TPTP Problem File: ITP013_3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP013_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ewords_2En2w__sub.p, bushy 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 : thm_2Ewords_2En2w__sub.p [Gau19]
% : HL406001_3.p [TPAP]
% Status : Theorem
% Rating : 0.00 v7.5.0
% Syntax : Number of formulae : 87 ( 21 unt; 41 typ; 0 def)
% Number of atoms : 110 ( 43 equ)
% Maximal formula atoms : 15 ( 1 avg)
% Number of connectives : 71 ( 7 ~; 3 |; 15 &)
% ( 26 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 33 ( 19 >; 14 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 38 ( 38 usr; 9 con; 0-4 aty)
% Number of variables : 143 ( 118 !; 1 ?; 143 :)
% ( 24 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $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(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_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_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_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: 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_2Ewords_2En2w_2E0,type,
c_2Ewords_2En2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2En2w_2E1,type,
c_2Ewords_2En2w_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__2comp_2E0,type,
c_2Ewords_2Eword__2comp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2Eword__2comp_2E1,type,
c_2Ewords_2Eword__2comp_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__add_2E0,type,
c_2Ewords_2Eword__add_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__add_2E2,type,
c_2Ewords_2Eword__add_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__sub_2E0,type,
c_2Ewords_2Eword__sub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__sub_2E2,type,
c_2Ewords_2Eword__sub_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
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_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_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_2D_2E0,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_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27a,X2_2E0: A_27a] : c_2Ebool_2ECOND_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ebool_2ECOND_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X2_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),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_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : c_2Ewords_2En2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum] : c_2Ewords_2En2w_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__2comp_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Ewords_2Eword__2comp_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__2comp_2E0(A_27b),X0_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__add_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__add_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Ewords_2Eword__add_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ewords_2Eword__add_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__sub_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__sub_2E0(A_27a),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_2Ebool_2ETRUTH,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( p(c_2Ebool_2ET_2E0)
=> p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
=> p(c_2Ebool_2ET_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(c_2Ebool_2EF_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(V0t_2E0) )
<=> p(c_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(c_2Ebool_2EF_2E0) )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] :
( ( V0x_2E0 = V0x_2E0 )
<=> p(c_2Ebool_2ET_2E0) ) ).
tff(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( ( V0x_2E0 = V1y_2E0 )
<=> ( V1y_2E0 = V0x_2E0 ) ) ).
tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = V0t_2E0 )
<=> p(V0t_2E0) )
& ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
<=> p(V0t_2E0) )
& ( ( c_2Ebool_2EF_2E0 = V0t_2E0 )
<=> ~ p(V0t_2E0) )
& ( ( V0t_2E0 = c_2Ebool_2EF_2E0 )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1_2E0: tyop_2Emin_2Ebool,V1t2_2E0: tyop_2Emin_2Ebool,V2t3_2E0: tyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> ( p(V1t2_2E0)
=> p(V2t3_2E0) ) )
<=> ( ( p(V0t1_2E0)
& p(V1t2_2E0) )
=> p(V2t3_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x_2E0: tyop_2Emin_2Ebool,V1x_27_2E0: tyop_2Emin_2Ebool,V2y_2E0: tyop_2Emin_2Ebool,V3y_27_2E0: tyop_2Emin_2Ebool] :
( ( ( V0x_2E0 = V1x_27_2E0 )
& ( p(V1x_27_2E0)
=> ( V2y_2E0 = V3y_27_2E0 ) ) )
=> ( ( p(V0x_2E0)
=> p(V2y_2E0) )
<=> ( p(V1x_27_2E0)
=> p(V3y_27_2E0) ) ) ) ).
tff(thm_2Ebool_2ECOND__CONG,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Ebool,V2x_2E0: A_27a,V3x_27_2E0: A_27a,V4y_2E0: A_27a,V5y_27_2E0: A_27a] :
( ( ( V0P_2E0 = V1Q_2E0 )
& ( p(V1Q_2E0)
=> ( V2x_2E0 = V3x_27_2E0 ) )
& ( ~ p(V1Q_2E0)
=> ( V4y_2E0 = V5y_27_2E0 ) ) )
=> ( c_2Ebool_2ECOND_2E3(A_27a,V0P_2E0,V2x_2E0,V4y_2E0) = c_2Ebool_2ECOND_2E3(A_27a,V1Q_2E0,V3x_27_2E0,V5y_27_2E0) ) ) ).
tff(thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a: $tType] :
( ! [V0t1_2E0: A_27a,V1t2_2E0: A_27a] : c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2ET_2E0,V0t1_2E0,V1t2_2E0) = V0t1_2E0
& ! [V2t1_2E0: A_27a,V3t2_2E0: A_27a] : c_2Ebool_2ECOND_2E3(A_27a,c_2Ebool_2EF_2E0,V2t1_2E0,V3t2_2E0) = V3t2_2E0 ) ).
tff(thm_2Ewords_2Eword__sub__def,axiom,
! [A_27a: $tType,V0v_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__sub_2E2(A_27a,V0v_2E0,V1w_2E0) = c_2Ewords_2Eword__add_2E2(A_27a,V0v_2E0,c_2Ewords_2Eword__2comp_2E1(A_27a,V1w_2E0)) ).
tff(thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Ewords_2Eword__add_2E2(A_27a,c_2Ewords_2Eword__2comp_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,V0m_2E0)),c_2Ewords_2Eword__2comp_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,V1n_2E0))) = c_2Ewords_2Eword__2comp_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2E_2B_2E2(V0m_2E0,V1n_2E0)))
& ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : c_2Ewords_2Eword__add_2E2(A_27b,c_2Ewords_2En2w_2E1(A_27b,V2m_2E0),c_2Ewords_2Eword__2comp_2E1(A_27b,c_2Ewords_2En2w_2E1(A_27b,V3n_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,V2m_2E0),c_2Ewords_2En2w_2E1(A_27b,c_2Earithmetic_2E_2D_2E2(V2m_2E0,V3n_2E0)),c_2Ewords_2Eword__2comp_2E1(A_27b,c_2Ewords_2En2w_2E1(A_27b,c_2Earithmetic_2E_2D_2E2(V3n_2E0,V2m_2E0)))) ) ).
tff(thm_2Ewords_2En2w__sub,conjecture,
! [A_27a: $tType,V0a_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1b_2E0,V0a_2E0))
=> ( c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2E_2D_2E2(V0a_2E0,V1b_2E0)) = c_2Ewords_2Eword__sub_2E2(A_27a,c_2Ewords_2En2w_2E1(A_27a,V0a_2E0),c_2Ewords_2En2w_2E1(A_27a,V1b_2E0)) ) ) ).
%------------------------------------------------------------------------------