ITP001 Axioms: ITP097+4.ax


%------------------------------------------------------------------------------
% File     : ITP097+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : comparison.ax [Gau19]
%          : HL4097+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  140 (  87 unt;   0 def)
%            Number of atoms       :  308 ( 224 equ)
%            Maximal formula atoms :   27 (   2 avg)
%            Number of connectives :  174 (   6   ~;   5   |;  65   &)
%                                         (  42 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  114 ( 114 usr;  60 con; 0-4 aty)
%            Number of variables   :  523 ( 522   !;   1   ?)
% SPC      : FOF_SAT_RFO_SEQ

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),X1_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2EListOrd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2EListOrd_2E1(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2EListOrd_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETO_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Etoto_2Etoto(A_27a),c_2Etoto_2ETO_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Etoto_2Etoto(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Etoto_2Etoto(A_27a)),c_2Etoto_2ETO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_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(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETO__inv_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2ETO__inv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETO__inv_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E1(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2ETO__inv_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2EternaryComparisons_2Eoption__compare_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Eoption__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Eoption__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELLEX_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2ETO__of__LinearOrder_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Etoto_2ETotOrd_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Etoto_2ETotOrd_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETotOrd_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Etoto_2ETotOrd_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2Eapto_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E1(s(tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2Eapto_2E0),s(tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Eoption__cmp2_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Ecomparison_2Eoption__cmp2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2Ecomparison_2Eoption__cmp2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecomparison_2Egood__cmp_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Ebool),c_2Ecomparison_2Egood__cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq2_2Ec_2EternaryComparisons_2Epair__compare_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Epair__compare_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)))),c_2EternaryComparisons_2Epair__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))),c_2Etoto_2ETO__of__LinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b,A_27d,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27d,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2EternaryComparisons_2Ebool__compare_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Ebool__compare_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2EternaryComparisons_2Echar__compare_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Echar__compare_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Estring_2Echar,X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Echar__compare_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Estring_2Echar,X1_2E0))) ).

fof(arityeq2_2Ec_2Etoto_2ElexTO_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ElexTO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)))),c_2Etoto_2ElexTO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))) ).

fof(arityeq2_2Ec_2EternaryComparisons_2Enum__compare_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Enum__compare_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Estring_2EORD_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),c_2Estring_2EORD_2E0),s(tyop_2Estring_2Echar,X0_2E0))) ).

fof(arityeq2_2Ec_2Ecomparison_2Eresp__equiv_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Ecomparison_2Eresp__equiv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EternaryComparisons_2Estring__compare_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Estring__compare_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Estring__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2EternaryComparisons_2Eordering,X1_2E0),s(tyop_2EternaryComparisons_2Eordering,X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2EternaryComparisons_2Eordering,X1_2E0))),s(tyop_2EternaryComparisons_2Eordering,X2_2E0))) ).

fof(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecomparison_2Eequiv__inj_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eequiv__inj_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Ecomparison_2Eequiv__inj_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecomparison_2Eoption__cmp2_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2Ecomparison_2Eoption__cmp2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecomparison_2Eoption__cmp2_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering))),c_2Ecomparison_2Eoption__cmp2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Eoption__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Eoption__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecomparison_2Eresp__equiv2_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Ecomparison_2Eresp__equiv2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ecomparison_2Eresp__equiv2_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool))),c_2Ecomparison_2Eresp__equiv2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X2_2E0))) ).

fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_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(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,X0_2E0] : s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b,A_27d,X0_2E0] : s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,X0_2E0] : s(A_27c,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27c),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b,A_27d,X0_2E0] : s(A_27d,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),A_27d),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0))) ).

fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2EternaryComparisons_2Eordering,X1_2E0),s(tyop_2EternaryComparisons_2Eordering,X2_2E0),s(tyop_2EternaryComparisons_2Eordering,X3_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering)))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2EternaryComparisons_2Eordering,X1_2E0))),s(tyop_2EternaryComparisons_2Eordering,X2_2E0))),s(tyop_2EternaryComparisons_2Eordering,X3_2E0))) ).

fof(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)))),c_2EternaryComparisons_2Epair__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0))) ).

fof(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),X3_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2EternaryComparisons_2Eordering)))),c_2EternaryComparisons_2Epair__compare_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27d),X3_2E0))) ).

fof(thm_2Ecomparison_2Egood__cmp__def,axiom,
    ! [A_27a,V0cmp_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
    <=> ( ! [V1x_2E0] : s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
        & ! [V2x_2E0,V3y_2E0] :
            ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
        & ! [V4x_2E0,V5y_2E0] :
            ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
          <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
        & ! [V6x_2E0,V7y_2E0,V8z_2E0] :
            ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
              & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
        & ! [V9x_2E0,V10y_2E0,V11z_2E0] :
            ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V9x_2E0))),s(A_27a,V10y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
              & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V10y_2E0))),s(A_27a,V11z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V9x_2E0))),s(A_27a,V11z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
        & ! [V12x_2E0,V13y_2E0,V14z_2E0] :
            ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V12x_2E0))),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
              & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V13y_2E0))),s(A_27a,V14z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V12x_2E0))),s(A_27a,V14z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
        & ! [V15x_2E0,V16y_2E0,V17z_2E0] :
            ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V15x_2E0))),s(A_27a,V16y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
              & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V16y_2E0))),s(A_27a,V17z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V15x_2E0))),s(A_27a,V17z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) ) ) ).

fof(thm_2Ecomparison_2Eresp__equiv__def,axiom,
    ! [A_27a,A_27b,A_27c,V0cmp_2E0,V1f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0))))
    <=> ! [V2k1_2E0,V3k2_2E0,V4v_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2k1_2E0))),s(A_27a,V3k2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_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)),V1f_2E0),s(A_27a,V2k1_2E0))),s(A_27b,V4v_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)),V1f_2E0),s(A_27a,V3k2_2E0))),s(A_27b,V4v_2E0))) ) ) ).

fof(thm_2Ecomparison_2Eresp__equiv2__def,axiom,
    ! [A_27a,A_27b,V0cmp_2E0,V1cmp2_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))))
    <=> ! [V3k1_2E0,V4k2_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3k1_2E0))),s(A_27a,V4k2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
         => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3k1_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4k2_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) ) ) ).

fof(thm_2Ecomparison_2Eequiv__inj__def,axiom,
    ! [A_27a,A_27b,V0cmp_2E0,V1cmp2_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eequiv__inj_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))))
    <=> ! [V3k1_2E0,V4k2_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3k1_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4k2_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
         => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3k1_2E0))),s(A_27a,V4k2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) ) ) ).

fof(thm_2Ecomparison_2Egood__cmp__thm,axiom,
    ! [A_27a,V0cmp_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
    <=> ( ! [V1x_2E0] : s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
        & ! [V2x_2E0,V3y_2E0,V4z_2E0] :
            ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
            <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
            & ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
                & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
             => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V4z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
            & ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
                & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
             => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V4z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) ) ) ) ).

fof(thm_2Ecomparison_2Ecmp__thms,axiom,
    ! [A_27a] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) != s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
      & ! [V0v0_2E0,V1v1_2E0,V2v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(A_27a,V0v0_2E0),s(A_27a,V1v1_2E0),s(A_27a,V2v2_2E0))) = s(A_27a,V0v0_2E0)
      & ! [V3v0_2E0,V4v1_2E0,V5v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0),s(A_27a,V3v0_2E0),s(A_27a,V4v1_2E0),s(A_27a,V5v2_2E0))) = s(A_27a,V4v1_2E0)
      & ! [V6v0_2E0,V7v1_2E0,V8v2_2E0] : s(A_27a,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0),s(A_27a,V6v0_2E0),s(A_27a,V7v1_2E0),s(A_27a,V8v2_2E0))) = s(A_27a,V8v2_2E0)
      & ! [V9a_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,V9a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
          | s(tyop_2EternaryComparisons_2Eordering,V9a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
          | s(tyop_2EternaryComparisons_2Eordering,V9a_2E0) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0) )
      & ! [V10cmp_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0))))
        <=> ( ! [V11x_2E0] : s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V11x_2E0))),s(A_27a,V11x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
            & ! [V12x_2E0,V13y_2E0] :
                ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V12x_2E0))),s(A_27a,V13y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
               => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V13y_2E0))),s(A_27a,V12x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
            & ! [V14x_2E0,V15y_2E0] :
                ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V14x_2E0))),s(A_27a,V15y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
              <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V15y_2E0))),s(A_27a,V14x_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
            & ! [V16x_2E0,V17y_2E0,V18z_2E0] :
                ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V16x_2E0))),s(A_27a,V17y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
                  & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V17y_2E0))),s(A_27a,V18z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
               => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V16x_2E0))),s(A_27a,V18z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
            & ! [V19x_2E0,V20y_2E0,V21z_2E0] :
                ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V19x_2E0))),s(A_27a,V20y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
                  & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V20y_2E0))),s(A_27a,V21z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
               => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V19x_2E0))),s(A_27a,V21z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
            & ! [V22x_2E0,V23y_2E0,V24z_2E0] :
                ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V22x_2E0))),s(A_27a,V23y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
                  & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V23y_2E0))),s(A_27a,V24z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
               => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V22x_2E0))),s(A_27a,V24z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
            & ! [V25x_2E0,V26y_2E0,V27z_2E0] :
                ( ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V25x_2E0))),s(A_27a,V26y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
                  & s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V26y_2E0))),s(A_27a,V27z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
               => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V10cmp_2E0),s(A_27a,V25x_2E0))),s(A_27a,V27z_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) ) ) ) ).

fof(thm_2Ecomparison_2Eoption__cmp__def,axiom,
    ! [A_27a,A_27b,V0v3_2E0,V1v2_2E0,V2v1_2E0,V3v0_2E0,V4c_2E0] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V3v0_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0v3_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2v1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1v2_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0),s(A_27a,V2v1_2E0))),s(A_27b,V1v2_2E0))) ) ).

fof(thm_2Ecomparison_2Eoption__cmp2__ind,axiom,
    ! [A_27a,A_27b,V0P_2E0] :
      ( ( ! [V1c_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))))
        & ! [V2c_2E0,V3v0_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V2c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V3v0_2E0))))))
        & ! [V4c_2E0,V5v3_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5v3_2E0))))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))))
        & ! [V6c_2E0,V7v1_2E0,V8v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V6c_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7v1_2E0))))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V8v2_2E0)))))) )
     => ! [V9v_2E0,V10v1_2E0,V11v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V9v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V10v1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V11v2_2E0)))) ) ).

fof(thm_2Ecomparison_2Eoption__cmp2__def,axiom,
    ! [A_27a,A_27b,V0y_2E0,V1x_27_2E0,V2x_2E0,V3cmp_2E0] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_27_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0)
      & s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_2E0),s(A_27a,V2x_2E0))),s(A_27b,V0y_2E0))) ) ).

fof(thm_2Ecomparison_2Epair__cmp__def,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,V0y_2E0,V1x_2E0,V2c2_2E0,V3c1_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3c1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V2c2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),V1x_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),V0y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3c1_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27c),V1x_2E0))))),s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27d),V0y_2E0))))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V2c2_2E0),s(A_27c,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27c),V1x_2E0))))),s(A_27d,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27d),V0y_2E0))))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))) ).

fof(thm_2Ecomparison_2Ebool__cmp__def,axiom,
    ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
    & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
    & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0)
    & s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) ) ).

fof(thm_2Ecomparison_2Enum__cmp__def,axiom,
    ! [F0_2E0] :
      ( ! [V0n1_2E0,V1n2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V0n1_2E0))),s(tyop_2Enum_2Enum,V1n2_2E0))))
        <=> s(tyop_2Enum_2Enum,V0n1_2E0) = s(tyop_2Enum_2Enum,V1n2_2E0) )
     => ! [V0n1_2E0,V1n2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V1n2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V0n1_2E0))),s(tyop_2Enum_2Enum,V1n2_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V1n2_2E0))),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0),s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EGREATER_2E0))))) ) ).

fof(thm_2Ecomparison_2Echar__cmp__def,axiom,
    ! [V0c1_2E0,V1c2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Echar__compare_2E2(s(tyop_2Estring_2Echar,V0c1_2E0),s(tyop_2Estring_2Echar,V1c2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V0c1_2E0))),s(tyop_2Enum_2Enum,c_2Estring_2EORD_2E1(s(tyop_2Estring_2Echar,V1c2_2E0))))) ).

fof(thm_2Ecomparison_2Estring__cmp__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Estring__compare_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Echar__compare_2E0))) ).

fof(thm_2Ecomparison_2ETotOrder__imp__good__cmp,axiom,
    ! [A_27a,V0cmp_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))) ) ).

fof(thm_2Ecomparison_2ETO__inv__invert,axiom,
    ! [A_27a,V0c_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))))
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2EternaryComparisons_2Eordering),c_2EternaryComparisons_2Einvert__comparison_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2EternaryComparisons_2Eordering),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))))))) ) ).

fof(thm_2Ecomparison_2Eoption__cmp2__TO__inv,axiom,
    ! [A_27a,V0c_2E0] : s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Ecomparison_2Eoption__cmp2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E1(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Eoption__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__inv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))))))) ).

fof(thm_2Ecomparison_2Elist__cmp__ListOrd,axiom,
    ! [A_27a,V0c_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))))
     => s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2EListOrd_2E1(s(tyop_2Etoto_2Etoto(A_27a),c_2Etoto_2ETO_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))))) ) ).

fof(thm_2Ecomparison_2ETotOrd__list__cmp,axiom,
    ! [A_27a,V0c_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0c_2E0)))))) ) ).

fof(thm_2Ecomparison_2Epair__cmp__lexTO,axiom,
    ! [A_27a,A_27b,V0R_2E0,V1V_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0R_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Etoto_2ETotOrd_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1V_2E0)))) )
     => s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Epair__compare_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1V_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ElexTO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1V_2E0))) ) ).

fof(thm_2Ecomparison_2Enum__cmp__numOrd,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Enum__compare_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2EnumOrd_2E0) ).

fof(thm_2Ecomparison_2Echar__cmp__charOrd,axiom,
    s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Echar__compare_2E0) = s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2EcharOrd_2E0) ).

fof(thm_2Ecomparison_2Estring__cmp__stringto,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Estring__compare_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E1(s(tyop_2Etoto_2Etoto(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Etoto_2Estringto_2E0))) ).

fof(thm_2Ecomparison_2Eoption__cmp__good,axiom,
    ! [A_27a,V0cmp_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Eoption__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))))) ) ).

fof(thm_2Ecomparison_2Eoption__cmp2__good,axiom,
    ! [A_27a,V0cmp_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Ecomparison_2Eoption__cmp2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))))) ) ).

fof(thm_2Ecomparison_2Elist__cmp__good,axiom,
    ! [A_27a,V0cmp_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))))) ) ).

fof(thm_2Ecomparison_2Epair__cmp__good,axiom,
    ! [A_27a,A_27b,V0cmp1_2E0,V1cmp2_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp1_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Epair__compare_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0)))))) ) ).

fof(thm_2Ecomparison_2Ebool__cmp__good,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Ebool__compare_2E0)))) ).

fof(thm_2Ecomparison_2Enum__cmp__good,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Enum__compare_2E0)))) ).

fof(thm_2Ecomparison_2Echar__cmp__good,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Echar__compare_2E0)))) ).

fof(thm_2Ecomparison_2Estring__cmp__good,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Estring__compare_2E0)))) ).

fof(thm_2Ecomparison_2Elist__cmp__cong,axiom,
    ! [A_27a,A_27b,V0cmp_2E0,V1l1_2E0,V2l2_2E0,V3cmp_27_2E0,V4l1_27_2E0,V5l2_27_2E0] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0)
        & s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27b),V5l2_27_2E0)
        & ! [V6x_2E0,V7x_27_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0))))))
              & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7x_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V5l2_27_2E0)))))) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7x_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7x_27_2E0))) ) )
     => s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V5l2_27_2E0))) ) ).

fof(thm_2Ecomparison_2Eoption__cmp__cong,axiom,
    ! [A_27a,A_27b,V0cmp_2E0,V1v1_2E0,V2v2_2E0,V3cmp_27_2E0,V4v1_27_2E0,V5v2_27_2E0] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),V1v1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V4v1_27_2E0)
        & s(tyop_2Eoption_2Eoption(A_27b),V2v2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V5v2_27_2E0)
        & ! [V6x_2E0,V7x_27_2E0] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V4v1_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0)))
              & s(tyop_2Eoption_2Eoption(A_27b),V5v2_27_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7x_27_2E0))) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7x_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7x_27_2E0))) ) )
     => s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1v1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2v2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V4v1_27_2E0),s(tyop_2Eoption_2Eoption(A_27b),V5v2_27_2E0))) ) ).

fof(thm_2Ecomparison_2Eoption__cmp2__cong,axiom,
    ! [A_27a,A_27b,V0cmp_2E0,V1v1_2E0,V2v2_2E0,V3cmp_27_2E0,V4v1_27_2E0,V5v2_27_2E0] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),V1v1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V4v1_27_2E0)
        & s(tyop_2Eoption_2Eoption(A_27b),V2v2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V5v2_27_2E0)
        & ! [V6x_2E0,V7x_27_2E0] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),V4v1_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0)))
              & s(tyop_2Eoption_2Eoption(A_27b),V5v2_27_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7x_27_2E0))) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7x_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7x_27_2E0))) ) )
     => s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1v1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2v2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V3cmp_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V4v1_27_2E0),s(tyop_2Eoption_2Eoption(A_27b),V5v2_27_2E0))) ) ).

fof(thm_2Ecomparison_2Epair__cmp__cong,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,V0cmp1_2E0,V1cmp2_2E0,V2v1_2E0,V3v2_2E0,V4cmp1_27_2E0,V5cmp2_27_2E0,V6v1_27_2E0,V7v2_27_2E0] :
      ( ( s(tyop_2Epair_2Eprod(A_27a,A_27c),V2v1_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27c),V6v1_27_2E0)
        & s(tyop_2Epair_2Eprod(A_27b,A_27d),V3v2_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27d),V7v2_27_2E0)
        & ! [V8a_2E0,V9b_2E0,V10c_2E0,V11d_2E0] :
            ( ( s(tyop_2Epair_2Eprod(A_27a,A_27c),V6v1_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V8a_2E0),s(A_27c,V9b_2E0)))
              & s(tyop_2Epair_2Eprod(A_27b,A_27d),V7v2_27_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,V10c_2E0),s(A_27d,V11d_2E0))) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp1_2E0),s(A_27a,V8a_2E0))),s(A_27b,V10c_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4cmp1_27_2E0),s(A_27a,V8a_2E0))),s(A_27b,V10c_2E0))) )
        & ! [V12a_2E0,V13b_2E0,V14c_2E0,V15d_2E0] :
            ( ( s(tyop_2Epair_2Eprod(A_27a,A_27c),V6v1_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V12a_2E0),s(A_27c,V13b_2E0)))
              & s(tyop_2Epair_2Eprod(A_27b,A_27d),V7v2_27_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,V14c_2E0),s(A_27d,V15d_2E0))) )
           => s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(A_27c,V13b_2E0))),s(A_27d,V15d_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V5cmp2_27_2E0),s(A_27c,V13b_2E0))),s(A_27d,V15d_2E0))) ) )
     => s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),V2v1_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),V3v2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V4cmp1_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2EternaryComparisons_2Eordering)),V5cmp2_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),V6v1_27_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27d),V7v2_27_2E0))) ) ).

fof(thm_2Ecomparison_2Egood__cmp__trans,axiom,
    ! [A_27a,A_27b,F1_2E0,F0_2E0] :
      ( ! [V0cmp_2E0,V1k_2E0,V3k_27_2E0,V4v_27_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V1k_2E0))),s(A_27a,V3k_27_2E0))),s(A_27b,V4v_27_2E0))))
        <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V1k_2E0))),s(A_27a,V3k_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
     => ( ! [V0cmp_2E0,V1k_2E0,V2v_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V1k_2E0))),s(A_27b,V2v_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V1k_2E0)))))
       => ! [V0cmp_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))))))) ) ) ) ).

fof(thm_2Ecomparison_2Egood__cmp__Less__trans,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0cmp_2E0,V1k_2E0,V2k_27_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V1k_2E0))),s(A_27a,V2k_27_2E0))))
        <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V1k_2E0))),s(A_27a,V2k_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
     => ! [V0cmp_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))))) ) ) ).

fof(thm_2Ecomparison_2Egood__cmp__Less__irrefl__trans,axiom,
    ! [A_27a,F1_2E0,F0_2E0] :
      ( ! [V0cmp_2E0,V3k_2E0,V4k_27_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V3k_2E0))),s(A_27a,V4k_27_2E0))))
        <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3k_2E0))),s(A_27a,V4k_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
     => ( ! [V0cmp_2E0,V1k_2E0,V2k_27_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V1k_2E0))),s(A_27a,V2k_27_2E0))))
          <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V1k_2E0))),s(A_27a,V2k_27_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2ELESS_2E0) )
       => ! [V0cmp_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))
           => ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))))))
              & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0)))))) ) ) ) ) ).

fof(thm_2Ecomparison_2Ebool__cmp__antisym,axiom,
    ! [V0x_2E0,V1y_2E0] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Ebool__compare_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Emin_2Ebool,V1y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
    <=> s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V1y_2E0) ) ).

fof(thm_2Ecomparison_2Enum__cmp__antisym,axiom,
    ! [V0x_2E0,V1y_2E0] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Enum__compare_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
    <=> s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,V1y_2E0) ) ).

fof(thm_2Ecomparison_2Echar__cmp__antisym,axiom,
    ! [V0x_2E0,V1y_2E0] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Echar__compare_2E2(s(tyop_2Estring_2Echar,V0x_2E0),s(tyop_2Estring_2Echar,V1y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
    <=> s(tyop_2Estring_2Echar,V0x_2E0) = s(tyop_2Estring_2Echar,V1y_2E0) ) ).

fof(thm_2Ecomparison_2Elist__cmp__antisym,axiom,
    ! [A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0] :
      ( ! [V3x_2E0,V4y_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
        <=> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) )
     => ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      <=> s(tyop_2Elist_2Elist(A_27a),V1x_2E0) = s(tyop_2Elist_2Elist(A_27a),V2y_2E0) ) ) ).

fof(thm_2Ecomparison_2Estring__cmp__antisym,axiom,
    ! [V0x_2E0,V1y_2E0] :
      ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Estring__compare_2E2(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
    <=> s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0x_2E0) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1y_2E0) ) ).

fof(thm_2Ecomparison_2Epair__cmp__antisym,axiom,
    ! [A_27a,A_27b,V0cmp1_2E0,V1cmp2_2E0,V2x_2E0,V3y_2E0] :
      ( ( ! [V4x_2E0,V5y_2E0] :
            ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp1_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
          <=> s(A_27a,V4x_2E0) = s(A_27a,V5y_2E0) )
        & ! [V6x_2E0,V7y_2E0] :
            ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(A_27b,V6x_2E0))),s(A_27b,V7y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
          <=> s(A_27b,V6x_2E0) = s(A_27b,V7y_2E0) ) )
     => ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Epair__compare_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V1cmp2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      <=> s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V3y_2E0) ) ) ).

fof(thm_2Ecomparison_2Eoption__cmp__antisym,axiom,
    ! [A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0] :
      ( ! [V3x_2E0,V4y_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
        <=> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) )
     => ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Eoption__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      <=> s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2y_2E0) ) ) ).

fof(thm_2Ecomparison_2Eoption__cmp2__antisym,axiom,
    ! [A_27a,V0cmp_2E0,V1x_2E0,V2y_2E0] :
      ( ! [V3x_2E0,V4y_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
        <=> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0) )
     => ( s(tyop_2EternaryComparisons_2Eordering,c_2Ecomparison_2Eoption__cmp2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
      <=> s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2y_2E0) ) ) ).

fof(thm_2Ecomparison_2Eantisym__resp__equiv,axiom,
    ! [A_27a,A_27b,A_27c,V0cmp_2E0,V1f_2E0] :
      ( ! [V2x_2E0,V3y_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
         => s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0))))
        & ! [V4cmp2_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Egood__cmp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),V4cmp2_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Ecomparison_2Eresp__equiv2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2EternaryComparisons_2Eordering)),V4cmp2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0)))) ) ) ) ).

fof(thm_2Ecomparison_2Elist__cmp__equal__list__rel,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0cmp_2E0,V3x_2E0,V4y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0))))
        <=> s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0) )
     => ! [V0cmp_2E0,V1l1_2E0,V2l2_2E0] :
          ( s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2EEQUAL_2E0)
        <=> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),V0cmp_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) ) ) ).

fof(thm_2Ecomparison_2ETO__of__LinearOrder__LLEX,axiom,
    ! [A_27a,V0R_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))
     => s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2ETO__of__LinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_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) ) ).

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