ITP001 Axioms: ITP039_7.ax
%------------------------------------------------------------------------------
% File : ITP039_7 : 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 : defCNF.ax [Gau19]
% : HL4039_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 101 ( 21 unt; 54 typ; 0 def)
% Number of atoms : 107 ( 38 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 63 ( 3 ~; 3 |; 24 &)
% ( 24 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 45 ( 26 >; 19 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 51 ( 51 usr; 13 con; 0-4 aty)
% Number of variables : 198 ( 161 !; 4 ?; 198 :)
% ( 33 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: ( $tType * $tType ) > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : 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))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2EdefCNF_2EDEF_2E0,type,
c_2EdefCNF_2EDEF_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool))) ).
tff(c_2EdefCNF_2EDEF_2E3,type,
c_2EdefCNF_2EDEF_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Esum_2EINL_2E0,type,
c_2Esum_2EINL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)) ).
tff(c_2Esum_2EINL_2E1,type,
c_2Esum_2EINL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Esum_2Esum(A_27a,A_27b) ) ).
tff(c_2Esum_2EINR_2E0,type,
c_2Esum_2EINR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)) ).
tff(c_2Esum_2EINR_2E1,type,
c_2Esum_2EINR_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Esum_2Esum(A_27a,A_27b) ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2EdefCNF_2EOK_2E0,type,
c_2EdefCNF_2EOK_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)) ).
tff(c_2EdefCNF_2EOK_2E2,type,
c_2EdefCNF_2EOK_2E2: ( tyop_2Enum_2Enum * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ) > tyop_2Emin_2Ebool ).
tff(c_2EdefCNF_2EOKDEF_2E0,type,
c_2EdefCNF_2EOKDEF_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)) ).
tff(c_2EdefCNF_2EOKDEF_2E2,type,
c_2EdefCNF_2EOKDEF_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))) ) > tyop_2Emin_2Ebool ).
tff(c_2Elist_2ESNOC_2E0,type,
c_2Elist_2ESNOC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ESNOC_2E2,type,
c_2Elist_2ESNOC_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2EdefCNF_2EUNIQUE_2E0,type,
c_2EdefCNF_2EUNIQUE_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))) ).
tff(c_2EdefCNF_2EUNIQUE_2E3,type,
c_2EdefCNF_2EUNIQUE_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum * tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(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(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [X0_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EdefCNF_2EDEF_2E3,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] : ( c_2EdefCNF_2EDEF_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),c_2EdefCNF_2EDEF_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0) ) ).
tff(arityeq2_2Ec_2EdefCNF_2EOK_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] : ( c_2EdefCNF_2EOK_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2EdefCNF_2EOK_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2EdefCNF_2EOKDEF_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] : ( c_2EdefCNF_2EOKDEF_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),c_2EdefCNF_2EOKDEF_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] : ( c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))),c_2Elist_2ESNOC_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2EdefCNF_2EUNIQUE_2E3,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] : ( c_2EdefCNF_2EUNIQUE_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),c_2EdefCNF_2EUNIQUE_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2EdefCNF_2EDEF__def,axiom,
( ! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] : ( c_2EdefCNF_2EDEF_2E3(V0v_2E0,V1n_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))) = c_2Ebool_2ET_2E0 )
& ! [V2v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3n_2E0: tyop_2Enum_2Enum,V4x_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V5xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( p(c_2EdefCNF_2EDEF_2E3(V2v_2E0,V3n_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V4x_2E0,V5xs_2E0)))
<=> ( p(c_2EdefCNF_2EUNIQUE_2E3(V2v_2E0,V3n_2E0,V4x_2E0))
& p(c_2EdefCNF_2EDEF_2E3(V2v_2E0,c_2Enum_2ESUC_2E1(V3n_2E0),V5xs_2E0)) ) ) ) ).
tff(thm_2EdefCNF_2EOKDEF__def,axiom,
( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2EdefCNF_2EOKDEF_2E2(V0n_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))) = c_2Ebool_2ET_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V3xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( p(c_2EdefCNF_2EOKDEF_2E2(V1n_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2x_2E0,V3xs_2E0)))
<=> ( p(c_2EdefCNF_2EOK_2E2(V1n_2E0,V2x_2E0))
& p(c_2EdefCNF_2EOKDEF_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V3xs_2E0)) ) ) ) ).
tff(thm_2EdefCNF_2EUNIQUE__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)))] :
( ( ! [V1v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum,V3conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4i_2E0: tyop_2Enum_2Enum,V5j_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0,V1v_2E0),V2n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V3conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4i_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5j_2E0)))))
& ! [V6v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V7n_2E0: tyop_2Enum_2Enum,V8conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9i_2E0: tyop_2Enum_2Enum,V10b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0,V6v_2E0),V7n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V8conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9i_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10b_2E0)))))
& ! [V11v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V12n_2E0: tyop_2Enum_2Enum,V13conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V14a_2E0: tyop_2Emin_2Ebool,V15j_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0,V11v_2E0),V12n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V13conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V14a_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V15j_2E0)))))
& ! [V16v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V17n_2E0: tyop_2Enum_2Enum,V18conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V19a_2E0: tyop_2Emin_2Ebool,V20b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0,V16v_2E0),V17n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V18conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V19a_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V20b_2E0))))) )
=> ! [V21v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V22v1_2E0: tyop_2Enum_2Enum,V23v2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V24v3_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V25v4_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),V0P_2E0,V21v_2E0),V22v1_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V23v2_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V24v3_2E0,V25v4_2E0)))) ) ).
tff(thm_2EdefCNF_2EUNIQUE__def,axiom,
! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum,V3i_2E0: tyop_2Enum_2Enum,V4conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V5b_2E0: tyop_2Emin_2Ebool,V6a_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2EdefCNF_2EUNIQUE_2E3(V0v_2E0,V1n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V4conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3i_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2j_2E0)))))
<=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V1n_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4conn_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V3i_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V2j_2E0)) ) )
& ( p(c_2EdefCNF_2EUNIQUE_2E3(V0v_2E0,V1n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V4conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3i_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5b_2E0)))))
<=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V1n_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4conn_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V3i_2E0)),V5b_2E0) ) )
& ( p(c_2EdefCNF_2EUNIQUE_2E3(V0v_2E0,V1n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V4conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V6a_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2j_2E0)))))
<=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V1n_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4conn_2E0,V6a_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V2j_2E0)) ) )
& ( p(c_2EdefCNF_2EUNIQUE_2E3(V0v_2E0,V1n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V4conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V6a_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5b_2E0)))))
<=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V1n_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4conn_2E0,V6a_2E0),V5b_2E0) ) ) ) ).
tff(thm_2EdefCNF_2EOK__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool))] :
( ( ! [V1n_2E0: tyop_2Enum_2Enum,V2conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3i_2E0: tyop_2Enum_2Enum,V4j_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),V0P_2E0,V1n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3i_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4j_2E0)))))
& ! [V5n_2E0: tyop_2Enum_2Enum,V6conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V7i_2E0: tyop_2Enum_2Enum,V8b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),V0P_2E0,V5n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V6conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7i_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V8b_2E0)))))
& ! [V9n_2E0: tyop_2Enum_2Enum,V10conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11a_2E0: tyop_2Emin_2Ebool,V12j_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),V0P_2E0,V9n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V10conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11a_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12j_2E0)))))
& ! [V13n_2E0: tyop_2Enum_2Enum,V14conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V15a_2E0: tyop_2Emin_2Ebool,V16b_2E0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),V0P_2E0,V13n_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V14conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V15a_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V16b_2E0))))) )
=> ! [V17v_2E0: tyop_2Enum_2Enum,V18v1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V19v2_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V20v3_2E0: tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),V0P_2E0,V17v_2E0),c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V18v1_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V19v2_2E0,V20v3_2E0)))) ) ).
tff(thm_2EdefCNF_2EOK__def,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Enum_2Enum,V3conn_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4b_2E0: tyop_2Emin_2Ebool,V5a_2E0: tyop_2Emin_2Ebool] :
( ( p(c_2EdefCNF_2EOK_2E2(V0n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V3conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2i_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1j_2E0)))))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,V0n_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V1j_2E0,V0n_2E0)) ) )
& ( c_2EdefCNF_2EOK_2E2(V0n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V3conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2i_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4b_2E0)))) = c_2Eprim__rec_2E_3C_2E2(V2i_2E0,V0n_2E0) )
& ( c_2EdefCNF_2EOK_2E2(V0n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V3conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5a_2E0),c_2Esum_2EINL_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1j_2E0)))) = c_2Eprim__rec_2E_3C_2E2(V1j_2E0,V0n_2E0) )
& ( c_2EdefCNF_2EOK_2E2(V0n_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V3conn_2E0,c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5a_2E0),c_2Esum_2EINR_2E1(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4b_2E0)))) = c_2Ebool_2ET_2E0 ) ) ).
tff(thm_2EdefCNF_2EDEF__SNOC,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),V3v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2EdefCNF_2EDEF_2E3(V3v_2E0,V0n_2E0,c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V1x_2E0,V2l_2E0)))
<=> ( p(c_2EdefCNF_2EDEF_2E3(V3v_2E0,V0n_2E0,V2l_2E0))
& p(c_2EdefCNF_2EUNIQUE_2E3(V3v_2E0,c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2l_2E0)),V1x_2E0)) ) ) ).
tff(thm_2EdefCNF_2EOKDEF__SNOC,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( p(c_2EdefCNF_2EOKDEF_2E2(V0n_2E0,c_2Elist_2ESNOC_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V1x_2E0,V2l_2E0)))
<=> ( p(c_2EdefCNF_2EOKDEF_2E2(V0n_2E0,V2l_2E0))
& p(c_2EdefCNF_2EOK_2E2(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V2l_2E0)),V1x_2E0)) ) ) ).
tff(thm_2EdefCNF_2ECONSISTENCY,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( p(c_2EdefCNF_2EOKDEF_2E2(V0n_2E0,V1l_2E0))
=> ? [V2v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2EdefCNF_2EDEF_2E3(V2v_2E0,V0n_2E0,V1l_2E0)) ) ).
tff(thm_2EdefCNF_2EBIGSTEP,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool,V2R_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V3v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3v_2E0))
=> ( V1Q_2E0 = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2R_2E0,V3v_2E0) ) )
=> ( ( ? [V4v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V4v_2E0))
& p(V1Q_2E0) )
<=> ? [V5v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V5v_2E0))
& p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2R_2E0,V5v_2E0)) ) ) ) ).
tff(thm_2EdefCNF_2EFINAL__DEF,axiom,
! [V0v_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Emin_2Ebool] :
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V1n_2E0) = V2x_2E0 )
<=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0v_2E0,V1n_2E0) = V2x_2E0 )
& p(c_2EdefCNF_2EDEF_2E3(V0v_2E0,c_2Enum_2ESUC_2E1(V1n_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Esum_2Esum(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))) ) ) ).
%------------------------------------------------------------------------------