%------------------------------------------------------------------------------
% File     : ITP015+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 syntactic export of thm_2Einteger__word_2Ei2w__0.p, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : thm_2Ebool_2ETRUTH.p [Gau20]
%          : HL407001+4.p [TPAP]

% Status   : Theorem
% Rating   : 0.78 v8.2.0, 0.83 v8.1.0, 0.86 v7.5.0
% Syntax   : Number of formulae    : 19036 (10939 unt;   0 def)
%            Number of atoms       : 46051 (24024 equ)
%            Maximal formula atoms :  912 (   2 avg)
%            Number of connectives : 29367 (2352   ~;1392   |;10361   &)
%                                         (6681 <=>;8581  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  360 (   6 avg)
%            Maximal term depth    :  260 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    : 3456 (3456 usr;1611 con; 0-9 aty)
%            Number of variables   : 88560 (74824   !;13736   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002+4.ax').
include('Axioms/ITP001/ITP003+4.ax').
include('Axioms/ITP001/ITP004+4.ax').
include('Axioms/ITP001/ITP005+4.ax').
include('Axioms/ITP001/ITP006+4.ax').
include('Axioms/ITP001/ITP007+4.ax').
include('Axioms/ITP001/ITP008+4.ax').
include('Axioms/ITP001/ITP009+4.ax').
include('Axioms/ITP001/ITP010+4.ax').
include('Axioms/ITP001/ITP011+4.ax').
include('Axioms/ITP001/ITP012+4.ax').
include('Axioms/ITP001/ITP013+4.ax').
include('Axioms/ITP001/ITP014+4.ax').
include('Axioms/ITP001/ITP015+4.ax').
include('Axioms/ITP001/ITP016+4.ax').
include('Axioms/ITP001/ITP017+4.ax').
include('Axioms/ITP001/ITP018+4.ax').
include('Axioms/ITP001/ITP019+4.ax').
include('Axioms/ITP001/ITP020+4.ax').
include('Axioms/ITP001/ITP021+4.ax').
include('Axioms/ITP001/ITP022+4.ax').
include('Axioms/ITP001/ITP023+4.ax').
include('Axioms/ITP001/ITP024+4.ax').
include('Axioms/ITP001/ITP025+4.ax').
include('Axioms/ITP001/ITP026+4.ax').
include('Axioms/ITP001/ITP027+4.ax').
include('Axioms/ITP001/ITP028+4.ax').
include('Axioms/ITP001/ITP029+4.ax').
include('Axioms/ITP001/ITP030+4.ax').
include('Axioms/ITP001/ITP031+4.ax').
include('Axioms/ITP001/ITP032+4.ax').
include('Axioms/ITP001/ITP033+4.ax').
include('Axioms/ITP001/ITP034+4.ax').
include('Axioms/ITP001/ITP035+4.ax').
include('Axioms/ITP001/ITP036+4.ax').
include('Axioms/ITP001/ITP037+4.ax').
include('Axioms/ITP001/ITP038+4.ax').
include('Axioms/ITP001/ITP039+4.ax').
include('Axioms/ITP001/ITP040+4.ax').
include('Axioms/ITP001/ITP041+4.ax').
include('Axioms/ITP001/ITP042+4.ax').
include('Axioms/ITP001/ITP043+4.ax').
include('Axioms/ITP001/ITP044+4.ax').
include('Axioms/ITP001/ITP045+4.ax').
include('Axioms/ITP001/ITP046+4.ax').
include('Axioms/ITP001/ITP047+4.ax').
include('Axioms/ITP001/ITP048+4.ax').
include('Axioms/ITP001/ITP049+4.ax').
include('Axioms/ITP001/ITP050+4.ax').
include('Axioms/ITP001/ITP051+4.ax').
include('Axioms/ITP001/ITP052+4.ax').
include('Axioms/ITP001/ITP053+4.ax').
include('Axioms/ITP001/ITP054+4.ax').
include('Axioms/ITP001/ITP055+4.ax').
include('Axioms/ITP001/ITP056+4.ax').
include('Axioms/ITP001/ITP057+4.ax').
include('Axioms/ITP001/ITP058+4.ax').
include('Axioms/ITP001/ITP059+4.ax').
include('Axioms/ITP001/ITP060+4.ax').
include('Axioms/ITP001/ITP061+4.ax').
include('Axioms/ITP001/ITP062+4.ax').
include('Axioms/ITP001/ITP063+4.ax').
include('Axioms/ITP001/ITP064+4.ax').
include('Axioms/ITP001/ITP065+4.ax').
include('Axioms/ITP001/ITP066+4.ax').
include('Axioms/ITP001/ITP067+4.ax').
include('Axioms/ITP001/ITP068+4.ax').
include('Axioms/ITP001/ITP069+4.ax').
include('Axioms/ITP001/ITP070+4.ax').
include('Axioms/ITP001/ITP071+4.ax').
include('Axioms/ITP001/ITP072+4.ax').
include('Axioms/ITP001/ITP073+4.ax').
include('Axioms/ITP001/ITP074+4.ax').
include('Axioms/ITP001/ITP075+4.ax').
include('Axioms/ITP001/ITP076+4.ax').
include('Axioms/ITP001/ITP077+4.ax').
include('Axioms/ITP001/ITP078+4.ax').
include('Axioms/ITP001/ITP079+4.ax').
include('Axioms/ITP001/ITP080+4.ax').
include('Axioms/ITP001/ITP081+4.ax').
include('Axioms/ITP001/ITP082+4.ax').
include('Axioms/ITP001/ITP083+4.ax').
include('Axioms/ITP001/ITP084+4.ax').
include('Axioms/ITP001/ITP085+4.ax').
include('Axioms/ITP001/ITP086+4.ax').
include('Axioms/ITP001/ITP087+4.ax').
include('Axioms/ITP001/ITP088+4.ax').
include('Axioms/ITP001/ITP089+4.ax').
include('Axioms/ITP001/ITP090+4.ax').
include('Axioms/ITP001/ITP091+4.ax').
include('Axioms/ITP001/ITP092+4.ax').
include('Axioms/ITP001/ITP093+4.ax').
include('Axioms/ITP001/ITP094+4.ax').
include('Axioms/ITP001/ITP095+4.ax').
include('Axioms/ITP001/ITP096+4.ax').
include('Axioms/ITP001/ITP097+4.ax').
include('Axioms/ITP001/ITP098+4.ax').
include('Axioms/ITP001/ITP099+4.ax').
include('Axioms/ITP001/ITP100+4.ax').
include('Axioms/ITP001/ITP101+4.ax').
include('Axioms/ITP001/ITP102+4.ax').
include('Axioms/ITP001/ITP103+4.ax').
include('Axioms/ITP001/ITP104+4.ax').
include('Axioms/ITP001/ITP105+4.ax').
include('Axioms/ITP001/ITP106+4.ax').
include('Axioms/ITP001/ITP107+4.ax').
include('Axioms/ITP001/ITP108+4.ax').
include('Axioms/ITP001/ITP109+4.ax').
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),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)))
     => s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).

fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : 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))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : 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))) = 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))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
    <=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).

fof(reserved_2Equant_2E_21,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(reserved_2Equant_2E_3F,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(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)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Estring_2ECHR_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Estring_2Echar,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),c_2Estring_2ECHR_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EINT__MAX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint),c_2Einteger__word_2EINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EINT__MIN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint),c_2Einteger__word_2EINT__MIN_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger_2ENum_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum),c_2Einteger_2ENum_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__exp_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__exp_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint)),c_2Einteger_2Eint__exp_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__mod_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mod_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Einteger_2Eint__mod_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq1_2Ec_2Einteger_2Eint__of__num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint),c_2Einteger_2Eint__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = 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,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Ew2i_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Einteger_2Eint),c_2Einteger__word_2Ew2i_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EUINT__MAX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint),c_2Einteger__word_2EUINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EfromString_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EfromString_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),c_2Einteger__word_2EfromString_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2ECONS_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = 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,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger_2Eint__neg_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__neg_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__add_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Einteger_2Eint__add_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__div_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__div_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Einteger_2Eint__div_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__mul_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mul_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Einteger_2Eint__mul_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__sub_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Einteger_2Eint__sub_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2EINT__MIN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Ewords_2EINT__MIN_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2EASCIInumbers_2Enum__from__dec__string_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2EASCIInumbers_2Enum__from__dec__string_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Ewords_2EINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2EUINT__MAX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Ewords_2EUINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger_2EABS_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2EABS_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__i2sw_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = 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_2Esaturate__i2sw_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__i2sw_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Einteger__word_2Esaturate__i2sw_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__i2w_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2w_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = 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_2Esaturate__i2w_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__i2w_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2w_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Einteger__word_2Esaturate__i2w_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__sw2sw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__sw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Einteger__word_2Esaturate__sw2sw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__sw2w_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__sw2w_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Einteger__word_2Esaturate__sw2w_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Esaturate__w2sw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__w2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Einteger__word_2Esaturate__w2sw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ewords_2Esw2sw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Einteger__word_2Ei2w_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Esw2sw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b,A_27c,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ewords_2Esw2sw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EtoString_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Einteger__word_2EtoString_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Einteger__word_2EtoString_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : 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))) = 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))) ).

fof(arityeq1_2Ec_2Einteger__word_2Ew2i_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Einteger_2Eint),c_2Einteger__word_2Ew2i_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Ew2w_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Ew2w_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Ew2w_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__abs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__abs_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = 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__abs_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__msb_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__msb_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27b),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27c),X0_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__ge_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__ge_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Einteger_2Eint__ge_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__gt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__gt_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Einteger_2Eint__gt_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__le_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Einteger_2Eint__le_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EINT__MAX_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27b),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27b),tyop_2Einteger_2Eint),c_2Einteger__word_2EINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ewords_2Esw2sw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger__word_2EINT__MIN_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27b),X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27b),tyop_2Einteger_2Eint),c_2Einteger__word_2EINT__MIN_2E0),s(tyop_2Ebool_2Eitself(A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2Einteger_2Eint__lt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Einteger_2Eint__lt_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger__word_2Esigned__saturate__add_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esigned__saturate__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Einteger__word_2Esigned__saturate__add_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger__word_2Esigned__saturate__sub_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esigned__saturate__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Einteger__word_2Esigned__saturate__sub_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Ewords_2Eword__add_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__asr_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__asr_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Ewords_2Eword__asr_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__ge_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__ge_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),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_2Emin_2Ebool)),c_2Ewords_2Eword__ge_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__gt_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__gt_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),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_2Emin_2Ebool)),c_2Ewords_2Eword__gt_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__le_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__le_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),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_2Emin_2Ebool)),c_2Ewords_2Eword__le_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__lt_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__lt_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),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_2Emin_2Ebool)),c_2Ewords_2Eword__lt_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__mul_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__mul_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Ewords_2Eword__mul_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger__word_2Eword__sdiv_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Eword__sdiv_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Einteger__word_2Eword__sdiv_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Einteger__word_2Eword__smod_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Eword__smod_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Einteger__word_2Eword__smod_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = 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))),c_2Ewords_2Eword__sub_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X2_2E0))) = 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,X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0),s(tyop_2Einteger_2Eint,X2_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))),s(tyop_2Einteger_2Eint,X2_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Ecombin_2EI_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Ecombin_2EI_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) ).

fof(arityeq1_2Ec_2EASCIInumbers_2Enum__to__dec__string_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__to__dec__string_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2EASCIInumbers_2Enum__to__dec__string_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Einteger_2Eint,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),X2_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Einteger_2Eint))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),X2_2E0))) ).

fof(thm_2Einteger__word_2EtoString__def,axiom,
    ! [V0i_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Einteger__word_2EtoString_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__to__dec__string_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__to__dec__string_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))) ).

fof(thm_2Einteger__word_2EfromString__primitive__def,axiom,
    ! [F4_2E0,F5_2E0,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V5v4_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Estring_2Echar,V5v4_2E0))))
        <=> s(tyop_2Estring_2Echar,V5v4_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))) )
     => ( ! [V5v4_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F5_2E0),s(tyop_2Estring_2Echar,V5v4_2E0))))
          <=> s(tyop_2Estring_2Echar,V5v4_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))) )
       => ( ! [V4t_2E0,V5v4_2E0] : s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint)),F3_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0))),s(tyop_2Estring_2Echar,V5v4_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Estring_2Echar,V5v4_2E0))),s(tyop_2Einteger_2Eint,c_2Ecombin_2EI_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0))))))))),s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F5_2E0),s(tyop_2Estring_2Echar,V5v4_2E0))),s(tyop_2Einteger_2Eint,c_2Ecombin_2EI_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0))))))))),s(tyop_2Einteger_2Eint,c_2Ecombin_2EI_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V5v4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0)))))))))))))
         => ( ! [V3v2_2E0,V4t_2E0] : s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),F2_2E0),s(tyop_2Estring_2Echar,V3v2_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint)),F3_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4t_2E0))),s(tyop_2Estring_2Echar,V3v2_2E0)))
           => ( ! [V1fromString_2E0,V2a_2E0] : s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),V1fromString_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2a_2E0))) = s(tyop_2Einteger_2Eint,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2a_2E0),s(tyop_2Einteger_2Eint,c_2Ecombin_2EI_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),F2_2E0)))
             => ( ! [V0R_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),V0R_2E0)))
               => s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),c_2Einteger__word_2EfromString_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),F1_2E0))) ) ) ) ) ) ) ).

fof(thm_2Einteger__word_2Ei2w__def,axiom,
    ! [A_27a,V0i_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_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,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))) ).

fof(thm_2Einteger__word_2Ew2i__def,axiom,
    ! [A_27a,V0w_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))))) ).

fof(thm_2Einteger__word_2EUINT__MAX__def,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ).

fof(thm_2Einteger__word_2EINT__MAX__def,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ).

fof(thm_2Einteger__word_2EINT__MIN__def,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ).

fof(thm_2Einteger__word_2Esaturate__i2w__def,axiom,
    ! [A_27a,V0i_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V0i_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__T_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))))) ).

fof(thm_2Einteger__word_2Esaturate__i2sw__def,axiom,
    ! [A_27a,V0i_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V0i_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__H_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__L_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))) ).

fof(thm_2Einteger__word_2Esaturate__sw2sw__def,axiom,
    ! [A_27a,A_27b,V0w_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__sw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))) ).

fof(thm_2Einteger__word_2Esaturate__w2sw__def,axiom,
    ! [A_27a,A_27b,V0w_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__w2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))))) ).

fof(thm_2Einteger__word_2Esaturate__sw2w__def,axiom,
    ! [A_27a,A_27b,V0w_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__sw2w_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))) ).

fof(thm_2Einteger__word_2Esigned__saturate__add__def,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esigned__saturate__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) ).

fof(thm_2Einteger__word_2Esigned__saturate__sub__def,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esigned__saturate__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2sw_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) ).

fof(thm_2Einteger__word_2Eword__sdiv__def,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Eword__sdiv_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__div_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) ).

fof(thm_2Einteger__word_2Eword__smod__def,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Eword__smod_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mod_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) ).

fof(thm_2Einteger__word_2EfromString__ind,axiom,
    ! [V0P_2E0] :
      ( ( ! [V1t_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0))))))
        & ! [V2t_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0))))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))))
        & ! [V3v4_2E0,V4v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V3v4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V4v1_2E0)))))) )
     => ! [V5v_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5v_2E0)))) ) ).

fof(thm_2Einteger__word_2EfromString__def,axiom,
    ! [F0_2E0,F1_2E0] :
      ( ! [V0v4_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Estring_2Echar,V0v4_2E0))))
        <=> s(tyop_2Estring_2Echar,V0v4_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))) )
     => ( ! [V0v4_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Estring_2Echar,V0v4_2E0))))
          <=> s(tyop_2Estring_2Echar,V0v4_2E0) = s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))) )
       => ! [V0v4_2E0,V1v1_2E0,V2t_2E0] :
            ( s(tyop_2Einteger_2Eint,c_2Einteger__word_2EfromString_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0)))))))
            & s(tyop_2Einteger_2Eint,c_2Einteger__word_2EfromString_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0)))))))
            & s(tyop_2Einteger_2Eint,c_2Einteger__word_2EfromString_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0)))))
            & s(tyop_2Einteger_2Eint,c_2Einteger__word_2EfromString_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0v4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1v1_2E0))))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Estring_2Echar,V0v4_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1v1_2E0))))))),s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Estring_2Echar,V0v4_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1v1_2E0))))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0v4_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1v1_2E0))))))))))) ) ) ) ).

fof(thm_2Einteger__word_2EONE__LE__TWOEXP,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) ).

fof(thm_2Einteger__word_2Ew2i__w2n__pos,axiom,
    ! [A_27a,V0w_2E0,V1n_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ).

fof(thm_2Einteger__word_2Ew2i__n2w__pos,axiom,
    ! [A_27a,V0n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) ) ).

fof(thm_2Einteger__word_2Ew2i__n2w__neg,axiom,
    ! [A_27a,V0n_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))))) ) ).

fof(thm_2Einteger__word_2Ei2w__w2i,axiom,
    ! [A_27a,V0w_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0) ).

fof(thm_2Einteger__word_2Ew2i__i2w,axiom,
    ! [A_27a,V0i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V0i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) = s(tyop_2Einteger_2Eint,V0i_2E0) ) ).

fof(thm_2Einteger__word_2Eword__msb__i2w,axiom,
    ! [A_27a,V0i_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mod_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))))) ).

fof(thm_2Einteger__word_2Ew2i__11,axiom,
    ! [A_27a,V0v_2E0,V1w_2E0] :
      ( s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0v_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0)))
    <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0v_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0) ) ).

fof(thm_2Einteger__word_2Eint__word__nchotomy,axiom,
    ! [A_27a,V0w_2E0] :
    ? [V1i_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V1i_2E0))) ).

fof(thm_2Einteger__word_2Ew2i__le,axiom,
    ! [A_27a,V0w_2E0] : p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Einteger__word_2Ew2i__ge,axiom,
    ! [A_27a,V0w_2E0] : p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0)))))) ).

fof(thm_2Einteger__word_2Eranged__int__word__nchotomy,axiom,
    ! [A_27a,V0w_2E0] :
    ? [V1i_2E0] :
      ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V1i_2E0)))
      & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V1i_2E0))))
      & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V1i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Einteger__word_2Esw2sw__i2w,axiom,
    ! [A_27a,A_27b,V0j_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V0j_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V0j_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0j_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0j_2E0))) ) ).

fof(thm_2Einteger__word_2Ew2w__i2w,axiom,
    ! [A_27a,A_27b,V0i_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Ew2w_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) ) ).

fof(thm_2Einteger__word_2EWORD__LTi,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__lt_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))) ).

fof(thm_2Einteger__word_2EWORD__GTi,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__gt_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__gt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))) ).

fof(thm_2Einteger__word_2EWORD__LEi,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__le_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))) ).

fof(thm_2Einteger__word_2EWORD__GEi,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__ge_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__ge_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))) ).

fof(thm_2Einteger__word_2Eword__add__i2w__w2n,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) ).

fof(thm_2Einteger__word_2Eword__add__i2w,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) ).

fof(thm_2Einteger__word_2Eword__sub__i2w__w2n,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) ).

fof(thm_2Einteger__word_2Eword__sub__i2w,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) ).

fof(thm_2Einteger__word_2Eword__mul__i2w__w2n,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mul_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__mul_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) ).

fof(thm_2Einteger__word_2Eword__mul__i2w,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mul_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__mul_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0))) ).

fof(thm_2Einteger__word_2Eword__i2w__add,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0a_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V1b_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint,V0a_2E0),s(tyop_2Einteger_2Eint,V1b_2E0))))) ).

fof(thm_2Einteger__word_2Eword__i2w__mul,axiom,
    ! [A_27a,V0a_2E0,V1b_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__mul_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0a_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V1b_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mul_2E2(s(tyop_2Einteger_2Eint,V0a_2E0),s(tyop_2Einteger_2Eint,V1b_2E0))))) ).

fof(thm_2Einteger__word_2EMULT__MINUS__ONE,axiom,
    ! [A_27a,V0i_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__mul_2E2(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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) ).

fof(thm_2Einteger__word_2Eword__0__w2i,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).

fof(thm_2Einteger__word_2Ew2i__eq__0,axiom,
    ! [A_27a,V0w_2E0] :
      ( s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
    <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).

fof(thm_2Einteger__word_2Ei2w__DIV,axiom,
    ! [A_27a,V0n_2E0,V1i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V1i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V1i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__div_2E2(s(tyop_2Einteger_2Eint,V1i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__exp_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__asr_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V1i_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) ) ).

fof(thm_2Einteger__word_2EINT__MIN__MONOTONIC,axiom,
    ! [A_27a,A_27b] :
      ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Einteger__word_2EINT__MAX__MONOTONIC,axiom,
    ! [A_27a,A_27b] :
      ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Einteger__word_2Ew2i__sw2sw__bounds,axiom,
    ! [A_27a,A_27b,V0w_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))))))
      & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Einteger__word_2Ew2i__i2w__id,axiom,
    ! [A_27a,A_27b,V0i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V0i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => ( s(tyop_2Einteger_2Eint,V0i_2E0) = s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0)))))
      <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) ) ) ).

fof(thm_2Einteger__word_2Ew2i__11__lift,axiom,
    ! [A_27a,A_27b,A_27c,V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0)))))) )
     => ( s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V1b_2E0)))
      <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0a_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Esw2sw_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V1b_2E0))) ) ) ).

fof(thm_2Einteger__word_2Ew2i__n2w__mod,axiom,
    ! [A_27a,V0n_2E0,V1m_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__mod_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__exp_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))) ) ).

fof(thm_2Einteger__word_2Eword__abs__w2i,axiom,
    ! [A_27a,V0w_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__abs_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))))))) ).

fof(thm_2Einteger__word_2Eword__abs__i2w,axiom,
    ! [A_27a,V0i_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,V0i_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,V0i_2E0),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__abs_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,V0i_2E0))))))) ) ).

fof(thm_2Einteger__word_2EINT__MIN,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))) ).

fof(thm_2Einteger__word_2EINT__MAX,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Einteger__word_2EUINT__MAX,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Einteger__word_2EINT__BOUND__ORDER,axiom,
    ! [A_27a] :
      ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))))) ) ).

fof(thm_2Einteger__word_2EINT__ZERO__LT__INT__MIN,axiom,
    ! [A_27a] : p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ).

fof(thm_2Einteger__word_2EINT__ZERO__LT__INT__MAX,axiom,
    ! [A_27a] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Einteger__word_2EINT__ZERO__LE__INT__MAX,axiom,
    ! [A_27a] : p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__le_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Einteger__word_2EINT__ZERO__LT__UINT__MAX,axiom,
    ! [A_27a] : p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Einteger__word_2Ew2i__1,axiom,
    ! [A_27a,F0_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,F0_2E0))
      <=> s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) )
     => s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,F0_2E0),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ) ).

fof(thm_2Einteger__word_2Ew2i__INT__MINw,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__L_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) ).

fof(thm_2Einteger__word_2Ew2i__UINT__MAXw,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__T_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ).

fof(thm_2Einteger__word_2Ew2i__INT__MAXw,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__H_2E0))) = s(tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))) ).

fof(thm_2Einteger__word_2Ew2i__minus__1,axiom,
    ! [A_27a] : s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(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,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) ).

fof(thm_2Einteger__word_2Ew2i__lt__0,axiom,
    ! [A_27a,V0w_2E0] : s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__lt_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) ).

fof(thm_2Einteger__word_2Ew2i__neg,axiom,
    ! [A_27a,V0w_2E0] :
      ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__L_2E0)
     => s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))))) ) ).

fof(thm_2Einteger__word_2Ei2w__0,conjecture,
    ! [A_27a] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).

%------------------------------------------------------------------------------