%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP015^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:53:42 AM UTC 2026
% Result : Theorem 2.58s 1.82s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 104 ( 76 unt; 0 typ; 4 def)
% Number of atoms : 463 ( 179 equ; 1 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 1747 ( 53 ~; 34 |; 34 &;1563 @)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 109 usr; 40 con; 0-3 aty)
% ( 51 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 61 ^; 93 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(type_def_9,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(type_def_10,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(func_def_4,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(func_def_5,type,
tyop_2Ebool_2Eitself: d > d ).
thf(func_def_6,type,
tyop_2Efcp_2Ecart: d > d > d ).
thf(func_def_7,type,
tyop_2Einteger_2Eint: d ).
thf(func_def_8,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_9,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_10,type,
tyop_2Enum_2Enum: d ).
thf(func_def_11,type,
s: d > u > du ).
thf(func_def_12,type,
app_2E2: du > du > u ).
thf(func_def_13,type,
combin_i_2E0: u ).
thf(func_def_14,type,
combin_k_2E0: u ).
thf(func_def_15,type,
combin_s_2E0: u ).
thf(func_def_16,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_17,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_18,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_20,type,
c_2Enum_2E0_2E0: u ).
thf(func_def_21,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(func_def_22,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(func_def_23,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_24,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_25,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_26,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_27,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_28,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_29,type,
c_2Ebool_2ECOND_2E0: u ).
thf(func_def_30,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(func_def_31,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_32,type,
c_2Earithmetic_2EMOD_2E0: u ).
thf(func_def_33,type,
c_2Earithmetic_2EMOD_2E2: du > du > u ).
thf(func_def_34,type,
c_2Einteger_2ENum_2E0: u ).
thf(func_def_35,type,
c_2Einteger_2ENum_2E1: du > u ).
thf(func_def_36,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_37,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_38,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_39,type,
c_2Ewords_2Edimword_2E0: u ).
thf(func_def_40,type,
c_2Ewords_2Edimword_2E1: du > u ).
thf(func_def_41,type,
c_2Einteger__word_2Ei2w_2E0: u ).
thf(func_def_42,type,
c_2Einteger__word_2Ei2w_2E1: du > u ).
thf(func_def_43,type,
c_2Einteger_2Eint__lt_2E0: u ).
thf(func_def_44,type,
c_2Einteger_2Eint__lt_2E2: du > du > u ).
thf(func_def_45,type,
c_2Einteger_2Eint__neg_2E0: u ).
thf(func_def_46,type,
c_2Einteger_2Eint__neg_2E1: du > u ).
thf(func_def_47,type,
c_2Einteger_2Eint__of__num_2E0: u ).
thf(func_def_48,type,
c_2Einteger_2Eint__of__num_2E1: du > u ).
thf(func_def_49,type,
c_2Ewords_2En2w_2E0: u ).
thf(func_def_50,type,
c_2Ewords_2En2w_2E1: du > u ).
thf(func_def_51,type,
c_2Ebool_2Ethe__value_2E0: u ).
thf(func_def_52,type,
c_2Ewords_2Eword__2comp_2E0: u ).
thf(func_def_53,type,
c_2Ewords_2Eword__2comp_2E1: du > u ).
thf(func_def_54,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_55,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_56,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_57,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_58,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_59,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_60,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_61,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(func_def_62,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(func_def_63,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(func_def_64,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(func_def_65,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_66,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(func_def_67,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_68,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(func_def_69,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(func_def_70,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_72,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(func_def_73,type,
mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(func_def_75,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_76,type,
mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_77,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_78,type,
mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_79,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_80,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_81,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_82,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_83,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(func_def_84,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(func_def_85,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(func_def_86,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > u ).
thf(func_def_87,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(func_def_88,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(func_def_89,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(func_def_90,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(func_def_91,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(func_def_92,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
thf(func_def_93,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(func_def_94,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_95,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_96,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_97,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_98,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_99,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_100,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(func_def_101,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(func_def_102,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(func_def_103,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(func_def_104,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_105,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(func_def_106,type,
j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_107,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(func_def_128,type,
sK1: d ).
thf(func_def_129,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f651,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f404,f435,f526,f626,f641]) ).
thf(f641,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f640]) ).
thf(f640,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f638]) ).
thf(f638,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f520,f319]) ).
thf(f319,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f318]) ).
thf(f318,definition,
( spl0_1
<=> ! [X1: $o] : ( $true = X1 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f520,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( $false
= ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ mono_2Ec_2Enum_2E0 ) ),
inference(not_proxy_clausification,[status(thm)],[f519]) ).
thf(f519,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ mono_2Ec_2Enum_2E0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f518]) ).
thf(f518,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( $true
= ( ^ [Y0: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ mono_2Ec_2Enum_2E0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ mono_2Ec_2Enum_2E0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f114]) ).
thf(f114,plain,
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ mono_2Ec_2Enum_2E0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f113]) ).
thf(f113,plain,
! [X0: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Eprim__rec_2E_3C @ X0 @ mono_2Ec_2Enum_2E0 ),
inference(rectify,[status(thm)],[f83]) ).
thf(f83,axiom,
! [X30: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Eprim__rec_2E_3C @ X30 @ mono_2Ec_2Enum_2E0 ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(f626,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f625]) ).
thf(f625,plain,
( $false
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f620]) ).
thf(f620,plain,
( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
!= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f375,f617]) ).
thf(f617,plain,
( ! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f616,f573]) ).
thf(f573,plain,
( ! [X2: u,X3: u,X1: d] :
( ( s @ X1 @ X3 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X2 ) @ ( s @ X1 @ X3 ) ) ) )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f507,f408]) ).
thf(f408,plain,
( ( mono_2Ec_2Ebool_2EF = $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f406]) ).
thf(f406,definition,
( spl0_6
<=> ( mono_2Ec_2Ebool_2EF = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f507,plain,
! [X2: u,X3: u,X1: d] :
( ( s @ X1 @ X3 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X2 ) @ ( s @ X1 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f506]) ).
thf(f506,plain,
! [X2: u,X3: u,X1: d] :
( ( ( s @ X1 @ X3 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X2 ) @ ( s @ X1 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f505]) ).
thf(f505,plain,
! [X2: u,X3: u,X1: d] :
( $true
= ( ^ [Y0: u] :
( ( s @ X1 @ Y0 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X2 ) @ ( s @ X1 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f504]) ).
thf(f504,plain,
! [X2: u,X1: d] :
( $true
= ( !! @ u
@ ^ [Y0: u] :
( ( s @ X1 @ Y0 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X2 ) @ ( s @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f503]) ).
thf(f503,plain,
! [X2: u,X1: d] :
( ( ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( ( s @ X1 @ Y1 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ Y0 ) @ ( s @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f502]) ).
thf(f502,plain,
! [X1: d] :
( $true
= ( !! @ u
@ ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( ( s @ X1 @ Y1 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ Y0 ) @ ( s @ X1 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
! [X1: d] :
( ( ( !! @ u
@ ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( ( s @ X1 @ Y1 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ Y0 ) @ ( s @ X1 @ Y1 ) ) ) ) ) )
& ( !! @ u
@ ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( ( s @ X1 @ Y1 )
= ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ Y1 ) @ ( s @ X1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f499]) ).
thf(f499,plain,
! [X1: d] :
( ( ^ [Y0: d] :
( ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ Y0 @ Y1 ) @ ( s @ Y0 @ Y2 ) ) ) ) ) )
& ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ Y0 @ Y2 ) @ ( s @ Y0 @ Y1 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f285]) ).
thf(f285,plain,
( ( !! @ d
@ ^ [Y0: d] :
( ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ Y0 @ Y1 ) @ ( s @ Y0 @ Y2 ) ) ) ) ) )
& ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ Y0 @ Y2 ) @ ( s @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f259,f267]) ).
thf(f267,plain,
mono_2Ec_2Ebool_2ET = $true,
inference(cnf_transformation,[status(thm)],[f98]) ).
thf(f98,plain,
mono_2Ec_2Ebool_2ET = $true,
inference(fool_elimination,[status(thm)],[f97]) ).
thf(f97,plain,
mono_2Ec_2Ebool_2ET,
inference(rectify,[status(thm)],[f71]) ).
thf(f71,axiom,
mono_2Ec_2Ebool_2ET,
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ebool_2ETRUTH) ).
thf(f259,plain,
( ( !! @ d
@ ^ [Y0: d] :
( ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ Y0 @ Y1 ) @ ( s @ Y0 @ Y2 ) ) ) ) ) )
& ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ Y0 @ Y2 ) @ ( s @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f152]) ).
thf(f152,plain,
( ( !! @ d
@ ^ [Y0: d] :
( ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ Y0 @ Y1 ) @ ( s @ Y0 @ Y2 ) ) ) ) ) )
& ( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( s @ Y0 @ Y2 )
= ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ Y0 @ Y2 ) @ ( s @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f151]) ).
thf(f151,plain,
! [X0: d] :
( ! [X1: u,X2: u] :
( ( s @ X0 @ X1 )
= ( s @ X0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X0 @ X1 ) @ ( s @ X0 @ X2 ) ) ) )
& ! [X3: u,X4: u] :
( ( s @ X0 @ X3 )
= ( s @ X0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X0 @ X4 ) @ ( s @ X0 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f78]) ).
thf(f78,axiom,
! [X0: d] :
( ! [X26: u,X27: u] :
( ( s @ X0 @ X26 )
= ( s @ X0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X0 @ X26 ) @ ( s @ X0 @ X27 ) ) ) )
& ! [X29: u,X28: u] :
( ( s @ X0 @ X29 )
= ( s @ X0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X0 @ X28 ) @ ( s @ X0 @ X29 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ebool_2Ebool__case__thm) ).
thf(f616,plain,
( ! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f568,f554]) ).
thf(f554,plain,
( ! [X0: mono_2Etyop_2Enum_2Enum] :
( $false
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f403,f263]) ).
thf(f263,plain,
( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
thf(f194,plain,
( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(fool_elimination,[status(thm)],[f79]) ).
thf(f79,axiom,
( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger_2EINT__NEG__0) ).
thf(f403,plain,
( ! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( $false
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f402]) ).
thf(f402,definition,
( spl0_5
<=> ! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( $false
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f568,plain,
! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f567,f455]) ).
thf(f455,plain,
! [X1: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
! [X1: d] :
( $true
= ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f453]) ).
thf(f453,plain,
! [X1: d] :
( $true
= ( ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f284]) ).
thf(f284,plain,
( ( !! @ d
@ ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f177]) ).
thf(f177,plain,
( ( !! @ d
@ ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f85]) ).
thf(f85,axiom,
! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ewords_2EWORD__NEG__0) ).
thf(f567,plain,
! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f558,f523]) ).
thf(f523,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f522]) ).
thf(f522,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( $true
= ( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f521]) ).
thf(f521,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( $true
= ( ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f261]) ).
thf(f261,plain,
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f168]) ).
thf(f168,plain,
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f167]) ).
thf(f167,plain,
! [X0: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X0 ) )
= X0 ),
inference(rectify,[status(thm)],[f81]) ).
thf(f81,axiom,
! [X30: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X30 ) )
= X30 ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(f558,plain,
! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f452,f263]) ).
thf(f452,plain,
! [X2: mono_2Etyop_2Einteger_2Eint,X1: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ X2 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X2 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X2 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f451]) ).
thf(f451,plain,
! [X2: mono_2Etyop_2Einteger_2Eint,X1: d] :
( $true
= ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ X2 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X2 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X2 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f450]) ).
thf(f450,plain,
! [X2: mono_2Etyop_2Einteger_2Eint,X1: d] :
( ( ^ [Y0: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ Y0 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ Y0 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ Y0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ Y0 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f449]) ).
thf(f449,plain,
! [X1: d] :
( ( !! @ mono_2Etyop_2Einteger_2Eint
@ ^ [Y0: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ Y0 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ Y0 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ Y0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f448]) ).
thf(f448,plain,
! [X1: d] :
( ( ^ [Y0: d] :
( !! @ mono_2Etyop_2Einteger_2Eint
@ ^ [Y1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ Y1 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ Y1 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ Y1 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f274]) ).
thf(f274,plain,
( $true
= ( !! @ d
@ ^ [Y0: d] :
( !! @ mono_2Etyop_2Einteger_2Eint
@ ^ [Y1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ Y1 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ Y1 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ Y1 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
thf(f162,plain,
( $true
= ( !! @ d
@ ^ [Y0: d] :
( !! @ mono_2Etyop_2Einteger_2Eint
@ ^ [Y1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ Y1 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ Y1 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ Y1 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f161]) ).
thf(f161,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ X0 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f82]) ).
thf(f82,axiom,
! [X32: mono_2Etyop_2Einteger_2Eint,X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X32 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ X32 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X32 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X32 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger__word_2Ei2w__def) ).
thf(f375,plain,
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
!= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f374]) ).
thf(f374,plain,
( $false
= ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f373]) ).
thf(f373,plain,
( $false
= ( ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f372]) ).
thf(f372,plain,
( $false
= ( !! @ d
@ ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f265]) ).
thf(f265,plain,
( ( ~ ( !! @ d
@ ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f231]) ).
thf(f231,plain,
( ( ~ ( !! @ d
@ ^ [Y0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f87]) ).
thf(f87,negated_conjecture,
~ ! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f86]) ).
thf(f86,conjecture,
! [X0: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger__word_2Ei2w__0) ).
thf(f526,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f525]) ).
thf(f525,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f524]) ).
thf(f524,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f400,f408]) ).
thf(f400,plain,
( ( mono_2Ec_2Ebool_2EF = $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f398]) ).
thf(f398,definition,
( spl0_4
<=> ( mono_2Ec_2Ebool_2EF = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f435,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f434,f406,f318]) ).
thf(f434,plain,
! [X1: $o] :
( ( mono_2Ec_2Ebool_2EF = $false )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f433]) ).
thf(f433,plain,
! [X1: $o] :
( $true
= ( mono_2Ec_2Ebool_2EF
=> X1 ) ),
inference(pi_clausification,[status(thm)],[f293]) ).
thf(f293,plain,
( $true
= ( !! @ $o @ ( (=>) @ mono_2Ec_2Ebool_2EF ) ) ),
inference(beta_eta_normalization,[status(thm)],[f272]) ).
thf(f272,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( mono_2Ec_2Ebool_2EF
=> Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
thf(f172,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( mono_2Ec_2Ebool_2EF
=> Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f171]) ).
thf(f171,plain,
! [X0: $o] :
( mono_2Ec_2Ebool_2EF
=> X0 ),
inference(rectify,[status(thm)],[f73]) ).
thf(f73,axiom,
! [X19: $o] :
( mono_2Ec_2Ebool_2EF
=> X19 ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ebool_2EFALSITY) ).
thf(f404,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f395,f402,f398]) ).
thf(f395,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EF = $true )
| ( $false
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f394]) ).
thf(f394,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f392]) ).
thf(f392,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f390]) ).
thf(f390,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f385]) ).
thf(f385,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( $true
= ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( ( mono_2Ec_2Enum_2E0 != X2 )
| ( mono_2Ec_2Enum_2E0 != X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f383]) ).
thf(f383,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( ( mono_2Ec_2Enum_2E0 != X2 )
| ( mono_2Ec_2Enum_2E0 != X1 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X2 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f382]) ).
thf(f382,plain,
! [X2: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ Y0 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( ( mono_2Ec_2Enum_2E0 != Y0 )
| ( mono_2Ec_2Enum_2E0 != X1 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f381]) ).
thf(f381,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ Y0 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( ( mono_2Ec_2Enum_2E0 != Y0 )
| ( mono_2Ec_2Enum_2E0 != X1 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f380]) ).
thf(f380,plain,
! [X1: mono_2Etyop_2Enum_2Enum] :
( $true
= ( ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y1: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ Y1 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= ( ( mono_2Ec_2Enum_2E0 != Y1 )
| ( mono_2Ec_2Enum_2E0 != Y0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f266]) ).
thf(f266,plain,
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y1: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ Y1 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= ( ( mono_2Ec_2Enum_2E0 != Y1 )
| ( mono_2Ec_2Enum_2E0 != Y0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f112]) ).
thf(f112,plain,
( ( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y0: mono_2Etyop_2Enum_2Enum] :
( !! @ mono_2Etyop_2Enum_2Enum
@ ^ [Y1: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ Y1 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= ( ( mono_2Ec_2Enum_2E0 != Y1 )
| ( mono_2Ec_2Enum_2E0 != Y0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y1 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ Y0 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ X0 @ X1 ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X0 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) )
<=> ( ( mono_2Ec_2Enum_2E0 != X1 )
| ( mono_2Ec_2Enum_2E0 != X0 ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) )
& ( ( mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X0 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X0 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f80]) ).
thf(f80,axiom,
! [X30: mono_2Etyop_2Enum_2Enum,X31: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X30 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X31 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ X30 @ X31 ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X30 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X31 ) )
<=> ( ( mono_2Ec_2Enum_2E0 != X31 )
| ( mono_2Ec_2Enum_2E0 != X30 ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X30 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X31 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X30 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X31 ) ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ X31 @ X30 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP015^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:20:59 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP015^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : HOL4 syntactic export of thm_2Einteger__word_2Ei2w__0.p, bushy mode
% 0.29/0.46 % Version : [BG+19] axioms.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.29/0.46 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [BG+19]
% 0.29/0.46 % Names : thm_2Einteger__word_2Ei2w__0.p [Gau19]
% 0.29/0.46 % : HL407001^1.p [TPAP]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 194 ( 72 unt; 108 typ; 0 def)
% 0.29/0.46 % Number of atoms : 134 ( 87 equ; 5 cnn)
% 0.29/0.46 % Maximal formula atoms : 8 ( 1 avg)
% 0.29/0.46 % Number of connectives : 1252 ( 5 ~; 2 |; 8 &;1211 @)
% 0.29/0.46 % ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 17 ( 4 avg)
% 0.29/0.46 % Number of types : 6 ( 5 usr)
% 0.29/0.46 % Number of type conns : 196 ( 196 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 105 ( 103 usr; 32 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 162 ( 0 ^; 161 !; 1 ?; 162 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(u,type,
% 0.29/0.46 u: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(d,type,
% 0.29/0.46 d: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(du,type,
% 0.29/0.46 du: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Etyop_2Einteger_2Eint,type,
% 0.29/0.46 mono_2Etyop_2Einteger_2Eint: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Etyop_2Enum_2Enum,type,
% 0.29/0.46 mono_2Etyop_2Enum_2Enum: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(tyop_2Ebool_2Eitself,type,
% 0.29/0.46 tyop_2Ebool_2Eitself: d > d ).
% 0.29/0.46
% 0.29/0.46 thf(tyop_2Efcp_2Ecart,type,
% 0.29/0.46 tyop_2Efcp_2Ecart: d > d > d ).
% 0.29/0.46
% 0.29/0.46 thf(tyop_2Einteger_2Eint,type,
% 0.29/0.46 tyop_2Einteger_2Eint: d ).
% 0.29/0.46
% 0.29/0.46 thf(tyop_2Emin_2Ebool,type,
% 0.29/0.46 tyop_2Emin_2Ebool: d ).
% 0.29/0.46
% 0.29/0.46 thf(tyop_2Emin_2Efun,type,
% 0.29/0.46 tyop_2Emin_2Efun: d > d > d ).
% 0.29/0.46
% 0.29/0.46 thf(tyop_2Enum_2Enum,type,
% 0.29/0.46 tyop_2Enum_2Enum: d ).
% 0.29/0.46
% 0.29/0.46 thf(s,type,
% 0.29/0.46 s: d > u > du ).
% 0.29/0.46
% 0.29/0.46 thf(app_2E2,type,
% 0.29/0.46 app_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(combin_i_2E0,type,
% 0.29/0.46 combin_i_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(combin_k_2E0,type,
% 0.29/0.46 combin_k_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(combin_s_2E0,type,
% 0.29/0.46 combin_s_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_21_2E0,type,
% 0.29/0.46 c_2Ebool_2E_21_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_21_2E1,type,
% 0.29/0.46 c_2Ebool_2E_21_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.29/0.46 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.29/0.46 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Enum_2E0_2E0,type,
% 0.29/0.46 c_2Enum_2E0_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Eprim__rec_2E_3C_2E0,type,
% 0.29/0.46 c_2Eprim__rec_2E_3C_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Eprim__rec_2E_3C_2E2,type,
% 0.29/0.46 c_2Eprim__rec_2E_3C_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Emin_2E_3D_2E0,type,
% 0.29/0.46 c_2Emin_2E_3D_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Emin_2E_3D_2E2,type,
% 0.29/0.46 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.29/0.46 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.29/0.46 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_3F_2E0,type,
% 0.29/0.46 c_2Ebool_2E_3F_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_3F_2E1,type,
% 0.29/0.46 c_2Ebool_2E_3F_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2ECOND_2E0,type,
% 0.29/0.46 c_2Ebool_2ECOND_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2ECOND_2E3,type,
% 0.29/0.46 c_2Ebool_2ECOND_2E3: du > du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2EF_2E0,type,
% 0.29/0.46 c_2Ebool_2EF_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Earithmetic_2EMOD_2E0,type,
% 0.29/0.46 c_2Earithmetic_2EMOD_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Earithmetic_2EMOD_2E2,type,
% 0.29/0.46 c_2Earithmetic_2EMOD_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2ENum_2E0,type,
% 0.29/0.46 c_2Einteger_2ENum_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2ENum_2E1,type,
% 0.29/0.46 c_2Einteger_2ENum_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2ET_2E0,type,
% 0.29/0.46 c_2Ebool_2ET_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.29/0.46 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.29/0.46 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ewords_2Edimword_2E0,type,
% 0.29/0.46 c_2Ewords_2Edimword_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ewords_2Edimword_2E1,type,
% 0.29/0.46 c_2Ewords_2Edimword_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger__word_2Ei2w_2E0,type,
% 0.29/0.46 c_2Einteger__word_2Ei2w_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger__word_2Ei2w_2E1,type,
% 0.29/0.46 c_2Einteger__word_2Ei2w_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2Eint__lt_2E0,type,
% 0.29/0.46 c_2Einteger_2Eint__lt_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2Eint__lt_2E2,type,
% 0.29/0.46 c_2Einteger_2Eint__lt_2E2: du > du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2Eint__neg_2E0,type,
% 0.29/0.46 c_2Einteger_2Eint__neg_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2Eint__neg_2E1,type,
% 0.29/0.46 c_2Einteger_2Eint__neg_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2Eint__of__num_2E0,type,
% 0.29/0.46 c_2Einteger_2Eint__of__num_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Einteger_2Eint__of__num_2E1,type,
% 0.29/0.46 c_2Einteger_2Eint__of__num_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ewords_2En2w_2E0,type,
% 0.29/0.46 c_2Ewords_2En2w_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ewords_2En2w_2E1,type,
% 0.29/0.46 c_2Ewords_2En2w_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2Ethe__value_2E0,type,
% 0.29/0.46 c_2Ebool_2Ethe__value_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ewords_2Eword__2comp_2E0,type,
% 0.29/0.46 c_2Ewords_2Eword__2comp_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ewords_2Eword__2comp_2E1,type,
% 0.29/0.46 c_2Ewords_2Eword__2comp_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_7E_2E0,type,
% 0.29/0.46 c_2Ebool_2E_7E_2E0: u ).
% 0.29/0.46
% 0.29/0.46 thf(c_2Ebool_2E_7E_2E1,type,
% 0.29/0.46 c_2Ebool_2E_7E_2E1: du > u ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
% 0.29/0.46 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.29/0.46 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Enum_2E0,type,
% 0.29/0.46 mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Eprim__rec_2E_3C,type,
% 0.29/0.46 mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.29/0.46 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Ebool_2EF,type,
% 0.29/0.46 mono_2Ec_2Ebool_2EF: $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Earithmetic_2EMOD,type,
% 0.29/0.46 mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Einteger_2ENum,type,
% 0.29/0.46 mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Ebool_2ET,type,
% 0.29/0.46 mono_2Ec_2Ebool_2ET: $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.29/0.46 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Einteger_2Eint__lt,type,
% 0.29/0.46 mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Einteger_2Eint__neg,type,
% 0.29/0.46 mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Einteger_2Eint__of__num,type,
% 0.29/0.46 mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.29/0.46 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
% 0.29/0.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Einteger_2Eint,type,
% 0.29/0.46 i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
% 0.29/0.46
% 0.29/0.46 thf(i_mono_2Etyop_2Enum_2Enum,type,
% 0.29/0.46 i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
% 0.29/0.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Einteger_2Eint,type,
% 0.29/0.46 j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
% 0.29/0.46
% 0.29/0.46 thf(j_mono_2Etyop_2Enum_2Enum,type,
% 0.29/0.46 j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.29/0.46 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.29/0.46 ( ! [V2x_2E0: u] :
% 0.29/0.46 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.29/0.46 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.29/0.46 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.29/0.46 ! [A_27a: d,V0x_2E0: u] :
% 0.29/0.46 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.29/0.46 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.29/0.46 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.29/0.46 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.29/0.46 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Eho_2Es__thm,axiom,
% 0.29/0.46 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.29/0.46 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.29/0.46 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.29/0.46 ! [V0: $o,V1: $o] :
% 0.29/0.46 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.29/0.46 <=> ( V0
% 0.29/0.46 & V1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.29/0.46 ! [V0: $o,V1: $o] :
% 0.29/0.46 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.29/0.46 <=> ( V0
% 0.29/0.46 | V1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Elogic_2E_7E,axiom,
% 0.29/0.46 ! [V0: $o] :
% 0.29/0.46 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.29/0.46 <=> ( (~) @ V0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.29/0.46 ! [V0: $o,V1: $o] :
% 0.29/0.46 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.29/0.46 <=> ( V0
% 0.29/0.46 => V1 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Elogic_2E_3D,axiom,
% 0.29/0.46 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.29/0.46 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.29/0.46 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Equant_2E_21,axiom,
% 0.29/0.46 ! [A_27a: d,V0f_2E0: u] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.29/0.46 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(reserved_2Equant_2E_3F,axiom,
% 0.29/0.46 ! [A_27a: d,V0f_2E0: u] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.29/0.46 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
% 0.29/0.46 ! [V0_2E0: u] :
% 0.29/0.46 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
% 0.29/0.46 = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.46 ! [V0: $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0: $o > $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.29/0.46 ! [V0: $o > $o > $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
% 0.29/0.46 = V0 ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0_2E0: u] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.29/0.46 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.29/0.46 ( ( ( s @ A_27a @ X0_2E0 )
% 0.29/0.46 = ( s @ A_27a @ X1_2E0 ) )
% 0.29/0.46 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0_2E0: u] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.29/0.46 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
% 0.29/0.46 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
% 0.29/0.46 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
% 0.29/0.46 ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X2_2E0 ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X2_2E0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0_2E0: u] :
% 0.29/0.46 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ X0_2E0 ) ) ) )
% 0.29/0.46 = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Ewords_2Edimword_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ c_2Einteger__word_2Ei2w_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a,axiom,
% 0.29/0.46 ! [A_27a: d,X0_2E0: u] :
% 0.29/0.46 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X0_2E0 ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.46 ! [V0: $o > $o,V1: $o] :
% 0.29/0.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0: $o > $o > $o,V1: $o] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.46 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.46 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.29/0.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
% 0.29/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
% 0.29/0.47 = ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
% 0.29/0.47 = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.47 ! [V0: $o > $o,V1: $o] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.47 ! [V0: $o > $o > $o,V1: $o] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
% 0.29/0.47 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( V0 @ V1 )
% 0.29/0.47 = ( V0 @ V1 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.29/0.47 mono_2Ec_2Ebool_2ET ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.29/0.47 ! [V0t1: $o,V1t2: $o] :
% 0.29/0.47 ( ( V0t1
% 0.29/0.47 => V1t2 )
% 0.29/0.47 => ( ( V1t2
% 0.29/0.47 => V0t1 )
% 0.29/0.47 => ( V0t1 = V1t2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2EFALSITY,axiom,
% 0.29/0.47 ! [V0t: $o] :
% 0.29/0.47 ( mono_2Ec_2Ebool_2EF
% 0.29/0.47 => V0t ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.29/0.47 ! [A_27a: d,V0x_2E0: u] :
% 0.29/0.47 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.29/0.47 = ( s @ A_27a @ V0x_2E0 ) )
% 0.29/0.47 <=> mono_2Ec_2Ebool_2ET ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.29/0.47 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 0.29/0.47 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.29/0.47 = ( s @ A_27a @ V1y_2E0 ) )
% 0.29/0.47 <=> ( ( s @ A_27a @ V1y_2E0 )
% 0.29/0.47 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 0.29/0.47 ! [V0t1: $o,V1t2: $o,V2t3: $o] :
% 0.29/0.47 ( ( V0t1
% 0.29/0.47 => ( V1t2
% 0.29/0.47 => V2t3 ) )
% 0.29/0.47 <=> ( ( V0t1
% 0.29/0.47 & V1t2 )
% 0.29/0.47 => V2t3 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2ECOND__CONG,axiom,
% 0.29/0.47 ! [A_27a: d,V0P: $o,V1Q: $o,V2x_2E0: u,V3x_27_2E0: u,V4y_2E0: u,V5y_27_2E0: u] :
% 0.29/0.47 ( ( ( V0P = V1Q )
% 0.29/0.47 & ( V1Q
% 0.29/0.47 => ( ( s @ A_27a @ V2x_2E0 )
% 0.29/0.47 = ( s @ A_27a @ V3x_27_2E0 ) ) )
% 0.29/0.47 & ( ( (~) @ V1Q )
% 0.29/0.47 => ( ( s @ A_27a @ V4y_2E0 )
% 0.29/0.47 = ( s @ A_27a @ V5y_27_2E0 ) ) ) )
% 0.29/0.47 => ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0P ) ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27a @ V4y_2E0 ) ) )
% 0.29/0.47 = ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1Q ) ) @ ( s @ A_27a @ V3x_27_2E0 ) @ ( s @ A_27a @ V5y_27_2E0 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ebool_2Ebool__case__thm,axiom,
% 0.29/0.47 ! [A_27a: d] :
% 0.29/0.47 ( ! [V0t1_2E0: u,V1t2_2E0: u] :
% 0.29/0.47 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) )
% 0.29/0.47 = ( s @ A_27a @ V0t1_2E0 ) )
% 0.29/0.47 & ! [V2t1_2E0: u,V3t2_2E0: u] :
% 0.29/0.47 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ A_27a @ V2t1_2E0 ) @ ( s @ A_27a @ V3t2_2E0 ) ) )
% 0.29/0.47 = ( s @ A_27a @ V3t2_2E0 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Einteger_2EINT__NEG__0,axiom,
% 0.29/0.47 ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
% 0.29/0.47 = ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Einteger_2EINT__LT__CALCULATE,axiom,
% 0.29/0.47 ! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
% 0.29/0.47 = ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) )
% 0.29/0.47 & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) )
% 0.29/0.47 = ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V0n ) )
% 0.29/0.47 & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
% 0.29/0.47 <=> ( ( (~) @ ( V0n = mono_2Ec_2Enum_2E0 ) )
% 0.29/0.47 | ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) ) ) )
% 0.29/0.47 & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) )
% 0.29/0.47 = mono_2Ec_2Ebool_2EF ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Einteger_2ENUM__OF__INT,axiom,
% 0.29/0.47 ! [V0n: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) )
% 0.29/0.47 = V0n ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Einteger__word_2Ei2w__def,axiom,
% 0.29/0.47 ! [A_27a: d,V0i: mono_2Etyop_2Einteger_2Eint] :
% 0.29/0.47 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0i ) ) ) )
% 0.29/0.47 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ V0i @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ V0i ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Eprim__rec_2ENOT__LESS__0,axiom,
% 0.29/0.47 ! [V0n: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ mono_2Ec_2Enum_2E0 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ewords_2En2w__11,axiom,
% 0.29/0.47 ! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
% 0.29/0.47 ( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) ) )
% 0.29/0.47 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) )
% 0.29/0.47 <=> ( ( mono_2Ec_2Earithmetic_2EMOD @ V0m @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
% 0.29/0.47 = ( mono_2Ec_2Earithmetic_2EMOD @ V1n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Ewords_2EWORD__NEG__0,axiom,
% 0.29/0.47 ! [A_27a: d] :
% 0.29/0.47 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
% 0.29/0.47 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(thm_2Einteger__word_2Ei2w__0,conjecture,
% 0.29/0.47 ! [A_27a: d] :
% 0.29/0.47 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
% 0.29/0.47 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.53/1.52 ---- Embedded in THF ---
% 2.53/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.53/1.52 %%% Generated on Tue Feb 24 08:21:00 EST 2026
% 2.53/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.53/1.52 %%% Logic specification used:
% 2.53/1.52 %%% thf(spec, logic, $$dhol).
% 2.53/1.52
% 2.53/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2DTF16294.p
% See solution above
% 2.53/1.52 ------------------------
% 2.53/1.55 ---- Cleaned THF ---
% 2.53/1.55 thf(u,type,
% 2.53/1.55 u: $tType ).
% 2.53/1.55
% 2.53/1.55 thf(d,type,
% 2.53/1.55 d: $tType ).
% 2.53/1.55
% 2.53/1.55 thf(du,type,
% 2.53/1.55 du: $tType ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Etyop_2Einteger_2Eint,type,
% 2.53/1.55 mono_2Etyop_2Einteger_2Eint: $tType ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Etyop_2Enum_2Enum,type,
% 2.53/1.55 mono_2Etyop_2Enum_2Enum: $tType ).
% 2.53/1.55
% 2.53/1.55 thf(tyop_2Ebool_2Eitself,type,
% 2.53/1.55 tyop_2Ebool_2Eitself: d > d ).
% 2.53/1.55
% 2.53/1.55 thf(tyop_2Efcp_2Ecart,type,
% 2.53/1.55 tyop_2Efcp_2Ecart: d > d > d ).
% 2.53/1.55
% 2.53/1.55 thf(tyop_2Einteger_2Eint,type,
% 2.53/1.55 tyop_2Einteger_2Eint: d ).
% 2.53/1.55
% 2.53/1.55 thf(tyop_2Emin_2Ebool,type,
% 2.53/1.55 tyop_2Emin_2Ebool: d ).
% 2.53/1.55
% 2.53/1.55 thf(tyop_2Emin_2Efun,type,
% 2.53/1.55 tyop_2Emin_2Efun: d > d > d ).
% 2.53/1.55
% 2.53/1.55 thf(tyop_2Enum_2Enum,type,
% 2.53/1.55 tyop_2Enum_2Enum: d ).
% 2.53/1.55
% 2.53/1.55 thf(s,type,
% 2.53/1.55 s: d > u > du ).
% 2.53/1.55
% 2.53/1.55 thf(app_2E2,type,
% 2.53/1.55 app_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(combin_i_2E0,type,
% 2.53/1.55 combin_i_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(combin_k_2E0,type,
% 2.53/1.55 combin_k_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(combin_s_2E0,type,
% 2.53/1.55 combin_s_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_21_2E0,type,
% 2.53/1.55 c_2Ebool_2E_21_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_21_2E1,type,
% 2.53/1.55 c_2Ebool_2E_21_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 2.53/1.55 c_2Ebool_2E_2F_5C_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 2.53/1.55 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Enum_2E0_2E0,type,
% 2.53/1.55 c_2Enum_2E0_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Eprim__rec_2E_3C_2E0,type,
% 2.53/1.55 c_2Eprim__rec_2E_3C_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Eprim__rec_2E_3C_2E2,type,
% 2.53/1.55 c_2Eprim__rec_2E_3C_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Emin_2E_3D_2E0,type,
% 2.53/1.55 c_2Emin_2E_3D_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Emin_2E_3D_2E2,type,
% 2.53/1.55 c_2Emin_2E_3D_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 2.53/1.55 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 2.53/1.55 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_3F_2E0,type,
% 2.53/1.55 c_2Ebool_2E_3F_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_3F_2E1,type,
% 2.53/1.55 c_2Ebool_2E_3F_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2ECOND_2E0,type,
% 2.53/1.55 c_2Ebool_2ECOND_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2ECOND_2E3,type,
% 2.53/1.55 c_2Ebool_2ECOND_2E3: du > du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2EF_2E0,type,
% 2.53/1.55 c_2Ebool_2EF_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Earithmetic_2EMOD_2E0,type,
% 2.53/1.55 c_2Earithmetic_2EMOD_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Earithmetic_2EMOD_2E2,type,
% 2.53/1.55 c_2Earithmetic_2EMOD_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2ENum_2E0,type,
% 2.53/1.55 c_2Einteger_2ENum_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2ENum_2E1,type,
% 2.53/1.55 c_2Einteger_2ENum_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2ET_2E0,type,
% 2.53/1.55 c_2Ebool_2ET_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 2.53/1.55 c_2Ebool_2E_5C_2F_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 2.53/1.55 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ewords_2Edimword_2E0,type,
% 2.53/1.55 c_2Ewords_2Edimword_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ewords_2Edimword_2E1,type,
% 2.53/1.55 c_2Ewords_2Edimword_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger__word_2Ei2w_2E0,type,
% 2.53/1.55 c_2Einteger__word_2Ei2w_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger__word_2Ei2w_2E1,type,
% 2.53/1.55 c_2Einteger__word_2Ei2w_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2Eint__lt_2E0,type,
% 2.53/1.55 c_2Einteger_2Eint__lt_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2Eint__lt_2E2,type,
% 2.53/1.55 c_2Einteger_2Eint__lt_2E2: du > du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2Eint__neg_2E0,type,
% 2.53/1.55 c_2Einteger_2Eint__neg_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2Eint__neg_2E1,type,
% 2.53/1.55 c_2Einteger_2Eint__neg_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2Eint__of__num_2E0,type,
% 2.53/1.55 c_2Einteger_2Eint__of__num_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Einteger_2Eint__of__num_2E1,type,
% 2.53/1.55 c_2Einteger_2Eint__of__num_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ewords_2En2w_2E0,type,
% 2.53/1.55 c_2Ewords_2En2w_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ewords_2En2w_2E1,type,
% 2.53/1.55 c_2Ewords_2En2w_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2Ethe__value_2E0,type,
% 2.53/1.55 c_2Ebool_2Ethe__value_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ewords_2Eword__2comp_2E0,type,
% 2.53/1.55 c_2Ewords_2Eword__2comp_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ewords_2Eword__2comp_2E1,type,
% 2.53/1.55 c_2Ewords_2Eword__2comp_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_7E_2E0,type,
% 2.53/1.55 c_2Ebool_2E_7E_2E0: u ).
% 2.53/1.55
% 2.53/1.55 thf(c_2Ebool_2E_7E_2E1,type,
% 2.53/1.55 c_2Ebool_2E_7E_2E1: du > u ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
% 2.53/1.55 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 2.53/1.55 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Enum_2E0,type,
% 2.53/1.55 mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Eprim__rec_2E_3C,type,
% 2.53/1.55 mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 2.53/1.55 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Ebool_2EF,type,
% 2.53/1.55 mono_2Ec_2Ebool_2EF: $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Earithmetic_2EMOD,type,
% 2.53/1.55 mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Einteger_2ENum,type,
% 2.53/1.55 mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Ebool_2ET,type,
% 2.53/1.55 mono_2Ec_2Ebool_2ET: $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 2.53/1.55 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Einteger_2Eint__lt,type,
% 2.53/1.55 mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Einteger_2Eint__neg,type,
% 2.53/1.55 mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Einteger_2Eint__of__num,type,
% 2.53/1.55 mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(mono_2Ec_2Ebool_2E_7E,type,
% 2.53/1.55 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
% 2.53/1.55 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Einteger_2Eint,type,
% 2.53/1.55 i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
% 2.53/1.55
% 2.53/1.55 thf(i_mono_2Etyop_2Enum_2Enum,type,
% 2.53/1.55 i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
% 2.53/1.55 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Einteger_2Eint,type,
% 2.53/1.55 j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
% 2.53/1.55
% 2.53/1.55 thf(j_mono_2Etyop_2Enum_2Enum,type,
% 2.53/1.55 j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Eho_2Eeq__ext,axiom,
% 2.53/1.55 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 2.53/1.55 ( ! [V2x_2E0: u] :
% 2.53/1.55 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 2.53/1.55 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Eho_2Ei__thm,axiom,
% 2.53/1.55 ! [A_27a: d,V0x_2E0: u] :
% 2.53/1.55 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Eho_2Ek__thm,axiom,
% 2.53/1.55 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 2.53/1.55 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Eho_2Es__thm,axiom,
% 2.53/1.55 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 2.53/1.55 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 2.53/1.55 ! [V0: $o,V1: $o] :
% 2.53/1.55 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 2.53/1.55 <=> ( V0
% 2.53/1.55 & V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 2.53/1.55 ! [V0: $o,V1: $o] :
% 2.53/1.55 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 2.53/1.55 <=> ( V0
% 2.53/1.55 | V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Elogic_2E_7E,axiom,
% 2.53/1.55 ! [V0: $o] :
% 2.53/1.55 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 2.53/1.55 <=> ( (~) @ V0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 2.53/1.55 ! [V0: $o,V1: $o] :
% 2.53/1.55 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 2.53/1.55 <=> ( V0
% 2.53/1.55 => V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Elogic_2E_3D,axiom,
% 2.53/1.55 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 2.53/1.55 <=> ( ( s @ A_27a @ V0_2E0 )
% 2.53/1.55 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Equant_2E_21,axiom,
% 2.53/1.55 ! [A_27a: d,V0f_2E0: u] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 2.53/1.55 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(reserved_2Equant_2E_3F,axiom,
% 2.53/1.55 ! [A_27a: d,V0f_2E0: u] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 2.53/1.55 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
% 2.53/1.55 ! [V0_2E0: u] :
% 2.53/1.55 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
% 2.53/1.55 = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: $o > $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.55 ! [V0: $o > $o > $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
% 2.53/1.55 = V0 ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 2.53/1.55 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.53/1.55 ( ( ( s @ A_27a @ X0_2E0 )
% 2.53/1.55 = ( s @ A_27a @ X1_2E0 ) )
% 2.53/1.55 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 2.53/1.55 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
% 2.53/1.55 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
% 2.53/1.55 ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X2_2E0 ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X2_2E0 ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.55 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ X0_2E0 ) ) ) )
% 2.53/1.55 = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Ewords_2Edimword_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ c_2Einteger__word_2Ei2w_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.55 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X0_2E0 ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: $o > $o,V1: $o] :
% 2.53/1.55 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: $o > $o > $o,V1: $o] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
% 2.53/1.55 = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: $o > $o,V1: $o] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: $o > $o > $o,V1: $o] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
% 2.53/1.55 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( V0 @ V1 )
% 2.53/1.55 = ( V0 @ V1 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2ETRUTH,axiom,
% 2.53/1.55 mono_2Ec_2Ebool_2ET ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 2.53/1.55 ! [V0t1: $o,V1t2: $o] :
% 2.53/1.55 ( ( V0t1
% 2.53/1.55 => V1t2 )
% 2.53/1.55 => ( ( V1t2
% 2.53/1.55 => V0t1 )
% 2.53/1.55 => ( V0t1 = V1t2 ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2EFALSITY,axiom,
% 2.53/1.55 ! [V0t: $o] :
% 2.53/1.55 ( mono_2Ec_2Ebool_2EF
% 2.53/1.55 => V0t ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 2.53/1.55 ! [A_27a: d,V0x_2E0: u] :
% 2.53/1.55 ( ( ( s @ A_27a @ V0x_2E0 )
% 2.53/1.55 = ( s @ A_27a @ V0x_2E0 ) )
% 2.53/1.55 <=> mono_2Ec_2Ebool_2ET ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 2.53/1.55 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 2.53/1.55 ( ( ( s @ A_27a @ V0x_2E0 )
% 2.53/1.55 = ( s @ A_27a @ V1y_2E0 ) )
% 2.53/1.55 <=> ( ( s @ A_27a @ V1y_2E0 )
% 2.53/1.55 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 2.53/1.55 ! [V0t1: $o,V1t2: $o,V2t3: $o] :
% 2.53/1.55 ( ( V0t1
% 2.53/1.55 => ( V1t2
% 2.53/1.55 => V2t3 ) )
% 2.53/1.55 <=> ( ( V0t1
% 2.53/1.55 & V1t2 )
% 2.53/1.55 => V2t3 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2ECOND__CONG,axiom,
% 2.53/1.55 ! [A_27a: d,V0P: $o,V1Q: $o,V2x_2E0: u,V3x_27_2E0: u,V4y_2E0: u,V5y_27_2E0: u] :
% 2.53/1.55 ( ( ( V0P = V1Q )
% 2.53/1.55 & ( V1Q
% 2.53/1.55 => ( ( s @ A_27a @ V2x_2E0 )
% 2.53/1.55 = ( s @ A_27a @ V3x_27_2E0 ) ) )
% 2.53/1.55 & ( ( (~) @ V1Q )
% 2.53/1.55 => ( ( s @ A_27a @ V4y_2E0 )
% 2.53/1.55 = ( s @ A_27a @ V5y_27_2E0 ) ) ) )
% 2.53/1.55 => ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0P ) ) @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27a @ V4y_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1Q ) ) @ ( s @ A_27a @ V3x_27_2E0 ) @ ( s @ A_27a @ V5y_27_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ebool_2Ebool__case__thm,axiom,
% 2.53/1.55 ! [A_27a: d] :
% 2.53/1.55 ( ! [V0t1_2E0: u,V1t2_2E0: u] :
% 2.53/1.55 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27a @ V0t1_2E0 ) )
% 2.53/1.55 & ! [V2t1_2E0: u,V3t2_2E0: u] :
% 2.53/1.55 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ A_27a @ V2t1_2E0 ) @ ( s @ A_27a @ V3t2_2E0 ) ) )
% 2.53/1.55 = ( s @ A_27a @ V3t2_2E0 ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Einteger_2EINT__NEG__0,axiom,
% 2.53/1.55 ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
% 2.53/1.55 = ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Einteger_2EINT__LT__CALCULATE,axiom,
% 2.53/1.55 ! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
% 2.53/1.55 = ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) )
% 2.53/1.55 & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) )
% 2.53/1.55 = ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V0n ) )
% 2.53/1.55 & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
% 2.53/1.55 <=> ( ( (~) @ ( V0n = mono_2Ec_2Enum_2E0 ) )
% 2.53/1.55 | ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) ) ) )
% 2.53/1.55 & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) )
% 2.53/1.55 = mono_2Ec_2Ebool_2EF ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Einteger_2ENUM__OF__INT,axiom,
% 2.53/1.55 ! [V0n: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) )
% 2.53/1.55 = V0n ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Einteger__word_2Ei2w__def,axiom,
% 2.53/1.55 ! [A_27a: d,V0i: mono_2Etyop_2Einteger_2Eint] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0i ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ V0i @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ V0i ) ) ) ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Eprim__rec_2ENOT__LESS__0,axiom,
% 2.53/1.55 ! [V0n: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ mono_2Ec_2Enum_2E0 ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ewords_2En2w__11,axiom,
% 2.53/1.55 ! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
% 2.53/1.55 ( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) )
% 2.53/1.55 <=> ( ( mono_2Ec_2Earithmetic_2EMOD @ V0m @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
% 2.53/1.55 = ( mono_2Ec_2Earithmetic_2EMOD @ V1n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Ewords_2EWORD__NEG__0,axiom,
% 2.53/1.55 ! [A_27a: d] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
% 2.53/1.55
% 2.53/1.55 thf(thm_2Einteger__word_2Ei2w__0,conjecture,
% 2.53/1.55 ! [A_27a: d] :
% 2.53/1.55 ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
% 2.53/1.55 = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A_27a ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
% 2.53/1.55 ------------------------
% 2.53/1.57 % (16414)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/2Mi)
% 2.53/1.57 % (16414)Instruction limit reached!
% 2.53/1.57 % (16414)------------------------------
% 2.53/1.57 % (16414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (16414)Termination reason: Unknown
% 2.53/1.57 % (16414)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (16414)Memory used [KB]: 1151
% 2.53/1.57 % (16414)Time elapsed: 0.002 s
% 2.53/1.57 % (16414)Instructions burned: 2 (million)
% 2.53/1.57 % (16414)------------------------------
% 2.53/1.57 % (16414)------------------------------
% 2.53/1.58 % (16416)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/18Mi)
% 2.53/1.58 % (16411)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/4Mi)
% 2.53/1.58 % (16410)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/183Mi)
% 2.53/1.58 % (16413)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/2Mi)
% 2.53/1.58 % (16415)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/275Mi)
% 2.53/1.58 % (16412)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/27Mi)
% 2.53/1.58 % (16413)Instruction limit reached!
% 2.53/1.58 % (16413)------------------------------
% 2.53/1.58 % (16413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (16413)Termination reason: Unknown
% 2.53/1.58 % (16413)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (16413)Memory used [KB]: 1151
% 2.53/1.58 % (16413)Time elapsed: 0.004 s
% 2.53/1.58 % (16413)Instructions burned: 3 (million)
% 2.53/1.58 % (16413)------------------------------
% 2.53/1.58 % (16413)------------------------------
% 2.53/1.58 % (16416)Instruction limit reached!
% 2.53/1.58 % (16416)------------------------------
% 2.53/1.58 % (16416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (16416)Termination reason: Unknown
% 2.53/1.58 % (16416)Termination phase: Property scanning
% 2.53/1.58
% 2.53/1.58 % (16416)Memory used [KB]: 1279
% 2.53/1.58 % (16416)Time elapsed: 0.008 s
% 2.53/1.58 % (16416)Instructions burned: 18 (million)
% 2.53/1.58 % (16416)------------------------------
% 2.53/1.58 % (16416)------------------------------
% 2.53/1.58 % (16411)Instruction limit reached!
% 2.53/1.58 % (16411)------------------------------
% 2.53/1.58 % (16411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (16411)Termination reason: Unknown
% 2.53/1.58 % (16411)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (16411)Memory used [KB]: 1151
% 2.53/1.58 % (16411)Time elapsed: 0.005 s
% 2.53/1.58 % (16411)Instructions burned: 5 (million)
% 2.53/1.58 % (16411)------------------------------
% 2.53/1.58 % (16411)------------------------------
% 2.53/1.59 % (16417)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/3Mi)
% 2.53/1.59 % (16417)Instruction limit reached!
% 2.53/1.59 % (16417)------------------------------
% 2.53/1.59 % (16417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (16417)Termination reason: Unknown
% 2.53/1.59 % (16417)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (16417)Memory used [KB]: 1151
% 2.53/1.59 % (16417)Time elapsed: 0.003 s
% 2.53/1.59 % (16417)Instructions burned: 4 (million)
% 2.53/1.59 % (16417)------------------------------
% 2.53/1.59 % (16417)------------------------------
% 2.53/1.59 % (16415)Refutation not found, incomplete strategy
% 2.53/1.59 % (16415)------------------------------
% 2.53/1.59 % (16415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (16415)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.59
% 2.53/1.59
% 2.53/1.59 % (16415)Memory used [KB]: 5628
% 2.53/1.59 % (16415)Time elapsed: 0.009 s
% 2.53/1.59 % (16415)Instructions burned: 12 (million)
% 2.53/1.59 % (16415)------------------------------
% 2.53/1.59 % (16415)------------------------------
% 2.53/1.59 % (16419)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/15Mi)
% 2.53/1.59 % (16412)Instruction limit reached!
% 2.53/1.59 % (16412)------------------------------
% 2.53/1.59 % (16412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (16412)Termination reason: Unknown
% 2.53/1.59 % (16412)Termination phase: Property scanning
% 2.53/1.59
% 2.53/1.59 % (16412)Memory used [KB]: 1279
% 2.53/1.59 % (16412)Time elapsed: 0.015 s
% 2.53/1.59 % (16412)Instructions burned: 27 (million)
% 2.53/1.59 % (16412)------------------------------
% 2.53/1.59 % (16412)------------------------------
% 2.58/1.60 % (16421)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/1041Mi)
% 2.58/1.60 % (16419)Instruction limit reached!
% 2.58/1.60 % (16419)------------------------------
% 2.58/1.60 % (16419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.60 % (16419)Termination reason: Unknown
% 2.58/1.60 % (16419)Termination phase: Property scanning
% 2.58/1.60
% 2.58/1.60 % (16419)Memory used [KB]: 1279
% 2.58/1.60 % (16419)Time elapsed: 0.006 s
% 2.58/1.60 % (16419)Instructions burned: 17 (million)
% 2.58/1.60 % (16419)------------------------------
% 2.58/1.60 % (16419)------------------------------
% 2.58/1.60 % (16418)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/37Mi)
% 2.58/1.60 % (16420)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/3Mi)
% 2.58/1.60 % (16420)Instruction limit reached!
% 2.58/1.60 % (16420)------------------------------
% 2.58/1.60 % (16420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.60 % (16420)Termination reason: Unknown
% 2.58/1.60 % (16420)Termination phase: shuffling
% 2.58/1.60
% 2.58/1.60 % (16420)Memory used [KB]: 1151
% 2.58/1.60 % (16420)Time elapsed: 0.004 s
% 2.58/1.60 % (16420)Instructions burned: 4 (million)
% 2.58/1.60 % (16420)------------------------------
% 2.58/1.60 % (16420)------------------------------
% 2.58/1.61 % (16424)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/3Mi)
% 2.58/1.61 % (16422)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/7Mi)
% 2.58/1.61 % (16424)Instruction limit reached!
% 2.58/1.61 % (16424)------------------------------
% 2.58/1.61 % (16424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (16424)Termination reason: Unknown
% 2.58/1.61 % (16424)Termination phase: shuffling
% 2.58/1.61
% 2.58/1.61 % (16424)Memory used [KB]: 1151
% 2.58/1.61 % (16424)Time elapsed: 0.002 s
% 2.58/1.61 % (16424)Instructions burned: 4 (million)
% 2.58/1.61 % (16424)------------------------------
% 2.58/1.61 % (16424)------------------------------
% 2.58/1.61 % (16422)Instruction limit reached!
% 2.58/1.61 % (16422)------------------------------
% 2.58/1.61 % (16422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (16422)Termination reason: Unknown
% 2.58/1.61 % (16422)Termination phase: Property scanning
% 2.58/1.61
% 2.58/1.61 % (16422)Memory used [KB]: 1151
% 2.58/1.61 % (16422)Time elapsed: 0.006 s
% 2.58/1.61 % (16422)Instructions burned: 7 (million)
% 2.58/1.61 % (16422)------------------------------
% 2.58/1.61 % (16422)------------------------------
% 2.58/1.61 % (16423)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/16Mi)
% 2.58/1.62 % (16426)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/7Mi)
% 2.58/1.62 % (16418)Instruction limit reached!
% 2.58/1.62 % (16418)------------------------------
% 2.58/1.62 % (16418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (16418)Termination reason: Unknown
% 2.58/1.62 % (16418)Termination phase: Property scanning
% 2.58/1.62
% 2.58/1.62 % (16418)Memory used [KB]: 1407
% 2.58/1.62 % (16418)Time elapsed: 0.020 s
% 2.58/1.62 % (16418)Instructions burned: 37 (million)
% 2.58/1.62 % (16418)------------------------------
% 2.58/1.62 % (16418)------------------------------
% 2.58/1.62 % (16426)Instruction limit reached!
% 2.58/1.62 % (16426)------------------------------
% 2.58/1.62 % (16426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (16426)Termination reason: Unknown
% 2.58/1.62 % (16426)Termination phase: shuffling
% 2.58/1.62
% 2.58/1.62 % (16426)Memory used [KB]: 1151
% 2.58/1.62 % (16426)Time elapsed: 0.004 s
% 2.58/1.62 % (16426)Instructions burned: 10 (million)
% 2.58/1.62 % (16426)------------------------------
% 2.58/1.62 % (16426)------------------------------
% 2.58/1.62 % (16425)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/3Mi)
% 2.58/1.62 % (16423)Instruction limit reached!
% 2.58/1.62 % (16423)------------------------------
% 2.58/1.62 % (16423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (16423)Termination reason: Unknown
% 2.58/1.62 % (16423)Termination phase: Property scanning
% 2.58/1.62
% 2.58/1.62 % (16423)Memory used [KB]: 1279
% 2.58/1.62 % (16423)Time elapsed: 0.011 s
% 2.58/1.62 % (16423)Instructions burned: 16 (million)
% 2.58/1.62 % (16423)------------------------------
% 2.58/1.62 % (16423)------------------------------
% 2.58/1.62 % (16425)Instruction limit reached!
% 2.58/1.62 % (16425)------------------------------
% 2.58/1.62 % (16425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (16425)Termination reason: Unknown
% 2.58/1.62 % (16425)Termination phase: shuffling
% 2.58/1.62
% 2.58/1.62 % (16425)Memory used [KB]: 1151
% 2.58/1.62 % (16425)Time elapsed: 0.004 s
% 2.58/1.62 % (16425)Instructions burned: 4 (million)
% 2.58/1.62 % (16425)------------------------------
% 2.58/1.62 % (16425)------------------------------
% 2.58/1.63 % (16427)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/3Mi)
% 2.58/1.63 % (16427)Instruction limit reached!
% 2.58/1.63 % (16427)------------------------------
% 2.58/1.63 % (16427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.63 % (16427)Termination reason: Unknown
% 2.58/1.63 % (16427)Termination phase: shuffling
% 2.58/1.63
% 2.58/1.63 % (16427)Memory used [KB]: 1151
% 2.58/1.63 % (16427)Time elapsed: 0.003 s
% 2.58/1.63 % (16427)Instructions burned: 3 (million)
% 2.58/1.63 % (16427)------------------------------
% 2.58/1.63 % (16427)------------------------------
% 2.58/1.63 % (16429)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/18Mi)
% 2.58/1.63 % (16429)Instruction limit reached!
% 2.58/1.63 % (16429)------------------------------
% 2.58/1.63 % (16429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.63 % (16429)Termination reason: Unknown
% 2.58/1.63 % (16429)Termination phase: Property scanning
% 2.58/1.63
% 2.58/1.63 % (16429)Memory used [KB]: 1279
% 2.58/1.63 % (16429)Time elapsed: 0.006 s
% 2.58/1.63 % (16429)Instructions burned: 19 (million)
% 2.58/1.63 % (16429)------------------------------
% 2.58/1.63 % (16429)------------------------------
% 2.58/1.64 % (16428)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/4Mi)
% 2.58/1.64 % (16430)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/710Mi)
% 2.58/1.64 % (16428)Instruction limit reached!
% 2.58/1.64 % (16428)------------------------------
% 2.58/1.64 % (16428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.64 % (16428)Termination reason: Unknown
% 2.58/1.64 % (16428)Termination phase: Property scanning
% 2.58/1.64
% 2.58/1.64 % (16428)Memory used [KB]: 1151
% 2.58/1.64 % (16428)Time elapsed: 0.005 s
% 2.58/1.64 % (16428)Instructions burned: 5 (million)
% 2.58/1.64 % (16428)------------------------------
% 2.58/1.64 % (16428)------------------------------
% 2.58/1.64 % (16431)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/6Mi)
% 2.58/1.64 % (16432)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/902Mi)
% 2.58/1.64 % (16433)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/21Mi)
% 2.58/1.64 % (16431)Instruction limit reached!
% 2.58/1.64 % (16431)------------------------------
% 2.58/1.64 % (16431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.64 % (16431)Termination reason: Unknown
% 2.58/1.64 % (16431)Termination phase: Property scanning
% 2.58/1.64
% 2.58/1.64 % (16431)Memory used [KB]: 1151
% 2.58/1.64 % (16431)Time elapsed: 0.006 s
% 2.58/1.64 % (16431)Instructions burned: 7 (million)
% 2.58/1.64 % (16431)------------------------------
% 2.58/1.64 % (16431)------------------------------
% 2.58/1.65 % (16433)Instruction limit reached!
% 2.58/1.65 % (16433)------------------------------
% 2.58/1.65 % (16433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.65 % (16433)Termination reason: Unknown
% 2.58/1.65 % (16433)Termination phase: SInE selection
% 2.58/1.65
% 2.58/1.65 % (16433)Memory used [KB]: 1279
% 2.58/1.65 % (16433)Time elapsed: 0.007 s
% 2.58/1.65 % (16433)Instructions burned: 21 (million)
% 2.58/1.65 % (16433)------------------------------
% 2.58/1.65 % (16433)------------------------------
% 2.58/1.66 % (16432)Refutation not found, incomplete strategy
% 2.58/1.66 % (16432)------------------------------
% 2.58/1.66 % (16432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.66 % (16432)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.66
% 2.58/1.66
% 2.58/1.66 % (16432)Memory used [KB]: 6140
% 2.58/1.66 % (16432)Time elapsed: 0.016 s
% 2.58/1.66 % (16432)Instructions burned: 45 (million)
% 2.58/1.66 % (16432)------------------------------
% 2.58/1.66 % (16432)------------------------------
% 2.58/1.66 % (16434)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/5Mi)
% 2.58/1.66 % (16435)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_16294 for (2999ds/6Mi)
% 2.58/1.66 % (16436)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/377Mi)
% 2.58/1.66 % (16434)Instruction limit reached!
% 2.58/1.66 % (16434)------------------------------
% 2.58/1.66 % (16434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.66 % (16434)Termination reason: Unknown
% 2.58/1.66 % (16434)Termination phase: shuffling
% 2.58/1.66
% 2.58/1.66 % (16434)Memory used [KB]: 1279
% 2.58/1.66 % (16434)Time elapsed: 0.005 s
% 2.58/1.66 % (16434)Instructions burned: 6 (million)
% 2.58/1.66 % (16434)------------------------------
% 2.58/1.66 % (16434)------------------------------
% 2.58/1.66 % (16435)Instruction limit reached!
% 2.58/1.66 % (16435)------------------------------
% 2.58/1.66 % (16435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.66 % (16435)Termination reason: Unknown
% 2.58/1.66 % (16435)Termination phase: shuffling
% 2.58/1.66
% 2.58/1.66 % (16435)Memory used [KB]: 1279
% 2.58/1.66 % (16435)Time elapsed: 0.004 s
% 2.58/1.66 % (16435)Instructions burned: 7 (million)
% 2.58/1.66 % (16435)------------------------------
% 2.58/1.66 % (16435)------------------------------
% 2.58/1.67 % (16437)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/779Mi)
% 2.58/1.67 % (16439)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/879Mi)
% 2.58/1.68 % (16438)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/19Mi)
% 2.58/1.68 % (16438)Instruction limit reached!
% 2.58/1.68 % (16438)------------------------------
% 2.58/1.68 % (16438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.68 % (16438)Termination reason: Unknown
% 2.58/1.68 % (16438)Termination phase: Property scanning
% 2.58/1.68
% 2.58/1.68 % (16438)Memory used [KB]: 1407
% 2.58/1.68 % (16438)Time elapsed: 0.009 s
% 2.58/1.68 % (16438)Instructions burned: 20 (million)
% 2.58/1.68 % (16438)------------------------------
% 2.58/1.68 % (16438)------------------------------
% 2.58/1.69 % (16410)Instruction limit reached!
% 2.58/1.69 % (16410)------------------------------
% 2.58/1.69 % (16410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.69 % (16410)Termination reason: Unknown
% 2.58/1.69 % (16410)Termination phase: Saturation
% 2.58/1.69
% 2.58/1.69 % (16410)Memory used [KB]: 6652
% 2.58/1.69 % (16410)Time elapsed: 0.110 s
% 2.58/1.69 % (16410)Instructions burned: 183 (million)
% 2.58/1.69 % (16410)------------------------------
% 2.58/1.69 % (16410)------------------------------
% 2.58/1.69 % (16440)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/17Mi)
% 2.58/1.70 % (16440)Instruction limit reached!
% 2.58/1.70 % (16440)------------------------------
% 2.58/1.70 % (16440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.70 % (16440)Termination reason: Unknown
% 2.58/1.70 % (16440)Termination phase: Property scanning
% 2.58/1.70
% 2.58/1.70 % (16440)Memory used [KB]: 1279
% 2.58/1.70 % (16440)Time elapsed: 0.007 s
% 2.58/1.70 % (16440)Instructions burned: 19 (million)
% 2.58/1.70 % (16440)------------------------------
% 2.58/1.70 % (16440)------------------------------
% 2.58/1.70 % (16441)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/3Mi)
% 2.58/1.70 % (16441)Instruction limit reached!
% 2.58/1.70 % (16441)------------------------------
% 2.58/1.70 % (16441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.70 % (16441)Termination reason: Unknown
% 2.58/1.70 % (16441)Termination phase: shuffling
% 2.58/1.70
% 2.58/1.70 % (16441)Memory used [KB]: 1151
% 2.58/1.70 % (16441)Time elapsed: 0.003 s
% 2.58/1.70 % (16441)Instructions burned: 4 (million)
% 2.58/1.70 % (16441)------------------------------
% 2.58/1.70 % (16441)------------------------------
% 2.58/1.71 % (16442)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/30Mi)
% 2.58/1.71 % (16443)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/127Mi)
% 2.58/1.72 % (16442)Instruction limit reached!
% 2.58/1.72 % (16442)------------------------------
% 2.58/1.72 % (16442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.72 % (16442)Termination reason: Unknown
% 2.58/1.72 % (16442)Termination phase: Property scanning
% 2.58/1.72
% 2.58/1.72 % (16442)Memory used [KB]: 1279
% 2.58/1.72 % (16442)Time elapsed: 0.011 s
% 2.58/1.72 % (16442)Instructions burned: 33 (million)
% 2.58/1.72 % (16442)------------------------------
% 2.58/1.72 % (16442)------------------------------
% 2.58/1.73 % (16444)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/100Mi)
% 2.58/1.73 % (16430)Refutation not found, incomplete strategy
% 2.58/1.73 % (16430)------------------------------
% 2.58/1.73 % (16430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.73 % (16430)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.73
% 2.58/1.73
% 2.58/1.73 % (16430)Memory used [KB]: 6268
% 2.58/1.73 % (16430)Time elapsed: 0.118 s
% 2.58/1.73 % (16430)Instructions burned: 182 (million)
% 2.58/1.73 % (16430)------------------------------
% 2.58/1.73 % (16430)------------------------------
% 2.58/1.74 % (16445)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/3Mi)
% 2.58/1.74 % (16445)Instruction limit reached!
% 2.58/1.74 % (16445)------------------------------
% 2.58/1.74 % (16445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.74 % (16445)Termination reason: Unknown
% 2.58/1.74 % (16445)Termination phase: shuffling
% 2.58/1.74
% 2.58/1.74 % (16445)Memory used [KB]: 1151
% 2.58/1.74 % (16445)Time elapsed: 0.002 s
% 2.58/1.74 % (16445)Instructions burned: 3 (million)
% 2.58/1.74 % (16445)------------------------------
% 2.58/1.74 % (16445)------------------------------
% 2.58/1.75 % (16446)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_16294 for (2998ds/20Mi)
% 2.58/1.76 % (16443)Instruction limit reached!
% 2.58/1.76 % (16443)------------------------------
% 2.58/1.76 % (16443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.76 % (16443)Termination reason: Unknown
% 2.58/1.76 % (16443)Termination phase: Saturation
% 2.58/1.76
% 2.58/1.76 % (16443)Memory used [KB]: 6268
% 2.58/1.76 % (16443)Time elapsed: 0.044 s
% 2.58/1.76 % (16443)Instructions burned: 128 (million)
% 2.58/1.76 % (16443)------------------------------
% 2.58/1.76 % (16443)------------------------------
% 2.58/1.76 % (16446)Refutation not found, incomplete strategy
% 2.58/1.76 % (16446)------------------------------
% 2.58/1.76 % (16446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.76 % (16446)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.76
% 2.58/1.76
% 2.58/1.76 % (16446)Memory used [KB]: 5628
% 2.58/1.76 % (16446)Time elapsed: 0.007 s
% 2.58/1.76 % (16446)Instructions burned: 16 (million)
% 2.58/1.76 % (16446)------------------------------
% 2.58/1.76 % (16446)------------------------------
% 2.58/1.76 % (16444)Instruction limit reached!
% 2.58/1.76 % (16444)------------------------------
% 2.58/1.76 % (16444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.76 % (16444)Termination reason: Unknown
% 2.58/1.76 % (16444)Termination phase: Saturation
% 2.58/1.76
% 2.58/1.76 % (16444)Memory used [KB]: 6268
% 2.58/1.76 % (16444)Time elapsed: 0.031 s
% 2.58/1.76 % (16444)Instructions burned: 100 (million)
% 2.58/1.76 % (16444)------------------------------
% 2.58/1.76 % (16444)------------------------------
% 2.58/1.77 % (16447)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_16294 for (2997ds/86Mi)
% 2.58/1.77 % (16448)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_16294 for (2997ds/107Mi)
% 2.58/1.77 % (16449)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_16294 for (2997ds/39Mi)
% 2.58/1.77 % (16436)Instruction limit reached!
% 2.58/1.77 % (16436)------------------------------
% 2.58/1.77 % (16436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.77 % (16436)Termination reason: Unknown
% 2.58/1.77 % (16436)Termination phase: Saturation
% 2.58/1.77
% 2.58/1.77 % (16436)Memory used [KB]: 6652
% 2.58/1.77 % (16436)Time elapsed: 0.116 s
% 2.58/1.77 % (16436)Instructions burned: 377 (million)
% 2.58/1.77 % (16436)------------------------------
% 2.58/1.77 % (16436)------------------------------
% 2.58/1.78 % (16449)Instruction limit reached!
% 2.58/1.78 % (16449)------------------------------
% 2.58/1.78 % (16449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.78 % (16449)Termination reason: Unknown
% 2.58/1.78 % (16449)Termination phase: Property scanning
% 2.58/1.78
% 2.58/1.78 % (16449)Memory used [KB]: 1407
% 2.58/1.78 % (16449)Time elapsed: 0.013 s
% 2.58/1.78 % (16449)Instructions burned: 41 (million)
% 2.58/1.78 % (16449)------------------------------
% 2.58/1.78 % (16449)------------------------------
% 2.58/1.78 % (16450)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_16294 for (2997ds/448Mi)
% 2.58/1.79 % (16451)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_16294 for (2997ds/46Mi)
% 2.58/1.80 % (16447)Instruction limit reached!
% 2.58/1.80 % (16447)------------------------------
% 2.58/1.80 % (16447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.80 % (16447)Termination reason: Unknown
% 2.58/1.80 % (16447)Termination phase: Saturation
% 2.58/1.80
% 2.58/1.80 % (16447)Memory used [KB]: 6268
% 2.58/1.80 % (16447)Time elapsed: 0.031 s
% 2.58/1.80 % (16447)Instructions burned: 87 (million)
% 2.58/1.80 % (16447)------------------------------
% 2.58/1.80 % (16447)------------------------------
% 2.58/1.81 % (16448)Instruction limit reached!
% 2.58/1.81 % (16448)------------------------------
% 2.58/1.81 % (16448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.81 % (16448)Termination reason: Unknown
% 2.58/1.81 % (16448)Termination phase: Saturation
% 2.58/1.81
% 2.58/1.81 % (16448)Memory used [KB]: 6396
% 2.58/1.81 % (16448)Time elapsed: 0.038 s
% 2.58/1.81 % (16448)Instructions burned: 107 (million)
% 2.58/1.81 % (16448)------------------------------
% 2.58/1.81 % (16448)------------------------------
% 2.58/1.81 % (16451)Instruction limit reached!
% 2.58/1.81 % (16451)------------------------------
% 2.58/1.81 % (16451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.81 % (16451)Termination reason: Unknown
% 2.58/1.81 % (16451)Termination phase: Saturation
% 2.58/1.81
% 2.58/1.81 % (16451)Memory used [KB]: 6012
% 2.58/1.81 % (16451)Time elapsed: 0.016 s
% 2.58/1.81 % (16451)Instructions burned: 46 (million)
% 2.58/1.81 % (16451)------------------------------
% 2.58/1.81 % (16451)------------------------------
% 2.58/1.81 % (16452)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_16294 for (2997ds/98Mi)
% 2.58/1.81 % (16450)First to succeed.
% 2.58/1.82 % (16450)Refutation found. Thanks to Tanya!
% 2.58/1.82 % SZS status Theorem for DTF2THF_16294
% 2.58/1.82 % SZS output start Proof for DTF2THF_16294
% 2.58/1.82 thf(type_def_5, type, d: $tType).
% 2.58/1.82 thf(type_def_7, type, u: $tType).
% 2.58/1.82 thf(type_def_8, type, du: $tType).
% 2.58/1.82 thf(type_def_9, type, mono_2Etyop_2Einteger_2Eint: $tType).
% 2.58/1.82 thf(type_def_10, type, mono_2Etyop_2Enum_2Enum: $tType).
% 2.58/1.82 thf(func_def_0, type, u: $tType).
% 2.58/1.82 thf(func_def_1, type, d: $tType).
% 2.58/1.82 thf(func_def_2, type, du: $tType).
% 2.58/1.82 thf(func_def_3, type, mono_2Etyop_2Einteger_2Eint: $tType).
% 2.58/1.82 thf(func_def_4, type, mono_2Etyop_2Enum_2Enum: $tType).
% 2.58/1.82 thf(func_def_5, type, tyop_2Ebool_2Eitself: d > d).
% 2.58/1.82 thf(func_def_6, type, tyop_2Efcp_2Ecart: d > d > d).
% 2.58/1.82 thf(func_def_7, type, tyop_2Einteger_2Eint: d).
% 2.58/1.82 thf(func_def_8, type, tyop_2Emin_2Ebool: d).
% 2.58/1.82 thf(func_def_9, type, tyop_2Emin_2Efun: d > d > d).
% 2.58/1.82 thf(func_def_10, type, tyop_2Enum_2Enum: d).
% 2.58/1.82 thf(func_def_11, type, s: d > u > du).
% 2.58/1.82 thf(func_def_12, type, app_2E2: du > du > u).
% 2.58/1.82 thf(func_def_13, type, combin_i_2E0: u).
% 2.58/1.82 thf(func_def_14, type, combin_k_2E0: u).
% 2.58/1.82 thf(func_def_15, type, combin_s_2E0: u).
% 2.58/1.82 thf(func_def_16, type, c_2Ebool_2E_21_2E0: u).
% 2.58/1.82 thf(func_def_17, type, c_2Ebool_2E_21_2E1: du > u).
% 2.58/1.82 thf(func_def_18, type, c_2Ebool_2E_2F_5C_2E0: u).
% 2.58/1.82 thf(func_def_19, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 2.58/1.82 thf(func_def_20, type, c_2Enum_2E0_2E0: u).
% 2.58/1.82 thf(func_def_21, type, c_2Eprim__rec_2E_3C_2E0: u).
% 2.58/1.82 thf(func_def_22, type, c_2Eprim__rec_2E_3C_2E2: du > du > u).
% 2.58/1.82 thf(func_def_23, type, c_2Emin_2E_3D_2E0: u).
% 2.58/1.82 thf(func_def_24, type, c_2Emin_2E_3D_2E2: du > du > u).
% 2.58/1.82 thf(func_def_25, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 2.58/1.82 thf(func_def_26, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 2.58/1.82 thf(func_def_27, type, c_2Ebool_2E_3F_2E0: u).
% 2.58/1.82 thf(func_def_28, type, c_2Ebool_2E_3F_2E1: du > u).
% 2.58/1.82 thf(func_def_29, type, c_2Ebool_2ECOND_2E0: u).
% 2.58/1.82 thf(func_def_30, type, c_2Ebool_2ECOND_2E3: du > du > du > u).
% 2.58/1.82 thf(func_def_31, type, c_2Ebool_2EF_2E0: u).
% 2.58/1.82 thf(func_def_32, type, c_2Earithmetic_2EMOD_2E0: u).
% 2.58/1.82 thf(func_def_33, type, c_2Earithmetic_2EMOD_2E2: du > du > u).
% 2.58/1.82 thf(func_def_34, type, c_2Einteger_2ENum_2E0: u).
% 2.58/1.82 thf(func_def_35, type, c_2Einteger_2ENum_2E1: du > u).
% 2.58/1.82 thf(func_def_36, type, c_2Ebool_2ET_2E0: u).
% 2.58/1.82 thf(func_def_37, type, c_2Ebool_2E_5C_2F_2E0: u).
% 2.58/1.82 thf(func_def_38, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 2.58/1.82 thf(func_def_39, type, c_2Ewords_2Edimword_2E0: u).
% 2.58/1.82 thf(func_def_40, type, c_2Ewords_2Edimword_2E1: du > u).
% 2.58/1.82 thf(func_def_41, type, c_2Einteger__word_2Ei2w_2E0: u).
% 2.58/1.82 thf(func_def_42, type, c_2Einteger__word_2Ei2w_2E1: du > u).
% 2.58/1.82 thf(func_def_43, type, c_2Einteger_2Eint__lt_2E0: u).
% 2.58/1.82 thf(func_def_44, type, c_2Einteger_2Eint__lt_2E2: du > du > u).
% 2.58/1.82 thf(func_def_45, type, c_2Einteger_2Eint__neg_2E0: u).
% 2.58/1.82 thf(func_def_46, type, c_2Einteger_2Eint__neg_2E1: du > u).
% 2.58/1.82 thf(func_def_47, type, c_2Einteger_2Eint__of__num_2E0: u).
% 2.58/1.82 thf(func_def_48, type, c_2Einteger_2Eint__of__num_2E1: du > u).
% 2.58/1.82 thf(func_def_49, type, c_2Ewords_2En2w_2E0: u).
% 2.58/1.82 thf(func_def_50, type, c_2Ewords_2En2w_2E1: du > u).
% 2.58/1.82 thf(func_def_51, type, c_2Ebool_2Ethe__value_2E0: u).
% 2.58/1.82 thf(func_def_52, type, c_2Ewords_2Eword__2comp_2E0: u).
% 2.58/1.82 thf(func_def_53, type, c_2Ewords_2Eword__2comp_2E1: du > u).
% 2.58/1.82 thf(func_def_54, type, c_2Ebool_2E_7E_2E0: u).
% 2.58/1.82 thf(func_def_55, type, c_2Ebool_2E_7E_2E1: du > u).
% 2.58/1.82 thf(func_def_56, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 2.58/1.82 thf(func_def_57, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 2.58/1.82 thf(func_def_58, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: (mono_2Etyop_2Einteger_2Eint > $o) > mono_2Etyop_2Einteger_2Eint > $o).
% 2.58/1.82 thf(func_def_59, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o).
% 2.58/1.82 thf(func_def_60, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_61, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_62, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: (mono_2Etyop_2Enum_2Enum > $o) > mono_2Etyop_2Enum_2Enum > $o).
% 2.58/1.82 thf(func_def_63, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o).
% 2.58/1.82 thf(func_def_64, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_65, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_66, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_67, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 2.58/1.82 thf(func_def_68, type, mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_69, type, mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o).
% 2.58/1.82 thf(func_def_70, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 2.58/1.82 thf(func_def_72, type, mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_73, type, mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_75, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 2.58/1.82 thf(func_def_76, type, mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o).
% 2.58/1.82 thf(func_def_77, type, mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_78, type, mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_79, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 2.58/1.82 thf(func_def_80, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 2.58/1.82 thf(func_def_81, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 2.58/1.82 thf(func_def_82, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 2.58/1.82 thf(func_def_83, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Einteger_2Eint > $o) > u).
% 2.58/1.82 thf(func_def_84, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o) > u).
% 2.58/1.82 thf(func_def_85, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint) > u).
% 2.58/1.82 thf(func_def_86, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum) > u).
% 2.58/1.82 thf(func_def_87, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Enum_2Enum > $o) > u).
% 2.58/1.82 thf(func_def_88, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o) > u).
% 2.58/1.82 thf(func_def_89, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > u).
% 2.58/1.82 thf(func_def_90, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint) > u).
% 2.58/1.82 thf(func_def_91, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > u).
% 2.58/1.82 thf(func_def_92, type, i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u).
% 2.58/1.82 thf(func_def_93, type, i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u).
% 2.58/1.82 thf(func_def_94, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 2.58/1.82 thf(func_def_95, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 2.58/1.82 thf(func_def_96, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 2.58/1.82 thf(func_def_97, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o).
% 2.58/1.82 thf(func_def_98, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o).
% 2.58/1.82 thf(func_def_99, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_100, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_101, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o).
% 2.58/1.82 thf(func_def_102, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o).
% 2.58/1.82 thf(func_def_103, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_104, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_105, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_106, type, j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint).
% 2.58/1.82 thf(func_def_107, type, j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum).
% 2.58/1.82 thf(func_def_128, type, sK1: d).
% 2.58/1.82 thf(func_def_129, type, ph2: !>[X0: $tType]:(X0)).
% 2.58/1.82 thf(f651,plain,(
% 2.58/1.82 $false),
% 2.58/1.82 inference(avatar_sat_refutation,[status(thm)],[f404,f435,f526,f626,f641])).
% 2.58/1.82 thf(f641,plain,(
% 2.58/1.82 ~spl0_1),
% 2.58/1.82 inference(avatar_contradiction_clause,[status(thm)],[f640])).
% 2.58/1.82 thf(f640,plain,(
% 2.58/1.82 $false | ~spl0_1),
% 2.58/1.82 inference(trivial_inequality_removal,[status(thm)],[f638])).
% 2.58/1.82 thf(f638,plain,(
% 2.58/1.82 ($false = $true) | ~spl0_1),
% 2.58/1.82 inference(superposition,[status(thm)],[f520,f319])).
% 2.58/1.82 thf(f319,plain,(
% 2.58/1.82 ( ! [X1 : $o] : (($true = X1)) ) | ~spl0_1),
% 2.58/1.82 inference(avatar_component_clause,[status(thm)],[f318])).
% 2.58/1.82 thf(f318,definition,(
% 2.58/1.82 spl0_1 <=> ! [X1 : $o] : ($true = X1)),
% 2.58/1.82 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.58/1.82 thf(f520,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (($false = (mono_2Ec_2Eprim__rec_2E_3C @ X1 @ mono_2Ec_2Enum_2E0))) )),
% 2.58/1.82 inference(not_proxy_clausification,[status(thm)],[f519])).
% 2.58/1.82 thf(f519,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (((~ (mono_2Ec_2Eprim__rec_2E_3C @ X1 @ mono_2Ec_2Enum_2E0)) = $true)) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f518])).
% 2.58/1.82 thf(f518,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (($true = ((^[Y0 : mono_2Etyop_2Enum_2Enum]: (~ (mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ mono_2Ec_2Enum_2E0))) @ X1))) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f260])).
% 2.58/1.82 thf(f260,plain,(
% 2.58/1.82 ((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: (~ (mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ mono_2Ec_2Enum_2E0)))) = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f114])).
% 2.58/1.82 thf(f114,plain,(
% 2.58/1.82 ((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: (~ (mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ mono_2Ec_2Enum_2E0)))) = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f113])).
% 2.58/1.82 thf(f113,plain,(
% 2.58/1.82 ! [X0 : mono_2Etyop_2Enum_2Enum] : (~ (mono_2Ec_2Eprim__rec_2E_3C @ X0 @ mono_2Ec_2Enum_2E0))),
% 2.58/1.82 inference(rectify,[status(thm)],[f83])).
% 2.58/1.82 thf(f83,axiom,(
% 2.58/1.82 ! [X30 : mono_2Etyop_2Enum_2Enum] : (~ (mono_2Ec_2Eprim__rec_2E_3C @ X30 @ mono_2Ec_2Enum_2E0))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Eprim__rec_2ENOT__LESS__0)).
% 2.58/1.82 thf(f626,plain,(
% 2.58/1.82 ~spl0_5 | ~spl0_6),
% 2.58/1.82 inference(avatar_contradiction_clause,[status(thm)],[f625])).
% 2.58/1.82 thf(f625,plain,(
% 2.58/1.82 $false | (~spl0_5 | ~spl0_6)),
% 2.58/1.82 inference(trivial_inequality_removal,[status(thm)],[f620])).
% 2.58/1.82 thf(f620,plain,(
% 2.58/1.82 ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) != (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0))))) | (~spl0_5 | ~spl0_6)),
% 2.58/1.82 inference(superposition,[status(thm)],[f375,f617])).
% 2.58/1.82 thf(f617,plain,(
% 2.58/1.82 ( ! [X0 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))) ) | (~spl0_5 | ~spl0_6)),
% 2.58/1.82 inference(forward_demodulation,[status(thm)],[f616,f573])).
% 2.58/1.82 thf(f573,plain,(
% 2.58/1.82 ( ! [X2 : u,X3 : u,X1 : d] : (((s @ X1 @ X3) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ $false)) @ (s @ X1 @ X2) @ (s @ X1 @ X3))))) ) | ~spl0_6),
% 2.58/1.82 inference(forward_demodulation,[status(thm)],[f507,f408])).
% 2.58/1.82 thf(f408,plain,(
% 2.58/1.82 (mono_2Ec_2Ebool_2EF = $false) | ~spl0_6),
% 2.58/1.82 inference(avatar_component_clause,[status(thm)],[f406])).
% 2.58/1.82 thf(f406,definition,(
% 2.58/1.82 spl0_6 <=> (mono_2Ec_2Ebool_2EF = $false)),
% 2.58/1.82 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 2.58/1.82 thf(f507,plain,(
% 2.58/1.82 ( ! [X2 : u,X3 : u,X1 : d] : (((s @ X1 @ X3) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ X2) @ (s @ X1 @ X3))))) )),
% 2.58/1.82 inference(equality_proxy_clausification,[status(thm)],[f506])).
% 2.58/1.82 thf(f506,plain,(
% 2.58/1.82 ( ! [X2 : u,X3 : u,X1 : d] : ((((s @ X1 @ X3) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ X2) @ (s @ X1 @ X3)))) = $true)) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f505])).
% 2.58/1.82 thf(f505,plain,(
% 2.58/1.82 ( ! [X2 : u,X3 : u,X1 : d] : (($true = ((^[Y0 : u]: ((s @ X1 @ Y0) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ X2) @ (s @ X1 @ Y0))))) @ X3))) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f504])).
% 2.58/1.82 thf(f504,plain,(
% 2.58/1.82 ( ! [X2 : u,X1 : d] : (($true = (!! @ u @ (^[Y0 : u]: ((s @ X1 @ Y0) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ X2) @ (s @ X1 @ Y0)))))))) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f503])).
% 2.58/1.82 thf(f503,plain,(
% 2.58/1.82 ( ! [X2 : u,X1 : d] : ((((^[Y0 : u]: (!! @ u @ (^[Y1 : u]: ((s @ X1 @ Y1) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ Y0) @ (s @ X1 @ Y1))))))) @ X2) = $true)) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f502])).
% 2.58/1.82 thf(f502,plain,(
% 2.58/1.82 ( ! [X1 : d] : (($true = (!! @ u @ (^[Y0 : u]: (!! @ u @ (^[Y1 : u]: ((s @ X1 @ Y1) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ Y0) @ (s @ X1 @ Y1)))))))))) )),
% 2.58/1.82 inference(binary_proxy_clausification,[status(thm)],[f500])).
% 2.58/1.82 thf(f500,plain,(
% 2.58/1.82 ( ! [X1 : d] : ((((!! @ u @ (^[Y0 : u]: (!! @ u @ (^[Y1 : u]: ((s @ X1 @ Y1) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X1 @ Y0) @ (s @ X1 @ Y1)))))))) & (!! @ u @ (^[Y0 : u]: (!! @ u @ (^[Y1 : u]: ((s @ X1 @ Y1) = (s @ X1 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ $true)) @ (s @ X1 @ Y1) @ (s @ X1 @ Y0))))))))) = $true)) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f499])).
% 2.58/1.82 thf(f499,plain,(
% 2.58/1.82 ( ! [X1 : d] : ((((^[Y0 : d]: ((!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ Y0 @ Y1) @ (s @ Y0 @ Y2)))))))) & (!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ $true)) @ (s @ Y0 @ Y2) @ (s @ Y0 @ Y1)))))))))) @ X1) = $true)) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f285])).
% 2.58/1.82 thf(f285,plain,(
% 2.58/1.82 ((!! @ d @ (^[Y0 : d]: ((!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ Y0 @ Y1) @ (s @ Y0 @ Y2)))))))) & (!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ $true)) @ (s @ Y0 @ Y2) @ (s @ Y0 @ Y1))))))))))) = $true)),
% 2.58/1.82 inference(definition_unfolding,[status(thm)],[f259,f267])).
% 2.58/1.82 thf(f267,plain,(
% 2.58/1.82 (mono_2Ec_2Ebool_2ET = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f98])).
% 2.58/1.82 thf(f98,plain,(
% 2.58/1.82 (mono_2Ec_2Ebool_2ET = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f97])).
% 2.58/1.82 thf(f97,plain,(
% 2.58/1.82 mono_2Ec_2Ebool_2ET),
% 2.58/1.82 inference(rectify,[status(thm)],[f71])).
% 2.58/1.82 thf(f71,axiom,(
% 2.58/1.82 mono_2Ec_2Ebool_2ET),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ebool_2ETRUTH)).
% 2.58/1.82 thf(f259,plain,(
% 2.58/1.82 ((!! @ d @ (^[Y0 : d]: ((!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ Y0 @ Y1) @ (s @ Y0 @ Y2)))))))) & (!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ (s @ Y0 @ Y2) @ (s @ Y0 @ Y1))))))))))) = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f152])).
% 2.58/1.82 thf(f152,plain,(
% 2.58/1.82 ((!! @ d @ (^[Y0 : d]: ((!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ Y0 @ Y1) @ (s @ Y0 @ Y2)))))))) & (!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: ((s @ Y0 @ Y2) = (s @ Y0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ (s @ Y0 @ Y2) @ (s @ Y0 @ Y1))))))))))) = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f151])).
% 2.58/1.82 thf(f151,plain,(
% 2.58/1.82 ! [X0 : d] : (! [X1 : u,X2 : u] : ((s @ X0 @ X1) = (s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ (s @ X0 @ X1) @ (s @ X0 @ X2)))) & ! [X3 : u,X4 : u] : ((s @ X0 @ X3) = (s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X0 @ X4) @ (s @ X0 @ X3)))))),
% 2.58/1.82 inference(rectify,[status(thm)],[f78])).
% 2.58/1.82 thf(f78,axiom,(
% 2.58/1.82 ! [X0 : d] : (! [X26 : u,X27 : u] : ((s @ X0 @ X26) = (s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ (s @ X0 @ X26) @ (s @ X0 @ X27)))) & ! [X29 : u,X28 : u] : ((s @ X0 @ X29) = (s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X0 @ X28) @ (s @ X0 @ X29)))))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ebool_2Ebool__case__thm)).
% 2.58/1.82 thf(f616,plain,(
% 2.58/1.82 ( ! [X0 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ $false)) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))))) ) | ~spl0_5),
% 2.58/1.82 inference(forward_demodulation,[status(thm)],[f568,f554])).
% 2.58/1.82 thf(f554,plain,(
% 2.58/1.82 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : (($false = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X0) @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) ) | ~spl0_5),
% 2.58/1.82 inference(superposition,[status(thm)],[f403,f263])).
% 2.58/1.82 thf(f263,plain,(
% 2.58/1.82 ((mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f194])).
% 2.58/1.82 thf(f194,plain,(
% 2.58/1.82 ((mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f79])).
% 2.58/1.82 thf(f79,axiom,(
% 2.58/1.82 ((mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger_2EINT__NEG__0)).
% 2.58/1.82 thf(f403,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (($false = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) ) | ~spl0_5),
% 2.58/1.82 inference(avatar_component_clause,[status(thm)],[f402])).
% 2.58/1.82 thf(f402,definition,(
% 2.58/1.82 spl0_5 <=> ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ($false = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))),
% 2.58/1.82 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 2.58/1.82 thf(f568,plain,(
% 2.58/1.82 ( ! [X0 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0) @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))))) )),
% 2.58/1.82 inference(forward_demodulation,[status(thm)],[f567,f455])).
% 2.58/1.82 thf(f455,plain,(
% 2.58/1.82 ( ! [X1 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))) )),
% 2.58/1.82 inference(equality_proxy_clausification,[status(thm)],[f454])).
% 2.58/1.82 thf(f454,plain,(
% 2.58/1.82 ( ! [X1 : d] : (($true = ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0))))))))) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f453])).
% 2.58/1.82 thf(f453,plain,(
% 2.58/1.82 ( ! [X1 : d] : (($true = ((^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))))) @ X1))) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f284])).
% 2.58/1.82 thf(f284,plain,(
% 2.58/1.82 ((!! @ d @ (^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0))))))))) = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f177])).
% 2.58/1.82 thf(f177,plain,(
% 2.58/1.82 ((!! @ d @ (^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0))))))))) = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f85])).
% 2.58/1.82 thf(f85,axiom,(
% 2.58/1.82 ! [X0 : d] : ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ewords_2EWORD__NEG__0)).
% 2.58/1.82 thf(f567,plain,(
% 2.58/1.82 ( ! [X0 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0) @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))))))) )),
% 2.58/1.82 inference(forward_demodulation,[status(thm)],[f558,f523])).
% 2.58/1.82 thf(f523,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = X1)) )),
% 2.58/1.82 inference(equality_proxy_clausification,[status(thm)],[f522])).
% 2.58/1.82 thf(f522,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (($true = ((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = X1))) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f521])).
% 2.58/1.82 thf(f521,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (($true = ((^[Y0 : mono_2Etyop_2Enum_2Enum]: ((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = Y0)) @ X1))) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f261])).
% 2.58/1.82 thf(f261,plain,(
% 2.58/1.82 ((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: ((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = Y0))) = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f168])).
% 2.58/1.82 thf(f168,plain,(
% 2.58/1.82 ((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: ((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = Y0))) = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f167])).
% 2.58/1.82 thf(f167,plain,(
% 2.58/1.82 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ X0)) = X0)),
% 2.58/1.82 inference(rectify,[status(thm)],[f81])).
% 2.58/1.82 thf(f81,axiom,(
% 2.58/1.82 ! [X30 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ X30)) = X30)),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger_2ENUM__OF__INT)).
% 2.58/1.82 thf(f558,plain,(
% 2.58/1.82 ( ! [X0 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0) @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))))))))) )),
% 2.58/1.82 inference(superposition,[status(thm)],[f452,f263])).
% 2.58/1.82 thf(f452,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X1 : d] : (((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ X2 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ X2)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ X2))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ X2)))))) )),
% 2.58/1.82 inference(equality_proxy_clausification,[status(thm)],[f451])).
% 2.58/1.82 thf(f451,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X1 : d] : (($true = ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ X2 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ X2)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ X2))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ X2))))))) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f450])).
% 2.58/1.82 thf(f450,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X1 : d] : ((((^[Y0 : mono_2Etyop_2Einteger_2Eint]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ Y0 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ Y0)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ Y0))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ Y0)))))) @ X2) = $true)) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f449])).
% 2.58/1.82 thf(f449,plain,(
% 2.58/1.82 ( ! [X1 : d] : (((!! @ mono_2Etyop_2Einteger_2Eint @ (^[Y0 : mono_2Etyop_2Einteger_2Eint]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ Y0 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ Y0)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ Y0))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ Y0))))))) = $true)) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f448])).
% 2.58/1.82 thf(f448,plain,(
% 2.58/1.82 ( ! [X1 : d] : ((((^[Y0 : d]: (!! @ mono_2Etyop_2Einteger_2Eint @ (^[Y1 : mono_2Etyop_2Einteger_2Eint]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ Y1 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ Y1)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ Y1))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ Y1)))))))) @ X1) = $true)) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f274])).
% 2.58/1.82 thf(f274,plain,(
% 2.58/1.82 ($true = (!! @ d @ (^[Y0 : d]: (!! @ mono_2Etyop_2Einteger_2Eint @ (^[Y1 : mono_2Etyop_2Einteger_2Eint]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ Y1 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ Y1)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ Y1))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ Y1))))))))))),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f162])).
% 2.58/1.82 thf(f162,plain,(
% 2.58/1.82 ($true = (!! @ d @ (^[Y0 : d]: (!! @ mono_2Etyop_2Einteger_2Eint @ (^[Y1 : mono_2Etyop_2Einteger_2Eint]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ Y1 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ Y1)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ Y1))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ Y1))))))))))),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f161])).
% 2.58/1.82 thf(f161,plain,(
% 2.58/1.82 ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : d] : ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ X0 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ X0)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ X0))))))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ X0)))))),
% 2.58/1.82 inference(rectify,[status(thm)],[f82])).
% 2.58/1.82 thf(f82,axiom,(
% 2.58/1.82 ! [X32 : mono_2Etyop_2Einteger_2Eint,X0 : d] : ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ X32)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (mono_2Ec_2Einteger_2Eint__lt @ X32 @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2Eword__2comp_2E1 @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ (mono_2Ec_2Einteger_2Eint__neg @ X32)))))))) @ (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Einteger_2ENum @ X32))))))))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger__word_2Ei2w__def)).
% 2.58/1.82 thf(f375,plain,(
% 2.58/1.82 ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) != (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))),
% 2.58/1.82 inference(equality_proxy_clausification,[status(thm)],[f374])).
% 2.58/1.82 thf(f374,plain,(
% 2.58/1.82 ($false = ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ sK1) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))))))),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f373])).
% 2.58/1.82 thf(f373,plain,(
% 2.58/1.82 ($false = ((^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))) @ sK1))),
% 2.58/1.82 inference(sigma_clausification,[status(thm)],[f372])).
% 2.58/1.82 thf(f372,plain,(
% 2.58/1.82 ($false = (!! @ d @ (^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0)))))))))),
% 2.58/1.82 inference(not_proxy_clausification,[status(thm)],[f265])).
% 2.58/1.82 thf(f265,plain,(
% 2.58/1.82 ((~ (!! @ d @ (^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))))) = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f231])).
% 2.58/1.82 thf(f231,plain,(
% 2.58/1.82 ((~ (!! @ d @ (^[Y0 : d]: ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ Y0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))))) = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f87])).
% 2.58/1.82 thf(f87,negated_conjecture,(
% 2.58/1.82 ~! [X0 : d] : ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))),
% 2.58/1.82 inference(negated_conjecture,[status(cth)],[f86])).
% 2.58/1.82 thf(f86,conjecture,(
% 2.58/1.82 ! [X0 : d] : ((s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Ewords_2En2w_2E1 @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0)))) = (s @ (tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X0) @ (c_2Einteger__word_2Ei2w_2E1 @ (s @ tyop_2Einteger_2Eint @ (i_mono_2Etyop_2Einteger_2Eint @ (mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0))))))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger__word_2Ei2w__0)).
% 2.58/1.82 thf(f526,plain,(
% 2.58/1.82 ~spl0_4 | ~spl0_6),
% 2.58/1.82 inference(avatar_contradiction_clause,[status(thm)],[f525])).
% 2.58/1.82 thf(f525,plain,(
% 2.58/1.82 $false | (~spl0_4 | ~spl0_6)),
% 2.58/1.82 inference(trivial_inequality_removal,[status(thm)],[f524])).
% 2.58/1.82 thf(f524,plain,(
% 2.58/1.82 ($false = $true) | (~spl0_4 | ~spl0_6)),
% 2.58/1.82 inference(backward_demodulation,[status(thm)],[f400,f408])).
% 2.58/1.82 thf(f400,plain,(
% 2.58/1.82 (mono_2Ec_2Ebool_2EF = $true) | ~spl0_4),
% 2.58/1.82 inference(avatar_component_clause,[status(thm)],[f398])).
% 2.58/1.82 thf(f398,definition,(
% 2.58/1.82 spl0_4 <=> (mono_2Ec_2Ebool_2EF = $true)),
% 2.58/1.82 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 2.58/1.82 thf(f435,plain,(
% 2.58/1.82 spl0_1 | spl0_6),
% 2.58/1.82 inference(avatar_split_clause,[status(thm)],[f434,f406,f318])).
% 2.58/1.82 thf(f434,plain,(
% 2.58/1.82 ( ! [X1 : $o] : ((mono_2Ec_2Ebool_2EF = $false) | ($true = X1)) )),
% 2.58/1.82 inference(binary_proxy_clausification,[status(thm)],[f433])).
% 2.58/1.82 thf(f433,plain,(
% 2.58/1.82 ( ! [X1 : $o] : (($true = (mono_2Ec_2Ebool_2EF => X1))) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f293])).
% 2.58/1.82 thf(f293,plain,(
% 2.58/1.82 ($true = (!! @ $o @ (=> @ mono_2Ec_2Ebool_2EF)))),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f272])).
% 2.58/1.82 thf(f272,plain,(
% 2.58/1.82 ($true = (!! @ $o @ (^[Y0 : $o]: (mono_2Ec_2Ebool_2EF => Y0))))),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f172])).
% 2.58/1.82 thf(f172,plain,(
% 2.58/1.82 ($true = (!! @ $o @ (^[Y0 : $o]: (mono_2Ec_2Ebool_2EF => Y0))))),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f171])).
% 2.58/1.82 thf(f171,plain,(
% 2.58/1.82 ! [X0 : $o] : (mono_2Ec_2Ebool_2EF => X0)),
% 2.58/1.82 inference(rectify,[status(thm)],[f73])).
% 2.58/1.82 thf(f73,axiom,(
% 2.58/1.82 ! [X19 : $o] : (mono_2Ec_2Ebool_2EF => X19)),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Ebool_2EFALSITY)).
% 2.58/1.82 thf(f404,plain,(
% 2.58/1.82 spl0_4 | spl0_5),
% 2.58/1.82 inference(avatar_split_clause,[status(thm)],[f395,f402,f398])).
% 2.58/1.82 thf(f395,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Ebool_2EF = $true) | ($false = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) )),
% 2.58/1.82 inference(binary_proxy_clausification,[status(thm)],[f394])).
% 2.58/1.82 thf(f394,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) )),
% 2.58/1.82 inference(equality_proxy_clausification,[status(thm)],[f392])).
% 2.58/1.82 thf(f392,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) = $true)) )),
% 2.58/1.82 inference(binary_proxy_clausification,[status(thm)],[f390])).
% 2.58/1.82 thf(f390,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X2)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) = $true)) )),
% 2.58/1.82 inference(binary_proxy_clausification,[status(thm)],[f385])).
% 2.58/1.82 thf(f385,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (($true = ((((mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X2)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X2)) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = ((~ (mono_2Ec_2Enum_2E0 = X2)) | (~ (mono_2Ec_2Enum_2E0 = X1))))))) )),
% 2.58/1.82 inference(binary_proxy_clausification,[status(thm)],[f383])).
% 2.58/1.82 thf(f383,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (((((((mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X2) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X2)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X2)) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = ((~ (mono_2Ec_2Enum_2E0 = X2)) | (~ (mono_2Ec_2Enum_2E0 = X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X2) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = (mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X1))) = $true)) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f382])).
% 2.58/1.82 thf(f382,plain,(
% 2.58/1.82 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((^[Y0 : mono_2Etyop_2Enum_2Enum]: (((((mono_2Ec_2Eprim__rec_2E_3C @ X1 @ Y0) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = ((~ (mono_2Ec_2Enum_2E0 = Y0)) | (~ (mono_2Ec_2Enum_2E0 = X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = (mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ X1)))) @ X2) = $true)) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f381])).
% 2.58/1.82 thf(f381,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: (((((mono_2Ec_2Eprim__rec_2E_3C @ X1 @ Y0) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = ((~ (mono_2Ec_2Enum_2E0 = Y0)) | (~ (mono_2Ec_2Enum_2E0 = X1))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = (mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ X1))))) = $true)) )),
% 2.58/1.82 inference(beta_eta_normalization,[status(thm)],[f380])).
% 2.58/1.82 thf(f380,plain,(
% 2.58/1.82 ( ! [X1 : mono_2Etyop_2Enum_2Enum] : (($true = ((^[Y0 : mono_2Etyop_2Enum_2Enum]: (!! @ mono_2Etyop_2Enum_2Enum @ (^[Y1 : mono_2Etyop_2Enum_2Enum]: (((((mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ Y1) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1)) @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = ((~ (mono_2Ec_2Enum_2E0 = Y1)) | (~ (mono_2Ec_2Enum_2E0 = Y0))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1) @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = (mono_2Ec_2Eprim__rec_2E_3C @ Y1 @ Y0)))))) @ X1))) )),
% 2.58/1.82 inference(pi_clausification,[status(thm)],[f266])).
% 2.58/1.82 thf(f266,plain,(
% 2.58/1.82 ((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: (!! @ mono_2Etyop_2Enum_2Enum @ (^[Y1 : mono_2Etyop_2Enum_2Enum]: (((((mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ Y1) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1)) @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = ((~ (mono_2Ec_2Enum_2E0 = Y1)) | (~ (mono_2Ec_2Enum_2E0 = Y0))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1) @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = (mono_2Ec_2Eprim__rec_2E_3C @ Y1 @ Y0))))))) = $true)),
% 2.58/1.82 inference(cnf_transformation,[status(thm)],[f112])).
% 2.58/1.82 thf(f112,plain,(
% 2.58/1.82 ((!! @ mono_2Etyop_2Enum_2Enum @ (^[Y0 : mono_2Etyop_2Enum_2Enum]: (!! @ mono_2Etyop_2Enum_2Enum @ (^[Y1 : mono_2Etyop_2Enum_2Enum]: (((((mono_2Ec_2Eprim__rec_2E_3C @ Y0 @ Y1) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1)) @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = ((~ (mono_2Ec_2Enum_2E0 = Y1)) | (~ (mono_2Ec_2Enum_2E0 = Y0))))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ Y1) @ (mono_2Ec_2Einteger_2Eint__of__num @ Y0)) = (mono_2Ec_2Eprim__rec_2E_3C @ Y1 @ Y0))))))) = $true)),
% 2.58/1.82 inference(fool_elimination,[status(thm)],[f111])).
% 2.58/1.82 thf(f111,plain,(
% 2.58/1.82 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X0) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) = (mono_2Ec_2Eprim__rec_2E_3C @ X0 @ X1)) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X0)) @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)) <=> ((~ (mono_2Ec_2Enum_2E0 = X1)) | (~ (mono_2Ec_2Enum_2E0 = X0)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X0) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))) & ((mono_2Ec_2Eprim__rec_2E_3C @ X1 @ X0) = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X0)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X1)))))),
% 2.58/1.82 inference(rectify,[status(thm)],[f80])).
% 2.58/1.82 thf(f80,axiom,(
% 2.58/1.82 ! [X30 : mono_2Etyop_2Enum_2Enum,X31 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X30) @ (mono_2Ec_2Einteger_2Eint__of__num @ X31)) = (mono_2Ec_2Eprim__rec_2E_3C @ X30 @ X31)) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X30)) @ (mono_2Ec_2Einteger_2Eint__of__num @ X31)) <=> ((~ (mono_2Ec_2Enum_2E0 = X31)) | (~ (mono_2Ec_2Enum_2E0 = X30)))) & (mono_2Ec_2Ebool_2EF = (mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__of__num @ X30) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X31)))) & ((mono_2Ec_2Einteger_2Eint__lt @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X30)) @ (mono_2Ec_2Einteger_2Eint__neg @ (mono_2Ec_2Einteger_2Eint__of__num @ X31))) = (mono_2Ec_2Eprim__rec_2E_3C @ X31 @ X30)))),
% 2.58/1.82 file('/export/starexec/sandbox2/tmp/tmp.iQKsZ7jdSM/DTF2THF_16294.p',thm_2Einteger_2EINT__LT__CALCULATE)).
% 2.58/1.82 % SZS output end Proof for DTF2THF_16294
% 2.58/1.82 % (16450)------------------------------
% 2.58/1.82 % (16450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.82 % (16450)Termination reason: Refutation
% 2.58/1.82
% 2.58/1.82 % (16450)Memory used [KB]: 6524
% 2.58/1.82 % (16450)Time elapsed: 0.033 s
% 2.58/1.82 % (16450)Instructions burned: 99 (million)
% 2.58/1.82 % (16450)------------------------------
% 2.58/1.82 % (16450)------------------------------
% 2.58/1.82 % (16409)Success in time 0.26 s
%------------------------------------------------------------------------------