ITP001 Axioms: ITP073_7.ax
%------------------------------------------------------------------------------
% File : ITP073_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 : quotient_sum.ax [Gau19]
% : HL4073_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 119 ( 44 unt; 46 typ; 0 def)
% Number of atoms : 136 ( 60 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 66 ( 3 ~; 3 |; 9 &)
% ( 13 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 23 >; 21 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 44 ( 44 usr; 6 con; 0-7 aty)
% Number of variables : 482 ( 415 !; 1 ?; 482 :)
% ( 66 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $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_2Esum_2E_2B_2B_2E0,type,
c_2Esum_2E_2B_2B_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)))) ).
tff(c_2Esum_2E_2B_2B_2E2,type,
c_2Esum_2E_2B_2B_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) ) > tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)) ) ).
tff(c_2Esum_2E_2B_2B_2E3,type,
c_2Esum_2E_2B_2B_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) * tyop_2Esum_2Esum(A_27a,A_27b) ) > tyop_2Esum_2Esum(A_27c,A_27d) ) ).
tff(c_2Equotient__sum_2E_2B_2B_2B_2E0,type,
c_2Equotient__sum_2E_2B_2B_2B_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)))) ).
tff(c_2Equotient__sum_2E_2B_2B_2B_2E2,type,
c_2Equotient__sum_2E_2B_2B_2B_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)) ) ).
tff(c_2Equotient__sum_2E_2B_2B_2B_2E4,type,
c_2Equotient__sum_2E_2B_2B_2B_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Esum_2Esum(A_27a,A_27b) * tyop_2Esum_2Esum(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Equotient_2E_2D_2D_3E_2E0,type,
c_2Equotient_2E_2D_2D_3E_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)))) ).
tff(c_2Equotient_2E_2D_2D_3E_2E3,type,
c_2Equotient_2E_2D_2D_3E_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) * tyop_2Emin_2Efun(A_27c,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27d) ) ).
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_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_2Equotient_2E_3D_3D_3D_3E_2E0,type,
c_2Equotient_2E_3D_3D_3D_3E_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))) ).
tff(c_2Equotient_2E_3D_3D_3D_3E_2E4,type,
c_2Equotient_2E_3D_3D_3D_3E_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,A_27b) ) > 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_2Equotient_2EEQUIV_2E0,type,
c_2Equotient_2EEQUIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Equotient_2EEQUIV_2E1,type,
c_2Equotient_2EEQUIV_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,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_2Esum_2EISL_2E0,type,
c_2Esum_2EISL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) ).
tff(c_2Esum_2EISL_2E1,type,
c_2Esum_2EISL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Esum_2Esum(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).
tff(c_2Esum_2EISR_2E0,type,
c_2Esum_2EISR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) ).
tff(c_2Esum_2EISR_2E1,type,
c_2Esum_2EISR_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Esum_2Esum(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).
tff(c_2Equotient_2EQUOTIENT_2E0,type,
c_2Equotient_2EQUOTIENT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Equotient_2EQUOTIENT_2E3,type,
c_2Equotient_2EQUOTIENT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: 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_2Esum_2E_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Esum_2E_2B_2B_2E2(A_27a,A_27c,A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d))),c_2Esum_2E_2B_2B_2E0(A_27a,A_27c,A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27d)] : ( c_2Esum_2E_2B_2B_2E2(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d))),c_2Esum_2E_2B_2B_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Esum_2E_2B_2B_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2Esum_2E_2B_2B_2E3(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d))),c_2Esum_2E_2B_2B_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27f_20mono_2EA_27h,axiom,
! [A_27b: $tType,A_27d: $tType,A_27f: $tType,A_27h: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27f),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27h)] : ( c_2Esum_2E_2B_2B_2E2(A_27b,A_27d,A_27f,A_27h,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27f,A_27h)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27f,A_27h))),c_2Esum_2E_2B_2B_2E0(A_27b,A_27d,A_27f,A_27h),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] : ( c_2Esum_2E_2B_2B_2E2(A_27c,A_27d,A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b))),c_2Esum_2E_2B_2B_2E0(A_27c,A_27d,A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Esum_2E_2B_2B_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0: tyop_2Esum_2Esum(A_27c,A_27d)] : ( c_2Esum_2E_2B_2B_2E3(A_27c,A_27d,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b))),c_2Esum_2E_2B_2B_2E0(A_27c,A_27d,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27e_20mono_2EA_27g_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,A_27e: $tType,A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27g,A_27c)] : ( c_2Esum_2E_2B_2B_2E2(A_27e,A_27g,A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27e,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27a,A_27c))),c_2Esum_2E_2B_2B_2E0(A_27e,A_27g,A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27e_20mono_2EA_27g_20mono_2EA_27f_20mono_2EA_27h,axiom,
! [A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,X0_2E0: tyop_2Emin_2Efun(A_27e,A_27f),X1_2E0: tyop_2Emin_2Efun(A_27g,A_27h)] : ( c_2Esum_2E_2B_2B_2E2(A_27e,A_27g,A_27f,A_27h,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27f,A_27h)),app_2E2(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27f,A_27h))),c_2Esum_2E_2B_2B_2E0(A_27e,A_27g,A_27f,A_27h),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Equotient__sum_2E_2B_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Equotient__sum_2E_2B_2B_2B_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Equotient__sum_2E_2B_2B_2B_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Esum_2Esum(A_27a,A_27b),X3_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Equotient__sum_2E_2B_2B_2B_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Equotient__sum_2E_2B_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))] : ( c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool))),c_2Equotient__sum_2E_2B_2B_2B_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Equotient__sum_2E_2B_2B_2B_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))] : ( c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool))),c_2Equotient__sum_2E_2B_2B_2B_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2EA_27f_20mono_2EA_27e_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27e: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27e),X1_2E0: tyop_2Emin_2Efun(A_27f,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27e,A_27f)] : ( c_2Equotient_2E_2D_2D_3E_2E3(A_27a,A_27f,A_27e,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Equotient_2E_2D_2D_3E_2E0(A_27a,A_27f,A_27e,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27h_20mono_2EA_27g_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,A_27g: $tType,A_27h: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27g),X1_2E0: tyop_2Emin_2Efun(A_27h,A_27d),X2_2E0: tyop_2Emin_2Efun(A_27g,A_27h)] : ( c_2Equotient_2E_2D_2D_3E_2E3(A_27c,A_27h,A_27g,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27h,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27g),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Equotient_2E_2D_2D_3E_2E0(A_27c,A_27h,A_27g,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27e_2CA_27g_29_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27d_29_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28A_27f_2CA_27h_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27a,A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27f,A_27h)),X2_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d))] : ( c_2Equotient_2E_2D_2D_3E_2E3(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27f,A_27h),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27f,A_27h)),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27f,A_27h)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27f,A_27h))),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27f,A_27h)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27f,A_27h)))),c_2Equotient_2E_2D_2D_3E_2E0(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27f,A_27h)),X0_2E0),X1_2E0),X2_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_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(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X3_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),X3_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d))] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),X0_2E0),X1_2E0),X2_2E0),X3_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(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Equotient_2EEQUIV_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Equotient_2EEQUIV_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Equotient_2EEQUIV_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Esum_2EINL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c] : ( c_2Esum_2EINL_2E1(A_27c,A_27d,X0_2E0) = app_2E2(A_27c,tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b] : ( c_2Esum_2EINR_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27d] : ( c_2Esum_2EINR_2E1(A_27c,A_27d,X0_2E0) = app_2E2(A_27d,tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2Esum_2EISL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Esum_2EISL_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Esum_2Esum(A_27c,A_27d)] : ( c_2Esum_2EISL_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool,c_2Esum_2EISL_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : ( c_2Esum_2EISR_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Esum_2EISR_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Esum_2Esum(A_27c,A_27d)] : ( c_2Esum_2EISR_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool,c_2Esum_2EISR_2E0(A_27c,A_27d),X0_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27e,axiom,
! [A_27a: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27e),X2_2E0: tyop_2Emin_2Efun(A_27e,A_27a)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27e,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27e,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27a),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27a,A_27e),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27b,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27f,axiom,
! [A_27b: $tType,A_27f: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27f),X2_2E0: tyop_2Emin_2Efun(A_27f,A_27b)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27f,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27b,A_27f),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27c_20mono_2EA_27g,axiom,
! [A_27c: $tType,A_27g: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27g),X2_2E0: tyop_2Emin_2Efun(A_27g,A_27c)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27c,A_27g,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27g,A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,A_27g),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27g),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27c,A_27g),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27d_20mono_2EA_27h,axiom,
! [A_27d: $tType,A_27h: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27h),X2_2E0: tyop_2Emin_2Efun(A_27h,A_27d)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27d,A_27h,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27h,A_27d),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27d,A_27h),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,A_27d),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27h),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,A_27d),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27d,A_27h),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),X2_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b))] : ( c_2Equotient_2EQUOTIENT_2E3(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),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_2Equotient__sum_2ESUM__REL__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ( ! [V1R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3a1_2E0: A_27a,V4a2_2E0: A_27a] : p(app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),V0P_2E0,V1R1_2E0),V2R2_2E0),c_2Esum_2EINL_2E1(A_27a,A_27b,V3a1_2E0)),c_2Esum_2EINL_2E1(A_27a,A_27b,V4a2_2E0)))
& ! [V5R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V6R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V7b1_2E0: A_27b,V8b2_2E0: A_27b] : p(app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),V0P_2E0,V5R1_2E0),V6R2_2E0),c_2Esum_2EINR_2E1(A_27a,A_27b,V7b1_2E0)),c_2Esum_2EINR_2E1(A_27a,A_27b,V8b2_2E0)))
& ! [V9R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V10R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V11a1_2E0: A_27a,V12b2_2E0: A_27b] : p(app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),V0P_2E0,V9R1_2E0),V10R2_2E0),c_2Esum_2EINL_2E1(A_27a,A_27b,V11a1_2E0)),c_2Esum_2EINR_2E1(A_27a,A_27b,V12b2_2E0)))
& ! [V13R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V14R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V15b1_2E0: A_27b,V16a2_2E0: A_27a] : p(app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),V0P_2E0,V13R1_2E0),V14R2_2E0),c_2Esum_2EINR_2E1(A_27a,A_27b,V15b1_2E0)),c_2Esum_2EINL_2E1(A_27a,A_27b,V16a2_2E0))) )
=> ! [V17v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V18v1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V19v2_2E0: tyop_2Esum_2Esum(A_27a,A_27b),V20v3_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] : p(app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),V0P_2E0,V17v_2E0),V18v1_2E0),V19v2_2E0),V20v3_2E0)) ) ).
tff(thm_2Equotient__sum_2ESUM__REL__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0b2_2E0: A_27b,V1b1_2E0: A_27b,V2a2_2E0: A_27a,V3a1_2E0: A_27a,V4R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V5R1_2E0,V4R2_2E0,c_2Esum_2EINL_2E1(A_27a,A_27b,V3a1_2E0),c_2Esum_2EINL_2E1(A_27a,A_27b,V2a2_2E0)) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5R1_2E0,V3a1_2E0),V2a2_2E0) )
& ( c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V5R1_2E0,V4R2_2E0,c_2Esum_2EINR_2E1(A_27a,A_27b,V1b1_2E0),c_2Esum_2EINR_2E1(A_27a,A_27b,V0b2_2E0)) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4R2_2E0,V1b1_2E0),V0b2_2E0) )
& ( c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V5R1_2E0,V4R2_2E0,c_2Esum_2EINL_2E1(A_27a,A_27b,V3a1_2E0),c_2Esum_2EINR_2E1(A_27a,A_27b,V0b2_2E0)) = c_2Ebool_2EF_2E0 )
& ( c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V5R1_2E0,V4R2_2E0,c_2Esum_2EINR_2E1(A_27a,A_27b,V1b1_2E0),c_2Esum_2EINL_2E1(A_27a,A_27b,V2a2_2E0)) = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Equotient__sum_2ESUM__REL__EQ,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27a,A_27b,c_2Emin_2E_3D_2E0(A_27a),c_2Emin_2E_3D_2E0(A_27b)) = c_2Emin_2E_3D_2E0(tyop_2Esum_2Esum(A_27a,A_27b)) ) ).
tff(thm_2Equotient__sum_2ESUM__EQUIV,axiom,
! [A_27a: $tType,A_27b: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Equotient_2EEQUIV_2E1(A_27a,V0R1_2E0))
=> ( p(c_2Equotient_2EEQUIV_2E1(A_27b,V1R2_2E0))
=> p(c_2Equotient_2EEQUIV_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27a,A_27b,V0R1_2E0,V1R2_2E0))) ) ) ).
tff(thm_2Equotient__sum_2ESUM__QUOTIENT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> p(c_2Equotient_2EQUOTIENT_2E3(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d),c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27a,A_27b,V0R1_2E0,V3R2_2E0),c_2Esum_2E_2B_2B_2E2(A_27a,A_27b,A_27c,A_27d,V1abs1_2E0,V4abs2_2E0),c_2Esum_2E_2B_2B_2E2(A_27c,A_27d,A_27a,A_27b,V2rep1_2E0,V5rep2_2E0))) ) ) ).
tff(thm_2Equotient__sum_2EINL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6a_2E0: A_27c] : ( c_2Esum_2EINL_2E1(A_27c,A_27d,V6a_2E0) = c_2Esum_2E_2B_2B_2E3(A_27a,A_27b,A_27c,A_27d,V1abs1_2E0,V4abs2_2E0,c_2Esum_2EINL_2E1(A_27a,A_27b,app_2E2(A_27c,A_27a,V2rep1_2E0,V6a_2E0))) ) ) ) ).
tff(thm_2Equotient__sum_2EINL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6a1_2E0: A_27a,V7a2_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R1_2E0,V6a1_2E0),V7a2_2E0))
=> p(c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V0R1_2E0,V3R2_2E0,c_2Esum_2EINL_2E1(A_27a,A_27b,V6a1_2E0),c_2Esum_2EINL_2E1(A_27a,A_27b,V7a2_2E0))) ) ) ) ).
tff(thm_2Equotient__sum_2EINR__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6b_2E0: A_27d] : ( c_2Esum_2EINR_2E1(A_27c,A_27d,V6b_2E0) = c_2Esum_2E_2B_2B_2E3(A_27a,A_27b,A_27c,A_27d,V1abs1_2E0,V4abs2_2E0,c_2Esum_2EINR_2E1(A_27a,A_27b,app_2E2(A_27d,A_27b,V5rep2_2E0,V6b_2E0))) ) ) ) ).
tff(thm_2Equotient__sum_2EINR__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6b1_2E0: A_27b,V7b2_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R2_2E0,V6b1_2E0),V7b2_2E0))
=> p(c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V0R1_2E0,V3R2_2E0,c_2Esum_2EINR_2E1(A_27a,A_27b,V6b1_2E0),c_2Esum_2EINR_2E1(A_27a,A_27b,V7b2_2E0))) ) ) ) ).
tff(thm_2Equotient__sum_2EISL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6a_2E0: tyop_2Esum_2Esum(A_27c,A_27d)] : ( c_2Esum_2EISL_2E1(A_27c,A_27d,V6a_2E0) = c_2Esum_2EISL_2E1(A_27a,A_27b,c_2Esum_2E_2B_2B_2E3(A_27c,A_27d,A_27a,A_27b,V2rep1_2E0,V5rep2_2E0,V6a_2E0)) ) ) ) ).
tff(thm_2Equotient__sum_2EISL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6a1_2E0: tyop_2Esum_2Esum(A_27a,A_27b),V7a2_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] :
( p(c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V0R1_2E0,V3R2_2E0,V6a1_2E0,V7a2_2E0))
=> ( c_2Esum_2EISL_2E1(A_27a,A_27b,V6a1_2E0) = c_2Esum_2EISL_2E1(A_27a,A_27b,V7a2_2E0) ) ) ) ) ).
tff(thm_2Equotient__sum_2EISR__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6a_2E0: tyop_2Esum_2Esum(A_27c,A_27d)] : ( c_2Esum_2EISR_2E1(A_27c,A_27d,V6a_2E0) = c_2Esum_2EISR_2E1(A_27a,A_27b,c_2Esum_2E_2B_2B_2E3(A_27c,A_27d,A_27a,A_27b,V2rep1_2E0,V5rep2_2E0,V6a_2E0)) ) ) ) ).
tff(thm_2Equotient__sum_2EISR__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6a1_2E0: tyop_2Esum_2Esum(A_27a,A_27b),V7a2_2E0: tyop_2Esum_2Esum(A_27a,A_27b)] :
( p(c_2Equotient__sum_2E_2B_2B_2B_2E4(A_27a,A_27b,V0R1_2E0,V3R2_2E0,V6a1_2E0,V7a2_2E0))
=> ( c_2Esum_2EISR_2E1(A_27a,A_27b,V6a1_2E0) = c_2Esum_2EISR_2E1(A_27a,A_27b,V7a2_2E0) ) ) ) ) ).
tff(thm_2Equotient__sum_2ESUM__MAP__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27e),V2rep1_2E0: tyop_2Emin_2Efun(A_27e,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27e,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27f),V5rep2_2E0: tyop_2Emin_2Efun(A_27f,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27f,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6R3_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V7abs3_2E0: tyop_2Emin_2Efun(A_27c,A_27g),V8rep3_2E0: tyop_2Emin_2Efun(A_27g,A_27c)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27c,A_27g,V6R3_2E0,V7abs3_2E0,V8rep3_2E0))
=> ! [V9R4_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V10abs4_2E0: tyop_2Emin_2Efun(A_27d,A_27h),V11rep4_2E0: tyop_2Emin_2Efun(A_27h,A_27d)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27d,A_27h,V9R4_2E0,V10abs4_2E0,V11rep4_2E0))
=> ! [V12f_2E0: tyop_2Emin_2Efun(A_27e,A_27f),V13g_2E0: tyop_2Emin_2Efun(A_27g,A_27h)] : ( c_2Esum_2E_2B_2B_2E2(A_27e,A_27g,A_27f,A_27h,V12f_2E0,V13g_2E0) = c_2Equotient_2E_2D_2D_3E_2E3(tyop_2Esum_2Esum(A_27e,A_27g),tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27f,A_27h),c_2Esum_2E_2B_2B_2E2(A_27e,A_27g,A_27a,A_27c,V2rep1_2E0,V8rep3_2E0),c_2Esum_2E_2B_2B_2E2(A_27b,A_27d,A_27f,A_27h,V4abs2_2E0,V10abs4_2E0),c_2Esum_2E_2B_2B_2E2(A_27a,A_27c,A_27b,A_27d,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,A_27f,A_27e,A_27b,V1abs1_2E0,V5rep2_2E0,V12f_2E0),c_2Equotient_2E_2D_2D_3E_2E3(A_27c,A_27h,A_27g,A_27d,V7abs3_2E0,V11rep4_2E0,V13g_2E0))) ) ) ) ) ) ).
tff(thm_2Equotient__sum_2ESUM__MAP__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,A_27f: $tType,A_27g: $tType,A_27h: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27e),V2rep1_2E0: tyop_2Emin_2Efun(A_27e,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27e,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27f),V5rep2_2E0: tyop_2Emin_2Efun(A_27f,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27f,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6R3_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V7abs3_2E0: tyop_2Emin_2Efun(A_27c,A_27g),V8rep3_2E0: tyop_2Emin_2Efun(A_27g,A_27c)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27c,A_27g,V6R3_2E0,V7abs3_2E0,V8rep3_2E0))
=> ! [V9R4_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V10abs4_2E0: tyop_2Emin_2Efun(A_27d,A_27h),V11rep4_2E0: tyop_2Emin_2Efun(A_27h,A_27d)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27d,A_27h,V9R4_2E0,V10abs4_2E0,V11rep4_2E0))
=> ! [V12f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V13f2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V14g1_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V15g2_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,A_27b,V0R1_2E0,V3R2_2E0,V12f1_2E0,V13f2_2E0))
& p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27c,A_27d,V6R3_2E0,V9R4_2E0,V14g1_2E0,V15g2_2E0)) )
=> p(c_2Equotient_2E_3D_3D_3D_3E_2E4(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d),c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27a,A_27c,V0R1_2E0,V6R3_2E0),c_2Equotient__sum_2E_2B_2B_2B_2E2(A_27b,A_27d,V3R2_2E0,V9R4_2E0),c_2Esum_2E_2B_2B_2E2(A_27a,A_27c,A_27b,A_27d,V12f1_2E0,V14g1_2E0),c_2Esum_2E_2B_2B_2E2(A_27a,A_27c,A_27b,A_27d,V13f2_2E0,V15g2_2E0))) ) ) ) ) ) ).
%------------------------------------------------------------------------------