 = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
tff(c_0_54,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_nnf,[status(thm)],[c_0_43]) ).
tcf(c_0_55,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum,X37: mono_2Etyop_2Enum_2Enum,X36: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X37,X36))
| ( X33 != mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X35,X36),X37) )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X33,X36) = X37 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
tff(c_0_56,plain,
! [X140: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X140,mono_2Ec_2Enum_2E0_2E0) = X140 ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD__0]) ).
tff(c_0_57,plain,
! [X311: mono_2Etyop_2Enum_2Enum,X312: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2A_2E2(X311,X312) = mono_2Ec_2Earithmetic_2E_2A_2E2(X312,X311) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMULT__COMM]) ).
tcf(c_0_58,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(X33))),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
tcf(c_0_59,plain,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2ETWO]) ).
tcf(c_0_60,plain,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
tcf(c_0_61,negated_conjecture,
mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) != mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
tcf(c_0_62,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X33)) = mono_2Ec_2Ebool_2EF_2E0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
tcf(c_0_63,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X35: mono_2Etyop_2Enum_2Enum,X33: mono_2Etyop_2Enum_2Enum,X7: mono_2Etyop_2Emin_2Ebool] :
( p(X7)
| ( X7 = X6 )
| ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X6,X33,X35) = X33 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
tcf(c_0_64,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
tcf(c_0_65,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X36: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X36,X35))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X33,X35),X36),X35) = X36 ) ),
inference(er,[status(thm)],[c_0_55]) ).
tcf(c_0_66,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2B_2E2(X33,mono_2Ec_2Enum_2E0_2E0) = X33,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
tcf(c_0_67,plain,
! [X35: mono_2Etyop_2Enum_2Enum,X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2A_2E2(X33,X35) = mono_2Ec_2Earithmetic_2E_2A_2E2(X35,X33),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
tcf(c_0_68,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33))
| ( X33 = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk2_1(X33)) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_69,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(X33)) = mono_2Ec_2Ebool_2ET_2E0,
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
tcf(c_0_70,plain,
mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_47]),c_0_60]) ).
tff(c_0_71,plain,
! [X130: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X130) = mono_2Ec_2Earithmetic_2E_2B_2E2(X130,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD1]) ).
tcf(c_0_72,negated_conjecture,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)) != mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_47]),c_0_60]) ).
tcf(c_0_73,plain,
! [X35: mono_2Etyop_2Enum_2Enum,X33: mono_2Etyop_2Enum_2Enum,X6: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = mono_2Ec_2Ebool_2EF_2E0 )
| ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X6,X33,X35) = X33 ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_62]),c_0_64]) ).
tcf(c_0_74,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X35))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X33,X35),X35) = mono_2Ec_2Enum_2E0_2E0 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
tcf(c_0_75,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33))
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(esk2_1(X33),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = X33 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
tcf(c_0_76,plain,
mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Ebool_2ET_2E0,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
tcf(c_0_77,plain,
! [X1: d,X3: u,X4: u] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X1,X3),s(X1,X4))) = s(X1,X4),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tcf(c_0_78,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Enum_2ESUC_2E1(X33) = mono_2Ec_2Earithmetic_2E_2B_2E2(X33,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
tff(c_0_79,plain,
! [X135: mono_2Etyop_2Enum_2Enum,X137: mono_2Etyop_2Enum_2Enum,X138: mono_2Etyop_2Enum_2Enum] :
( ( p(mono_2Ec_2Earithmetic_2EODD_2E1(X137))
| ( X137 != mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X138)) ) )
& ( ( X135 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk3_1(X135))) )
| ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X135)) ) ),
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])])])])])]) ).
tff(c_0_80,plain,
! [X309: mono_2Etyop_2Enum_2Enum,X310: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2ESUC_2E1(X309),mono_2Ec_2Enum_2ESUC_2E1(X310)) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X309,X310) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__MONO__EQ]) ).
tcf(c_0_81,negated_conjecture,
( ( mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) != mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0) = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
tcf(c_0_82,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X33,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Enum_2E0_2E0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_51])]) ).
tcf(c_0_83,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] : s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2EF_2E0,X33,X35))) = s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X35)),
inference(spm,[status(thm)],[c_0_77,c_0_31]) ).
tcf(c_0_84,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2B_2E2(X33,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(X33),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_47]),c_0_60]) ).
tcf(c_0_85,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X33))
| ( X33 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk3_1(X33))) ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
tcf(c_0_86,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2ESUC_2E1(X33),mono_2Ec_2Enum_2ESUC_2E1(X35)) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X33,X35),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
tcf(c_0_87,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33))
| p(mono_2Ec_2Earithmetic_2EODD_2E1(X33)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_88,negated_conjecture,
mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0) = mono_2Ec_2Ebool_2EF_2E0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_36]) ).
tcf(c_0_89,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2EF_2E0,X33,X35) = X35,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_83]),c_0_40]) ).
tcf(c_0_90,plain,
! [X33: mono_2Etyop_2Enum_2Enum,X35: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),X35))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(X33,X35)),X35) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(spm,[status(thm)],[c_0_65,c_0_84]) ).
tcf(c_0_91,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X33))
| ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(esk3_1(X33),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))) = X33 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_67]) ).
tcf(c_0_92,plain,
! [X33: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2ESUC_2E1(X33),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X33,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)),
inference(spm,[status(thm)],[c_0_86,c_0_70]) ).
tcf(c_0_93,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X33))
| ( mono_2Ec_2Earithmetic_2EODD_2E1(X33) = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_87]) ).
tcf(c_0_94,negated_conjecture,
mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) != mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_88]),c_0_89]) ).
tcf(c_0_95,plain,
! [X33: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X33))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X33,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_69]),c_0_51])]) ).
tcf(c_0_96,negated_conjecture,
mono_2Ec_2Earithmetic_2EODD_2E1(esk1_0) = mono_2Ec_2Ebool_2ET_2E0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_88]),c_0_64]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_51])]),
[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
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 21:37:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.46 Running first-order theorem proving
% 0.11/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/16.71 % Version: 3.5.1
% 0.20/16.71 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.20/16.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/16.71 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.20/16.71 % Starting new_bool_3 with 600s (2) cores
% 0.20/16.71 % Starting new_bool_1 with 300s (1) cores
% 0.20/16.71 % Starting sh5l with 300s (1) cores
% 0.20/16.71 % sh5l with pid 3606345 completed with status 0
% 0.20/16.71 % Result found by sh5l
% 0.20/16.71 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.20/16.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/16.71 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.20/16.71 % Starting new_bool_3 with 600s (2) cores
% 0.20/16.71 % Starting new_bool_1 with 300s (1) cores
% 0.20/16.71 % Starting sh5l with 300s (1) cores
% 0.20/16.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.20/16.71 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/16.71 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.20/16.71 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/16.71 % Starting SubtermCWHack with 31s (1) cores
% 0.20/16.71 % SubtermCWHack with pid 3606349 completed with status 0
% 0.20/16.71 % Result found by SubtermCWHack
% 0.20/16.71 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.20/16.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/16.71 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.20/16.71 % Starting new_bool_3 with 600s (2) cores
% 0.20/16.71 % Starting new_bool_1 with 300s (1) cores
% 0.20/16.71 % Starting sh5l with 300s (1) cores
% 0.20/16.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.20/16.71 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/16.71 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.20/16.71 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/16.71 % Starting SubtermCWHack with 31s (1) cores
% 0.20/16.71 % Preprocessing time : 0.003 s
% 0.20/16.71
% 0.20/16.71 % Proof found!
% 0.20/16.71 % SZS status Theorem
% 0.20/16.71 % SZS output start CNFRefutation
% See solution above
% 0.20/16.71 % Parsed axioms : 253
% 0.20/16.71 % Removed by relevancy pruning/SinE : 142
% 0.20/16.71 % Initial clauses : 409
% 0.20/16.71 % Removed in clause preprocessing : 247
% 0.20/16.71 % Initial clauses in saturation : 162
% 0.20/16.71 % Processed clauses : 24690
% 0.20/16.71 % ...of these trivial : 37
% 0.20/16.71 % ...subsumed : 23038
% 0.20/16.71 % ...remaining for further processing : 1615
% 0.20/16.71 % Other redundant clauses eliminated : 38162
% 0.20/16.71 % Clauses deleted for lack of memory : 0
% 0.20/16.71 % Backward-subsumed : 151
% 0.20/16.71 % Backward-rewritten : 70
% 0.20/16.71 % Generated clauses : 1390130
% 0.20/16.71 % ...of the previous two non-redundant : 1271561
% 0.20/16.71 % ...aggressively subsumed : 0
% 0.20/16.71 % Contextual simplify-reflections : 48
% 0.20/16.71 % Paramodulations : 1348777
% 0.20/16.71 % Factorizations : 3190
% 0.20/16.71 % NegExts : 0
% 0.20/16.71 % Equation resolutions : 38163
% 0.20/16.71 % Disequality decompositions : 0
% 0.20/16.71 % Total rewrite steps : 117849
% 0.20/16.71 % ...of those cached : 115255
% 0.20/16.71 % Propositional unsat checks : 0
% 0.20/16.71 % Propositional check models : 0
% 0.20/16.71 % Propositional check unsatisfiable : 0
% 0.20/16.71 % Propositional clauses : 0
% 0.20/16.71 % Propositional clauses after purity: 0
% 0.20/16.71 % Propositional unsat core size : 0
% 0.20/16.71 % Propositional preprocessing time : 0.000
% 0.20/16.71 % Propositional encoding time : 0.000
% 0.20/16.71 % Propositional solver time : 0.000
% 0.20/16.71 % Success case prop preproc time : 0.000
% 0.20/16.71 % Success case prop encoding time : 0.000
% 0.20/16.71 % Success case prop solver time : 0.000
% 0.20/16.71 % Current number of processed clauses : 1383
% 0.20/16.71 % Positive orientable unit clauses : 117
% 0.20/16.71 % Positive unorientable unit clauses: 1
% 0.20/16.71 % Negative unit clauses : 2
% 0.20/16.71 % Non-unit-clauses : 1263
% 0.20/16.71 % Current number of unprocessed clauses: 1241745
% 0.20/16.71 % ...number of literals in the above : 7070954
% 0.20/16.71 % Current number of archived formulas : 0
% 0.20/16.71 % Current number of archived clauses : 221
% 0.20/16.71 % Clause-clause subsumption calls (NU) : 1536857
% 0.20/16.71 % Rec. Clause-clause subsumption calls : 322520
% 0.20/16.71 % Non-unit clause-clause subsumptions : 22305
% 0.20/16.71 % Unit Clause-clause subsumption calls : 1805
% 0.20/16.71 % Rewrite failures with RHS unbound : 0
% 0.20/16.71 % BW rewrite match attempts : 183
% 0.20/16.71 % BW rewrite match successes : 34
% 0.20/16.71 % Condensation attempts : 0
% 0.20/16.71 % Condensation successes : 0
% 0.20/16.71 % Termbank termtop insertions : 17632122
% 0.20/16.71 % Search garbage collected termcells : 3378
% 0.20/16.71
% 0.20/16.71 % -------------------------------------------------
% 0.20/16.71 % User time : 15.006 s
% 0.20/16.71 % System time : 0.708 s
% 0.20/16.71 % Total time : 15.715 s
% 0.20/16.71 % Maximum resident set size: 4720 pages
% 0.20/16.71
% 0.20/16.71 % -------------------------------------------------
% 0.20/16.71 % User time : 15.020 s
% 0.20/16.71 % System time : 0.717 s
% 0.20/16.71 % Total time : 15.736 s
% 0.20/16.71 % Maximum resident set size: 5120 pages
% 0.20/16.71 % E exiting
%------------------------------------------------------------------------------