TPTP Problem File: SWW478+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW478+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 479, 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_l479 [Bla11]
% Status : Theorem
% Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0
% Syntax : Number of formulae : 213 ( 92 unt; 0 def)
% Number of atoms : 410 ( 181 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 276 ( 79 ~; 6 |; 19 &)
% ( 48 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 196 ( 196 usr; 62 con; 0-5 aty)
% Number of variables : 781 ( 771 !; 10 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 16:05:57
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (14)
fof(gsy_c_SmallStep_Oassigned,axiom,
! [B_1_1,B_2_1] : is_bool(assigned(B_1_1,B_2_1)) ).
fof(gsy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,axiom,
! [B_1_1,B_2_1,B_3] : is_bool(widen_2090681816t_char(B_1_1,B_2_1,B_3)) ).
fof(gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,axiom,
! [B_1_1,B_2_1] : is_bool(wf_pro755087577t_char(B_1_1,B_2_1)) ).
fof(gsy_c_WellTypeRT_OWTrt,axiom,
! [B_1_1,B_2_1,B_3,B_4,B_5] : is_bool(wTrt(B_1_1,B_2_1,B_3,B_4,B_5)) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_bool(hAPP_bool_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_f1001225811y_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_001,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__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f61040418l_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__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__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,axiom,
! [B_1_1,B_2_1] : is_bool(member840932460on_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,axiom,
! [B_1_1,B_2_1] : is_bool(member763590124on_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,hypothesis,
! [B_1_1,B_2_1] : is_bool(member773094996on_val(B_1_1,B_2_1)) ).
%----Relevant facts (167)
fof(fact_0_InitBlockRed_I3_J,axiom,
hAPP_l207779698on_val(l_a,v_1) = some_val(v_2) ).
fof(fact_1_InitBlockRed_I1_J,axiom,
hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) ).
fof(fact_2_fun__upd__triv,axiom,
! [F,X_1] : fun_up1149430426on_val(F,X_1,hAPP_l207779698on_val(F,X_1)) = F ).
fof(fact_3_fun__upd__triv,axiom,
! [F,X_1] : fun_up424764369ion_ty(F,X_1,hAPP_l512744617ion_ty(F,X_1)) = F ).
fof(fact_4_assms,axiom,
hBOOL(wf_pro755087577t_char(wf_J_mdecl,p)) ).
fof(fact_5_map__upd__Some__unfold,axiom,
! [M,A_10,B_1,X_1,Y_1] :
( hAPP_l207779698on_val(fun_up1149430426on_val(M,A_10,some_val(B_1)),X_1) = some_val(Y_1)
<=> ( ( X_1 = A_10
& B_1 = Y_1 )
| ( X_1 != A_10
& hAPP_l207779698on_val(M,X_1) = some_val(Y_1) ) ) ) ).
fof(fact_6_map__upd__Some__unfold,axiom,
! [M,A_10,B_1,X_1,Y_1] :
( hAPP_l512744617ion_ty(fun_up424764369ion_ty(M,A_10,some_ty(B_1)),X_1) = some_ty(Y_1)
<=> ( ( X_1 = A_10
& B_1 = Y_1 )
| ( X_1 != A_10
& hAPP_l512744617ion_ty(M,X_1) = some_ty(Y_1) ) ) ) ).
fof(fact_7_map__upd__triv,axiom,
! [T,K,X_1] :
( hAPP_l207779698on_val(T,K) = some_val(X_1)
=> fun_up1149430426on_val(T,K,some_val(X_1)) = T ) ).
fof(fact_8_map__upd__triv,axiom,
! [T,K,X_1] :
( hAPP_l512744617ion_ty(T,K) = some_ty(X_1)
=> fun_up424764369ion_ty(T,K,some_ty(X_1)) = T ) ).
fof(fact_9_map__upd__eqD1,axiom,
! [M,A_10,X_1,N,Y_1] :
( fun_up1149430426on_val(M,A_10,some_val(X_1)) = fun_up1149430426on_val(N,A_10,some_val(Y_1))
=> X_1 = Y_1 ) ).
fof(fact_10_map__upd__eqD1,axiom,
! [M,A_10,X_1,N,Y_1] :
( fun_up424764369ion_ty(M,A_10,some_ty(X_1)) = fun_up424764369ion_ty(N,A_10,some_ty(Y_1))
=> X_1 = Y_1 ) ).
fof(fact_11_InitBlockRed_I2_J,axiom,
! [Ta,Ea] :
( hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v)))))
=> ( hBOOL(wTrt(p,ha,Ea,ea,Ta))
=> ? [T_5] :
( hBOOL(wTrt(p,h_a,Ea,e_a,T_5))
& hBOOL(widen_2090681816t_char(p,T_5,Ta)) ) ) ) ).
fof(fact_12_prod__induct4,axiom,
! [X_1,Pa] :
( ! [A_15,B,C_1,D_1] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_1),D_1)))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
fof(fact_13_prod__cases4,axiom,
! [Y_1] :
~ ! [A_15,B,C_1,D_1] : Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_1),D_1))) ).
fof(fact_14_InitBlockRed_I4_J,axiom,
hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,e),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la))) ).
fof(fact_15_Pair__inject,axiom,
! [A_10,B_1,A_9,B_2] :
( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_9),B_2)
=> ~ ( A_10 = A_9
=> B_1 != B_2 ) ) ).
fof(fact_16_Pair__inject,axiom,
! [A_10,B_1,A_9,B_2] :
( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_9),B_2)
=> ~ ( A_10 = A_9
=> B_1 != B_2 ) ) ).
fof(fact_17_Pair__inject,axiom,
! [A_10,B_1,A_9,B_2] :
( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_9),B_2)
=> ~ ( A_10 = A_9
=> B_1 != B_2 ) ) ).
fof(fact_18_Pair__eq,axiom,
! [A_10,B_1,A_9,B_2] :
( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_9),B_2)
<=> ( A_10 = A_9
& B_1 = B_2 ) ) ).
fof(fact_19_Pair__eq,axiom,
! [A_10,B_1,A_9,B_2] :
( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_9),B_2)
<=> ( A_10 = A_9
& B_1 = B_2 ) ) ).
fof(fact_20_Pair__eq,axiom,
! [A_10,B_1,A_9,B_2] :
( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_9),B_2)
<=> ( A_10 = A_9
& B_1 = B_2 ) ) ).
fof(fact_21_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ! [A_15,B] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B))) ) ).
fof(fact_22_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ! [A_15,B] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B))) ) ).
fof(fact_23_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ! [A_15,B] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B))) ) ).
fof(fact_24_fun__upd__def,axiom,
! [F,B_1,A_10,X] :
( ( X = A_10
=> hAPP_l207779698on_val(fun_up1149430426on_val(F,A_10,B_1),X) = B_1 )
& ( X != A_10
=> hAPP_l207779698on_val(fun_up1149430426on_val(F,A_10,B_1),X) = hAPP_l207779698on_val(F,X) ) ) ).
fof(fact_25_fun__upd__def,axiom,
! [F,B_1,A_10,X] :
( ( X = A_10
=> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,A_10,B_1),X) = B_1 )
& ( X != A_10
=> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,A_10,B_1),X) = hAPP_l512744617ion_ty(F,X) ) ) ).
fof(fact_26_fun__upd__idem,axiom,
! [F,X_1,Y_1] :
( hAPP_l207779698on_val(F,X_1) = Y_1
=> fun_up1149430426on_val(F,X_1,Y_1) = F ) ).
fof(fact_27_fun__upd__idem,axiom,
! [F,X_1,Y_1] :
( hAPP_l512744617ion_ty(F,X_1) = Y_1
=> fun_up424764369ion_ty(F,X_1,Y_1) = F ) ).
fof(fact_28_fun__upd__other,axiom,
! [F,Y_1,Z,X_1] :
( Z != X_1
=> hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = hAPP_l207779698on_val(F,Z) ) ).
fof(fact_29_fun__upd__other,axiom,
! [F,Y_1,Z,X_1] :
( Z != X_1
=> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = hAPP_l512744617ion_ty(F,Z) ) ).
fof(fact_30_fun__upd__twist,axiom,
! [M,B_1,D,A_10,C] :
( A_10 != C
=> fun_up1149430426on_val(fun_up1149430426on_val(M,A_10,B_1),C,D) = fun_up1149430426on_val(fun_up1149430426on_val(M,C,D),A_10,B_1) ) ).
fof(fact_31_fun__upd__twist,axiom,
! [M,B_1,D,A_10,C] :
( A_10 != C
=> fun_up424764369ion_ty(fun_up424764369ion_ty(M,A_10,B_1),C,D) = fun_up424764369ion_ty(fun_up424764369ion_ty(M,C,D),A_10,B_1) ) ).
fof(fact_32_fun__upd__apply,axiom,
! [F,Y_1,Z,X_1] :
( ( Z = X_1
=> hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = Y_1 )
& ( Z != X_1
=> hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = hAPP_l207779698on_val(F,Z) ) ) ).
fof(fact_33_fun__upd__apply,axiom,
! [F,Y_1,Z,X_1] :
( ( Z = X_1
=> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = Y_1 )
& ( Z != X_1
=> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = hAPP_l512744617ion_ty(F,Z) ) ) ).
fof(fact_34_fun__upd__same,axiom,
! [F,X_1,Y_1] : hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),X_1) = Y_1 ).
fof(fact_35_fun__upd__same,axiom,
! [F,X_1,Y_1] : hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),X_1) = Y_1 ).
fof(fact_36_fun__upd__upd,axiom,
! [F,X_1,Y_1,Z] : fun_up1149430426on_val(fun_up1149430426on_val(F,X_1,Y_1),X_1,Z) = fun_up1149430426on_val(F,X_1,Z) ).
fof(fact_37_fun__upd__upd,axiom,
! [F,X_1,Y_1,Z] : fun_up424764369ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),X_1,Z) = fun_up424764369ion_ty(F,X_1,Z) ).
fof(fact_38_fun__upd__idem__iff,axiom,
! [F,X_1,Y_1] :
( fun_up1149430426on_val(F,X_1,Y_1) = F
<=> hAPP_l207779698on_val(F,X_1) = Y_1 ) ).
fof(fact_39_fun__upd__idem__iff,axiom,
! [F,X_1,Y_1] :
( fun_up424764369ion_ty(F,X_1,Y_1) = F
<=> hAPP_l512744617ion_ty(F,X_1) = Y_1 ) ).
fof(fact_40_widen__refl,axiom,
! [P_3,T_4] : hBOOL(widen_2090681816t_char(P_3,T_4,T_4)) ).
fof(fact_41_red__preserves__hconf,axiom,
! [Ea,Ta,Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
=> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)) ) ) ) ).
fof(fact_42_red__preserves__lconf,axiom,
! [Ea,Ta,Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea))
=> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)) ) ) ) ).
fof(fact_43_prod__cases3,axiom,
! [Y_1] :
~ ! [A_15,B,C_1] : Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),C_1)) ).
fof(fact_44_prod__cases3,axiom,
! [Y_1] :
~ ! [A_15,B,C_1] : Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B),C_1)) ).
fof(fact_45_prod__induct3,axiom,
! [X_1,Pa] :
( ! [A_15,B,C_1] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),C_1))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
fof(fact_46_prod__induct3,axiom,
! [X_1,Pa] :
( ! [A_15,B,C_1] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B),C_1))))
=> hBOOL(hAPP_P1708370145l_bool(Pa,X_1)) ) ).
fof(fact_47_red__preserves__sconf,axiom,
! [Ea,Ta,Eb,S,E_b,S_1,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa)))
=> ( hBOOL(wTrt(Pa,hp(S),Ea,Eb,Ta))
=> ( hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S))
=> hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S_1)) ) ) ) ).
fof(fact_48_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X,Xa] :
( hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa),R_1))
<=> hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_49_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X,Xa] :
( hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Xa),R_1))
<=> hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Xa),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_50_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X,Xa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Xa),R_1))
<=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Xa),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_51_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_15,B] : Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) ).
fof(fact_52_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_15,B] : Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) ).
fof(fact_53_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_15,B] : Y_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) ).
fof(fact_54_widen__trans,axiom,
! [T_3,P_2,S_2,U_1] :
( hBOOL(widen_2090681816t_char(P_2,S_2,U_1))
=> ( hBOOL(widen_2090681816t_char(P_2,U_1,T_3))
=> hBOOL(widen_2090681816t_char(P_2,S_2,T_3)) ) ) ).
fof(fact_55_InitBlockRed_I5_J,axiom,
hBOOL(wTrt(p,ha,e,block_list_char(v_1,t_1,seq_list_char(lAss_list_char(v_1,val_list_char(v)),ea)),t)) ).
fof(fact_56_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ? [A_15,B] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B))) ) ).
fof(fact_57_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ? [A_15,B] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B))) ) ).
fof(fact_58_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ? [A_15,B] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B))) ) ).
fof(fact_59_PairE,axiom,
! [P_1] :
~ ! [X,Y] : P_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) ).
fof(fact_60_PairE,axiom,
! [P_1] :
~ ! [X,Y] : P_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) ).
fof(fact_61_PairE,axiom,
! [P_1] :
~ ! [X,Y] : P_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) ).
fof(fact_62_internal__split__conv,axiom,
! [C,A_10,B_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc2128769400l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
<=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,A_10),B_1)) ) ).
fof(fact_63_sconf__def,axiom,
! [Pa,Ea,S] :
( hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,cOMBS_570216337l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,cOMBB_383678192on_val),hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,fconj),hconf_97414254t_char(Pa))),hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,cOMBC_832625297y_bool),lconf_496643946t_char(Pa))),Ea))),S)) ) ).
fof(fact_64_prod__caseI,axiom,
! [F1,A_10,B_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A_10),B_1))
=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) ) ).
fof(fact_65_prod__caseI,axiom,
! [F1,A_10,B_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A_10),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) ) ).
fof(fact_66_prod__caseI,axiom,
! [F1,A_10,B_1] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) ) ).
fof(fact_67_splitI,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1))
=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) ) ).
fof(fact_68_splitI,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) ) ).
fof(fact_69_splitI,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) ) ).
fof(fact_70_splitD,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)) ) ).
fof(fact_71_splitD,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)) ) ).
fof(fact_72_splitD,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)) ) ).
fof(fact_73_split__weak__cong,axiom,
! [C,P_1,Q_2] :
( P_1 = Q_2
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),Q_2)) ) ) ).
fof(fact_74_split__weak__cong,axiom,
! [C,P_1,Q_2] :
( P_1 = Q_2
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1))
<=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),Q_2)) ) ) ).
fof(fact_75_split__weak__cong,axiom,
! [C,P_1,Q_2] :
( P_1 = Q_2
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),Q_2)) ) ) ).
fof(fact_76_internal__split__def,axiom,
produc399384568l_bool = produc1815960045l_bool ).
fof(fact_77_internal__split__def,axiom,
produc1988544340l_bool = produc1911463199l_bool ).
fof(fact_78_internal__split__def,axiom,
produc2128769400l_bool = produc1958875245l_bool ).
fof(fact_79_split__twice,axiom,
! [F,G,P_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P789556885on_val(hAPP_f1520199827on_val(produc1174947465on_val,G),P_1)))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,hAPP_f1825030711l_bool(cOMBB_877741809on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).
fof(fact_80_split__twice,axiom,
! [F,G,P_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P1760219823on_val(hAPP_f394183983on_val(produc1003071703on_val,G),P_1)))
<=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,hAPP_f881985847l_bool(cOMBB_1083177073on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).
fof(fact_81_split__twice,axiom,
! [F,G,P_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_f1309113673on_val(produc901351817on_val,G),P_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,hAPP_f1233687287l_bool(cOMBB_171276332on_val,hAPP_f1930574389l_bool(produc1815960045l_bool,F))),G)),P_1)) ) ).
fof(fact_82_split__twice,axiom,
! [F,G,P_1] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P2024243179on_val(hAPP_f204556415on_val(produc1148763895on_val,G),P_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,hAPP_f2052660463l_bool(cOMBB_1292453606on_val,hAPP_f635218277l_bool(produc1911463199l_bool,F))),G)),P_1)) ) ).
fof(fact_83_split__part,axiom,
! [Pa,Q_1,X] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f546724245l_bool(hAPP_f917296015l_bool(cOMBB_740252943t_char,hAPP_f1308714617l_bool(cOMBB_338347573on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X))
<=> ( hBOOL(Pa)
& hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,Q_1),X)) ) ) ).
fof(fact_84_split__part,axiom,
! [Pa,Q_1,X] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f641257349l_bool(hAPP_f2032347769l_bool(cOMBB_466903633on_val,hAPP_f1560238713l_bool(cOMBB_672625589on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X))
<=> ( hBOOL(Pa)
& hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,Q_1),X)) ) ) ).
fof(fact_85_split__part,axiom,
! [Pa,Q_1,X] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,hAPP_f1863694447l_bool(cOMBB_383678192on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X))
<=> ( hBOOL(Pa)
& hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Q_1),X)) ) ) ).
fof(fact_86_prod_Osimps_I2_J,axiom,
! [F1,A_10,B_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
<=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A_10),B_1)) ) ).
fof(fact_87_prod_Osimps_I2_J,axiom,
! [F1,A_10,B_1] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A_10),B_1)) ) ).
fof(fact_88_prod_Osimps_I2_J,axiom,
! [F1,A_10,B_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A_10),B_1)) ) ).
fof(fact_89_split__conv,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))
<=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)) ) ).
fof(fact_90_split__conv,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))
<=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)) ) ).
fof(fact_91_split__conv,axiom,
! [F,A_10,B_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))
<=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)) ) ).
fof(fact_92_split__eta,axiom,
! [F] : hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,hAPP_f2057883639l_bool(cOMBB_1750801836on_val,F)),produc899768717on_val)) = F ).
fof(fact_93_split__eta,axiom,
! [F] : hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1342895119l_bool(hAPP_f639265145l_bool(cOMBB_364363975on_val,hAPP_f365540729l_bool(cOMBB_1466662571on_val,F)),produc1441475159on_val)) = F ).
fof(fact_94_split__eta,axiom,
! [F] : hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f439412817l_bool(hAPP_f1725502637l_bool(cOMBB_1027621637t_char,hAPP_f10074679l_bool(cOMBB_1759207793on_val,F)),produc1259058957on_val)) = F ).
fof(fact_95_red__reds_OInitBlockRed,axiom,
! [Ta,V_a,Eb,Hb,Lb,Va_1,Va,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( hAPP_l207779698on_val(L_b,Va_1) = some_val(V_a)
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))),red(Pa))) ) ) ).
fof(fact_96_red__reds_ORedInitBlock,axiom,
! [Va_1,Ta,Va,U,S,Pa] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),val_list_char(U)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(U)),S)),red(Pa))) ).
fof(fact_97_splitI2,axiom,
! [C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B)
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C,A_15),B)) )
=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1)) ) ).
fof(fact_98_splitI2,axiom,
! [C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B)
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C,A_15),B)) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1)) ) ).
fof(fact_99_splitI2,axiom,
! [C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B)
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,A_15),B)) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1)) ) ).
fof(fact_100_splitE,axiom,
! [C,P_1] :
( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1))
=> ~ ! [X,Y] :
( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y)
=> ~ hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C,X),Y)) ) ) ).
fof(fact_101_splitE,axiom,
! [C,P_1] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1))
=> ~ ! [X,Y] :
( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y)
=> ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C,X),Y)) ) ) ).
fof(fact_102_splitE,axiom,
! [C,P_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1))
=> ~ ! [X,Y] :
( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y)
=> ~ hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,X),Y)) ) ) ).
fof(fact_103_WTrtBlock,axiom,
! [Pa,Hb,Ea,Va_1,Ta,Eb,T_a] :
( hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,some_ty(Ta)),Eb,T_a))
=> hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a)) ) ).
fof(fact_104_mem__splitI,axiom,
! [Z,C,A_10,B_1] :
( hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,A_10),B_1)))
=> hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))) ) ).
fof(fact_105_mem__splitI,axiom,
! [Z,C,A_10,B_1] :
( hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,A_10),B_1)))
=> hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))) ) ).
fof(fact_106_mem__splitI,axiom,
! [Z,C,A_10,B_1] :
( hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,A_10),B_1)))
=> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))) ) ).
fof(fact_107_mem__splitI,axiom,
! [Z,C,A_10,B_1] :
( hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,A_10),B_1)))
=> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))) ) ).
fof(fact_108_mem__splitI,axiom,
! [Z,C,A_10,B_1] :
( hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,A_10),B_1)))
=> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))) ) ).
fof(fact_109_mem__splitI,axiom,
! [Z,C,A_10,B_1] :
( hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,A_10),B_1)))
=> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))) ) ).
fof(fact_110_WTrtSeq,axiom,
! [E_2,T_2,Pa,Hb,Ea,E_1,T_1] :
( hBOOL(wTrt(Pa,Hb,Ea,E_1,T_1))
=> ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2))
=> hBOOL(wTrt(Pa,Hb,Ea,seq_list_char(E_1,E_2),T_2)) ) ) ).
fof(fact_111_red__reds_OSeqRed,axiom,
! [E_2,Eb,S,E_b,S_1,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa)))
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_1)),red(Pa))) ) ).
fof(fact_112_red__reds_OLAssRed,axiom,
! [Va_1,Eb,S,E_b,S_1,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa)))
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_1)),red(Pa))) ) ).
fof(fact_113_red__reds_ORedSeq,axiom,
! [Va,E_2,S,Pa] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(val_list_char(Va),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S)),red(Pa))) ).
fof(fact_114_red__reds_ORedBlock,axiom,
! [Va_1,Ta,U,S,Pa] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,val_list_char(U))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(U)),S)),red(Pa))) ).
fof(fact_115_mem__splitE,axiom,
! [Z,C,P_1] :
( hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),P_1)))
=> ~ ! [X,Y] :
( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y)
=> ~ hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,X),Y))) ) ) ).
fof(fact_116_mem__splitE,axiom,
! [Z,C,P_1] :
( hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),P_1)))
=> ~ ! [X,Y] :
( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y)
=> ~ hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,X),Y))) ) ) ).
fof(fact_117_mem__splitE,axiom,
! [Z,C,P_1] :
( hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),P_1)))
=> ~ ! [X,Y] :
( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y)
=> ~ hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,X),Y))) ) ) ).
fof(fact_118_mem__splitE,axiom,
! [Z,C,P_1] :
( hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),P_1)))
=> ~ ! [X,Y] :
( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y)
=> ~ hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,X),Y))) ) ) ).
fof(fact_119_mem__splitE,axiom,
! [Z,C,P_1] :
( hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),P_1)))
=> ~ ! [X,Y] :
( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y)
=> ~ hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,X),Y))) ) ) ).
fof(fact_120_mem__splitE,axiom,
! [Z,C,P_1] :
( hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),P_1)))
=> ~ ! [X,Y] :
( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y)
=> ~ hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,X),Y))) ) ) ).
fof(fact_121_mem__splitI2,axiom,
! [Z,C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B)
=> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,A_15),B))) )
=> hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),P_1))) ) ).
fof(fact_122_mem__splitI2,axiom,
! [Z,C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B)
=> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,A_15),B))) )
=> hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),P_1))) ) ).
fof(fact_123_mem__splitI2,axiom,
! [Z,C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B)
=> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,A_15),B))) )
=> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),P_1))) ) ).
fof(fact_124_mem__splitI2,axiom,
! [Z,C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B)
=> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,A_15),B))) )
=> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),P_1))) ) ).
fof(fact_125_mem__splitI2,axiom,
! [Z,C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B)
=> hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,A_15),B))) )
=> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),P_1))) ) ).
fof(fact_126_mem__splitI2,axiom,
! [Z,C,P_1] :
( ! [A_15,B] :
( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B)
=> hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,A_15),B))) )
=> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),P_1))) ) ).
fof(fact_127_red__reds_ORedLAss,axiom,
! [Va_1,Va,Hb,Lb,Pa] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,val_list_char(Va))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va))))),red(Pa))) ).
fof(fact_128_cond__split__eta,axiom,
! [G,F] :
( ! [X,Y] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,X),Y))
<=> hBOOL(hAPP_P159683425l_bool(G,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y))) )
=> hAPP_f2121594859l_bool(produc1958875245l_bool,F) = G ) ).
fof(fact_129_cond__split__eta,axiom,
! [G,F] :
( ! [X,Y] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,X),Y))
<=> hBOOL(hAPP_P282169671l_bool(G,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y))) )
=> hAPP_f635218277l_bool(produc1911463199l_bool,F) = G ) ).
fof(fact_130_cond__split__eta,axiom,
! [G,F] :
( ! [X,Y] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,X),Y))
<=> hBOOL(hAPP_P1708370145l_bool(G,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y))) )
=> hAPP_f1930574389l_bool(produc1815960045l_bool,F) = G ) ).
fof(fact_131_splitE2,axiom,
! [Q_1,Pa,Z] :
( hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Pa),Z)))
=> ~ ! [X,Y] :
( Z = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y)
=> ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,X),Y))) ) ) ).
fof(fact_132_splitE2,axiom,
! [Q_1,Pa,Z] :
( hBOOL(hAPP_bool_bool(Q_1,hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,Pa),Z)))
=> ~ ! [X,Y] :
( Z = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y)
=> ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,X),Y))) ) ) ).
fof(fact_133_splitE2,axiom,
! [Q_1,Pa,Z] :
( hBOOL(hAPP_bool_bool(Q_1,hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,Pa),Z)))
=> ~ ! [X,Y] :
( Z = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y)
=> ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,X),Y))) ) ) ).
fof(fact_134_exp_Osimps_I143_J,axiom,
! [A_14,Ty_7,Exp_13,A_13,Exp_12] : block_list_char(A_14,Ty_7,Exp_13) != lAss_list_char(A_13,Exp_12) ).
fof(fact_135_exp_Osimps_I196_J,axiom,
! [A_12,Ty_6,Exp_11,Exp1_7,Exp2_7] : block_list_char(A_12,Ty_6,Exp_11) != seq_list_char(Exp1_7,Exp2_7) ).
fof(fact_136_exp_Osimps_I3_J,axiom,
! [Val_7,Val_6] :
( val_list_char(Val_7) = val_list_char(Val_6)
<=> Val_7 = Val_6 ) ).
fof(fact_137_exp_Osimps_I11_J,axiom,
! [Exp1_6,Exp2_6,Exp1_5,Exp2_5] :
( seq_list_char(Exp1_6,Exp2_6) = seq_list_char(Exp1_5,Exp2_5)
<=> ( Exp1_6 = Exp1_5
& Exp2_6 = Exp2_5 ) ) ).
fof(fact_138_exp_Osimps_I6_J,axiom,
! [A_10,Exp_10,A_9,Exp_9] :
( lAss_list_char(A_10,Exp_10) = lAss_list_char(A_9,Exp_9)
<=> ( A_10 = A_9
& Exp_10 = Exp_9 ) ) ).
fof(fact_139_mem__def,axiom,
! [X_1,A_11] :
( hBOOL(member763590124on_val(X_1,A_11))
<=> hBOOL(hAPP_P159683425l_bool(A_11,X_1)) ) ).
fof(fact_140_mem__def,axiom,
! [X_1,A_11] :
( hBOOL(member840932460on_val(X_1,A_11))
<=> hBOOL(hAPP_P1708370145l_bool(A_11,X_1)) ) ).
fof(fact_141_mem__def,axiom,
! [X_1,A_11] :
( hBOOL(member773094996on_val(X_1,A_11))
<=> hBOOL(hAPP_P282169671l_bool(A_11,X_1)) ) ).
fof(fact_142_exp_Osimps_I10_J,axiom,
! [A_10,Ty_5,Exp_10,A_9,Ty_4,Exp_9] :
( block_list_char(A_10,Ty_5,Exp_10) = block_list_char(A_9,Ty_4,Exp_9)
<=> ( A_10 = A_9
& Ty_5 = Ty_4
& Exp_10 = Exp_9 ) ) ).
fof(fact_143_exp_Osimps_I84_J,axiom,
! [Val_5,Exp1_4,Exp2_4] : val_list_char(Val_5) != seq_list_char(Exp1_4,Exp2_4) ).
fof(fact_144_exp_Osimps_I74_J,axiom,
! [Val_4,A_8,Exp_8] : val_list_char(Val_4) != lAss_list_char(A_8,Exp_8) ).
fof(fact_145_exp_Osimps_I85_J,axiom,
! [Exp1_3,Exp2_3,Val_3] : seq_list_char(Exp1_3,Exp2_3) != val_list_char(Val_3) ).
fof(fact_146_exp_Osimps_I75_J,axiom,
! [A_7,Exp_7,Val_2] : lAss_list_char(A_7,Exp_7) != val_list_char(Val_2) ).
fof(fact_147_exp_Osimps_I82_J,axiom,
! [Val_1,A_6,Ty_3,Exp_6] : val_list_char(Val_1) != block_list_char(A_6,Ty_3,Exp_6) ).
fof(fact_148_exp_Osimps_I83_J,axiom,
! [A_5,Ty_2,Exp_5,Val] : block_list_char(A_5,Ty_2,Exp_5) != val_list_char(Val) ).
fof(fact_149_exp_Osimps_I145_J,axiom,
! [Exp1_2,Exp2_2,A_4,Exp_4] : seq_list_char(Exp1_2,Exp2_2) != lAss_list_char(A_4,Exp_4) ).
fof(fact_150_exp_Osimps_I144_J,axiom,
! [A_3,Exp_3,Exp1_1,Exp2_1] : lAss_list_char(A_3,Exp_3) != seq_list_char(Exp1_1,Exp2_1) ).
fof(fact_151_exp_Osimps_I197_J,axiom,
! [Exp1,Exp2,A_2,Ty_1,Exp_2] : seq_list_char(Exp1,Exp2) != block_list_char(A_2,Ty_1,Exp_2) ).
fof(fact_152_exp_Osimps_I142_J,axiom,
! [A_1,Exp_1,A,Ty,Exp] : lAss_list_char(A_1,Exp_1) != block_list_char(A,Ty,Exp) ).
fof(fact_153_redp__redsp_OInitBlockRed,axiom,
! [Ta,V_a,Pa,Eb,Hb,Lb,Va_1,Va,E_b,H_b,L_b] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va)))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
=> ( hAPP_l207779698on_val(L_b,Va_1) = some_val(V_a)
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ).
fof(fact_154_red__reds_OBlockRedSome,axiom,
! [Ta,Va,Eb,Hb,Lb,Va_1,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
=> ( hAPP_l207779698on_val(L_b,Va_1) = some_val(Va)
=> ( ~ hBOOL(assigned(Va_1,Eb))
=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))),red(Pa))) ) ) ) ).
fof(fact_155_redp__redsp_OSeqRed,axiom,
! [E_2,Pa,Eb,S,E_b,S_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Eb,E_2),S),seq_list_char(E_b,E_2)),S_1)) ) ).
fof(fact_156_redp__redsp_OLAssRed,axiom,
! [Va_1,Pa,Eb,S,E_b,S_1] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,Eb),S),lAss_list_char(Va_1,E_b)),S_1)) ) ).
fof(fact_157_redp__redsp_OBlockRedNone,axiom,
! [Ta,Pa,Eb,Hb,Lb,Va_1,E_b,H_b,L_b] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
=> ( hAPP_l207779698on_val(L_b,Va_1) = none_val
=> ( ~ hBOOL(assigned(Va_1,Eb))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ) ).
fof(fact_158_redp__redsp_ORedSeq,axiom,
! [Pa,Va,E_2,S] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(val_list_char(Va),E_2),S),E_2),S)) ).
fof(fact_159_map__upd__nonempty,axiom,
! [T,K,X_1] :
~ ! [X] : hAPP_l207779698on_val(fun_up1149430426on_val(T,K,some_val(X_1)),X) = none_val ).
fof(fact_160_map__upd__nonempty,axiom,
! [T,K,X_1] :
~ ! [X] : hAPP_l512744617ion_ty(fun_up424764369ion_ty(T,K,some_ty(X_1)),X) = none_ty ).
fof(fact_161_redp__redsp_ORedBlock,axiom,
! [Pa,Va_1,Ta,U,S] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,val_list_char(U)),S),val_list_char(U)),S)) ).
fof(fact_162_empty__upd__none,axiom,
! [X_1,X] : hAPP_l207779698on_val(fun_up1149430426on_val(cOMBK_1097134891t_char(none_val),X_1,none_val),X) = none_val ).
fof(fact_163_empty__upd__none,axiom,
! [X_1,X] : hAPP_l512744617ion_ty(fun_up424764369ion_ty(cOMBK_1294242658t_char(none_ty),X_1,none_ty),X) = none_ty ).
fof(fact_164_redp__redsp_OBlockRedSome,axiom,
! [Ta,Va,Pa,Eb,Hb,Lb,Va_1,E_b,H_b,L_b] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
=> ( hAPP_l207779698on_val(L_b,Va_1) = some_val(Va)
=> ( ~ hBOOL(assigned(Va_1,Eb))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ) ).
fof(fact_165_redp__red__eq,axiom,
! [Pa,X,Xa,Xb,Xc] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,X,Xa),Xb),Xc))
<=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xb),Xc)),red(Pa))) ) ).
fof(fact_166_redp__redsp_ORedInitBlock,axiom,
! [Pa,Va_1,Ta,Va,U,S] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),val_list_char(U))),S),val_list_char(U)),S)) ).
%----Helper facts (31)
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(P) ) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(Q) ) ).
fof(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_,axiom,
! [P,Q] : hAPP_l512744617ion_ty(cOMBK_1294242658t_char(P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis,axiom,
! [P,Q] : hAPP_l207779698on_val(cOMBK_1097134891t_char(P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O,axiom,
! [P,Q,R] : hAPP_f1033709212l_bool(hAPP_f1074020887l_bool(hAPP_f1863694447l_bool(cOMBB_383678192on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_f1033709212l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio,axiom,
! [P,Q,R] : hAPP_f1033709212l_bool(hAPP_f603925568l_bool(hAPP_f181262431l_bool(cOMBC_832625297y_bool,P),Q),R) = hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_f1145256474l_bool(hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f61040418l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It,axiom,
! [P,Q,R] : hAPP_P159683425l_bool(hAPP_f2134824737l_bool(hAPP_f1308714617l_bool(cOMBB_338347573on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_P159683425l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__,axiom,
! [P,Q,R] : hAPP_P1708370145l_bool(hAPP_f926562337l_bool(hAPP_f1560238713l_bool(cOMBB_672625589on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_P1708370145l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
! [P,Q,R] : hAPP_f1175813647l_bool(hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,P),Q),R) = hAPP_f603925568l_bool(hAPP_f1617787571l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It,axiom,
! [P,Q,R] : hAPP_f1033709212l_bool(hAPP_f1008932791l_bool(hAPP_f2057883639l_bool(cOMBB_1750801836on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_f1727192346on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M,axiom,
! [P,Q,R] : hAPP_f1175813647l_bool(hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,P),Q),R) = hAPP_f1074020887l_bool(P,hAPP_f1175813647l_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
! [P,Q,R] : hAPP_f1175813647l_bool(cOMBS_570216337l_bool(P,Q),R) = hAPP_f1074020887l_bool(hAPP_f1492320500l_bool(P,R),hAPP_f1175813647l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,axiom,
! [P,Q,R] : hAPP_f1033709212l_bool(hAPP_f318082871l_bool(hAPP_f1233687287l_bool(cOMBB_171276332on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_f1926378906on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
! [P,Q,R] : hAPP_f1492320500l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,P),Q),R) = hAPP_f1863694447l_bool(P,hAPP_f1145256474l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_002,axiom,
! [P,Q,R] : hAPP_f1617787571l_bool(hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,P),Q),R) = hAPP_f181262431l_bool(P,hAPP_f1213370163y_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_003,axiom,
! [P,Q,R] : hAPP_P159683425l_bool(hAPP_f1301559543l_bool(hAPP_f1825030711l_bool(cOMBB_877741809on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P1776198677on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_004,axiom,
! [P,Q,R] : hAPP_P159683425l_bool(hAPP_f489055607l_bool(hAPP_f10074679l_bool(cOMBB_1759207793on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_P604205461on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_005,axiom,
! [P,Q,R] : hAPP_P1708370145l_bool(hAPP_f1712766199l_bool(hAPP_f881985847l_bool(cOMBB_1083177073on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P789556885on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O,axiom,
! [P,Q,R] : hAPP_e1833980889l_bool(hAPP_f546724245l_bool(hAPP_f917296015l_bool(cOMBB_740252943t_char,P),Q),R) = hAPP_f2134824737l_bool(P,hAPP_e1833980889l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_006,axiom,
! [P,Q,R] : hAPP_f1175813647l_bool(hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,P),Q),R) = hAPP_f1008932791l_bool(P,hAPP_f1849790461on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_007,axiom,
! [P,Q,R] : hAPP_f1175813647l_bool(hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,P),Q),R) = hAPP_f318082871l_bool(P,hAPP_f1840640125on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
! [P,Q,R] : hAPP_f1033709212l_bool(hAPP_f524589473l_bool(hAPP_f2052660463l_bool(cOMBB_1292453606on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_f602593190on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_008,axiom,
! [P,Q,R] : hAPP_e1833980889l_bool(hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,P),Q),R) = hAPP_f1301559543l_bool(P,hAPP_e108155315on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_009,axiom,
! [P,Q,R] : hAPP_e1833980889l_bool(hAPP_f439412817l_bool(hAPP_f1725502637l_bool(cOMBB_1027621637t_char,P),Q),R) = hAPP_f489055607l_bool(P,hAPP_e1659493427on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__010,axiom,
! [P,Q,R] : hAPP_P1708370145l_bool(hAPP_f204771371l_bool(hAPP_f365540729l_bool(cOMBB_1466662571on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_P1886180715on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,axiom,
! [P,Q,R] : hAPP_P1116729363l_bool(hAPP_f641257349l_bool(hAPP_f2032347769l_bool(cOMBB_466903633on_val,P),Q),R) = hAPP_f926562337l_bool(P,hAPP_P1116729363l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_011,axiom,
! [P,Q,R] : hAPP_f1175813647l_bool(hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,P),Q),R) = hAPP_f524589473l_bool(P,hAPP_f600512025on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___012,axiom,
! [P,Q,R] : hAPP_P1116729363l_bool(hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,P),Q),R) = hAPP_f1712766199l_bool(P,hAPP_P2083594489on_val(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___013,axiom,
! [P,Q,R] : hAPP_P1116729363l_bool(hAPP_f1342895119l_bool(hAPP_f639265145l_bool(cOMBB_364363975on_val,P),Q),R) = hAPP_f204771371l_bool(P,hAPP_P1870962205on_val(Q,R)) ).
%----Conjectures (1)
fof(conj_0,conjecture,
hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) ).
%------------------------------------------------------------------------------