ITP001 Axioms: ITP117+4.ax
%------------------------------------------------------------------------------
% File : ITP117+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 : numRing.ax [Gau19]
% : HL4117+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 110 ( 93 unt; 0 def)
% Number of atoms : 281 ( 234 equ)
% Maximal formula atoms : 91 ( 2 avg)
% Number of connectives : 175 ( 4 ~; 3 |; 132 &)
% ( 29 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 4 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 175 ( 175 usr; 92 con; 0-4 aty)
% Number of variables : 379 ( 378 !; 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_2Enum_2ESUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiiSUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Enumeral_2EiDUB_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Enumeral_2EiZ_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiZ_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_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_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EODD_2E1,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__merge_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__merge_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__merge_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq4_2Ec_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0))) = s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum))))),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__prod_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__prod_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__prod_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__scalar_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__scalar_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar2_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__scalar2_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__scalar2_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__scalar3_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__scalar3_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))))),c_2Ecanonical_2Ecanonical__sum__scalar3_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Ecanonical__sum__simplify_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Ecanonical__sum__simplify_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__simplify_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Eics__aux_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Ecanonical_2Eics__aux_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)))),c_2Ecanonical_2Eics__aux_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Einterp__cs_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__cs_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Ecanonical_2Einterp__cs_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Einterp__m_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Einterp__m_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)))),c_2Ecanonical_2Einterp__m_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Einterp__sp_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__sp_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Ecanonical_2Einterp__sp_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Einterp__vl_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__vl_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Einterp__vl_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Esemi__ring_2Eis__semi__ring_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Esemi__ring_2Eis__semi__ring_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Esemi__ring_2Eis__semi__ring_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Eivl__aux_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Eivl__aux_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)))),c_2Ecanonical_2Eivl__aux_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Emonom__insert_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Emonom__insert_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))))),c_2Ecanonical_2Emonom__insert_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2EnumRing_2Enum__canonical__sum__simplify_2E1,axiom,
! [X0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__canonical__sum__simplify_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2EnumRing_2Enum__spolynom__normalize_2E1,axiom,
! [X0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__spolynom__normalize_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecanonical_2ECons__varlist_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2ECons__varlist_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq3_2Ec_2Ecanonical_2ECons__monom_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2ECons__monom_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2ESPconst_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPconst_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)),c_2Ecanonical_2ESPconst_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2ESPvar_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPvar_2E1(s(tyop_2Equote_2Eindex,X0_2E0))) = s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)),c_2Ecanonical_2ESPvar_2E0),s(tyop_2Equote_2Eindex,X0_2E0))) ).
fof(arityeq2_2Ec_2Ecanonical_2ESPmult_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPmult_2E2(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum))),c_2Ecanonical_2ESPmult_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecanonical_2ESPplus_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPplus_2E2(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum))),c_2Ecanonical_2ESPplus_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq1_2Ec_2EnumRing_2Enum__spolynom__simplify_2E1,axiom,
! [X0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__simplify_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__spolynom__simplify_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Espolynom__normalize_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Espolynom__normalize_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Espolynom__normalize_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Espolynom__simplify_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Espolynom__simplify_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Espolynom__simplify_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecanonical_2Evarlist__insert_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Evarlist__insert_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Evarlist__insert_2E0),s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),X0_2E0))) ).
fof(arityeq3_2Ec_2EnumRing_2Enum__ivl__aux_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Equote_2Eindex,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2EnumRing_2Enum__ivl__aux_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Equote_2Eindex,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__interp__sp_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__sp_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,X0_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Equote_2Evarmap__find_2E0),s(tyop_2Equote_2Eindex,X0_2E0))),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq3_2Ec_2EnumRing_2Enum__ics__aux_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2EnumRing_2Enum__ics__aux_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__interp__vl_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__vl_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))) ).
fof(arityeq3_2Ec_2EnumRing_2Enum__interp__m_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2EnumRing_2Enum__interp__m_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_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_2EnumRing_2Enum__canonical__sum__merge_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__merge_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__prod_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__prod_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__scalar2_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__scalar2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq3_2Ec_2EnumRing_2Enum__canonical__sum__scalar3_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2EnumRing_2Enum__canonical__sum__scalar3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__canonical__sum__scalar_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__scalar_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__interp__cs_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__cs_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) ).
fof(arityeq2_2Ec_2EnumRing_2Enum__varlist__insert_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__varlist__insert_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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_2Enum_2Enum_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) ).
fof(arityeq3_2Ec_2EnumRing_2Enum__monom__insert_2E3,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2EnumRing_2Enum__monom__insert_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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_2Enum_2Enum_29,axiom,
! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X3_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),X3_2E0))) ).
fof(thm_2EnumRing_2Enum__interp__sp__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__sp_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__sp_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__spolynom__simplify__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__spolynom__simplify_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Espolynom__simplify_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__spolynom__normalize__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__spolynom__normalize_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Espolynom__normalize_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__interp__cs__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__cs_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__cs_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__ics__aux__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2EnumRing_2Enum__ics__aux_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Ecanonical_2Eics__aux_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__interp__m__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2EnumRing_2Enum__interp__m_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Einterp__m_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__interp__vl__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2EnumRing_2Enum__interp__vl_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum)),c_2Ecanonical_2Einterp__vl_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__ivl__aux__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2EnumRing_2Enum__ivl__aux_2E0) = s(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Enum_2Enum))),c_2Ecanonical_2Eivl__aux_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__canonical__sum__simplify__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2EnumRing_2Enum__canonical__sum__simplify_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)),c_2Ecanonical_2Ecanonical__sum__simplify_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__canonical__sum__prod__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__prod_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__prod_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__canonical__sum__scalar3__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2EnumRing_2Enum__canonical__sum__scalar3_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Ecanonical__sum__scalar3_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__canonical__sum__scalar2__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__scalar2_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__scalar2_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__canonical__sum__scalar__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__scalar_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__scalar_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__varlist__insert__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__varlist__insert_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Evarlist__insert_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__monom__insert__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2EnumRing_2Enum__monom__insert_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum)))),c_2Ecanonical_2Emonom__insert_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__canonical__sum__merge__def,axiom,
s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2EnumRing_2Enum__canonical__sum__merge_2E0) = s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum))),c_2Ecanonical_2Ecanonical__sum__merge_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))) ).
fof(thm_2EnumRing_2Enum__semi__ring,axiom,
p(s(tyop_2Emin_2Ebool,c_2Esemi__ring_2Eis__semi__ring_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0)))))) ).
fof(thm_2EnumRing_2Enum__ring__thms,axiom,
! [A_27a,F2_2E0,F1_2E0,F0_2E0] :
( ! [V105c_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V105c_2E0))))
<=> s(tyop_2Enum_2Enum,V105c_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) )
=> ( ! [V105c_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Enum_2Enum,V105c_2E0))))
<=> s(tyop_2Enum_2Enum,V105c_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
=> ( ! [V24x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V24x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
=> ( p(s(tyop_2Emin_2Ebool,c_2Esemi__ring_2Eis__semi__ring_2E1(s(tyop_2Esemi__ring_2Esemi__ring(tyop_2Enum_2Enum),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0))))))
& ! [V0vm_2E0,V1p_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V0vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V1p_2E0))) = s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V0vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__simplify_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V1p_2E0)))))
& ! [V2vm_2E0,V3c_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V2vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPconst_2E1(s(tyop_2Enum_2Enum,V3c_2E0))))) = s(tyop_2Enum_2Enum,V3c_2E0)
& ! [V4vm_2E0,V5i_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V4vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPvar_2E1(s(tyop_2Equote_2Eindex,V5i_2E0))))) = s(tyop_2Enum_2Enum,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V5i_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V4vm_2E0)))
& ! [V6vm_2E0,V7p1_2E0,V8p2_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V6vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPplus_2E2(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V7p1_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V8p2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V6vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V7p1_2E0))),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V6vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V8p2_2E0)))))
& ! [V9vm_2E0,V10p1_2E0,V11p2_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V9vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPmult_2E2(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V10p1_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V11p2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V9vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V10p1_2E0))),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__sp_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V9vm_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V11p2_2E0)))))
& ! [V12x_2E0,V13v2_2E0,V14v1_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,V12x_2E0),s(tyop_2Equote_2Evarmap(A_27a),V14v1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V13v2_2E0))))) = s(A_27a,V12x_2E0)
& ! [V15x_2E0,V16v2_2E0,V17v1_2E0,V18i1_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,c_2Equote_2ERight__idx_2E1(s(tyop_2Equote_2Eindex,V18i1_2E0))),s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2ENode__vm_2E3(s(A_27a,V15x_2E0),s(tyop_2Equote_2Evarmap(A_27a),V17v1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V16v2_2E0))))) = s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V18i1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V16v2_2E0)))
& ! [V19x_2E0,V20v2_2E0,V21v1_2E0,V22i1_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,c_2Equote_2ELeft__idx_2E1(s(tyop_2Equote_2Eindex,V22i1_2E0))),s(tyop_2Equote_2Evarmap(A_27a),c_2Equote_2ENode__vm_2E3(s(A_27a,V19x_2E0),s(tyop_2Equote_2Evarmap(A_27a),V21v1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V20v2_2E0))))) = s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V22i1_2E0),s(tyop_2Equote_2Evarmap(A_27a),V21v1_2E0)))
& ! [V23i_2E0] : s(A_27a,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V23i_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)))
& ! [V25t2_2E0,V26t1_2E0,V27l2_2E0,V28l1_2E0,V29c2_2E0,V30c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V30c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V28l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V26t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V29c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V27l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V25t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V28l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V27l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V30c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V28l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V26t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V29c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V27l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V25t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V30c1_2E0),s(tyop_2Enum_2Enum,V29c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V28l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V26t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V25t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V29c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V27l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V30c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V28l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V26t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V25t2_2E0)))))))
& ! [V31t2_2E0,V32t1_2E0,V33l2_2E0,V34l1_2E0,V35c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V35c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V34l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V32t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V33l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V31t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V34l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V33l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V35c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V34l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V32t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V33l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V31t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V35c1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V34l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V32t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V31t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V33l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V35c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V34l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V32t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V31t2_2E0)))))))
& ! [V36t2_2E0,V37t1_2E0,V38l2_2E0,V39l1_2E0,V40c2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V39l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V37t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V40c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V38l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V36t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V39l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V38l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V39l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V37t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V40c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V38l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V36t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V40c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V39l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V37t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V36t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V40c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V38l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V39l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V37t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V36t2_2E0)))))))
& ! [V41t2_2E0,V42t1_2E0,V43l2_2E0,V44l1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V44l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V42t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V43l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V41t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V44l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V43l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V44l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V42t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V43l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V41t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_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),V44l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V42t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V41t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V43l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V44l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V42t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V41t2_2E0)))))))
& ! [V45s1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V45s1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V45s1_2E0)
& ! [V46v6_2E0,V47v5_2E0,V48v4_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V48v4_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V47v5_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V46v6_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V48v4_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V47v5_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V46v6_2E0)))
& ! [V49v8_2E0,V50v7_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V50v7_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V49v8_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V50v7_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V49v8_2E0)))
& ! [V51t2_2E0,V52l2_2E0,V53l1_2E0,V54c2_2E0,V55c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V55c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V53l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V54c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V52l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V51t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V53l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V52l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V55c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V53l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V54c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V52l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V51t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V55c1_2E0),s(tyop_2Enum_2Enum,V54c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V53l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V51t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V54c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V52l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V55c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V53l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V51t2_2E0)))))))
& ! [V56t2_2E0,V57l2_2E0,V58l1_2E0,V59c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V59c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V58l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V57l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V56t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V58l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V57l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V59c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V58l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V57l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V56t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V59c1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V58l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V56t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V57l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V59c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V58l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V56t2_2E0)))))))
& ! [V60l1_2E0,V61c1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V61c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V61c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V60l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)))
& ! [V62t2_2E0,V63l2_2E0,V64l1_2E0,V65c2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V64l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V65c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V63l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V62t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V64l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V63l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V64l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V65c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V63l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V62t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V65c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V64l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V62t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V65c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V63l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V64l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V62t2_2E0)))))))
& ! [V66t2_2E0,V67l2_2E0,V68l1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V68l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V67l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V66t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),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),V68l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V67l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V68l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V67l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V66t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_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),V68l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V66t2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V67l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V68l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V66t2_2E0)))))))
& ! [V69l1_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__varlist__insert_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V69l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V69l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)))
& ! [V70c0_2E0,V71c_2E0,V72l_2E0,V73t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar_2E2(s(tyop_2Enum_2Enum,V70c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V71c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V72l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V73t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V70c0_2E0),s(tyop_2Enum_2Enum,V71c_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V72l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar_2E2(s(tyop_2Enum_2Enum,V70c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V73t_2E0)))))
& ! [V74c0_2E0,V75l_2E0,V76t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar_2E2(s(tyop_2Enum_2Enum,V74c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V75l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V76t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V74c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V75l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar_2E2(s(tyop_2Enum_2Enum,V74c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V76t_2E0)))))
& ! [V77c0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar_2E2(s(tyop_2Enum_2Enum,V77c0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)
& ! [V78l0_2E0,V79c_2E0,V80l_2E0,V81t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V78l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V79c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V80l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V81t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V79c_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),V78l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V80l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V78l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V81t_2E0)))))
& ! [V82l0_2E0,V83l_2E0,V84t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V82l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V83l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V84t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__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),V82l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V83l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V82l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V84t_2E0)))))
& ! [V85l0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V85l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)
& ! [V86c0_2E0,V87l0_2E0,V88c_2E0,V89l_2E0,V90t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,V86c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V87l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V88c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V89l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V90t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V86c0_2E0),s(tyop_2Enum_2Enum,V88c_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),V87l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V89l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,V86c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V87l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V90t_2E0)))))
& ! [V91c0_2E0,V92l0_2E0,V93l_2E0,V94t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,V91c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V92l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V93l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V94t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__monom__insert_2E3(s(tyop_2Enum_2Enum,V91c0_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),V92l0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V93l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,V91c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V92l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V94t_2E0)))))
& ! [V95c0_2E0,V96l0_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,V95c0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V96l0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)
& ! [V97c1_2E0,V98l1_2E0,V99t1_2E0,V100s2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V97c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V98l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V99t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V100s2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar3_2E3(s(tyop_2Enum_2Enum,V97c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V98l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V100s2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V99t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V100s2_2E0)))))
& ! [V101l1_2E0,V102t1_2E0,V103s2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V101l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V102t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V103s2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__scalar2_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V101l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V103s2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V102t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V103s2_2E0)))))
& ! [V104s2_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V104s2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)
& ! [V105c_2E0,V106l_2E0,V107t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V105c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V106l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V107t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Enum_2Enum,V105c_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V107t_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Enum_2Enum,V105c_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V106l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V107t_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V105c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V106l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V107t_2E0)))))))))
& ! [V108l_2E0,V109t_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V108l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V109t_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V108l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V109t_2E0)))))
& s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)
& ! [V110vm_2E0,V111x_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V110vm_2E0),s(tyop_2Equote_2Eindex,V111x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))) = s(tyop_2Enum_2Enum,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V111x_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V110vm_2E0)))
& ! [V112vm_2E0,V113x_2E0,V114x_27_2E0,V115t_27_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V112vm_2E0),s(tyop_2Equote_2Eindex,V113x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V114x_27_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V115t_27_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Equote_2Evarmap__find_2E2(s(tyop_2Equote_2Eindex,V113x_2E0),s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V112vm_2E0))),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V112vm_2E0),s(tyop_2Equote_2Eindex,V114x_27_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V115t_27_2E0)))))
& ! [V116vm_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V116vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
& ! [V117vm_2E0,V118x_2E0,V119t_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V117vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V118x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V119t_2E0))))) = s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V117vm_2E0),s(tyop_2Equote_2Eindex,V118x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V119t_2E0)))
& ! [V120vm_2E0,V121c_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V120vm_2E0),s(tyop_2Enum_2Enum,V121c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))) = s(tyop_2Enum_2Enum,V121c_2E0)
& ! [V122vm_2E0,V123c_2E0,V124x_2E0,V125t_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V122vm_2E0),s(tyop_2Enum_2Enum,V123c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V124x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V125t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V123c_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ivl__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V122vm_2E0),s(tyop_2Equote_2Eindex,V124x_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V125t_2E0)))))
& ! [V126vm_2E0,V127a_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V126vm_2E0),s(tyop_2Enum_2Enum,V127a_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Enum_2Enum,V127a_2E0)
& ! [V128vm_2E0,V129a_2E0,V130l_2E0,V131t_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V128vm_2E0),s(tyop_2Enum_2Enum,V129a_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V130l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V131t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V129a_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V128vm_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V128vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V130l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V131t_2E0)))))
& ! [V132vm_2E0,V133a_2E0,V134c_2E0,V135l_2E0,V136t_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V132vm_2E0),s(tyop_2Enum_2Enum,V133a_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V134c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V135l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V136t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V133a_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V132vm_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V132vm_2E0),s(tyop_2Enum_2Enum,V134c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V135l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V136t_2E0)))))
& ! [V137vm_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V137vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V138vm_2E0,V139l_2E0,V140t_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V138vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V139l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V140t_2E0))))) = s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V138vm_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__vl_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V138vm_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V139l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V140t_2E0)))
& ! [V141vm_2E0,V142c_2E0,V143l_2E0,V144t_2E0] : s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__cs_2E2(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V141vm_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V142c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V143l_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V144t_2E0))))) = s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__ics__aux_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V141vm_2E0),s(tyop_2Enum_2Enum,c_2EnumRing_2Enum__interp__m_2E3(s(tyop_2Equote_2Evarmap(tyop_2Enum_2Enum),V141vm_2E0),s(tyop_2Enum_2Enum,V142c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V143l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),V144t_2E0)))
& ! [V145i_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPvar_2E1(s(tyop_2Equote_2Eindex,V145i_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ECONS_2E2(s(tyop_2Equote_2Eindex,V145i_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)))
& ! [V146c_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPconst_2E1(s(tyop_2Enum_2Enum,V146c_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ECons__monom_2E3(s(tyop_2Enum_2Enum,V146c_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),c_2Elist_2ENIL_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2Ecanonical_2ENil__monom_2E0)))
& ! [V147l_2E0,V148r_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPplus_2E2(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V147l_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V148r_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__merge_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V147l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V148r_2E0)))))
& ! [V149l_2E0,V150r_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),c_2Ecanonical_2ESPmult_2E2(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V149l_2E0),s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V150r_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__prod_2E2(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V149l_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V150r_2E0)))))
& ! [V151x_2E0] : s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__simplify_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V151x_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__canonical__sum__simplify_2E1(s(tyop_2Ecanonical_2Ecanonical__sum(tyop_2Enum_2Enum),c_2EnumRing_2Enum__spolynom__normalize_2E1(s(tyop_2Ecanonical_2Espolynom(tyop_2Enum_2Enum),V151x_2E0))))) ) ) ) ) ).
fof(thm_2EnumRing_2Enum__rewrites,axiom,
! [V0n_2E0] :
( ! [V1n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0)
& ! [V2n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0)
& ! [V3n_2E0,V4m_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))))))
& ! [V5n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V5n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V6n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V7n_2E0,V8m_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V7n_2E0),s(tyop_2Enum_2Enum,V8m_2E0)))))
& ! [V9n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V9n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V10n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V10n_2E0)
& ! [V11n_2E0,V12m_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V12m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V11n_2E0),s(tyop_2Enum_2Enum,V12m_2E0)))))
& ! [V13n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V13n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V14n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V14n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V15n_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V15n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
& ! [V16n_2E0,V17m_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V16n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V16n_2E0),s(tyop_2Enum_2Enum,V17m_2E0)))))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))
& ! [V18n_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V18n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V18n_2E0)))))
& s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
& ! [V19n_2E0] : s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V19n_2E0)))))
& ! [V20n_2E0] :
( s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V20n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
<=> s(tyop_2Enum_2Enum,V20n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) )
& ! [V21n_2E0] :
( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V21n_2E0)))
<=> s(tyop_2Enum_2Enum,V21n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) )
& ! [V22n_2E0,V23m_2E0] :
( s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V22n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V23m_2E0)))
<=> s(tyop_2Enum_2Enum,V22n_2E0) = s(tyop_2Enum_2Enum,V23m_2E0) )
& ! [V24n_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V24n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [V25n_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V25n_2E0)))
& ! [V26n_2E0,V27m_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V26n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V27m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V26n_2E0),s(tyop_2Enum_2Enum,V27m_2E0)))
& ! [V28n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V28n_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [V29n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V29n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V29n_2E0)))
& ! [V30n_2E0,V31m_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V30n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V31m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V31m_2E0),s(tyop_2Enum_2Enum,V30n_2E0)))
& ! [V32n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V32n_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V33n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V33n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V33n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))
& ! [V34n_2E0,V35m_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V34n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V35m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V34n_2E0),s(tyop_2Enum_2Enum,V35m_2E0)))
& ! [V36n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V36n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
& ! [V37n_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V37n_2E0))))
<=> s(tyop_2Enum_2Enum,V37n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
& ! [V38n_2E0,V39m_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V38n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V39m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V39m_2E0),s(tyop_2Enum_2Enum,V38n_2E0)))
& ! [V40n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V40n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V40n_2E0)))
& ! [V41n_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V41n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V41n_2E0)))
& ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
& ! [V42n_2E0,V43m_2E0] :
( ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V42n_2E0)))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V42n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V42n_2E0)))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V42n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V42n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V43m_2E0)))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V42n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V43m_2E0)))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V42n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V43m_2E0)))
<=> s(tyop_2Enum_2Enum,V42n_2E0) = s(tyop_2Enum_2Enum,V43m_2E0) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V42n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V43m_2E0)))
<=> s(tyop_2Enum_2Enum,V42n_2E0) = s(tyop_2Enum_2Enum,V43m_2E0) ) )
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))
& ! [V44n_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V44n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V44n_2E0)))
& ! [V45n_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V45n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V45n_2E0)))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))
& ! [V46n_2E0,V47m_2E0] :
( s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V46n_2E0))))) = s(tyop_2Enum_2Enum,V46n_2E0)
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V46n_2E0)
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V46n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V46n_2E0)))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V46n_2E0)))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V46n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V46n_2E0)))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V46n_2E0)))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0)))))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V46n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V47m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V46n_2E0),s(tyop_2Enum_2Enum,V47m_2E0))))))) )
& ! [V48n_2E0,V49m_2E0] :
( s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V48n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)
& s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V48n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)
& s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V48n_2E0))),s(tyop_2Enum_2Enum,V49m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V48n_2E0),s(tyop_2Enum_2Enum,V49m_2E0))))),s(tyop_2Enum_2Enum,V49m_2E0)))))
& s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V48n_2E0))),s(tyop_2Enum_2Enum,V49m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V48n_2E0),s(tyop_2Enum_2Enum,V49m_2E0))),s(tyop_2Enum_2Enum,V49m_2E0))))))) )
& ! [V50n_2E0] :
( s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V50n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V50n_2E0)))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V50n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V50n_2E0)))))
& s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) )
& ( s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_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) ) ).
%------------------------------------------------------------------------------