%------------------------------------------------------------------------------
% File     : ITP129+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : ratRing.ax [Gau19]
%          : HL4129+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  104 (  88 unt;   0 def)
%            Number of atoms       :  187 ( 151 equ)
%            Maximal formula atoms :   62 (   1 avg)
%            Number of connectives :   86 (   3   ~;   3   |;  58   &)
%                                         (  15 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   65 (   3 avg)
%            Maximal term depth    :   18 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  164 ( 164 usr;  88 con; 0-5 aty)
%            Number of variables   :  318 ( 317   !;   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_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

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

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

fof(arityeq1_2Ec_2EringNorm_2Einterp__p_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Einterp__p_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EringNorm_2Einterp__p_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2Erat_2Erat__of__num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erat_2Erat),c_2Erat_2Erat__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq5_2Ec_2Ering_2Erecordtype_2Ering_2E5_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Erat_2Erat,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),X4_2E0))) = s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),tyop_2Ering_2Ering(tyop_2Erat_2Erat)))))),c_2Ering_2Erecordtype_2Ering_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Erat_2Erat,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),X4_2E0))) ).

fof(arityeq1_2Ec_2Ering_2Eis__ring_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Ebool),c_2Ering_2Eis__ring_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Epolynom__normalize_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Epolynom__normalize_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Epolynom__normalize_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Epolynom__simplify_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Epolynom__simplify_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Epolynom__simplify_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__merge_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__merge_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__merge_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__prod_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__prod_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__prod_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__scalar_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__scalar_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar2_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__scalar2_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__scalar2_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__scalar3_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__scalar3_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))))),c_2EringNorm_2Er__canonical__sum__scalar3_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__canonical__sum__simplify_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__canonical__sum__simplify_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__simplify_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__ics__aux_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EringNorm_2Er__ics__aux_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)))),c_2EringNorm_2Er__ics__aux_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__interp__cs_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__cs_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EringNorm_2Er__interp__cs_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__interp__m_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__interp__m_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)))),c_2EringNorm_2Er__interp__m_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__interp__sp_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__sp_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EringNorm_2Er__interp__sp_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__interp__vl_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__vl_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__interp__vl_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__ivl__aux_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__ivl__aux_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)))),c_2EringNorm_2Er__ivl__aux_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__monom__insert_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__monom__insert_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))))),c_2EringNorm_2Er__monom__insert_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__spolynom__normalize_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__spolynom__normalize_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__spolynom__normalize_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__spolynom__simplify_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__spolynom__simplify_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__spolynom__simplify_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2Er__varlist__insert_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__varlist__insert_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__varlist__insert_2E0),s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2Erat_2Erat__ainv_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erat_2Erat,c_2Erat_2Erat__ainv_2E1(s(tyop_2Erat_2Erat,X0_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0),s(tyop_2Erat_2Erat,X0_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__interp__p_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EratRing_2Erat__interp__p_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2EPconst_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPconst_2E1(s(tyop_2Erat_2Erat,X0_2E0))) = s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),c_2EringNorm_2EPconst_2E0),s(tyop_2Erat_2Erat,X0_2E0))) ).

fof(arityeq1_2Ec_2EratRing_2Erat__polynom__normalize_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__polynom__normalize_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2EPopp_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),c_2EringNorm_2EPopp_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EringNorm_2EPvar_2E1_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0] : s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,X0_2E0))) = s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),c_2EringNorm_2EPvar_2E0),s(tyop_2Equote_2Eindex,X0_2E0))) ).

fof(arityeq2_2Ec_2EringNorm_2EPmult_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat))),c_2EringNorm_2EPmult_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq2_2Ec_2EringNorm_2EPplus_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat))),c_2EringNorm_2EPplus_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq1_2Ec_2EratRing_2Erat__polynom__simplify_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__simplify_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__polynom__simplify_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq1_2Ec_2EratRing_2Erat__r__canonical__sum__simplify_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__canonical__sum__simplify_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecanonical_2ECons__varlist_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2Ecanonical_2ECons__varlist_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq3_2Ec_2Ecanonical_2ECons__monom_2E3_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2Ecanonical_2ECons__monom_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex))),c_2Elist_2ECONS_2E0),s(tyop_2Equote_2Eindex,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))) ).

fof(arityeq2_2Ec_2Erat_2Erat__add_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Erat_2Erat,X1_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Erat_2Erat,X1_2E0))) ).

fof(arityeq3_2Ec_2EratRing_2Erat__r__ics__aux_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Erat_2Erat,X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__ics__aux_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Erat_2Erat,X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__interp__vl_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__interp__vl_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))) ).

fof(arityeq3_2Ec_2EratRing_2Erat__r__interp__m_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Erat_2Erat,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__interp__m_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Erat_2Erat,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) ).

fof(arityeq2_2Ec_2Erat_2Erat__mul_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Erat_2Erat,X1_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Erat_2Erat,X1_2E0))) ).

fof(arityeq3_2Ec_2EratRing_2Erat__r__ivl__aux_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Equote_2Eindex,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__ivl__aux_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Equote_2Eindex,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) ).

fof(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2Etyop_2Erat_2Erat,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erat_2Erat,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,X0_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2Equote_2Evarmap__find_2E0),s(tyop_2Equote_2Eindex,X0_2E0))),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__merge_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__merge_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__prod_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__prod_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__scalar2_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq3_2Ec_2EratRing_2Erat__r__canonical__sum__scalar3_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__canonical__sum__scalar_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__scalar_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__interp__cs_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Erat_2Erat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__interp__cs_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq2_2Ec_2EratRing_2Erat__r__varlist__insert_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__varlist__insert_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))) ).

fof(arityeq3_2Ec_2EternaryComparisons_2Elist__merge_2E3_2Emono_2Etyop_2Equote_2Eindex,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Elist_2Elist(tyop_2Equote_2Eindex)))),c_2EternaryComparisons_2Elist__merge_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) ).

fof(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,X0_2E0),s(tyop_2Equote_2Evarmap(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27a)),c_2Equote_2Evarmap__find_2E0),s(tyop_2Equote_2Eindex,X0_2E0))),s(tyop_2Equote_2Evarmap(A_27a),X1_2E0))) ).

fof(arityeq3_2Ec_2Equote_2ENode__vm_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2ENode__vm_2E3(s(A_27a,X0_2E0),s(tyop_2Equote_2Evarmap(A_27a),X1_2E0),s(tyop_2Equote_2Evarmap(A_27a),X2_2E0))) = s(tyop_2Equote_2Evarmap(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)))),c_2Equote_2ENode__vm_2E0),s(A_27a,X0_2E0))),s(tyop_2Equote_2Evarmap(A_27a),X1_2E0))),s(tyop_2Equote_2Evarmap(A_27a),X2_2E0))) ).

fof(arityeq1_2Ec_2Equote_2ELeft__idx_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Equote_2Eindex,c_2Equote_2ELeft__idx_2E1(s(tyop_2Equote_2Eindex,X0_2E0))) = s(tyop_2Equote_2Eindex,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),c_2Equote_2ELeft__idx_2E0),s(tyop_2Equote_2Eindex,X0_2E0))) ).

fof(arityeq1_2Ec_2Equote_2ERight__idx_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Equote_2Eindex,c_2Equote_2ERight__idx_2E1(s(tyop_2Equote_2Eindex,X0_2E0))) = s(tyop_2Equote_2Eindex,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),c_2Equote_2ERight__idx_2E0),s(tyop_2Equote_2Eindex,X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) ).

fof(arityeq3_2Ec_2EratRing_2Erat__r__monom__insert_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EratRing_2Erat__r__monom__insert_2E0),s(tyop_2Erat_2Erat,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))) ).

fof(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) ).

fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X3_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),X3_2E0))) ).

fof(thm_2EratRing_2Erat__interp__p__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EratRing_2Erat__interp__p_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Einterp__p_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__polynom__simplify__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__polynom__simplify_2E0) = s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Epolynom__simplify_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__polynom__normalize__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__polynom__normalize_2E0) = s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Epolynom__normalize_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__canonical__sum__merge__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__merge_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__merge_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__monom__insert__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EratRing_2Erat__r__monom__insert_2E0) = s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__monom__insert_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__varlist__insert__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__varlist__insert_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__varlist__insert_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__canonical__sum__scalar__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__scalar_2E0) = s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__scalar_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__canonical__sum__scalar2__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__scalar2_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__canonical__sum__scalar3__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E0) = s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)))),c_2EringNorm_2Er__canonical__sum__scalar3_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__canonical__sum__prod__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__canonical__sum__prod_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat))),c_2EringNorm_2Er__canonical__sum__prod_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__canonical__sum__simplify__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__canonical__sum__simplify_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__canonical__sum__simplify_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__ivl__aux__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__ivl__aux_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__ivl__aux_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__interp__vl__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__interp__vl_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__vl_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__interp__m__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__interp__m_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Erat_2Erat))),c_2EringNorm_2Er__interp__m_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__ics__aux__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EratRing_2Erat__r__ics__aux_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat))),c_2EringNorm_2Er__ics__aux_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__interp__cs__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__interp__cs_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__cs_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__spolynom__normalize__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__spolynom__normalize_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__spolynom__normalize_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__spolynom__simplify__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__spolynom__simplify_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat)),c_2EringNorm_2Er__spolynom__simplify_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2Erat__r__interp__sp__def,axiom,
    s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EratRing_2Erat__r__interp__sp_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Erat_2Erat),tyop_2Erat_2Erat)),c_2EringNorm_2Er__interp__sp_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))) ).

fof(thm_2EratRing_2ERAT__IS__RING,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0)))))) ).

fof(thm_2EratRing_2Erat__ring__thms,axiom,
    ! [A_27a,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V107c_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Erat_2Erat,V107c_2E0))))
        <=> s(tyop_2Erat_2Erat,V107c_2E0) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) )
     => ( ! [V107c_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Erat_2Erat,V107c_2E0))))
          <=> s(tyop_2Erat_2Erat,V107c_2E0) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ( ! [V26x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V26x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
         => ( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(tyop_2Erat_2Erat),c_2Ering_2Erecordtype_2Ering_2E5(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__add_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat)),c_2Erat_2Erat__mul_2E0),s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Erat_2Erat),c_2Erat_2Erat__ainv_2E0))))))
            & ! [V0vm_2E0,V1p_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V0vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V1p_2E0))) = s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V0vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__simplify_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V1p_2E0)))))
            & ! [V2vm_2E0,V3c_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V2vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPconst_2E1(s(tyop_2Erat_2Erat,V3c_2E0))))) = s(tyop_2Erat_2Erat,V3c_2E0)
            & ! [V4vm_2E0,V5i_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V4vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V5i_2E0))))) = s(tyop_2Erat_2Erat,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V5i_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V4vm_2E0)))
            & ! [V6vm_2E0,V7p1_2E0,V8p2_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V6vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V7p1_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V8p2_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V6vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V7p1_2E0))),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V6vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V8p2_2E0)))))
            & ! [V9vm_2E0,V10p1_2E0,V11p2_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V9vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V10p1_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V11p2_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V9vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V10p1_2E0))),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V9vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V11p2_2E0)))))
            & ! [V12vm_2E0,V13p1_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V12vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V13p1_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__ainv_2E1(s(tyop_2Erat_2Erat,c_2EratRing_2Erat__interp__p_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V12vm_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V13p1_2E0)))))
            & ! [V14x_2E0,V15v2_2E0,V16v1_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,c_2Equote_2EEnd__idx_2E0),s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2ENode__vm_2E3(s(A_27a,V14x_2E0),s(tyop_2Equote_2Evarmap(A_27a),V16v1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V15v2_2E0))))) = s(A_27a,V14x_2E0)
            & ! [V17x_2E0,V18v2_2E0,V19v1_2E0,V20i1_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,c_2Equote_2ERight__idx_2E1(s(tyop_2Equote_2Eindex,V20i1_2E0))),s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2ENode__vm_2E3(s(A_27a,V17x_2E0),s(tyop_2Equote_2Evarmap(A_27a),V19v1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V18v2_2E0))))) = s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V20i1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V18v2_2E0)))
            & ! [V21x_2E0,V22v2_2E0,V23v1_2E0,V24i1_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,c_2Equote_2ELeft__idx_2E1(s(tyop_2Equote_2Eindex,V24i1_2E0))),s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2ENode__vm_2E3(s(A_27a,V21x_2E0),s(tyop_2Equote_2Evarmap(A_27a),V23v1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V22v2_2E0))))) = s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V24i1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V23v1_2E0)))
            & ! [V25i_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V25i_2E0),s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2EEmpty__vm_2E0))) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0)))
            & ! [V27t2_2E0,V28t1_2E0,V29l2_2E0,V30l1_2E0,V31c2_2E0,V32c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V32c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V30l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V28t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V31c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V29l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V27t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V30l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V29l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V32c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V30l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V28t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V31c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V29l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V27t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,V32c1_2E0),s(tyop_2Erat_2Erat,V31c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V30l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V28t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V27t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V31c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V29l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V32c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V30l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V28t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V27t2_2E0)))))))
            & ! [V33t2_2E0,V34t1_2E0,V35l2_2E0,V36l1_2E0,V37c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V37c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V36l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V34t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V35l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V33t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V36l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V35l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V37c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V36l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V34t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V35l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V33t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,V37c1_2E0),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V36l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V34t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V33t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V35l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V37c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V36l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V34t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V33t2_2E0)))))))
            & ! [V38t2_2E0,V39t1_2E0,V40l2_2E0,V41l1_2E0,V42c2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V41l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V39t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V42c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V40l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V38t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V41l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V40l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V41l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V39t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V42c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V40l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V38t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erat_2Erat,V42c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V41l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V39t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V38t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V42c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V40l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V41l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V39t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V38t2_2E0)))))))
            & ! [V43t2_2E0,V44t1_2E0,V45l2_2E0,V46l1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V46l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V44t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V45l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V43t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V46l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V45l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V46l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V44t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V45l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V43t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V46l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V44t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V43t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V45l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V46l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V44t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V43t2_2E0)))))))
            & ! [V47s1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V47s1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V47s1_2E0)
            & ! [V48v6_2E0,V49v5_2E0,V50v4_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V50v4_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V49v5_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V48v6_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V50v4_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V49v5_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V48v6_2E0)))
            & ! [V51v8_2E0,V52v7_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V52v7_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V51v8_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V52v7_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V51v8_2E0)))
            & ! [V53t2_2E0,V54l2_2E0,V55l1_2E0,V56c2_2E0,V57c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V57c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V55l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V56c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V54l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V53t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V55l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V54l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V57c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V55l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V56c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V54l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V53t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,V57c1_2E0),s(tyop_2Erat_2Erat,V56c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V55l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V53t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V56c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V54l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V57c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V55l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V53t2_2E0)))))))
            & ! [V58t2_2E0,V59l2_2E0,V60l1_2E0,V61c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V61c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V59l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V58t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V59l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V61c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V59l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V58t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,V61c1_2E0),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V58t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V59l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V61c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V58t2_2E0)))))))
            & ! [V62l1_2E0,V63c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V63c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V62l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V63c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V62l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)))
            & ! [V64t2_2E0,V65l2_2E0,V66l1_2E0,V67c2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V66l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V67c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V65l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V64t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V66l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V65l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V66l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V67c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V65l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V64t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erat_2Erat,V67c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V66l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V64t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V67c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V65l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V66l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V64t2_2E0)))))))
            & ! [V68t2_2E0,V69l2_2E0,V70l1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V70l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V69l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V68t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V70l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V69l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V70l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V69l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V68t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V70l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V68t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V69l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V70l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V68t2_2E0)))))))
            & ! [V71l1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V71l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V71l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)))
            & ! [V72c0_2E0,V73c_2E0,V74l_2E0,V75t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(s(tyop_2Erat_2Erat,V72c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V73c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V74l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V75t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(s(tyop_2Erat_2Erat,V72c0_2E0),s(tyop_2Erat_2Erat,V73c_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V74l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(s(tyop_2Erat_2Erat,V72c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V75t_2E0)))))
            & ! [V76c0_2E0,V77l_2E0,V78t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(s(tyop_2Erat_2Erat,V76c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V77l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V78t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V76c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V77l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(s(tyop_2Erat_2Erat,V76c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V78t_2E0)))))
            & ! [V79c0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar_2E2(s(tyop_2Erat_2Erat,V79c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)
            & ! [V80l0_2E0,V81c_2E0,V82l_2E0,V83t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V80l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V81c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V82l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V83t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V81c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),c_2Equote_2Eindex__lt_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V80l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V82l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V80l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V83t_2E0)))))
            & ! [V84l0_2E0,V85l_2E0,V86t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V84l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V85l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V86t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),c_2Equote_2Eindex__lt_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V84l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V85l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V84l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V86t_2E0)))))
            & ! [V87l0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V87l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)
            & ! [V88c0_2E0,V89l0_2E0,V90c_2E0,V91l_2E0,V92t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,V88c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V89l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V90c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V91l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V92t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(s(tyop_2Erat_2Erat,V88c0_2E0),s(tyop_2Erat_2Erat,V90c_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),c_2Equote_2Eindex__lt_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V89l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V91l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,V88c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V89l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V92t_2E0)))))
            & ! [V93c0_2E0,V94l0_2E0,V95l_2E0,V96t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,V93c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V94l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V95l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V96t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__monom__insert_2E3(s(tyop_2Erat_2Erat,V93c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2EternaryComparisons_2Elist__merge_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),c_2Equote_2Eindex__lt_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V94l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V95l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,V93c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V94l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V96t_2E0)))))
            & ! [V97c0_2E0,V98l0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,V97c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V98l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)
            & ! [V99c1_2E0,V100l1_2E0,V101t1_2E0,V102s2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V99c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V100l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V101t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V102s2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,V99c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V100l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V102s2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V101t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V102s2_2E0)))))
            & ! [V103l1_2E0,V104t1_2E0,V105s2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V103l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V104t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V105s2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V103l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V105s2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V104t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V105s2_2E0)))))
            & ! [V106s2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V106s2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)
            & ! [V107c_2E0,V108l_2E0,V109t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V107c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V108l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V109t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Erat_2Erat,V107c_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V109t_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erat_2Erat,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Erat_2Erat,V107c_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V108l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V109t_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V107c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V108l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V109t_2E0)))))))))
            & ! [V110l_2E0,V111t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V110l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V111t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V110l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V111t_2E0)))))
            & s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)
            & ! [V112vm_2E0,V113x_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V112vm_2E0),s(tyop_2Equote_2Eindex,V113x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))) = s(tyop_2Erat_2Erat,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V113x_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V112vm_2E0)))
            & ! [V114vm_2E0,V115x_2E0,V116x_27_2E0,V117t_27_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V114vm_2E0),s(tyop_2Equote_2Eindex,V115x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V116x_27_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V117t_27_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(s(tyop_2Erat_2Erat,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V115x_2E0),s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V114vm_2E0))),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V114vm_2E0),s(tyop_2Equote_2Eindex,V116x_27_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V117t_27_2E0)))))
            & ! [V118vm_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V118vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
            & ! [V119vm_2E0,V120x_2E0,V121t_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V119vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V120x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V121t_2E0))))) = s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V119vm_2E0),s(tyop_2Equote_2Eindex,V120x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V121t_2E0)))
            & ! [V122vm_2E0,V123c_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V122vm_2E0),s(tyop_2Erat_2Erat,V123c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))) = s(tyop_2Erat_2Erat,V123c_2E0)
            & ! [V124vm_2E0,V125c_2E0,V126x_2E0,V127t_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V124vm_2E0),s(tyop_2Erat_2Erat,V125c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V126x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V127t_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__mul_2E2(s(tyop_2Erat_2Erat,V125c_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V124vm_2E0),s(tyop_2Equote_2Eindex,V126x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V127t_2E0)))))
            & ! [V128vm_2E0,V129a_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V128vm_2E0),s(tyop_2Erat_2Erat,V129a_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Erat_2Erat,V129a_2E0)
            & ! [V130vm_2E0,V131a_2E0,V132l_2E0,V133t_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V130vm_2E0),s(tyop_2Erat_2Erat,V131a_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V132l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V133t_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,V131a_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V130vm_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V130vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V132l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V133t_2E0)))))
            & ! [V134vm_2E0,V135a_2E0,V136c_2E0,V137l_2E0,V138t_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V134vm_2E0),s(tyop_2Erat_2Erat,V135a_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V136c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V137l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V138t_2E0))))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__add_2E2(s(tyop_2Erat_2Erat,V135a_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V134vm_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V134vm_2E0),s(tyop_2Erat_2Erat,V136c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V137l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V138t_2E0)))))
            & ! [V139vm_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V139vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
            & ! [V140vm_2E0,V141l_2E0,V142t_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V140vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V141l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V142t_2E0))))) = s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V140vm_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V140vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V141l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V142t_2E0)))
            & ! [V143vm_2E0,V144c_2E0,V145l_2E0,V146t_2E0] : s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V143vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V144c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V145l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V146t_2E0))))) = s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V143vm_2E0),s(tyop_2Erat_2Erat,c_2EratRing_2Erat__r__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Erat_2Erat),V143vm_2E0),s(tyop_2Erat_2Erat,V144c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V145l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),V146t_2E0)))
            & ! [V147i_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V147i_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V147i_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)))
            & ! [V148c_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPconst_2E1(s(tyop_2Erat_2Erat,V148c_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Erat_2Erat,V148c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2Ecanonical_2ENil__monom_2E0)))
            & ! [V149pl_2E0,V150pr_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V149pl_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V150pr_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V149pl_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V150pr_2E0)))))
            & ! [V151pl_2E0,V152pr_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V151pl_2E0),s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V152pr_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V151pl_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V152pr_2E0)))))
            & ! [V153p_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V153p_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__scalar3_2E3(s(tyop_2Erat_2Erat,c_2Erat_2Erat__ainv_2E1(s(tyop_2Erat_2Erat,c_2Erat_2Erat__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V153p_2E0)))))
            & ! [V154x_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__simplify_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V154x_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__r__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Erat_2Erat),c_2EratRing_2Erat__polynom__normalize_2E1(s(tyop_2EringNorm_2Epolynom(tyop_2Erat_2Erat),V154x_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) ) ).

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