%------------------------------------------------------------------------------
% File     : ITP066+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    : lbtree.ax [Gau19]
%          : HL4066+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  137 (  75 unt;   0 def)
%            Number of atoms       :  348 ( 175 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  215 (   4   ~;  20   |;  85   &)
%                                         (  39 <=>;  67  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :   18 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  116 ( 116 usr;  59 con; 0-4 aty)
%            Number of variables   :  673 ( 592   !;  81   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

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

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

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

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

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).

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

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

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

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

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

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

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

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

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

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elbtree_2Elbtree_28A_27b_29_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2ELfrep_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Elbtree_2ELfrep_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elbtree_2ELfrep_2E0),s(A_27a,X0_2E0))) ).

fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2ESOME_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_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_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

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

fof(arityeq1_2Ec_2Elbtree_2Ebf__flatten_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Ellist_2Ellist(A_27a)),c_2Elbtree_2Ebf__flatten_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) ).

fof(arityeq3_2Ec_2Elbtree_2ENd_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X2_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elbtree_2ENd_2E0),s(A_27a,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X2_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2Efinite_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Elbtree_2Efinite_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Elbtree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),X1_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Elbtree_2Elbtree(A_27a))),c_2Elbtree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),X1_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2Efinite_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),c_2Elbtree_2Efinite_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),X0_2E0))) ).

fof(arityeq3_2Ec_2Elbtree_2ENd_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),X1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),X2_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Elbtree_2Elbtree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Elbtree_2Elbtree(A_27b)))),c_2Elbtree_2ENd_2E0),s(A_27b,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),X1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),X2_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2Eis__lbtree_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__lbtree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Elbtree_2Eis__lbtree_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2Elbtree__abs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Elbtree__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Elbtree_2Elbtree(A_27a)),c_2Elbtree_2Elbtree__abs_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2Elbtree__rep_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2Elbtree__rep_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),c_2Elbtree_2Elbtree__rep_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) ).

fof(arityeq3_2Ec_2Elbtree_2ENdrep_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2ENdrep_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),c_2Elbtree_2ENdrep_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),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(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27a),X0_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_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).

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

fof(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) ).

fof(arityeq1_2Ec_2Elbtree_2Emem_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Elbtree_2Emem_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),c_2Elbtree_2Emem_2E0),s(A_27a,X0_2E0))) ).

fof(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELCONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27b_29_29_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))) ).

fof(arityeq2_2Ec_2Ellist_2Eexists_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),c_2Ellist_2Eexists_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elbtree_2Emap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27b))),c_2Elbtree_2Emap_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elbtree_2Emem_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),c_2Elbtree_2Emem_2E0),s(A_27a,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elbtree_2Emindepth_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Elbtree_2Emindepth_2E0),s(A_27a,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Elbtree_2Eoptmin_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Eoptmin_2E2(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Elbtree_2Eoptmin_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27b_29_20mono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))),X1_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))),tyop_2Elbtree_2Elbtree(A_27b))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27b_29_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b))),X1_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b))),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b))),tyop_2Elbtree_2Elbtree(A_27b))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b))),X1_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(A_27b,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27b),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27b_29,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),tyop_2Elbtree_2Elbtree(A_27b)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0))) ).

fof(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq1_2Ec_2Ewhile_2ELEAST_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq3_2Ec_2Elbtree_2Edepth_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Elbtree_2Edepth_2E0),s(A_27a,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq3_2Ec_2Elbtree_2Elbtree__case_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Elbtree_2Elbtree__case_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),X1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),c_2Elbtree_2Elbtree__case_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),X1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),X2_2E0))) ).

fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) ).

fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),X2_2E0))) ).

fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27b_29_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ).

fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Elbtree_2Elbtree_28A_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a))),X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),X2_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Elbtree_2Elbtree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Elbtree_2Elbtree(A_27b)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a))),X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),X2_2E0))) ).

fof(arityeq3_2Ec_2Elbtree_2Epath__follow_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),c_2Elbtree_2Epath__follow_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).

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

fof(arityeq4_2Ec_2Elbtree_2ENdrep_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2ENdrep_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),c_2Elbtree_2ENdrep_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X3_2E0))) ).

fof(arityeq4_2Ec_2Elbtree_2Eis__mmindex_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Elbtree_2Eis__mmindex_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) ).

fof(thm_2Elbtree_2ELfrep__def,axiom,
    ! [A_27a,A_27b,V0x_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Elbtree_2ELfrep_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ).

fof(thm_2Elbtree_2ENdrep__def,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V1t1_2E0,V2t2_2E0,V4v_2E0,V5xs_2E0] : s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0))),s(tyop_2Emin_2Ebool,V4v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V4v_2E0),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5xs_2E0))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5xs_2E0)))))
     => ! [V0a_2E0,V1t1_2E0,V2t2_2E0,V3x_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2ENdrep_2E4(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0a_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1t1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t2_2E0))))) ) ).

fof(thm_2Elbtree_2Eis__lbtree__def,axiom,
    ! [A_27a,V0t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__lbtree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V0t_2E0))))
    <=> ? [V1P_2E0] :
          ( ! [V2t_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t_2E0))))
             => ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2ELfrep_2E0)
                | ? [V3a_2E0,V4t1_2E0,V5t2_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V4t1_2E0))))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V5t2_2E0))))
                    & s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V2t_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2ENdrep_2E3(s(A_27a,V3a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V4t1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V5t2_2E0))) ) ) )
          & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V0t_2E0)))) ) ) ).

fof(thm_2Elbtree_2Elbtree__TY__DEF,axiom,
    ! [A_27a] :
    ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Elbtree_2Eis__lbtree_2E0),s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),V0rep_2E0)))) ).

fof(thm_2Elbtree_2Elbtree__absrep,axiom,
    ! [A_27a] :
      ( ! [V0a_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Elbtree__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2Elbtree__rep_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V0a_2E0))))) = s(tyop_2Elbtree_2Elbtree(A_27a),V0a_2E0)
      & ! [V1r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__lbtree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1r_2E0))))
        <=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2Elbtree__rep_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Elbtree__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),V1r_2E0) ) ) ).

fof(thm_2Elbtree_2Epath__follow__def,axiom,
    ! [A_27a,A_27b,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V2g_2E0,V4h_2E0,V5t_2E0,V9y_2E0,V10z_2E0] : s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,V4h_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0))),s(A_27b,V9y_2E0))),s(A_27b,V10z_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0),s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V4h_2E0),s(A_27b,V9y_2E0),s(A_27b,V10z_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0)))
     => ( ! [V2g_2E0,V4h_2E0,V5t_2E0,V7a_2E0,V8v2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,V4h_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0))),s(A_27a,V7a_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27b),V8v2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),V8v2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,V4h_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0)))))
       => ( ! [V2g_2E0,V4h_2E0,V5t_2E0,V6v_2E0] : s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,V4h_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),V6v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),V6v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Eoption_2Eoption(A_27a)))))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,V4h_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0)))))
         => ( ! [V0g_2E0,V1x_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V0g_2E0),s(A_27b,V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V0g_2E0),s(A_27b,V1x_2E0)))))
            & ! [V2g_2E0,V3x_2E0,V4h_2E0,V5t_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Elbtree_2Epath__follow_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0),s(A_27b,V3x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,V4h_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0),s(A_27b,V3x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)),tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27b)))),V2g_2E0))),s(tyop_2Emin_2Ebool,V4h_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5t_2E0))))) ) ) ) ) ).

fof(thm_2Elbtree_2ELf__def,axiom,
    ! [A_27a] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Elbtree__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2ELfrep_2E0))) ).

fof(thm_2Elbtree_2ENd__def,axiom,
    ! [A_27a,V0a_2E0,V1t1_2E0,V2t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Elbtree__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2ENdrep_2E3(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2Elbtree__rep_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Elbtree_2Elbtree__rep_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0))))))) ).

fof(thm_2Elbtree_2Elbtree__case__def,axiom,
    ! [A_27a,A_27b,F0_2E0,F2_2E0,F3_2E0,F1_2E0] :
      ( ! [V2t_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))))
        <=> s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ELf_2E0) )
     => ( ! [V2t_2E0,V6t1_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),V6t1_2E0))))
          <=> ? [V7a_2E0,V8t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V7a_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V8t2_2E0))) )
       => ( ! [V2t_2E0,V9t2_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),V9t2_2E0))))
            <=> ? [V10a_2E0,V11t1_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V9t2_2E0))) )
         => ( ! [V2t_2E0,V3a_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))),s(A_27b,V3a_2E0))))
              <=> ? [V4t1_2E0,V5t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V4t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V5t2_2E0))) )
           => ! [V0e_2E0,V1f_2E0,V2t_2E0] : s(A_27a,c_2Elbtree_2Elbtree__case_2E3(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),V1f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))),s(A_27a,V0e_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),V1f_2E0),s(A_27b,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))))))),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))))))),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))))))))) ) ) ) ) ).

fof(thm_2Elbtree_2Emem__def,axiom,
    ! [A_27a,V0x_2E0,V1x_27_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1x_27_2E0))))
    <=> ! [V2mem_27_2E0] :
          ( ! [V3a0_2E0,V4a1_2E0] :
              ( ( ? [V5t1_2E0,V6t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),V4a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V3a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t2_2E0)))
                | ? [V7b_2E0,V8t1_2E0,V9t2_2E0] :
                    ( s(tyop_2Elbtree_2Elbtree(A_27a),V4a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V7b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V9t2_2E0)))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2mem_27_2E0),s(A_27a,V3a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V8t1_2E0)))) )
                | ? [V10b_2E0,V11t1_2E0,V12t2_2E0] :
                    ( s(tyop_2Elbtree_2Elbtree(A_27a),V4a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0)))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2mem_27_2E0),s(A_27a,V3a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0)))) ) )
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2mem_27_2E0),s(A_27a,V3a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V4a1_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2mem_27_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1x_27_2E0)))) ) ) ).

fof(thm_2Elbtree_2Emap__def,axiom,
    ! [A_27a,A_27b,V0f_2E0] :
      ( s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ELf_2E0)
      & ! [V1a_2E0,V2t1_2E0,V3t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))) ) ).

fof(thm_2Elbtree_2Efinite__def,axiom,
    ! [A_27a,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V0x_2E0))))
    <=> ! [V1finite_27_2E0] :
          ( ! [V2a0_2E0] :
              ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V2a0_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)
                | ? [V3a_2E0,V4t1_2E0,V5t2_2E0] :
                    ( s(tyop_2Elbtree_2Elbtree(A_27a),V2a0_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V4t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t2_2E0)))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V1finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V4t1_2E0))))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V1finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t2_2E0)))) ) )
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V1finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2a0_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V1finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0x_2E0)))) ) ) ).

fof(thm_2Elbtree_2Ebf__flatten__def,axiom,
    ! [A_27a] :
      ( s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)
      & ! [V0ts_2E0] : s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0ts_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0ts_2E0)))
      & ! [V1a_2E0,V2t1_2E0,V3t2_2E0,V4ts_2E0] : s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V4ts_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1a_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V4ts_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ENIL_2E0))))))))))) ) ).

fof(thm_2Elbtree_2Edepth__def,axiom,
    ! [A_27a,V0x_2E0,V1x_27_2E0,V2x_27_27_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1x_27_2E0),s(tyop_2Enum_2Enum,V2x_27_27_2E0))))
    <=> ! [V3depth_27_2E0] :
          ( ! [V4a0_2E0,V5a1_2E0,V6a2_2E0] :
              ( ( ? [V7t1_2E0,V8t2_2E0] :
                    ( s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V4a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0)))
                    & s(tyop_2Enum_2Enum,V6a2_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
                | ? [V9m_2E0,V10a_2E0,V11t1_2E0,V12t2_2E0] :
                    ( s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0)))
                    & s(tyop_2Enum_2Enum,V6a2_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V9m_2E0)))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V4a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0))),s(tyop_2Enum_2Enum,V9m_2E0)))) )
                | ? [V13m_2E0,V14a_2E0,V15t1_2E0,V16t2_2E0] :
                    ( s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V14a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V15t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V16t2_2E0)))
                    & s(tyop_2Enum_2Enum,V6a2_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V13m_2E0)))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V4a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V16t2_2E0))),s(tyop_2Enum_2Enum,V13m_2E0)))) ) )
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V4a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V5a1_2E0))),s(tyop_2Enum_2Enum,V6a2_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3depth_27_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1x_27_2E0))),s(tyop_2Enum_2Enum,V2x_27_27_2E0)))) ) ) ).

fof(thm_2Elbtree_2Emindepth__def,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0x_2E0,V1t_2E0,V2n_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))
     => ! [V0x_2E0,V1t_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0),s(A_27a,V0x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) ) ).

fof(thm_2Elbtree_2Eis__mmindex__def,axiom,
    ! [A_27a,V0f_2E0,V1l_2E0,V2n_2E0,V3d_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3d_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
        & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V3d_2E0)))
        & ! [V4i_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
           => ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0)
              | ? [V5d_27_2E0] :
                  ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V5d_27_2E0)))
                  & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V5d_27_2E0))))
                  & ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))
                   => p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V5d_27_2E0)))) ) ) ) ) ) ) ).

fof(thm_2Elbtree_2Elbtree__cases,axiom,
    ! [A_27a,V0t_2E0] :
      ( s(tyop_2Elbtree_2Elbtree(A_27a),V0t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)
      | ? [V1a_2E0,V2t1_2E0,V3t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),V0t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))) ) ).

fof(thm_2Elbtree_2ELf__NOT__Nd,axiom,
    ! [A_27a,V0t2_2E0,V1t1_2E0,V2a_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0) != s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V2a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0))) ).

fof(thm_2Elbtree_2ENd__11,axiom,
    ! [A_27a,V0u2_2E0,V1u1_2E0,V2t2_2E0,V3t1_2E0,V4a2_2E0,V5a1_2E0] :
      ( s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1u1_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V4a2_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0u2_2E0)))
    <=> ( s(A_27a,V5a1_2E0) = s(A_27a,V4a2_2E0)
        & s(tyop_2Elbtree_2Elbtree(A_27a),V3t1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0)
        & s(tyop_2Elbtree_2Elbtree(A_27a),V1u1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),V0u2_2E0) ) ) ).

fof(thm_2Elbtree_2Elbtree__ue__Axiom,axiom,
    ! [A_27a,A_27b,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V4b_2E0,V1g_2E0,V6y_2E0,V7z_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))))),F3_2E0),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0))),s(A_27a,V6y_2E0))),s(A_27a,V7z_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V4b_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0),s(A_27a,V6y_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0),s(A_27a,V7z_2E0)))))
     => ( ! [V1g_2E0,V4b_2E0,V5v2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27a),V5v2_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),V5v2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b))))),F3_2E0),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0)))))
       => ( ! [V1g_2E0,V3v_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0))),s(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),V3v_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),V3v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Elbtree_2Elbtree(A_27b)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0)))))
         => ( ! [V0f_2E0,V1g_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0))))
              <=> ! [V2x_2E0] : s(tyop_2Elbtree_2Elbtree(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)))),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ELf_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elbtree_2Elbtree(A_27b))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),V1g_2E0))))) )
           => ! [V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elbtree_2Elbtree(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Epair_2Eprod(A_27a,A_27a)))),V0f_2E0)))))) ) ) ) ) ).

fof(thm_2Elbtree_2Elbtree__case__thm,axiom,
    ! [A_27a,A_27b,V0t2_2E0,V1t1_2E0,V2f_2E0,V3e_2E0,V4a_2E0] :
      ( s(A_27a,c_2Elbtree_2Elbtree__case_2E3(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),V2f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ELf_2E0))) = s(A_27a,V3e_2E0)
      & s(A_27a,c_2Elbtree_2Elbtree__case_2E3(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),V2f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V4a_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V0t2_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27b),A_27a))),V2f_2E0),s(A_27b,V4a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),V1t1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27b),V0t2_2E0))) ) ).

fof(thm_2Elbtree_2Elbtree__bisimulation,axiom,
    ! [A_27a,V0t_2E0,V1u_2E0] :
      ( s(tyop_2Elbtree_2Elbtree(A_27a),V0t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),V1u_2E0)
    <=> ? [V2R_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1u_2E0))))
          & ! [V3t_2E0,V4u_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V4u_2E0))))
             => ( ( s(tyop_2Elbtree_2Elbtree(A_27a),V3t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)
                  & s(tyop_2Elbtree_2Elbtree(A_27a),V4u_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0) )
                | ? [V5a_2E0,V6t1_2E0,V7u1_2E0,V8t2_2E0,V9u2_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V7u1_2E0))))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V9u2_2E0))))
                    & s(tyop_2Elbtree_2Elbtree(A_27a),V3t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0)))
                    & s(tyop_2Elbtree_2Elbtree(A_27a),V4u_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7u1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V9u2_2E0))) ) ) ) ) ) ).

fof(thm_2Elbtree_2Elbtree__strong__bisimulation,axiom,
    ! [A_27a,V0t_2E0,V1u_2E0] :
      ( s(tyop_2Elbtree_2Elbtree(A_27a),V0t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),V1u_2E0)
    <=> ? [V2R_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V1u_2E0))))
          & ! [V3t_2E0,V4u_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V4u_2E0))))
             => ( s(tyop_2Elbtree_2Elbtree(A_27a),V3t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),V4u_2E0)
                | ? [V5a_2E0,V6t1_2E0,V7u1_2E0,V8t2_2E0,V9u2_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V7u1_2E0))))
                    & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V9u2_2E0))))
                    & s(tyop_2Elbtree_2Elbtree(A_27a),V3t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0)))
                    & s(tyop_2Elbtree_2Elbtree(A_27a),V4u_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7u1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V9u2_2E0))) ) ) ) ) ) ).

fof(thm_2Elbtree_2Emem__rules,axiom,
    ! [A_27a] :
      ( ! [V0a_2E0,V1t1_2E0,V2t2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0))))))
      & ! [V3a_2E0,V4b_2E0,V5t1_2E0,V6t2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t1_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V4b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t2_2E0)))))) )
      & ! [V7a_2E0,V8b_2E0,V9t1_2E0,V10t2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V7a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V10t2_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V7a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V8b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V9t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V10t2_2E0)))))) ) ) ).

fof(thm_2Elbtree_2Emem__ind,axiom,
    ! [A_27a,V0mem_27_2E0] :
      ( ( ! [V1a_2E0,V2t1_2E0,V3t2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V1a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))))
        & ! [V4a_2E0,V5b_2E0,V6t1_2E0,V7t2_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t2_2E0)))))) )
        & ! [V8a_2E0,V9b_2E0,V10t1_2E0,V11t2_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V8a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V11t2_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V8a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V9b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V10t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t2_2E0)))))) ) )
     => ! [V12a0_2E0,V13a1_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V12a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13a1_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V12a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V13a1_2E0)))) ) ) ).

fof(thm_2Elbtree_2Emem__strongind,axiom,
    ! [A_27a,V0mem_27_2E0] :
      ( ( ! [V1a_2E0,V2t1_2E0,V3t2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V1a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))))
        & ! [V4a_2E0,V5b_2E0,V6t1_2E0,V7t2_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V4a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t2_2E0)))))) )
        & ! [V8a_2E0,V9b_2E0,V10t1_2E0,V11t2_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V8a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t2_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V8a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V11t2_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V8a_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V9b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V10t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t2_2E0)))))) ) )
     => ! [V12a0_2E0,V13a1_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V12a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13a1_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool)),V0mem_27_2E0),s(A_27a,V12a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V13a1_2E0)))) ) ) ).

fof(thm_2Elbtree_2Emem__cases,axiom,
    ! [A_27a,V0a0_2E0,V1a1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0))))
    <=> ( ? [V2t1_2E0,V3t2_2E0] : s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))
        | ? [V4b_2E0,V5t1_2E0,V6t2_2E0] :
            ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V4b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t2_2E0)))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V5t1_2E0)))) )
        | ? [V7b_2E0,V8t1_2E0,V9t2_2E0] :
            ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V7b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V9t2_2E0)))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V9t2_2E0)))) ) ) ) ).

fof(thm_2Elbtree_2Emem__thm,axiom,
    ! [A_27a,V0t2_2E0,V1t1_2E0,V2b_2E0,V3a_2E0] :
      ( s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      & ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V2b_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0))))))
      <=> ( s(A_27a,V3a_2E0) = s(A_27a,V2b_2E0)
          | p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0))))
          | p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0)))) ) ) ) ).

fof(thm_2Elbtree_2Emap__eq__Lf,axiom,
    ! [A_27a,A_27b,V0t_2E0,V1f_2E0] :
      ( ( s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V0t_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)
      <=> s(tyop_2Elbtree_2Elbtree(A_27b),V0t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ELf_2E0) )
      & ( s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V0t_2E0)))
      <=> s(tyop_2Elbtree_2Elbtree(A_27b),V0t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ELf_2E0) ) ) ).

fof(thm_2Elbtree_2Emap__eq__Nd,axiom,
    ! [A_27a,A_27b,V0t2_2E0,V1t1_2E0,V2t_2E0,V3f_2E0,V4a_2E0] :
      ( s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V4a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0)))
    <=> ? [V5a_27_2E0,V6t1_27_2E0,V7t2_27_2E0] :
          ( s(tyop_2Elbtree_2Elbtree(A_27b),V2t_2E0) = s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V5a_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V6t1_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V7t2_27_2E0)))
          & s(A_27a,V4a_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(A_27b,V5a_27_2E0)))
          & s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V6t1_27_2E0)))
          & s(tyop_2Elbtree_2Elbtree(A_27a),V0t2_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V7t2_27_2E0))) ) ) ).

fof(thm_2Elbtree_2Efinite__rules,axiom,
    ! [A_27a] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))))
      & ! [V0a_2E0,V1t1_2E0,V2t2_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0)))))) ) ) ).

fof(thm_2Elbtree_2Efinite__ind,axiom,
    ! [A_27a,V0finite_27_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))))
        & ! [V1a_2E0,V2t1_2E0,V3t2_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))))) ) )
     => ! [V4a0_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V4a0_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V4a0_2E0)))) ) ) ).

fof(thm_2Elbtree_2Efinite__strongind,axiom,
    ! [A_27a,V0finite_27_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))))
        & ! [V1a_2E0,V2t1_2E0,V3t2_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))))) ) )
     => ! [V4a0_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V4a0_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),V0finite_27_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V4a0_2E0)))) ) ) ).

fof(thm_2Elbtree_2Efinite__cases,axiom,
    ! [A_27a,V0a0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V0a0_2E0))))
    <=> ( s(tyop_2Elbtree_2Elbtree(A_27a),V0a0_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0)
        | ? [V1a_2E0,V2t1_2E0,V3t2_2E0] :
            ( s(tyop_2Elbtree_2Elbtree(A_27a),V0a0_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0)))) ) ) ) ).

fof(thm_2Elbtree_2Efinite__thm,axiom,
    ! [A_27a,A_27b,V0t2_2E0,V1t1_2E0,V2a_2E0] :
      ( s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      & ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),c_2Elbtree_2ENd_2E3(s(A_27b,V2a_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V0t2_2E0))))))
      <=> ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),V1t1_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),V0t2_2E0)))) ) ) ) ).

fof(thm_2Elbtree_2Efinite__map,axiom,
    ! [A_27a,A_27b,V0t_2E0,V1f_2E0] : s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2Emap_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elbtree_2Elbtree(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elbtree_2Efinite_2E1(s(tyop_2Elbtree_2Elbtree(A_27b),V0t_2E0))) ).

fof(thm_2Elbtree_2Ebf__flatten__eq__lnil,axiom,
    ! [A_27a,V0l_2E0] :
      ( s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0l_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)
    <=> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0l_2E0)))) ) ).

fof(thm_2Elbtree_2Ebf__flatten__append,axiom,
    ! [A_27a,V0l2_2E0,V1l1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V1l1_2E0))))
     => s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V1l1_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0l2_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0l2_2E0))) ) ).

fof(thm_2Elbtree_2EEXISTS__FIRST,axiom,
    ! [A_27a,V0P_2E0,V1l_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))
     => ? [V2l1_2E0,V3x_2E0,V4l2_2E0] :
          ( s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l2_2E0)))))
          & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))))
          & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) ) ) ).

fof(thm_2Elbtree_2Eexists__bf__flatten,axiom,
    ! [A_27a,V0x_2E0,V1tlist_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V1tlist_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Elbtree_2Emem_2E1(s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V1tlist_2E0)))) ) ).

fof(thm_2Elbtree_2Edepth__rules,axiom,
    ! [A_27a] :
      ( ! [V0x_2E0,V1t1_2E0,V2t2_2E0] : p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t2_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
      & ! [V3m_2E0,V4x_2E0,V5a_2E0,V6t1_2E0,V7t2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V4x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V4x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V5a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V6t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t2_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3m_2E0)))))) )
      & ! [V8m_2E0,V9x_2E0,V10a_2E0,V11t1_2E0,V12t2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V9x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0),s(tyop_2Enum_2Enum,V8m_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V9x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V8m_2E0)))))) ) ) ).

fof(thm_2Elbtree_2Edepth__ind,axiom,
    ! [A_27a,V0depth_27_2E0] :
      ( ( ! [V1x_2E0,V2t1_2E0,V3t2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
        & ! [V4m_2E0,V5x_2E0,V6a_2E0,V7t1_2E0,V8t2_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0))),s(tyop_2Enum_2Enum,V4m_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V6a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4m_2E0)))))) )
        & ! [V9m_2E0,V10x_2E0,V11a_2E0,V12t1_2E0,V13t2_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0))),s(tyop_2Enum_2Enum,V9m_2E0))))
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V11a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V9m_2E0)))))) ) )
     => ! [V14a0_2E0,V15a1_2E0,V16a2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V14a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0),s(tyop_2Enum_2Enum,V16a2_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V14a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0))),s(tyop_2Enum_2Enum,V16a2_2E0)))) ) ) ).

fof(thm_2Elbtree_2Edepth__strongind,axiom,
    ! [A_27a,V0depth_27_2E0] :
      ( ( ! [V1x_2E0,V2t1_2E0,V3t2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
        & ! [V4m_2E0,V5x_2E0,V6a_2E0,V7t1_2E0,V8t2_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V5x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0))),s(tyop_2Enum_2Enum,V4m_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V5x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V6a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4m_2E0)))))) )
        & ! [V9m_2E0,V10x_2E0,V11a_2E0,V12t1_2E0,V13t2_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V10x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0),s(tyop_2Enum_2Enum,V9m_2E0))))
              & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0))),s(tyop_2Enum_2Enum,V9m_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V10x_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V11a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V13t2_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V9m_2E0)))))) ) )
     => ! [V14a0_2E0,V15a1_2E0,V16a2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V14a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0),s(tyop_2Enum_2Enum,V16a2_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0depth_27_2E0),s(A_27a,V14a0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),V15a1_2E0))),s(tyop_2Enum_2Enum,V16a2_2E0)))) ) ) ).

fof(thm_2Elbtree_2Edepth__cases,axiom,
    ! [A_27a,V0a0_2E0,V1a1_2E0,V2a2_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0),s(tyop_2Enum_2Enum,V2a2_2E0))))
    <=> ( ? [V3t1_2E0,V4t2_2E0] :
            ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V4t2_2E0)))
            & s(tyop_2Enum_2Enum,V2a2_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
        | ? [V5m_2E0,V6a_2E0,V7t1_2E0,V8t2_2E0] :
            ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V6a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V8t2_2E0)))
            & s(tyop_2Enum_2Enum,V2a2_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V5m_2E0)))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V7t1_2E0),s(tyop_2Enum_2Enum,V5m_2E0)))) )
        | ? [V9m_2E0,V10a_2E0,V11t1_2E0,V12t2_2E0] :
            ( s(tyop_2Elbtree_2Elbtree(A_27a),V1a1_2E0) = s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V10a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V11t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0)))
            & s(tyop_2Enum_2Enum,V2a2_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V9m_2E0)))
            & p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0a0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V12t2_2E0),s(tyop_2Enum_2Enum,V9m_2E0)))) ) ) ) ).

fof(thm_2Elbtree_2Emem__depth,axiom,
    ! [A_27a,V0x_2E0,V1t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))))
     => ? [V2n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) ) ).

fof(thm_2Elbtree_2Edepth__mem,axiom,
    ! [A_27a,V0x_2E0,V1t_2E0,V2n_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0)))) ) ).

fof(thm_2Elbtree_2Eoptmin__ind,axiom,
    ! [V0P_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))))
        & ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))))
        & ! [V2y_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V2y_2E0))))))
        & ! [V3x_2E0,V4y_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V4y_2E0)))))) )
     => ! [V5v_2E0,V6v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V5v_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V6v1_2E0)))) ) ).

fof(thm_2Elbtree_2Eoptmin__def,axiom,
    ! [V0y_2E0,V1x_2E0] :
      ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Eoptmin_2E2(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0)
      & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Eoptmin_2E2(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V1x_2E0)))
      & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Eoptmin_2E2(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0y_2E0)))
      & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Eoptmin_2E2(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))) ) ).

fof(thm_2Elbtree_2Emindepth__thm,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0x_2E0,V3a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V3a_2E0))))
        <=> s(A_27a,V0x_2E0) = s(A_27a,V3a_2E0) )
     => ! [V0x_2E0,V1t2_2E0,V2t1_2E0,V3a_2E0] :
          ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0)
          & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V3a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t2_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0x_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Eoptmin_2E2(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t2_2E0))))))))) ) ) ).

fof(thm_2Elbtree_2Emem__mindepth,axiom,
    ! [A_27a,V0x_2E0,V1t_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Emem_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))))
     => ? [V2n_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) ) ).

fof(thm_2Elbtree_2Emindepth__depth,axiom,
    ! [A_27a,V0x_2E0,V1t_2E0,V2n_2E0] :
      ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Elbtree_2Emindepth_2E2(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))
     => p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Edepth_2E3(s(A_27a,V0x_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) ) ).

fof(thm_2Elbtree_2Emmindex__EXISTS,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V1f_2E0,V2e_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0))),s(A_27a,V2e_2E0))))
        <=> ? [V3n_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0),s(A_27a,V2e_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V3n_2E0))) )
     => ! [V0l_2E0,V1f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))
         => ? [V4i_2E0,V5m_2E0] : p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,V5m_2E0)))) ) ) ).

fof(thm_2Elbtree_2Emmindex__unique,axiom,
    ! [A_27a,V0m_2E0,V1l_2E0,V2i_2E0,V3f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))
     => ! [V4j_2E0,V5n_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Elbtree_2Eis__mmindex_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Enum_2Enum,V4j_2E0),s(tyop_2Enum_2Enum,V5n_2E0))))
        <=> ( s(tyop_2Enum_2Enum,V4j_2E0) = s(tyop_2Enum_2Enum,V2i_2E0)
            & s(tyop_2Enum_2Enum,V5n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) ) ) ) ).

fof(thm_2Elbtree_2Emem__bf__flatten,axiom,
    ! [A_27a,V0x_2E0,V1tlist_2E0] : s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V1tlist_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Ebool),c_2Elbtree_2Emem_2E1(s(A_27a,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V1tlist_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) ) ).

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