ITP001 Axioms: ITP015+4.ax


%------------------------------------------------------------------------------
% File     : ITP015+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : prim_rec.ax [Gau19]
%          : HL4015+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   92 (  45 unt;   0 def)
%            Number of atoms       :  179 (  84 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   98 (  11   ~;   6   |;  20   &)
%                                         (  28 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :   14 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   61 (  61 usr;  31 con; 0-4 aty)
%            Number of variables   :  279 ( 270   !;   9   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_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_3F_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2Einv__image_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Eprim__rec_2Ewellfounded_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eprim__rec_2Ewellfounded_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq3_2Ec_2Eprim__rec_2ESIMP__REC_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eprim__rec_2ESIMP__REC_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq3_2Ec_2Eprim__rec_2EPRIM__REC_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eprim__rec_2EPRIM__REC_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq4_2Ec_2Eprim__rec_2EPRIM__REC__FUN_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2EPRIM__REC__FUN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_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_2Eprim__rec_2EPRIM__REC__FUN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2EPRIM__REC__FUN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2EPRIM__REC__FUN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Eprim__rec_2ESIMP__REC_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2ESIMP__REC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2ESIMP__REC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq3_2Ec_2Eprim__rec_2Emeasure_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Emeasure_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq4_2Ec_2Eprim__rec_2ESIMP__REC__REL_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Eprim__rec_2ESIMP__REC__REL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) ).

fof(thm_2Eprim__rec_2ELESS__DEF,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
    <=> ? [V2P_2E0] :
          ( ! [V3n_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) )
          & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))
          & ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ) ).

fof(thm_2Eprim__rec_2EPRE__DEF,axiom,
    ! [F0_2E0,F1_2E0] :
      ( ! [V0m_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))
        <=> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
     => ( ! [V0m_2E0,V1n_2E0] :
            ( p(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)),F1_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))
          <=> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) )
       => ! [V0m_2E0] : s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(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)),F1_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))))) ) ) ).

fof(thm_2Eprim__rec_2ESIMP__REC__REL,axiom,
    ! [A_27a,V0fun_2E0,V1x_2E0,V2f_2E0,V3n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))
    <=> ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V1x_2E0)
        & ! [V4m_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))) ) ) ) ).

fof(thm_2Eprim__rec_2ESIMP__REC,axiom,
    ! [A_27a,V0x_2E0,V1f_27_2E0,V2n_2E0] :
    ? [V3g_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))
      & s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) ) ).

fof(thm_2Eprim__rec_2EPRIM__REC__FUN,axiom,
    ! [A_27a,F1_2E0,F0_2E0] :
      ( ! [V1f_2E0,V3fun_2E0,V4n_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0)))
     => ( ! [V0x_2E0,V2n_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,V0x_2E0)
       => ! [V0x_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2EPRIM__REC__FUN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2ESIMP__REC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))))) ) ) ).

fof(thm_2Eprim__rec_2EPRIM__REC,axiom,
    ! [A_27a,V0x_2E0,V1f_2E0,V2m_2E0] : s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) ).

fof(thm_2Eprim__rec_2Ewellfounded__def,axiom,
    ! [A_27a,V0R_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
    <=> ~ ? [V1f_2E0] :
          ! [V2n_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)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) ) ).

fof(thm_2Eprim__rec_2Emeasure__def,axiom,
    ! [A_27a] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0))) ).

fof(thm_2Eprim__rec_2EINV__SUC__EQ,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))
    <=> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) ) ).

fof(thm_2Eprim__rec_2EPRE,axiom,
    ( s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
    & ! [V0m_2E0] : s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))) = s(tyop_2Enum_2Enum,V0m_2E0) ) ).

fof(thm_2Eprim__rec_2ELESS__REFL,axiom,
    ! [V0n_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) ).

fof(thm_2Eprim__rec_2ESUC__LESS,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ).

fof(thm_2Eprim__rec_2ENOT__LESS__0,axiom,
    ! [V0n_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) ).

fof(thm_2Eprim__rec_2ELESS__0,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) ).

fof(thm_2Eprim__rec_2ELESS__0__0,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) ).

fof(thm_2Eprim__rec_2ELESS__MONO,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) ) ).

fof(thm_2Eprim__rec_2ELESS__MONO__REV,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ).

fof(thm_2Eprim__rec_2ELESS__MONO__EQ,axiom,
    ! [V0m_2E0,V1n_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) ).

fof(thm_2Eprim__rec_2ETC__IM__RTC__SUC,axiom,
    ! [F1_2E0,F0_2E0] :
      ( ! [V4x_2E0,V5y_2E0] :
          ( p(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)),F1_2E0),s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,V5y_2E0))))
        <=> s(tyop_2Enum_2Enum,V5y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4x_2E0))) )
     => ( ! [V2x_2E0,V3y_2E0] :
            ( p(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)),F0_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,V3y_2E0))))
          <=> s(tyop_2Enum_2Enum,V3y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))) )
       => ! [V0m_2E0,V1n_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) ) ) ).

fof(thm_2Eprim__rec_2ERTC__IM__TC,axiom,
    ! [A_27a,F1_2E0,F0_2E0] :
      ( ! [V0f_2E0,V5x_2E0,V6y_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0))))
        <=> s(A_27a,V6y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5x_2E0))) )
     => ( ! [V0f_2E0,V3x_2E0,V4y_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))))
          <=> s(A_27a,V4y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3x_2E0))) )
       => ! [V0f_2E0,V1m_2E0,V2n_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V1m_2E0))),s(A_27a,V2n_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,V1m_2E0),s(A_27a,V2n_2E0))) ) ) ).

fof(thm_2Eprim__rec_2ELESS__ALT,axiom,
    ! [F0_2E0] :
      ( ! [V0x_2E0,V1y_2E0] :
          ( p(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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))
        <=> s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) )
     => s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0))) ) ).

fof(thm_2Eprim__rec_2ELESS__SUC__REFL,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) ).

fof(thm_2Eprim__rec_2ELESS__SUC,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) ) ).

fof(thm_2Eprim__rec_2ELESS__LEMMA1,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))
     => ( s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0)
        | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ) ).

fof(thm_2Eprim__rec_2ELESS__LEMMA2,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( ( s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0)
        | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) ) ).

fof(thm_2Eprim__rec_2ELESS__THM,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))
    <=> ( s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0)
        | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ) ).

fof(thm_2Eprim__rec_2ELESS__SUC__IMP,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))
     => ( s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0)
       => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ) ).

fof(thm_2Eprim__rec_2EEQ__LESS,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0)
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ).

fof(thm_2Eprim__rec_2ESUC__ID,axiom,
    ! [V0n_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) != s(tyop_2Enum_2Enum,V0n_2E0) ).

fof(thm_2Eprim__rec_2ENOT__LESS__EQ,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0)
     => ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) ) ).

fof(thm_2Eprim__rec_2ELESS__NOT__EQ,axiom,
    ! [V0m_2E0,V1n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))
     => s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) ) ).

fof(thm_2Eprim__rec_2ESIMP__REC__EXISTS,axiom,
    ! [A_27a,V0x_2E0,V1f_2E0,V2n_2E0] :
    ? [V3fun_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) ).

fof(thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE,axiom,
    ! [A_27a,V0x_2E0,V1f_2E0,V2g1_2E0,V3g2_2E0,V4m1_2E0,V5m2_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g1_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4m1_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))) )
     => ! [V6n_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V4m1_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))) )
         => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g1_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) ) ) ).

fof(thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0x_2E0,V1f_2E0,V2n_2E0,V3y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V3y_2E0))))
        <=> ? [V4g_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))
              & s(A_27a,V3y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) ) )
     => ! [V0x_2E0,V1f_2E0,V2n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))) ) ).

fof(thm_2Eprim__rec_2ELESS__SUC__SUC,axiom,
    ! [V0m_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) ) ).

fof(thm_2Eprim__rec_2ESIMP__REC__THM,axiom,
    ! [A_27a,V0x_2E0,V1f_2E0] :
      ( s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0x_2E0)
      & ! [V2m_2E0] : s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))) ) ).

fof(thm_2Eprim__rec_2EPRIM__REC__EQN,axiom,
    ! [A_27a,V0x_2E0,V1f_2E0] :
      ( ! [V2n_2E0] : s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,V0x_2E0)
      & ! [V3m_2E0,V4n_2E0] : s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3m_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0))) ) ).

fof(thm_2Eprim__rec_2EPRIM__REC__THM,axiom,
    ! [A_27a,V0x_2E0,V1f_2E0] :
      ( s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0x_2E0)
      & ! [V2m_2E0] : s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))),s(tyop_2Enum_2Enum,V2m_2E0))) ) ).

fof(thm_2Eprim__rec_2EDC,axiom,
    ! [A_27a,V0P_2E0,V1R_2E0,V2a_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2a_2E0))))
        & ! [V3x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))
           => ? [V4y_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4y_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)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) ) ) )
     => ? [V5f_2E0] :
          ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V2a_2E0)
          & ! [V6n_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0)))))))) ) ) ) ).

fof(thm_2Eprim__rec_2Enum__Axiom__old,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0e_2E0,V1f_2E0,V2fn1_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0))))
        <=> ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0e_2E0)
            & ! [V3n_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0))) ) )
     => ! [V0e_2E0,V1f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0)))))) ) ).

fof(thm_2Eprim__rec_2Enum__Axiom,axiom,
    ! [A_27a,V0e_2E0,V1f_2E0] :
    ? [V2fn_2E0] :
      ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0e_2E0)
      & ! [V3n_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) ) ).

fof(thm_2Eprim__rec_2EWF__IFF__WELLFOUNDED,axiom,
    ! [A_27a,V0R_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) ).

fof(thm_2Eprim__rec_2EWF__PRED,axiom,
    ! [F0_2E0] :
      ( ! [V0x_2E0,V1y_2E0] :
          ( p(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)),F0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))
        <=> s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) )
     => p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0)))) ) ).

fof(thm_2Eprim__rec_2EWF__LESS,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0)))) ).

fof(thm_2Eprim__rec_2EWF__measure,axiom,
    ! [A_27a,V0m_2E0] : p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0)))))) ).

fof(thm_2Eprim__rec_2Emeasure__thm,axiom,
    ! [A_27a,V0f_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Emeasure_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2y_2E0))))) ).

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) ) ).

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