%------------------------------------------------------------------------------
% File     : ITP112+4 : TPTP v8.2.0. 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    : patricia_casts.ax [Gau19]
%          : HL4112+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  193 ( 164 unt;   0 def)
%            Number of atoms       :  244 ( 196 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   54 (   3   ~;   4   |;   8   &)
%                                         (  22 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :   26 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  210 ( 210 usr; 111 con; 0-3 aty)
%            Number of variables   :  552 ( 543   !;   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_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia_2EDEPTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia_2EDEPTH_2E1(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum),c_2Epatricia_2EDEPTH_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) = s(tyop_2Epatricia_2Eptree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Epatricia_2Eptree(A_27b)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2EDEPTHw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2EDEPTHw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum),c_2Epatricia__casts_2EDEPTHw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2CA_27a_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a))),c_2Elist_2EFOLDL_2E1(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a)))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_2CA_27b_29_20mono_2Etyop_2Epatricia__casts_2Eword__ptree_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Elist_2EFOLDL_2E1(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2EKEYSs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2EKEYSs_2E1(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epatricia__casts_2EKEYSs_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2EKEYSw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2EKEYSw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Epatricia__casts_2EKEYSw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEw_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Epatricia__casts_2ETRAVERSEw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEs_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epatricia__casts_2ETRAVERSEs_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))) ).

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

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

fof(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia_2ESIZE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia_2ESIZE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum),c_2Epatricia_2ESIZE_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ESIZEw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2ESIZEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum),c_2Epatricia__casts_2ESIZEw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) ).

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

fof(arityeq1_2Ec_2Epatricia__casts_2ESKIP1_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2ESKIP1_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ESKIP1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).

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

fof(arityeq3_2Ec_2EASCIInumbers_2En2s_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2En2s_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2EASCIInumbers_2En2s_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),c_2Epatricia__casts_2ESOME__PTREE_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EADD_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2EADD_2E2(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epatricia_2Eptree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epatricia_2Eptree(A_27b))),c_2Epatricia_2EADD_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2EREMOVE_2E2(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27b))),c_2Epatricia_2EREMOVE_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b,A_27c,X0_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b)),c_2Epatricia__casts_2ESOME__PTREE_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,X0_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),X0_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia_2Eptree(A_27a)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2ETRANSFORM_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2ETRANSFORM_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia_2Eptree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia_2Eptree(A_27b))),c_2Epatricia_2ETRANSFORM_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EINSERT__PTREE_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EINSERT__PTREE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))),c_2Epatricia_2EINSERT__PTREE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),c_2Epatricia__casts_2ESOME__PTREE_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EPTREE__OF__NUMSET_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EPTREE__OF__NUMSET_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))),c_2Epatricia_2EPTREE__OF__NUMSET_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27c,axiom,
    ! [A_27c,X0_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EUNION__PTREE_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EUNION__PTREE_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))),c_2Epatricia_2EUNION__PTREE_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EPEEKs_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia__casts_2EPEEKs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(A_27a))),c_2Epatricia__casts_2EPEEKs_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).

fof(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EPEEKw_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia__casts_2EPEEKw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Epatricia__casts_2EPEEKw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a)),c_2Epatricia__casts_2ESOME__PTREE_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X0_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Epatricia_2Eptree(A_27a)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EWord__ptree_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a))),c_2Epatricia__casts_2EWord__ptree_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27a),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E1(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epatricia__casts_2ETRAVERSEs_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Epatricia__casts_2ETRAVERSEw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2Enum__to__string_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2Enum__to__string_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2Enum__to__string_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Epatricia__casts_2Estring__to__num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EWord__ptree_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Epatricia__casts_2EWord__ptree_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2Eptree__size_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia_2Eptree__size_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum)),c_2Epatricia_2Eptree__size_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq2_2Ec_2Enumposrep_2El2n_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Enumposrep_2El2n_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EADD_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia_2EADD_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Epatricia_2Eptree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Epatricia_2Eptree(A_27a))),c_2Epatricia_2EADD_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EADDs_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2EADDs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))),c_2Epatricia__casts_2EADDs_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Eone_2Eone,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Eone_2Eone,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EADDs_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EADDs_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))),c_2Epatricia__casts_2EADDs_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EADDw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EADDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Epatricia__casts_2EADDw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Eone_2Eone,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Eone_2Eone,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EADDw_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EADDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))),c_2Epatricia__casts_2EADDw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Elogroot_2ELOG_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2E_3E_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EEVERY__LEAF_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia_2EEVERY__LEAF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool)),c_2Epatricia_2EEVERY__LEAF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EEVERY__LEAFw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EEVERY__LEAFw_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2EEVERY__LEAFw_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EEXISTS__LEAF_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia_2EEXISTS__LEAF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool)),c_2Epatricia_2EEXISTS__LEAF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EEXISTS__LEAFw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EEXISTS__LEAFw_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2EEXISTS__LEAFw_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EFINDs_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(A_27a,c_2Epatricia__casts_2EFINDs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),c_2Epatricia__casts_2EFINDs_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EFINDw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2Epatricia__casts_2EFINDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),A_27a)),c_2Epatricia__casts_2EFINDw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EINSERT__PTREEs_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EINSERT__PTREEs_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))),c_2Epatricia__casts_2EINSERT__PTREEs_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EINSERT__PTREEw_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EINSERT__PTREEw_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))),c_2Epatricia__casts_2EINSERT__PTREEw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EIN__PTREE_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia_2EIN__PTREE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),c_2Epatricia_2EIN__PTREE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EIN__PTREEs_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EIN__PTREEs_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2EIN__PTREEs_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EIN__PTREEw_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EIN__PTREEw_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2EIN__PTREEw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Epatricia_2ETRAVERSE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Epatricia_2ETRAVERSE_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq1_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Epatricia_2ETRAVERSE_2E1(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Epatricia_2ETRAVERSE_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia_2EPEEK_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),c_2Epatricia_2EPEEK_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Epatricia_2EPEEK_2E2(s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b))),c_2Epatricia_2EPEEK_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EPEEKw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Epatricia__casts_2EPEEKw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Epatricia__casts_2EPEEKw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))),c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))),c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Esorting_2EQSORT_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)))),c_2Esorting_2EQSORT_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Esorting_2EQSORT_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Esorting_2EQSORT_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia_2EREMOVE_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27a))),c_2Epatricia_2EREMOVE_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EREMOVEs_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2EREMOVEs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epatricia_2Eptree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epatricia_2Eptree(A_27a))),c_2Epatricia__casts_2EREMOVEs_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EREMOVEw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EREMOVEw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Epatricia__casts_2EREMOVEw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2ETRANSFORMw_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),c_2Epatricia__casts_2ETRANSFORMw_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b))),c_2Epatricia__casts_2ETRANSFORMw_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28A_27b_29_29_29_20mono_2Etyop_2Epatricia__casts_2Eword__ptree_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2EUNION__PTREEw_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EUNION__PTREEw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))),c_2Epatricia__casts_2EUNION__PTREEw_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E0),s(tyop_2Eone_2Eone,X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ECONS_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Epatricia__casts_2Eword__ptree__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(A_27c,c_2Epatricia__casts_2Eword__ptree__CASE_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),A_27c)),c_2Epatricia__casts_2Eword__ptree__CASE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),X1_2E0))) ).

fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28A_27b_29_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),X2_2E0))) ).

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

fof(arityeq3_2Ec_2EASCIInumbers_2Es2n_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Es2n_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum))),c_2EASCIInumbers_2Es2n_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0))) ).

fof(arityeq3_2Ec_2Epatricia__casts_2Eword__ptree__size_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Eword__ptree__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum))),c_2Epatricia__casts_2Eword__ptree__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X2_2E0))) ).

fof(thm_2Epatricia__casts_2ESKIP1__def,axiom,
    ! [V0c_2E0,V1s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2ESKIP1_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V0c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1s_2E0) ).

fof(thm_2Epatricia__casts_2Estring__to__num__def,axiom,
    ! [V0s_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2EASCIInumbers_2Es2n_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2EORD_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))))) ).

fof(thm_2Epatricia__casts_2Enum__to__string__def,axiom,
    ! [V0n_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2Enum__to__string_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2ESKIP1_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2En2s_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),c_2Estring_2ECHR_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) ).

fof(thm_2Epatricia__casts_2EPEEKs__def,axiom,
    ! [A_27a,V0t_2E0,V1w_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia__casts_2EPEEKs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia_2EPEEK_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))))) ).

fof(thm_2Epatricia__casts_2EFINDs__def,axiom,
    ! [A_27a,V0t_2E0,V1w_2E0] : s(A_27a,c_2Epatricia__casts_2EFINDs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia__casts_2EPEEKs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))))) ).

fof(thm_2Epatricia__casts_2EADDs__def,axiom,
    ! [A_27a,V0t_2E0,V1w_2E0,V2d_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2EADDs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0),s(A_27a,V2d_2E0))))) = s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia_2EADD_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))),s(A_27a,V2d_2E0))))) ).

fof(thm_2Epatricia__casts_2EADD__LISTs__def,axiom,
    ! [A_27a] : s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a))),c_2Epatricia__casts_2EADD__LISTs_2E0) = s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a))),c_2Elist_2EFOLDL_2E1(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))),c_2Epatricia__casts_2EADDs_2E0))) ).

fof(thm_2Epatricia__casts_2EREMOVEs__def,axiom,
    ! [A_27a,V0t_2E0,V1w_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2EREMOVEs_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))) = s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia_2EREMOVE_2E2(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0),s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1w_2E0))))) ).

fof(thm_2Epatricia__casts_2ETRAVERSEs__def,axiom,
    ! [A_27a,V0t_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E1(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2Enum__to__string_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Epatricia_2ETRAVERSE_2E1(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2EKEYSs__def,axiom,
    ! [A_27a,V0t_2E0] : s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2EKEYSs_2E1(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Esorting_2EQSORT_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Estring_2Estring__lt_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E1(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2EIN__PTREEs__def,axiom,
    ! [V0w_2E0,V1t_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EIN__PTREEs_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0w_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epatricia_2EIN__PTREE_2E2(s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0w_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V1t_2E0))) ).

fof(thm_2Epatricia__casts_2EINSERT__PTREEs__def,axiom,
    ! [V0w_2E0,V1t_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EINSERT__PTREEs_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0w_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V1t_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EINSERT__PTREE_2E2(s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0w_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V1t_2E0))) ).

fof(thm_2Epatricia__casts_2ESTRINGSET__OF__PTREE__def,axiom,
    ! [V0t_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V0t_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2EPTREE__OF__STRINGSET__def,axiom,
    ! [V0t_2E0,V1s_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V0t_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EPTREE__OF__NUMSET_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V0t_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),V1s_2E0))))) ).

fof(thm_2Epatricia__casts_2Eword__ptree__TY__DEF,axiom,
    ! [A_27a,A_27b,F1_2E0,F0_2E0] :
      ( ! [V6n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),F1_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),c_2Eind__type_2EBOTTOM_2E0)
     => ( ! [V1a0_27_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),V1a0_27_2E0))))
          <=> ! [V2_27word__ptree_27_2E0] :
                ( ! [V3a0_27_2E0] :
                    ( ? [V4a0_2E0,V5a1_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V4a0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V5a1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),F1_2E0)))
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),V2_27word__ptree_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),V3a0_27_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),V2_27word__ptree_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),V1a0_27_2E0)))) ) )
       => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),V0rep_2E0)))) ) ) ).

fof(thm_2Epatricia__casts_2Eword__ptree__case__def,axiom,
    ! [A_27a,A_27b,A_27c,V0a0_2E0,V1a1_2E0,V2f_2E0] : s(A_27c,c_2Epatricia__casts_2Eword__ptree__CASE_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V0a0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V1a1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V2f_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V0a0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),V1a1_2E0))) ).

fof(thm_2Epatricia__casts_2Eword__ptree__size__def,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1f1_2E0,V2a0_2E0,V3a1_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Eword__ptree__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1f1_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2a0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V3a1_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epatricia_2Eptree__size_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1f1_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V3a1_2E0))))) ).

fof(thm_2Epatricia__casts_2ETHE__PTREE__def,axiom,
    ! [A_27a,A_27b,V0a_2E0,V1t_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),V0a_2E0),s(tyop_2Epatricia_2Eptree(A_27a),V1t_2E0))))) = s(tyop_2Epatricia_2Eptree(A_27a),V1t_2E0) ).

fof(thm_2Epatricia__casts_2ESOME__PTREE__def,axiom,
    ! [A_27a,A_27b,V0t_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),V0t_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),V0t_2E0))) ).

fof(thm_2Epatricia__casts_2EWordEmpty__def,axiom,
    ! [A_27a,A_27b] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWordEmpty_2E0) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2EEmpty_2E0))) ).

fof(thm_2Epatricia__casts_2EPEEKw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0,V1w_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Epatricia__casts_2EPEEKw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Epatricia_2EPEEK_2E2(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))),s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))))) ).

fof(thm_2Epatricia__casts_2EFINDw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0,V1w_2E0] : s(A_27a,c_2Epatricia__casts_2EFINDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),V0t_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V1w_2E0))) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Epatricia__casts_2EPEEKw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),V0t_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V1w_2E0))))) ).

fof(thm_2Epatricia__casts_2EADDw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0,V1w_2E0,V2d_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EADDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0),s(A_27b,V2d_2E0))))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2EADD_2E2(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))),s(A_27b,V2d_2E0))))))) ).

fof(thm_2Epatricia__casts_2EADD__LISTw__def,axiom,
    ! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Epatricia__casts_2EADD__LISTw_2E0) = s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Elist_2EFOLDL_2E1(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Epatricia__casts_2EADDw_2E0))) ).

fof(thm_2Epatricia__casts_2EREMOVEw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0,V1w_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EREMOVEw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2EREMOVE_2E2(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))),s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))))))) ).

fof(thm_2Epatricia__casts_2ETRAVERSEw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2En2w_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Epatricia_2ETRAVERSE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))))))) ).

fof(thm_2Epatricia__casts_2EKEYSw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0] : s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2EKEYSw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Esorting_2EQSORT_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),c_2Ewords_2Eword__lo_2E0),s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2ETRANSFORMw__def,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1t_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),c_2Epatricia__casts_2ETRANSFORMw_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),V1t_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia_2ETRANSFORM_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),V1t_2E0))))))) ).

fof(thm_2Epatricia__casts_2EEVERY__LEAFw__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0P_2E0,V2k_2E0,V3d_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))),s(A_27b,V3d_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V2k_2E0))))),s(A_27b,V3d_2E0)))
     => ! [V0P_2E0,V1t_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EEVERY__LEAFw_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epatricia_2EEVERY__LEAF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1t_2E0))))) ) ).

fof(thm_2Epatricia__casts_2EEXISTS__LEAFw__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0P_2E0,V2k_2E0,V3d_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))),s(A_27b,V3d_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,V2k_2E0))))),s(A_27b,V3d_2E0)))
     => ! [V0P_2E0,V1t_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EEXISTS__LEAFw_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epatricia_2EEXISTS__LEAF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1t_2E0))))) ) ).

fof(thm_2Epatricia__casts_2ESIZEw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2ESIZEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))) = s(tyop_2Enum_2Enum,c_2Epatricia_2ESIZE_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2EDEPTHw__def,axiom,
    ! [A_27a,A_27b,V0t_2E0] : s(tyop_2Enum_2Enum,c_2Epatricia__casts_2EDEPTHw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))) = s(tyop_2Enum_2Enum,c_2Epatricia_2EDEPTH_2E1(s(tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2EIN__PTREEw__def,axiom,
    ! [A_27a,V0w_2E0,V1t_2E0] : s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EIN__PTREEw_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epatricia_2EIN__PTREE_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1t_2E0))))) ).

fof(thm_2Epatricia__casts_2EINSERT__PTREEw__def,axiom,
    ! [A_27a,V0w_2E0,V1t_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EINSERT__PTREEw_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1t_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EINSERT__PTREE_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1t_2E0))))))) ).

fof(thm_2Epatricia__casts_2EWORDSET__OF__PTREE__def,axiom,
    ! [A_27a,V0t_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V0t_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V0t_2E0))))) ).

fof(thm_2Epatricia__casts_2EUNION__PTREEw__def,axiom,
    ! [A_27a,A_27b,A_27c,V0t1_2E0,V1t2_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EUNION__PTREEw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),V0t1_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),V1t2_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EUNION__PTREE_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),V0t1_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),V1t2_2E0))))))) ).

fof(thm_2Epatricia__casts_2EPTREE__OF__WORDSET__def,axiom,
    ! [A_27a,V0t_2E0,V1s_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V0t_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia_2EPTREE__OF__NUMSET_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V0t_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),V1s_2E0))))))) ).

fof(thm_2Epatricia__casts_2Edatatype__word__ptree,axiom,
    ! [A_27a,A_27b,V0word__ptree_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),tyop_2Emin_2Ebool),V0word__ptree_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Epatricia__casts_2EWord__ptree_2E0)))))) ).

fof(thm_2Epatricia__casts_2Eword__ptree__11,axiom,
    ! [A_27a,A_27b,V0a0_2E0,V1a1_2E0,V2a0_27_2E0,V3a1_27_2E0] :
      ( s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V0a0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V1a1_2E0))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2a0_27_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V3a1_27_2E0)))
    <=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V0a0_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2a0_27_2E0)
        & s(tyop_2Epatricia_2Eptree(A_27b),V1a1_2E0) = s(tyop_2Epatricia_2Eptree(A_27b),V3a1_27_2E0) ) ) ).

fof(thm_2Epatricia__casts_2Eword__ptree__nchotomy,axiom,
    ! [A_27a,A_27b,V0ww_2E0] :
    ? [V1f_2E0,V2p_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0ww_2E0) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V1f_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V2p_2E0))) ).

fof(thm_2Epatricia__casts_2Eword__ptree__Axiom,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0] :
    ? [V1fn_2E0] :
    ! [V2a0_2E0,V3a1_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),A_27c),V1fn_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2a0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V3a1_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2a0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),V3a1_2E0))) ).

fof(thm_2Epatricia__casts_2Eword__ptree__induction,axiom,
    ! [A_27a,A_27b,V0P_2E0] :
      ( ! [V1f_2E0,V2p_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V1f_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V2p_2E0))))))
     => ! [V3w_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V3w_2E0)))) ) ).

fof(thm_2Epatricia__casts_2Eword__ptree__case__cong,axiom,
    ! [A_27a,A_27b,A_27c,V0f_27_2E0,V1M_2E0,V2M_27_2E0,V3f_2E0] :
      ( ( s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1M_2E0) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V2M_27_2E0)
        & ! [V4a0_2E0,V5a1_2E0] :
            ( s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V2M_27_2E0) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V4a0_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V5a1_2E0)))
           => s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V4a0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),V5a1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V0f_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V4a0_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),V5a1_2E0))) ) )
     => s(A_27c,c_2Epatricia__casts_2Eword__ptree__CASE_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1M_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V3f_2E0))) = s(A_27c,c_2Epatricia__casts_2Eword__ptree__CASE_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V2M_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V0f_27_2E0))) ) ).

fof(thm_2Epatricia__casts_2Eword__ptree__case__eq,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1v_2E0,V2f_2E0] :
      ( s(A_27c,c_2Epatricia__casts_2Eword__ptree__CASE_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V2f_2E0))) = s(A_27c,V1v_2E0)
    <=> ? [V3f_27_2E0,V4p_2E0] :
          ( s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V0x_2E0) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EWord__ptree_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V3f_27_2E0),s(tyop_2Epatricia_2Eptree(A_27b),V4p_2E0)))
          & s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V3f_27_2E0))),s(tyop_2Epatricia_2Eptree(A_27b),V4p_2E0))) = s(A_27c,V1v_2E0) ) ) ).

fof(thm_2Epatricia__casts_2EADD__INSERT__STRING,axiom,
    ! [V0w_2E0,V1v_2E0,V2t_2E0] : s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EADDs_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V2t_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0w_2E0),s(tyop_2Eone_2Eone,V1v_2E0))))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2EADDs_2E2(s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V2t_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0w_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))))) ).

fof(thm_2Epatricia__casts_2El2n__APPEND,axiom,
    ! [V0b_2E0,V1l1_2E0,V2l2_2E0] : s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0))))),s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0))))))) ).

fof(thm_2Epatricia__casts_2El2n__LENGTH,axiom,
    ! [V0b_2E0,V1l_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l_2E0)))))))) ) ).

fof(thm_2Epatricia__casts_2El2n__11,axiom,
    ! [V0b_2E0,V1l1_2E0,V2l2_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E1(s(tyop_2Enum_2Enum,V0b_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E1(s(tyop_2Enum_2Enum,V0b_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0)))) )
     => ( s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumposrep_2El2n_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0)))))))
      <=> s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l1_2E0) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0) ) ) ).

fof(thm_2Epatricia__casts_2EEVERY__MAP__ORD,axiom,
    ! [V0l_2E0] : p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2EORD_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0l_2E0)))))) ).

fof(thm_2Epatricia__casts_2EMAP__11,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1l1_2E0,V2l2_2E0] :
      ( ! [V3x_2E0,V4y_2E0] :
          ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0)))
        <=> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) )
     => ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))
      <=> s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) ) ) ).

fof(thm_2Epatricia__casts_2EREVERSE__11,axiom,
    ! [A_27a,V0l1_2E0,V1l2_2E0] :
      ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))
    <=> s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) ) ).

fof(thm_2Epatricia__casts_2Estring__to__num__11,axiom,
    ! [V0s_2E0,V1t_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0)))
    <=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0) ) ).

fof(thm_2Epatricia__casts_2EIMAGE__string__to__num,axiom,
    ! [V0n_2E0] :
      ( ( s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
        | ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))),s(tyop_2Enum_2Enum,V0n_2E0))))
          & s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) ) )
    <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) ) ).

fof(thm_2Epatricia__casts_2Estring__to__num__num__to__string,axiom,
    ! [V0n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))))
     => s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2Enum__to__string_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0) ) ).

fof(thm_2Epatricia__casts_2Enum__to__string__string__to__num,axiom,
    ! [V0s_2E0] : s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2Enum__to__string_2E1(s(tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0) ).

fof(thm_2Epatricia__casts_2EADD__INSERT__WORD,axiom,
    ! [A_27a,V0w_2E0,V1v_2E0,V2t_2E0] : s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EADDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V2t_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0),s(tyop_2Eone_2Eone,V1v_2E0))))) = s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2EADDw_2E2(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V2t_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))))) ).

fof(thm_2Epatricia__casts_2ETHE__PTREE__SOME__PTREE,axiom,
    ! [A_27a,A_27b,V0t_2E0] : s(tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),c_2Epatricia__casts_2ESOME__PTREE_2E1(s(tyop_2Epatricia_2Eptree(A_27a),V0t_2E0))))) = s(tyop_2Epatricia_2Eptree(A_27a),V0t_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) ) ).

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