ITP001 Axioms: ITP008+4.ax


%------------------------------------------------------------------------------
% File     : ITP008+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    : combin.ax [Gau19]
%          : HL4008+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  132 (  93 unt;   0 def)
%            Number of atoms       :  188 ( 140 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   64 (   8   ~;   4   |;  11   &)
%                                         (  25 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :   14 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   65 (  65 usr;  32 con; 0-4 aty)
%            Number of variables   :  571 ( 570   !;   1   ?)
% 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(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = 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_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(A_27a,X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27e,A_27f,X0_2E0] : s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,X0_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,A_27e)),c_2Ecombin_2EK_2E0),s(A_27e,X0_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b,A_27c,X0_2E0,X1_2E0] : s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b,A_27c,X0_2E0,X1_2E0] : s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2E_3A_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2Ecombin_2E_3A_3E_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Ecombin_2E_3A_3E_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,X0_2E0),s(A_27b,X1_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)),c_2Ecombin_2EFAIL_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)),c_2Ecombin_2EFCOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)),c_2Ecombin_2EFCOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,X0_2E0),s(A_27b,X1_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)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ELEFT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ELEFT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27c,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27b,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27c,X0_2E0,X1_2E0] : s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(A_27c,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EMONOID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2EMONOID_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ERIGHT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2ERIGHT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27b,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27c,X0_2E0,X1_2E0] : s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(A_27c,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = 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_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27d_20mono_2EA_27f,axiom,
    ! [A_27d,A_27f,X0_2E0] : s(tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E1(s(A_27d,X0_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27f,A_27d)),c_2Ecombin_2EK_2E0),s(A_27d,X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27d,axiom,
    ! [A_27d,A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27c,X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27c,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_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))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0),s(A_27c,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))),s(A_27c,X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27c,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))),s(A_27b,X2_2E0))) ).

fof(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0))) ).

fof(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27d,c_2Ecombin_2EUPDATE_2E4(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27c,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27c,X3_2E0))) ).

fof(thm_2Ecombin_2EK__DEF,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1x_27_2E0] : s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0))) = s(A_27a,V0x_2E0) ).

fof(thm_2Ecombin_2ES__DEF,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0] : s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_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)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_2E0))))) ).

fof(thm_2Ecombin_2EI__DEF,axiom,
    ! [A_27a] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E0))) ).

fof(thm_2Ecombin_2EC__DEF,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0] : s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27b,V1x_27_2E0),s(A_27a,V2x_27_27_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)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,V1x_27_2E0))) ).

fof(thm_2Ecombin_2EW__DEF,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1x_27_2E0] : s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0x_2E0),s(A_27a,V1x_27_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0x_2E0),s(A_27a,V1x_27_2E0))),s(A_27a,V1x_27_2E0))) ).

fof(thm_2Ecombin_2Eo__DEF,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0))))) ).

fof(thm_2Ecombin_2EAPP__DEF,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1f_2E0] : s(A_27a,c_2Ecombin_2E_3A_3E_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))) ).

fof(thm_2Ecombin_2EUPDATE__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0a_2E0,V3x_27_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)),F0_2E0),s(A_27a,V0a_2E0))),s(A_27a,V3x_27_2E0))))
        <=> s(A_27a,V0a_2E0) = s(A_27a,V3x_27_2E0) )
     => ! [V0a_2E0,V1b_2E0,V2x_2E0,V3x_27_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(A_27a,V0a_2E0))),s(A_27a,V3x_27_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0))))) ) ).

fof(thm_2Ecombin_2EASSOC__DEF,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))))
    <=> ! [V1x_2E0,V2y_2E0,V3z_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0))) ) ).

fof(thm_2Ecombin_2ECOMM__DEF,axiom,
    ! [A_27a,A_27b,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0))))
    <=> ! [V1x_2E0,V2y_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0))) ) ).

fof(thm_2Ecombin_2EFCOMM__DEF,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0))))
    <=> ! [V2x_2E0,V3y_2E0,V4z_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0),s(A_27c,V2x_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)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,V4z_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)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0),s(A_27c,V2x_2E0))),s(A_27a,V3y_2E0))))),s(A_27b,V4z_2E0))) ) ).

fof(thm_2Ecombin_2ERIGHT__ID__DEF,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1e_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27b,V1e_2E0))))
    <=> ! [V2x_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)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V1e_2E0))) = s(A_27a,V2x_2E0) ) ).

fof(thm_2Ecombin_2ELEFT__ID__DEF,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1e_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0))))
    <=> ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0))),s(A_27b,V2x_2E0))) = s(A_27b,V2x_2E0) ) ).

fof(thm_2Ecombin_2EMONOID__DEF,axiom,
    ! [A_27a,V0f_2E0,V1e_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))) ) ) ).

fof(thm_2Ecombin_2EFAIL__DEF,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1x_27_2E0] : s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0))) = s(A_27a,V0x_2E0) ).

fof(thm_2Ecombin_2Eo__THM,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(A_27c,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(A_27c,V2x_2E0))))) ).

fof(thm_2Ecombin_2Eo__ASSOC,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1g_2E0,V2h_2E0] : s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),V2h_2E0))) ).

fof(thm_2Ecombin_2Eo__ABS__L,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V1f_2E0,V3x_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_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0))),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V3x_2E0)))
     => ! [V0g_2E0,V1f_2E0,V2x_2E0] : s(A_27c,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V2x_2E0))))) ) ).

fof(thm_2Ecombin_2Eo__ABS__R,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V0g_2E0,V3x_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_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0)))
     => ! [V0g_2E0,V1f_2E0,V2x_2E0] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))))) ) ).

fof(thm_2Ecombin_2EK__THM,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).

fof(thm_2Ecombin_2ES__THM,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,c_2Ecombin_2ES_2E3(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(thm_2Ecombin_2ES__ABS__L,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V1f_2E0,V3x_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0)))
     => ! [V0g_2E0,V1f_2E0,V2x_2E0] : s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))))) ) ).

fof(thm_2Ecombin_2ES__ABS__R,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V0g_2E0,V3x_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_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0)))
     => ! [V0g_2E0,V1f_2E0,V2x_2E0] : s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))))) ) ).

fof(thm_2Ecombin_2EC__THM,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1x_2E0,V2y_2E0] : s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27b,V1x_2E0),s(A_27a,V2y_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,V2y_2E0))),s(A_27b,V1x_2E0))) ).

fof(thm_2Ecombin_2EC__ABS__L,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V1f_2E0,V3x_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0)))
     => ! [V0y_2E0,V1f_2E0,V2x_2E0] : s(A_27b,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27c,V0y_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,V0y_2E0))) ) ).

fof(thm_2Ecombin_2EW__THM,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1x_2E0] : s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))) ).

fof(thm_2Ecombin_2EI__THM,axiom,
    ! [A_27a,V0x_2E0] : s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).

fof(thm_2Ecombin_2EI__o__ID,axiom,
    ! [A_27a,A_27b,V0f_2E0] :
      ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)
      & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ).

fof(thm_2Ecombin_2EK__o__THM,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27e,A_27f] :
      ( ! [V0f_2E0,V1v_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_2E0)))
      & ! [V2f_2E0,V3v_2E0] : s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V2f_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E1(s(A_27d,V3v_2E0))))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V2f_2E0),s(A_27d,V3v_2E0))))) ) ).

fof(thm_2Ecombin_2EUPDATE__APPLY,axiom,
    ! [A_27a,A_27b,A_27c,A_27d] :
      ( ! [V0a_2E0,V1x_2E0,V2f_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0a_2E0))) = s(A_27b,V1x_2E0)
      & ! [V3a_2E0,V4b_2E0,V5x_2E0,V6f_2E0] :
          ( s(A_27c,V3a_2E0) != s(A_27c,V4b_2E0)
         => s(A_27d,c_2Ecombin_2EUPDATE_2E4(s(A_27c,V3a_2E0),s(A_27d,V5x_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))) ) ) ).

fof(thm_2Ecombin_2EAPPLY__UPDATE__THM,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1a_2E0,V3c_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)),F0_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3c_2E0))))
        <=> s(A_27a,V1a_2E0) = s(A_27a,V3c_2E0) )
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] : s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(A_27a,V1a_2E0))),s(A_27a,V3c_2E0))),s(A_27b,V2b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0))))) ) ).

fof(thm_2Ecombin_2EUPDATE__COMMUTES,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4d_2E0] :
      ( s(A_27a,V1a_2E0) != s(A_27a,V2b_2E0)
     => s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) ) ).

fof(thm_2Ecombin_2EUPDATE__EQ,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) ).

fof(thm_2Ecombin_2EUPDATE__APPLY__ID,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0] :
      ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))) = s(A_27b,V2b_2E0)
    <=> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ).

fof(thm_2Ecombin_2EUPDATE__APPLY__IMP__ID,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1b_2E0,V2a_2E0] :
      ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2a_2E0))) = s(A_27b,V1b_2E0)
     => s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ).

fof(thm_2Ecombin_2EAPPLY__UPDATE__ID,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ).

fof(thm_2Ecombin_2EUPD11__SAME__BASE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0,V4d_2E0] :
      ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))
    <=> ( ( s(A_27a,V1a_2E0) = s(A_27a,V2b_2E0)
          & s(A_27b,V3c_2E0) = s(A_27b,V4d_2E0) )
        | ( s(A_27a,V1a_2E0) != s(A_27a,V2b_2E0)
          & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)
          & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ) ) ).

fof(thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1f1_2E0,V2f2_2E0,V3a_2E0,V4b_2E0,V5c_2E0] :
      ( s(A_27d,V4b_2E0) != s(A_27d,V5c_2E0)
     => s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V4b_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))) != s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V5c_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))) ) ).

fof(thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0,V3c_2E0] :
      ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))
    <=> s(A_27b,V2b_2E0) = s(A_27b,V3c_2E0) ) ).

fof(thm_2Ecombin_2EUPD__SAME__KEY__UNWIND,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2a_2E0,V3b_2E0,V4c_2E0] :
      ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V4c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0)))
     => ( s(A_27b,V3b_2E0) = s(A_27b,V4c_2E0)
        & ! [V5v_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0))) ) ) ).

fof(thm_2Ecombin_2EGEN__LET__RAND,axiom,
    ! [A_27a,A_27b,A_27c,V0v_2E0,V1f_2E0,V2P_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_2E0))))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(A_27c,V0v_2E0))) ).

fof(thm_2Ecombin_2EGEN__LET__RATOR,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1v_2E0,V2f_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1v_2E0))),s(A_27c,V0x_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27c,V0x_2E0))),s(A_27b,V1v_2E0))) ).

fof(thm_2Ecombin_2ELET__FORALL__ELIM,axiom,
    ! [A_27a,V0v_2E0,V1f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_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_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,V0v_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))))) ).

fof(thm_2Ecombin_2EGEN__literal__case__RAND,axiom,
    ! [A_27a,A_27b,A_27c,V0v_2E0,V1f_2E0,V2P_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_2E0))))) = s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(A_27c,V0v_2E0))) ).

fof(thm_2Ecombin_2EGEN__literal__case__RATOR,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1v_2E0,V2f_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1v_2E0))),s(A_27c,V0x_2E0))) = s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27c,V0x_2E0))),s(A_27b,V1v_2E0))) ).

fof(thm_2Ecombin_2Eliteral__case__FORALL__ELIM,axiom,
    ! [A_27a,V0v_2E0,V1f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_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_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,V0v_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))))) ).

fof(thm_2Ecombin_2EASSOC__CONJ,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0)))) ).

fof(thm_2Ecombin_2EASSOC__SYM,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))))
    <=> ! [V1x_2E0,V2y_2E0,V3z_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) ) ).

fof(thm_2Ecombin_2EASSOC__DISJ,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0)))) ).

fof(thm_2Ecombin_2EFCOMM__ASSOC,axiom,
    ! [A_27a,V0f_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))) ).

fof(thm_2Ecombin_2EMONOID__CONJ__T,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_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,c_2Ebool_2ET_2E0)))) ).

fof(thm_2Ecombin_2EMONOID__DISJ__F,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_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,c_2Ebool_2EF_2E0)))) ).

fof(thm_2Ecombin_2EFAIL__THM,axiom,
    ! [A_27a,A_27b,V0y_2E0,V1x_2E0] : s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(A_27a,V1x_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) ) ).

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