TPTP Problem File: SWW476+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW476+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 197, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_100_fofmg_l197 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.4.0, 0.96 v5.3.0
% Syntax : Number of formulae : 345 ( 98 unt; 0 def)
% Number of atoms : 774 ( 365 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 526 ( 97 ~; 2 |; 12 &)
% ( 40 <=>; 375 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 204 ( 204 usr; 16 con; 0-5 aty)
% Number of variables : 1373 (1331 !; 42 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:33:21
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (40)
fof(gsy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J,axiom,
! [B_1_1] : is_bool(final_list_char(B_1_1)) ).
fof(gsy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,axiom,
! [B_1_1,B_2_1] : is_bool(hconf_97414254t_char(B_1_1,B_2_1)) ).
fof(gsy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,axiom,
! [B_1_1,B_2_1,B_3_1,B_4_1] : is_bool(lconf_496643946t_char(B_1_1,B_2_1,B_3_1,B_4_1)) ).
fof(gsy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J,axiom,
! [B_1_1] : is_bool(distinct_list_char(B_1_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a52822260ion_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oo,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a1834344429ion_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a283687028t_char(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olis,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a839443437t_char(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a2039389316_ty_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Ova,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a1073113293ty_val(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a1880637950ion_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty,hypothesis,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_all2_ty_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_a1462908359ion_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_List_Olist__all2_000tc__Value__Oval_000tc__Type__Oty,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(list_all2_val_ty(B_1_1,B_2_1,B_3_1)) ).
fof(gsy_c_Objects_Ohext,axiom,
! [B_1_1,B_2_1] : is_bool(hext(B_1_1,B_2_1)) ).
fof(gsy_c_WellTypeRT_OWTrt,hypothesis,
! [B_1_1,B_2_1,B_3_1,B_4_1,B_5] : is_bool(wTrt(B_1_1,B_2_1,B_3_1,B_4_1,B_5)) ).
fof(gsy_c_WellTypeRT_OWTrts,axiom,
! [B_1_1,B_2_1,B_3_1,B_4_1,B_5] : is_bool(wTrts(B_1_1,B_2_1,B_3_1,B_4_1,B_5)) ).
fof(gsy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_e544220455r_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Type__Oty_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_ty_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1033709212l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1715346603l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P1708370145l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P92196306r_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P1235399154l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P1907982426r_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P2118621157r_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P159683425l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P282169671l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,axiom,
! [B_1_1,B_2_1] : is_bool(member_exp_list_char(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__List__Olist_Itc__String__Ochar_J,axiom,
! [B_1_1,B_2_1] : is_bool(member_list_char(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__Option__Ooption_Itc__Type__Oty_J,axiom,
! [B_1_1,B_2_1] : is_bool(member_option_ty(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__Type__Oty,axiom,
! [B_1_1,B_2_1] : is_bool(member_ty(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__Value__Oval,axiom,
! [B_1_1,B_2_1] : is_bool(member_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,axiom,
! [B_1_1,B_2_1] : is_bool(member773094996on_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String,axiom,
! [B_1_1,B_2_1] : is_bool(member1420286996t_char(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fu,axiom,
! [B_1_1,B_2_1] : is_bool(member1322055188on_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_I,axiom,
! [B_1_1,B_2_1] : is_bool(member125098544t_char(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr,axiom,
! [B_1_1,B_2_1] : is_bool(member1161907014t_char(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_,axiom,
! [B_1_1,B_2_1] : is_bool(member563141460on_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_It,axiom,
! [B_1_1,B_2_1] : is_bool(member808015754on_val(B_1_1,B_2_1)) ).
%----Relevant facts (300)
fof(fact_0_widens__refl,axiom,
! [Pa,Xs] : hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Xs,Xs)) ).
fof(fact_1_widen__refl,axiom,
! [P_3,T_4] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),T_4),T_4)) ).
fof(fact_2_widens__trans,axiom,
! [Us,Pa,Ss,Tsa] :
( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Tsa))
=> ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Us))
=> hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Us)) ) ) ).
fof(fact_3_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_all2_val_ty(Pa,Xs,Ys))
=> size_size_list_val(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_4_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
=> size_size_list_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_5_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a283687028t_char(Pa,Xs,Ys))
=> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_6_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a1073113293ty_val(Pa,Xs,Ys))
=> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ).
fof(fact_7_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a2039389316_ty_ty(Pa,Xs,Ys))
=> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_8_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a839443437t_char(Pa,Xs,Ys))
=> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_9_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a52822260ion_ty(Pa,Xs,Ys))
=> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_10_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a1462908359ion_ty(Pa,Xs,Ys))
=> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_11_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a1880637950ion_ty(Pa,Xs,Ys))
=> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_12_list__all2__lengthD,axiom,
! [Pa,Xs,Ys] :
( hBOOL(list_a1834344429ion_ty(Pa,Xs,Ys))
=> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_13_length__map,axiom,
! [F,Xs] : size_size_list_val(hAPP_l1892737211st_val(map_list_char_val(F),Xs)) = size_s2113983095t_char(Xs) ).
fof(fact_14_length__map,axiom,
! [F,Xs] : size_s1143674878t_char(hAPP_l732421366t_char(map_va1934808527t_char(F),Xs)) = size_size_list_val(Xs) ).
fof(fact_15_length__map,axiom,
! [F,Xs] : size_s1050794909ion_ty(hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs)) = size_size_list_ty(Xs) ).
fof(fact_16_length__map,axiom,
! [F,Xs] : size_s1050794909ion_ty(hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs)) = size_size_list_val(Xs) ).
fof(fact_17_length__map,axiom,
! [F,Xs] : size_s1050794909ion_ty(hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs)) = size_s1143674878t_char(Xs) ).
fof(fact_18_length__map,axiom,
! [F,Xs] : size_s1050794909ion_ty(hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs)) = size_s2113983095t_char(Xs) ).
fof(fact_19_length__map,axiom,
! [F,Xs] : size_s1143674878t_char(hAPP_l330149622t_char(map_op1779340173t_char(F),Xs)) = size_s1050794909ion_ty(Xs) ).
fof(fact_20_length__map,axiom,
! [F,Xs] : size_size_list_val(hAPP_l336371937st_val(map_option_ty_val(F),Xs)) = size_s1050794909ion_ty(Xs) ).
fof(fact_21_length__map,axiom,
! [F,Xs] : size_size_list_ty(hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs)) = size_s1050794909ion_ty(Xs) ).
fof(fact_22_length__map,axiom,
! [F,Xs] : size_s2113983095t_char(hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs)) = size_s1050794909ion_ty(Xs) ).
fof(fact_23_length__map,axiom,
! [F,Xs] : size_s2113983095t_char(hAPP_l407174677t_char(map_li1333403488t_char(F),Xs)) = size_s2113983095t_char(Xs) ).
fof(fact_24_length__map,axiom,
! [F,Xs] : size_s1699857438on_val(hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs)) = size_s1699857438on_val(Xs) ).
fof(fact_25_length__map,axiom,
! [F,Xs] : size_size_list_val(hAPP_l228474410st_val(map_option_val_val(F),Xs)) = size_s1595297126on_val(Xs) ).
fof(fact_26_length__map,axiom,
! [F,Xs] : size_s1595297126on_val(hAPP_l297961988on_val(map_li50976719on_val(F),Xs)) = size_s2113983095t_char(Xs) ).
fof(fact_27_length__map,axiom,
! [F,Xs] : size_s1050794909ion_ty(hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs)) = size_s1050794909ion_ty(Xs) ).
fof(fact_28_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys)
=> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_29_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys)
=> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_30_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys)
=> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_31_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_32_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ).
fof(fact_33_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_34_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ).
fof(fact_35_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_36_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l1607890493on_val(map_ex1598883030on_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_37_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_38_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l2011456725t_char(map_ex101166958t_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_39_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1539861698st_val(map_ex740158547ar_val(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_40_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l2065413838t_char(map_ex2109939687t_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_41_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l110066169ist_ty(map_exp_list_char_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_42_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys)
=> size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ).
fof(fact_43_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l382831894on_val(map_va527586287on_val(G),Ys)
=> size_s1699857438on_val(Xs) = size_size_list_val(Ys) ) ).
fof(fact_44_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys)
=> size_s1595297126on_val(Xs) = size_size_list_val(Ys) ) ).
fof(fact_45_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l761459294on_val(map_val_option_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ).
fof(fact_46_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ).
fof(fact_47_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ).
fof(fact_48_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l1085267864ist_ty(map_val_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ).
fof(fact_49_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys)
=> size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ).
fof(fact_50_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys)
=> size_s1143674878t_char(Xs) = size_size_list_val(Ys) ) ).
fof(fact_51_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys)
=> size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_52_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l1634001311on_val(map_ty891785382on_val(G),Ys)
=> size_s1699857438on_val(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_53_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys)
=> size_s1595297126on_val(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_54_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l1014734695on_val(map_ty_option_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_55_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l578807295t_char(map_ty_exp_list_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_56_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_57_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_58_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_list_ty_list_ty(map_ty_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_59_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys)
=> size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_60_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys)
=> size_s1143674878t_char(Xs) = size_size_list_ty(Ys) ) ).
fof(fact_61_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l418486716on_val(map_li1100402823on_val(G),Ys)
=> size_s1699857438on_val(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_62_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys)
=> size_s1595297126on_val(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_63_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_64_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l740678812t_char(map_li1249123943t_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_65_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_66_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l1871878770ist_ty(map_list_char_ty(G),Ys)
=> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_67_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l2065413838t_char(map_ex2109939687t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys)
=> size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_68_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1557845365on_val(map_ex840371726on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1699857438on_val(Ys) ) ).
fof(fact_69_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1539861698st_val(map_ex740158547ar_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1595297126on_val(Ys) ) ).
fof(fact_70_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1607890493on_val(map_ex1598883030on_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys)
=> size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_71_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys)
=> size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_72_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_73_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_74_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l2011456725t_char(map_ex101166958t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_75_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1539861698st_val(map_ex740158547ar_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_76_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l2065413838t_char(map_ex2109939687t_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_77_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l110066169ist_ty(map_exp_list_char_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys)
=> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_78_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l922645359t_char(map_val_list_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys)
=> size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_79_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l382831894on_val(map_va527586287on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys)
=> size_size_list_val(Xs) = size_s1699857438on_val(Ys) ) ).
fof(fact_80_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l273806049st_val(map_val_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys)
=> size_size_list_val(Xs) = size_s1595297126on_val(Ys) ) ).
fof(fact_81_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l761459294on_val(map_val_option_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys)
=> size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_82_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l273806049st_val(map_val_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys)
=> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_83_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l922645359t_char(map_val_list_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys)
=> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_84_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1085267864ist_ty(map_val_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys)
=> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_85_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys)
=> size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_86_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys)
=> size_size_list_val(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_87_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l402740472t_char(map_ty_list_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys)
=> size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_88_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1634001311on_val(map_ty891785382on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys)
=> size_size_list_ty(Xs) = size_s1699857438on_val(Ys) ) ).
fof(fact_89_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1530663448st_val(map_ty_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys)
=> size_size_list_ty(Xs) = size_s1595297126on_val(Ys) ) ).
fof(fact_90_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1014734695on_val(map_ty_option_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys)
=> size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_91_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l578807295t_char(map_ty_exp_list_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys)
=> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_92_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1530663448st_val(map_ty_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys)
=> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_93_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l402740472t_char(map_ty_list_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys)
=> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_94_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_list_ty_list_ty(map_ty_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys)
=> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_95_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys)
=> size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_96_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys)
=> size_size_list_ty(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_97_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys)
=> size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_98_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l418486716on_val(map_li1100402823on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1699857438on_val(Ys) ) ).
fof(fact_99_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1595297126on_val(Ys) ) ).
fof(fact_100_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys)
=> size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_101_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_102_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l740678812t_char(map_li1249123943t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_103_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_104_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1871878770ist_ty(map_list_char_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ).
fof(fact_105_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys)
=> size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ).
fof(fact_106_map__eq__imp__length__eq,axiom,
! [F,Xs,G,Ys] :
( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys)
=> size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys) ) ).
fof(fact_107_prod__induct4,axiom,
! [X_1,Pa] :
( ! [A,B_1,C_3,D] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D)))))
=> hBOOL(hAPP_P92196306r_bool(Pa,X_1)) ) ).
fof(fact_108_prod__induct4,axiom,
! [X_1,Pa] :
( ! [A,B_1,C_3,D] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,produc1259058957on_val(B_1,produc899768717on_val(C_3,D)))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
fof(fact_109_prod__cases4,axiom,
! [Y_5] :
~ ! [A,B_1,C_3,D] : Y_5 != produc921874948t_char(A,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D))) ).
fof(fact_110_prod__cases4,axiom,
! [Y_3] :
~ ! [A,B_1,C_3,D] : Y_3 != produc1441475159on_val(A,produc1259058957on_val(B_1,produc899768717on_val(C_3,D))) ).
fof(fact_111_Pair__inject,axiom,
! [A_5,B_4,A_4,B_3] :
( produc921874948t_char(A_5,B_4) = produc921874948t_char(A_4,B_3)
=> ~ ( A_5 = A_4
=> B_4 != B_3 ) ) ).
fof(fact_112_Pair__inject,axiom,
! [A_5,B_4,A_4,B_3] :
( produc1909267824t_char(A_5,B_4) = produc1909267824t_char(A_4,B_3)
=> ~ ( A_5 = A_4
=> B_4 != B_3 ) ) ).
fof(fact_113_Pair__inject,axiom,
! [A_5,B_4,A_4,B_3] :
( produc1916172923t_char(A_5,B_4) = produc1916172923t_char(A_4,B_3)
=> ~ ( A_5 = A_4
=> B_4 != B_3 ) ) ).
fof(fact_114_Pair__inject,axiom,
! [A_1,B,A_3,B_2] :
( produc899768717on_val(A_1,B) = produc899768717on_val(A_3,B_2)
=> ~ ( A_1 = A_3
=> B != B_2 ) ) ).
fof(fact_115_Pair__inject,axiom,
! [A_1,B,A_3,B_2] :
( produc1441475159on_val(A_1,B) = produc1441475159on_val(A_3,B_2)
=> ~ ( A_1 = A_3
=> B != B_2 ) ) ).
fof(fact_116_Pair__inject,axiom,
! [A_1,B,A_3,B_2] :
( produc1259058957on_val(A_1,B) = produc1259058957on_val(A_3,B_2)
=> ~ ( A_1 = A_3
=> B != B_2 ) ) ).
fof(fact_117_Pair__inject,axiom,
! [A_1,B,A_3,B_2] :
( produc823076510on_val(A_1,B) = produc823076510on_val(A_3,B_2)
=> ~ ( A_1 = A_3
=> B != B_2 ) ) ).
fof(fact_118_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc921874948t_char(A_1,B) = produc921874948t_char(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_119_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc1909267824t_char(A_1,B) = produc1909267824t_char(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_120_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc1916172923t_char(A_1,B) = produc1916172923t_char(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_121_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc899768717on_val(A_1,B) = produc899768717on_val(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_122_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc1441475159on_val(A_1,B) = produc1441475159on_val(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_123_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc1259058957on_val(A_1,B) = produc1259058957on_val(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_124_Pair__eq,axiom,
! [A_1,B,A_3,B_2] :
( produc823076510on_val(A_1,B) = produc823076510on_val(A_3,B_2)
<=> ( A_1 = A_3
& B = B_2 ) ) ).
fof(fact_125_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,B_1))) ) ).
fof(fact_126_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,B_1))) ) ).
fof(fact_127_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A,B_1))) ) ).
fof(fact_128_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A,B_1))) ) ).
fof(fact_129_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,B_1))) ) ).
fof(fact_130_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,B_1))) ) ).
fof(fact_131_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
<=> ! [A,B_1] : hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A,B_1))) ) ).
fof(fact_132_neq__if__length__neq,axiom,
! [Xs_2,Ys_2] :
( size_s1050794909ion_ty(Xs_2) != size_s1050794909ion_ty(Ys_2)
=> Xs_2 != Ys_2 ) ).
fof(fact_133_neq__if__length__neq,axiom,
! [Xs_2,Ys_2] :
( size_s2113983095t_char(Xs_2) != size_s2113983095t_char(Ys_2)
=> Xs_2 != Ys_2 ) ).
fof(fact_134_neq__if__length__neq,axiom,
! [Xs_2,Ys_2] :
( size_size_list_ty(Xs_2) != size_size_list_ty(Ys_2)
=> Xs_2 != Ys_2 ) ).
fof(fact_135_neq__if__length__neq,axiom,
! [Xs_2,Ys_2] :
( size_size_list_val(Xs_2) != size_size_list_val(Ys_2)
=> Xs_2 != Ys_2 ) ).
fof(fact_136_neq__if__length__neq,axiom,
! [Xs_2,Ys_2] :
( size_s1143674878t_char(Xs_2) != size_s1143674878t_char(Ys_2)
=> Xs_2 != Ys_2 ) ).
fof(fact_137_list__all2__eq,axiom,
! [Xs,Ys] :
( Xs = Ys
<=> hBOOL(list_all2_ty_ty(fequal_ty,Xs,Ys)) ) ).
fof(fact_138_widen__trans,axiom,
! [T_3,P_2,S_2,U] :
( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_2),U))
=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),U),T_3))
=> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_2),T_3)) ) ) ).
fof(fact_139_prod__cases3,axiom,
! [Y_4] :
~ ! [A,B_1,C_3] : Y_4 != produc921874948t_char(A,produc1909267824t_char(B_1,C_3)) ).
fof(fact_140_prod__cases3,axiom,
! [Y_4] :
~ ! [A,B_1,C_3] : Y_4 != produc1909267824t_char(A,produc1916172923t_char(B_1,C_3)) ).
fof(fact_141_prod__cases3,axiom,
! [Y_3] :
~ ! [A,B_1,C_3] : Y_3 != produc1441475159on_val(A,produc1259058957on_val(B_1,C_3)) ).
fof(fact_142_prod__cases3,axiom,
! [Y_3] :
~ ! [A,B_1,C_3] : Y_3 != produc1259058957on_val(A,produc899768717on_val(B_1,C_3)) ).
fof(fact_143_prod__induct3,axiom,
! [X_1,Pa] :
( ! [A,B_1,C_3] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,produc1909267824t_char(B_1,C_3))))
=> hBOOL(hAPP_P92196306r_bool(Pa,X_1)) ) ).
fof(fact_144_prod__induct3,axiom,
! [X_1,Pa] :
( ! [A,B_1,C_3] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,produc1916172923t_char(B_1,C_3))))
=> hBOOL(hAPP_P1907982426r_bool(Pa,X_1)) ) ).
fof(fact_145_prod__induct3,axiom,
! [X_1,Pa] :
( ! [A,B_1,C_3] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,produc1259058957on_val(B_1,C_3))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
fof(fact_146_prod__induct3,axiom,
! [X_1,Pa] :
( ! [A,B_1,C_3] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,produc899768717on_val(B_1,C_3))))
=> hBOOL(hAPP_P1708370145l_bool(Pa,X_1)) ) ).
fof(fact_147_confs__conv__map,axiom,
! [Pa,Ha,Vsa_1,Ts_1] :
( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Ts_1))
<=> ? [Ts_2] :
( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts_2)
& hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts_1)) ) ) ).
fof(fact_148_list__all2__mono,axiom,
! [Q,Pa,Xs,Ys] :
( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
=> ( ! [Xs_1,Ys_1] :
( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,Xs_1),Ys_1))
=> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Xs_1),Ys_1)) )
=> hBOOL(list_all2_ty_ty(Q,Xs,Ys)) ) ) ).
fof(fact_149_list__all2__mono,axiom,
! [Q,Pa,Xs,Ys] :
( hBOOL(list_all2_val_ty(Pa,Xs,Ys))
=> ( ! [Xs_1,Ys_1] :
( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,Xs_1),Ys_1))
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Q,Xs_1),Ys_1)) )
=> hBOOL(list_all2_val_ty(Q,Xs,Ys)) ) ) ).
fof(fact_150_list__all2__refl,axiom,
! [Xs,Pa] :
( ! [X_2] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),X_2))
=> hBOOL(list_all2_ty_ty(Pa,Xs,Xs)) ) ).
fof(fact_151_list__all2__antisym,axiom,
! [Xs,Ys,Q,Pa] :
( ! [X_2,Y_1] :
( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),Y_1))
=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Y_1),X_2))
=> X_2 = Y_1 ) )
=> ( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
=> ( hBOOL(list_all2_ty_ty(Q,Ys,Xs))
=> Xs = Ys ) ) ) ).
fof(fact_152_Ex__list__of__length,axiom,
! [N_1] :
? [Xs_1] : size_s1050794909ion_ty(Xs_1) = N_1 ).
fof(fact_153_Ex__list__of__length,axiom,
! [N_1] :
? [Xs_1] : size_s1143674878t_char(Xs_1) = N_1 ).
fof(fact_154_Ex__list__of__length,axiom,
! [N_1] :
? [Xs_1] : size_size_list_val(Xs_1) = N_1 ).
fof(fact_155_Ex__list__of__length,axiom,
! [N_1] :
? [Xs_1] : size_size_list_ty(Xs_1) = N_1 ).
fof(fact_156_Ex__list__of__length,axiom,
! [N_1] :
? [Xs_1] : size_s2113983095t_char(Xs_1) = N_1 ).
fof(fact_157_conf__widen,axiom,
! [T_2,Pa,Ha,V_1,Ta] :
( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta))
=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T_2))
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),T_2)) ) ) ).
fof(fact_158_typeof__conf,axiom,
! [Pa,Ha,V_1,Ta] :
( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta)
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta)) ) ).
fof(fact_159_confs__widens,axiom,
! [Ts_1,Pa,Ha,Vsa_1,Tsa] :
( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Tsa))
=> ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Ts_1))
=> hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Ts_1)) ) ) ).
fof(fact_160_conf__def,axiom,
! [Pa,Ha,V_1,Ta] :
( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta))
<=> ? [T_1] :
( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_1)
& hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),Ta)) ) ) ).
fof(fact_161_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A,B_1))) ) ).
fof(fact_162_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,B_1))) ) ).
fof(fact_163_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,B_1))) ) ).
fof(fact_164_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A,B_1))) ) ).
fof(fact_165_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A,B_1))) ) ).
fof(fact_166_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,B_1))) ) ).
fof(fact_167_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
<=> ? [A,B_1] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,B_1))) ) ).
fof(fact_168_PairE,axiom,
! [P] :
~ ! [X_2,Y_1] : P != produc823076510on_val(X_2,Y_1) ).
fof(fact_169_PairE,axiom,
! [P] :
~ ! [X_2,Y_1] : P != produc1259058957on_val(X_2,Y_1) ).
fof(fact_170_PairE,axiom,
! [P] :
~ ! [X_2,Y_1] : P != produc1441475159on_val(X_2,Y_1) ).
fof(fact_171_PairE,axiom,
! [P] :
~ ! [X_2,Y_1] : P != produc899768717on_val(X_2,Y_1) ).
fof(fact_172_PairE,axiom,
! [P_1] :
~ ! [X_2,Y_1] : P_1 != produc1916172923t_char(X_2,Y_1) ).
fof(fact_173_PairE,axiom,
! [P_1] :
~ ! [X_2,Y_1] : P_1 != produc1909267824t_char(X_2,Y_1) ).
fof(fact_174_PairE,axiom,
! [P_1] :
~ ! [X_2,Y_1] : P_1 != produc921874948t_char(X_2,Y_1) ).
fof(fact_175_prod_Oexhaust,axiom,
! [Y_3] :
~ ! [A,B_1] : Y_3 != produc823076510on_val(A,B_1) ).
fof(fact_176_prod_Oexhaust,axiom,
! [Y_3] :
~ ! [A,B_1] : Y_3 != produc1259058957on_val(A,B_1) ).
fof(fact_177_prod_Oexhaust,axiom,
! [Y_3] :
~ ! [A,B_1] : Y_3 != produc1441475159on_val(A,B_1) ).
fof(fact_178_prod_Oexhaust,axiom,
! [Y_3] :
~ ! [A,B_1] : Y_3 != produc899768717on_val(A,B_1) ).
fof(fact_179_prod_Oexhaust,axiom,
! [Y_2] :
~ ! [A,B_1] : Y_2 != produc1916172923t_char(A,B_1) ).
fof(fact_180_prod_Oexhaust,axiom,
! [Y_2] :
~ ! [A,B_1] : Y_2 != produc1909267824t_char(A,B_1) ).
fof(fact_181_prod_Oexhaust,axiom,
! [Y_2] :
~ ! [A,B_1] : Y_2 != produc921874948t_char(A,B_1) ).
fof(fact_182_confs__hext,axiom,
! [H,Pa,Ha,Vsa_1,Tsa] :
( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Tsa))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,H),Vsa_1,Tsa)) ) ) ).
fof(fact_183_blocksEval,axiom,
! [Pa,Ea,Ha,L_1,E,H,L,Vsa_1,Ps,Tsa] :
( size_s2113983095t_char(Ps) = size_size_list_ty(Tsa)
=> ( size_s2113983095t_char(Ps) = size_size_list_val(Vsa_1)
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,blocks(produc921874948t_char(Ps,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),E),produc899768717on_val(H,L)))
=> ? [L_3] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Ps,Vsa_1))),E),produc899768717on_val(H,L_3))) ) ) ) ).
fof(fact_184_conf__hext,axiom,
! [Pa,V_1,Ta,Ha,H] :
( hBOOL(hext(Ha,H))
=> ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta))
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,H),V_1),Ta)) ) ) ).
fof(fact_185_hext__typeof__mono,axiom,
! [V_1,Ta,Ha,H] :
( hBOOL(hext(Ha,H))
=> ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta)
=> hAPP_val_option_ty(typeof_h(H),V_1) = hAPP_ty_option_ty(some_ty,Ta) ) ) ).
fof(fact_186_eval__hext,axiom,
! [Pa,Ea,Ha,L_1,E,H,L] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,L_1)),E),produc899768717on_val(H,L)))
=> hBOOL(hext(Ha,H)) ) ).
fof(fact_187_hext__refl,axiom,
! [Ha] : hBOOL(hext(Ha,Ha)) ).
fof(fact_188_WTrt__hext__mono,axiom,
! [H,Pa,Ha,E_1,Ea,Ta] :
( hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(wTrt(Pa,H,E_1,Ea,Ta)) ) ) ).
fof(fact_189_hext__trans,axiom,
! [H_1,Ha,H] :
( hBOOL(hext(Ha,H))
=> ( hBOOL(hext(H,H_1))
=> hBOOL(hext(Ha,H_1)) ) ) ).
fof(fact_190_WTrtVal,axiom,
! [Pa,E_1,Ha,V_1,Ta] :
( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta)
=> hBOOL(wTrt(Pa,Ha,E_1,hAPP_v834067052t_char(val_list_char,V_1),Ta)) ) ).
fof(fact_191_blocksFinal,axiom,
! [Ha,L_1,Pa,Ea,Vsa_1,Vsa,Tsa] :
( size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa)
=> ( size_size_list_val(Vsa_1) = size_size_list_ty(Tsa)
=> ( hBOOL(final_list_char(Ea))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).
fof(fact_192_WTrts__Val,axiom,
! [Pa,Ha,E_1,Vsa_1,Tsa] :
( hBOOL(wTrts(Pa,Ha,E_1,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa_1),Tsa))
<=> hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Tsa) ) ).
fof(fact_193_option_Oinject,axiom,
! [A_1,A_3] :
( hAPP_val_option_val(some_val,A_1) = hAPP_val_option_val(some_val,A_3)
<=> A_1 = A_3 ) ).
fof(fact_194_option_Oinject,axiom,
! [A_1,A_3] :
( hAPP_P1510515380on_val(some_P948696889on_val,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,A_3)
<=> A_1 = A_3 ) ).
fof(fact_195_option_Oinject,axiom,
! [A_1,A_3] :
( hAPP_ty_option_ty(some_ty,A_1) = hAPP_ty_option_ty(some_ty,A_3)
<=> A_1 = A_3 ) ).
fof(fact_196_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B)))
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B)) ) ).
fof(fact_197_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B)))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B)) ) ).
fof(fact_198_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B)))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B)) ) ).
fof(fact_199_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B)))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B)) ) ).
fof(fact_200_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B)))
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B)) ) ).
fof(fact_201_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B)))
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B)) ) ).
fof(fact_202_curryI,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B)))
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B)) ) ).
fof(fact_203_Val,axiom,
! [Pa,V_1,S_1] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1)) ).
fof(fact_204_eval__cases_I2_J,axiom,
! [Pa,V_1,S_1,E,S] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),E),S))
=> ~ ( E = hAPP_v834067052t_char(val_list_char,V_1)
=> S != S_1 ) ) ).
fof(fact_205_WTrts__hext__mono,axiom,
! [H,Pa,Ha,E_1,Es,Tsa] :
( hBOOL(wTrts(Pa,Ha,E_1,Es,Tsa))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(wTrts(Pa,H,E_1,Es,Tsa)) ) ) ).
fof(fact_206_WTrts__same__length,axiom,
! [Pa,Ha,E_1,Es,Tsa] :
( hBOOL(wTrts(Pa,Ha,E_1,Es,Tsa))
=> size_s1143674878t_char(Es) = size_size_list_ty(Tsa) ) ).
fof(fact_207_eval__final,axiom,
! [Pa,Ea,S_1,E,S] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S))
=> hBOOL(final_list_char(E)) ) ).
fof(fact_208_eval__finalId,axiom,
! [Pa,S_1,Ea] :
( hBOOL(final_list_char(Ea))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),Ea),S_1)) ) ).
fof(fact_209_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B))
=> hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))) ) ).
fof(fact_210_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B))
=> hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))) ) ).
fof(fact_211_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B))
=> hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))) ) ).
fof(fact_212_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B))
=> hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))) ) ).
fof(fact_213_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B))
=> hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))) ) ).
fof(fact_214_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B))
=> hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))) ) ).
fof(fact_215_curryE,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B))
=> hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))) ) ).
fof(fact_216_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B))
=> hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))) ) ).
fof(fact_217_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B))
=> hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))) ) ).
fof(fact_218_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B))
=> hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))) ) ).
fof(fact_219_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B))
=> hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))) ) ).
fof(fact_220_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B))
=> hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))) ) ).
fof(fact_221_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B))
=> hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))) ) ).
fof(fact_222_curryD,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B))
=> hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))) ) ).
fof(fact_223_red__hext__incr,axiom,
! [Ea,Ha,L_1,E,H,L,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> hBOOL(hext(Ha,H)) ) ).
fof(fact_224_rtrancl_Ortrancl__refl,axiom,
! [A_1,R] : hBOOL(member773094996on_val(produc1441475159on_val(A_1,A_1),transi2024712006on_val(R))) ).
fof(fact_225_r__into__rtrancl,axiom,
! [P,R] :
( hBOOL(member773094996on_val(P,R))
=> hBOOL(member773094996on_val(P,transi2024712006on_val(R))) ) ).
fof(fact_226_red__preserves__hconf,axiom,
! [E_1,Ta,Ea,Ha,L_1,E,H,L,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta))
=> ( hBOOL(hconf_97414254t_char(Pa,Ha))
=> hBOOL(hconf_97414254t_char(Pa,H)) ) ) ) ).
fof(fact_227_rtrancl__idemp,axiom,
! [R] : transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R) ).
fof(fact_228_converse__rtrancl__into__rtrancl,axiom,
! [C_2,A_1,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R))) ) ) ).
fof(fact_229_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_2,A_1,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),R))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R))) ) ) ).
fof(fact_230_rtrancl__trans,axiom,
! [C_2,A_1,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R))) ) ) ).
fof(fact_231_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A,B_1)),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_232_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R)))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(A,B_1)),transi61620055on_val(R)))
=> ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A),B_1))
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_233_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A,B_1)),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_234_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A,B_1)),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A),B_1))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_235_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R)))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(A,B_1)),transi1789604888t_char(R)))
=> ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Aa,Ba)),R))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A),B_1))
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_236_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R)))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(A,B_1)),transi1257872013t_char(R)))
=> ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Aa,Ba)),R))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A),B_1))
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_237_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R)))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(A,B_1)),transi122195895t_char(R)))
=> ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Aa,Ba)),R))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A),B_1))
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_238_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Aa,Ba),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_239_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R)))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Aa,Ba)),R))
=> ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Aa,Ba),produc823076510on_val(Bx,By)),transi61620055on_val(R)))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_240_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Aa,Ba),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_241_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Aa,Ba),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_242_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R)))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Aa,Ba)),R))
=> ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Aa,Ba),produc1916172923t_char(Bx,By)),transi1789604888t_char(R)))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_243_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R)))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Aa,Ba)),R))
=> ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Aa,Ba),produc1909267824t_char(Bx,By)),transi1257872013t_char(R)))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_244_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R)))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By))
=> ( ! [A,B_1,Aa,Ba] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Aa,Ba)),R))
=> ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Aa,Ba),produc921874948t_char(Bx,By)),transi122195895t_char(R)))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_245_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R)))
=> ( produc1259058957on_val(Xa_1,Xb) != produc1259058957on_val(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb),produc1259058957on_val(A,B_1)),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R))) ) ) ) ).
fof(fact_246_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb),produc823076510on_val(Za,Zb)),transi61620055on_val(R)))
=> ( produc823076510on_val(Xa_1,Xb) != produc823076510on_val(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb),produc823076510on_val(A,B_1)),R))
=> ~ hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Za,Zb)),transi61620055on_val(R))) ) ) ) ).
fof(fact_247_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb),produc1441475159on_val(Za,Zb)),transi910771962on_val(R)))
=> ( produc1441475159on_val(Xa_1,Xb) != produc1441475159on_val(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb),produc1441475159on_val(A,B_1)),R))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R))) ) ) ) ).
fof(fact_248_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb),produc899768717on_val(Za,Zb)),transi921647814on_val(R)))
=> ( produc899768717on_val(Xa_1,Xb) != produc899768717on_val(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb),produc899768717on_val(A,B_1)),R))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R))) ) ) ) ).
fof(fact_249_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R)))
=> ( produc1916172923t_char(Xa_1,Xb) != produc1916172923t_char(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb),produc1916172923t_char(A,B_1)),R))
=> ~ hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R))) ) ) ) ).
fof(fact_250_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R)))
=> ( produc1909267824t_char(Xa_1,Xb) != produc1909267824t_char(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb),produc1909267824t_char(A,B_1)),R))
=> ~ hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R))) ) ) ) ).
fof(fact_251_converse__rtranclE2,axiom,
! [Xa_1,Xb,Za,Zb,R] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb),produc921874948t_char(Za,Zb)),transi122195895t_char(R)))
=> ( produc921874948t_char(Xa_1,Xb) != produc921874948t_char(Za,Zb)
=> ~ ! [A,B_1] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb),produc921874948t_char(A,B_1)),R))
=> ~ hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Za,Zb)),transi122195895t_char(R))) ) ) ) ).
fof(fact_252_rtranclE,axiom,
! [A_1,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( A_1 != B
=> ~ ! [Y_1] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,Y_1),transi2024712006on_val(R)))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y_1,B),R)) ) ) ) ).
fof(fact_253_converse__rtranclE,axiom,
! [X_1,Z_1,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(X_1,Z_1),transi2024712006on_val(R)))
=> ( X_1 != Z_1
=> ~ ! [Y_1] :
( hBOOL(member773094996on_val(produc1441475159on_val(X_1,Y_1),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z_1),transi2024712006on_val(R))) ) ) ) ).
fof(fact_254_converse__rtrancl__induct,axiom,
! [Pa,A_1,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
=> ( ! [Y_1,Z] :
( hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,A_1)) ) ) ) ).
fof(fact_255_rtrancl__induct,axiom,
! [Pa,A_1,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,A_1))
=> ( ! [Y_1,Z] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,Y_1),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z),R))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Y_1))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).
fof(fact_256_red__preserves__lconf,axiom,
! [E_1,Ta,Ea,Ha,L_1,E,H,L,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta))
=> ( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1))
=> hBOOL(lconf_496643946t_char(Pa,H,L,E_1)) ) ) ) ).
fof(fact_257_blocksRedsFinal,axiom,
! [L_2,Ea,Ha,L_1,E,H,L,Pa,Vsa_1,Vsa,Tsa] :
( size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa)
=> ( size_size_list_val(Vsa_1) = size_size_list_ty(Tsa)
=> ( hBOOL(distinct_list_char(Vsa))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Vsa,Vsa_1))),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa))))
=> ( hBOOL(final_list_char(E))
=> ( L_2 = overri2012515291on_val(L,L_1,set_list_char(Vsa))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ).
fof(fact_258_map__eq__conv,axiom,
! [F,Xs,G] :
( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs)
<=> ! [X_2] :
( hBOOL(member_list_char(X_2,set_list_char(Xs)))
=> hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2) ) ) ).
fof(fact_259_map__eq__conv,axiom,
! [F,Xs,G] :
( hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs)
<=> ! [X_2] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2) ) ) ).
fof(fact_260_map__eq__conv,axiom,
! [F,Xs,G] :
( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs)
<=> ! [X_2] :
( hBOOL(member_ty(X_2,set_ty(Xs)))
=> hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2) ) ) ).
fof(fact_261_map__eq__conv,axiom,
! [F,Xs,G] :
( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs)
<=> ! [X_2] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2) ) ) ).
fof(fact_262_mem__def,axiom,
! [X_1,A_2] :
( hBOOL(member773094996on_val(X_1,A_2))
<=> hBOOL(hAPP_P282169671l_bool(A_2,X_1)) ) ).
fof(fact_263_lconf__hext,axiom,
! [H,Pa,Ha,L_1,E_1] :
( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(lconf_496643946t_char(Pa,H,L_1,E_1)) ) ) ).
fof(fact_264_lconf__def,axiom,
! [Pa,Ha,L_1,E_1] :
( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1))
<=> ! [V_3,V_2] :
( hAPP_l207779698on_val(L_1,V_3) = hAPP_val_option_val(some_val,V_2)
=> ? [T] :
( hAPP_l512744617ion_ty(E_1,V_3) = hAPP_ty_option_ty(some_ty,T)
& hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),T)) ) ) ) ).
fof(fact_265_blocksReds,axiom,
! [Ea,Ha,L_1,E,H,L,Pa,Vsa_1,Vsa,Tsa] :
( size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa)
=> ( size_size_list_val(Vsa_1) = size_size_list_ty(Tsa)
=> ( hBOOL(distinct_list_char(Vsa))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Vsa,Vsa_1))),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(the_val,L)),Vsa),E)))),produc899768717on_val(H,overri2012515291on_val(L,L_1,set_list_char(Vsa))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ).
fof(fact_266_List_Omap_Ocomp,axiom,
! [F,G] : comp_l1825390573t_char(map_option_val_val(F),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F,G)) ).
fof(fact_267_map__comp__map,axiom,
! [F,G] : comp_l1825390573t_char(map_option_val_val(F),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F,G)) ).
fof(fact_268_map__map,axiom,
! [F,G,Xs] : hAPP_l228474410st_val(map_option_val_val(F),hAPP_l297961988on_val(map_li50976719on_val(G),Xs)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F,G)),Xs) ).
fof(fact_269_List_Omap_Ocompositionality,axiom,
! [F,G,List] : hAPP_l228474410st_val(map_option_val_val(F),hAPP_l297961988on_val(map_li50976719on_val(G),List)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F,G)),List) ).
fof(fact_270_the_Osimps,axiom,
! [X_3] : hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_3)) = X_3 ).
fof(fact_271_the_Osimps,axiom,
! [X_1] : hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_1)) = X_1 ).
fof(fact_272_the_Osimps,axiom,
! [X_3] : hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_3)) = X_3 ).
fof(fact_273_ex__map__conv,axiom,
! [Ys,F] :
( ? [Xs_1] : Ys = hAPP_l1892737211st_val(map_list_char_val(F),Xs_1)
<=> ! [X_2] :
( hBOOL(member_val(X_2,set_val(Ys)))
=> ? [Xa] : X_2 = hAPP_list_char_val(F,Xa) ) ) ).
fof(fact_274_ex__map__conv,axiom,
! [Ys,F] :
( ? [Xs_1] : Ys = hAPP_l732421366t_char(map_va1934808527t_char(F),Xs_1)
<=> ! [X_2] :
( hBOOL(member_exp_list_char(X_2,set_exp_list_char(Ys)))
=> ? [Xa] : X_2 = hAPP_v834067052t_char(F,Xa) ) ) ).
fof(fact_275_ex__map__conv,axiom,
! [Ys,F] :
( ? [Xs_1] : Ys = hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs_1)
<=> ! [X_2] :
( hBOOL(member_option_ty(X_2,set_option_ty(Ys)))
=> ? [Xa] : X_2 = hAPP_ty_option_ty(F,Xa) ) ) ).
fof(fact_276_ex__map__conv,axiom,
! [Ys,F] :
( ? [Xs_1] : Ys = hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs_1)
<=> ! [X_2] :
( hBOOL(member_option_ty(X_2,set_option_ty(Ys)))
=> ? [Xa] : X_2 = hAPP_val_option_ty(F,Xa) ) ) ).
fof(fact_277_map__ext,axiom,
! [F,G,Xs] :
( ! [X_2] :
( hBOOL(member_list_char(X_2,set_list_char(Xs)))
=> hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2) )
=> hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) ) ).
fof(fact_278_map__ext,axiom,
! [F,G,Xs] :
( ! [X_2] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2) )
=> hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) ) ).
fof(fact_279_map__ext,axiom,
! [F,G,Xs] :
( ! [X_2] :
( hBOOL(member_ty(X_2,set_ty(Xs)))
=> hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2) )
=> hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) ) ).
fof(fact_280_map__ext,axiom,
! [F,G,Xs] :
( ! [X_2] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2) )
=> hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) ) ).
fof(fact_281_map__cong,axiom,
! [F,G,Xs,Ys] :
( Xs = Ys
=> ( ! [X_2] :
( hBOOL(member_list_char(X_2,set_list_char(Ys)))
=> hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2) )
=> hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) ) ) ).
fof(fact_282_map__cong,axiom,
! [F,G,Xs,Ys] :
( Xs = Ys
=> ( ! [X_2] :
( hBOOL(member_val(X_2,set_val(Ys)))
=> hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2) )
=> hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) ) ) ).
fof(fact_283_map__cong,axiom,
! [F,G,Xs,Ys] :
( Xs = Ys
=> ( ! [X_2] :
( hBOOL(member_ty(X_2,set_ty(Ys)))
=> hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2) )
=> hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) ) ) ).
fof(fact_284_map__cong,axiom,
! [F,G,Xs,Ys] :
( Xs = Ys
=> ( ! [X_2] :
( hBOOL(member_val(X_2,set_val(Ys)))
=> hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2) )
=> hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) ) ) ).
fof(fact_285_map__idI,axiom,
! [F,Xs] :
( ! [X_2] :
( hBOOL(member_list_char(X_2,set_list_char(Xs)))
=> hAPP_l1074208899t_char(F,X_2) = X_2 )
=> hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = Xs ) ).
fof(fact_286_map__idI,axiom,
! [F,Xs] :
( ! [X_2] :
( hBOOL(member773094996on_val(X_2,set_Pr1921835862on_val(Xs)))
=> hAPP_P918220497on_val(F,X_2) = X_2 )
=> hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = Xs ) ).
fof(fact_287_map__upds__apply__nontin,axiom,
! [F,Ys,X_1,Xs] :
( ~ hBOOL(member_list_char(X_1,set_list_char(Xs)))
=> hAPP_l207779698on_val(map_up1085636310ar_val(F,Xs,Ys),X_1) = hAPP_l207779698on_val(F,X_1) ) ).
fof(fact_288_map__upds__apply__nontin,axiom,
! [F,Ys,X_1,Xs] :
( ~ hBOOL(member_list_char(X_1,set_list_char(Xs)))
=> hAPP_l512744617ion_ty(map_up891053837har_ty(F,Xs,Ys),X_1) = hAPP_l512744617ion_ty(F,X_1) ) ).
fof(fact_289_Red__lcl__add,axiom,
! [L_0,Ea,Ha,L_1,E,H,L,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,L_1))),produc1259058957on_val(E,produc899768717on_val(H,map_ad325961431ar_val(L_0,L)))),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_290_map__add__find__right,axiom,
! [M,N,K,Xx] :
( hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,Xx)
=> hAPP_l207779698on_val(map_ad325961431ar_val(M,N),K) = hAPP_val_option_val(some_val,Xx) ) ).
fof(fact_291_map__add__assoc,axiom,
! [M1,M2,M3] : map_ad325961431ar_val(M1,map_ad325961431ar_val(M2,M3)) = map_ad325961431ar_val(map_ad325961431ar_val(M1,M2),M3) ).
fof(fact_292_map__add__upds,axiom,
! [M1,M2,Xs,Ys] : map_ad325961431ar_val(M1,map_up1085636310ar_val(M2,Xs,Ys)) = map_up1085636310ar_val(map_ad325961431ar_val(M1,M2),Xs,Ys) ).
fof(fact_293_map__add__upds,axiom,
! [M1,M2,Xs,Ys] : map_add_list_char_ty(M1,map_up891053837har_ty(M2,Xs,Ys)) = map_up891053837har_ty(map_add_list_char_ty(M1,M2),Xs,Ys) ).
fof(fact_294_red__lcl__add,axiom,
! [L_0,Ea,Ha,L_1,E,H,L,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,L_1))),produc1259058957on_val(E,produc899768717on_val(H,map_ad325961431ar_val(L_0,L)))),red(Pa))) ) ).
fof(fact_295_hext__def,axiom,
! [Ha,H] :
( hBOOL(hext(Ha,H))
<=> ! [A,C_1,Fs] :
( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs))
=> ? [Fs_1] : hAPP_n546249108on_val(H,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs_1)) ) ) ).
fof(fact_296_hext__objD,axiom,
! [A_1,C,Fs_2,Ha,H] :
( hBOOL(hext(Ha,H))
=> ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_2))
=> ? [Fs_1] : hAPP_n546249108on_val(H,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_1)) ) ) ).
fof(fact_297_hextI,axiom,
! [H,Ha] :
( ! [A,C_1,Fs] :
( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs))
=> ? [Fs_1] : hAPP_n546249108on_val(H,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs_1)) )
=> hBOOL(hext(Ha,H)) ) ).
fof(fact_298_TryRedsVal,axiom,
! [C,V,E_2,Ea,S_1,V_1,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(Ea,C,V),E_2),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_299_red__reds_OTryRed,axiom,
! [C,V,E_2,Ea,S_1,E,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(Ea,C,V),E_2),S_1),produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(E,C,V),E_2),S)),red(Pa))) ) ).
%----Helper facts (2)
fof(help_fequal_1_1_fequal_000tc__Type__Oty_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Type__Oty_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y)) ) ).
%----Conjectures (3)
fof(conj_0,hypothesis,
size_s2113983095t_char(vs_1) = size_size_list_ty(ts) ).
fof(conj_1,hypothesis,
size_size_list_val(vs) = size_size_list_ty(ts) ).
fof(conj_2,conjecture,
( hBOOL(wTrt(p,h,e_1,blocks(produc921874948t_char(vs_1,produc1909267824t_char(ts,produc1916172923t_char(vs,e)))),t))
<=> ( hBOOL(wTrt(p,h,map_up891053837har_ty(e_1,vs_1,ts),e,t))
& ? [Ts] :
( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(h)),vs) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts)
& hBOOL(list_all2_ty_ty(widen_2090681816t_char(p),Ts,ts)) ) ) ) ).
%------------------------------------------------------------------------------