TPTP Problem File: SWW477+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW477+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 346, 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_l346 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 182 ( 78 unt; 0 def)
% Number of atoms : 437 ( 110 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 357 ( 102 ~; 0 |; 16 &)
% ( 35 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 61 ( 61 usr; 16 con; 0-5 aty)
% Number of variables : 782 ( 764 !; 18 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:52:17
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (19)
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,B_4] : is_bool(lconf_496643946t_char(B_1_1,B_2_1,B_3,B_4)) ).
fof(gsy_c_Objects_Ohext,axiom,
! [B_1_1,B_2_1] : is_bool(hext(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,hypothesis,
! [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__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__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_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P1221872711l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P378063101l_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_,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__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)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option,axiom,
! [B_1_1,B_2_1] : is_bool(member2032527242on_val(B_1_1,B_2_1)) ).
fof(gsy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List,axiom,
! [B_1_1,B_2_1] : is_bool(member712690550on_val(B_1_1,B_2_1)) ).
%----Relevant facts (162)
fof(fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096,axiom,
hBOOL(wTrt(p,ha,e,ea,nt)) ).
fof(fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX,axiom,
! [Ta] :
( hBOOL(wTrt(p,ha,e,ea,Ta))
=> ? [U_1] :
( hBOOL(wTrt(p,h_a,e,e_a,U_1))
& hBOOL(widen_2090681816t_char(p,U_1,Ta)) ) ) ).
fof(fact_2_assms,axiom,
hBOOL(wf_pro755087577t_char(wf_J_mdecl,p)) ).
fof(fact_3_IH,axiom,
! [Ta,Ea] :
( hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,Ea),produc899768717on_val(ha,la)))
=> ( hBOOL(wTrt(p,ha,Ea,ea,Ta))
=> ? [U_1] :
( hBOOL(wTrt(p,h_a,Ea,e_a,U_1))
& hBOOL(widen_2090681816t_char(p,U_1,Ta)) ) ) ) ).
fof(fact_4_conf,axiom,
hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,e),produc899768717on_val(ha,la))) ).
fof(fact_5_wt,axiom,
hBOOL(wTrt(p,ha,e,fAss_list_char(ea,f,d,e_2),t)) ).
fof(fact_6_WTrtFAccNT,axiom,
! [Fa,Da,Ta,Pa,Hb,Ea,Eb] :
( hBOOL(wTrt(Pa,Hb,Ea,Eb,nt))
=> hBOOL(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da),Ta)) ) ).
fof(fact_7_FAssRed1_I2_J,axiom,
! [Ta,Ea] :
( hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,Ea),produc899768717on_val(ha,la)))
=> ( hBOOL(wTrt(p,ha,Ea,ea,Ta))
=> ? [T_3] :
( hBOOL(wTrt(p,h_a,Ea,e_a,T_3))
& hBOOL(widen_2090681816t_char(p,T_3,Ta)) ) ) ) ).
fof(fact_8_red,axiom,
hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(ea,produc899768717on_val(ha,la)),produc1259058957on_val(e_a,produc899768717on_val(h_a,l_a))),red(p))) ).
fof(fact_9_FAssRed1_I4_J,axiom,
hBOOL(wTrt(p,ha,e,fAss_list_char(ea,f,d,e_2),t)) ).
fof(fact_10_FAssRed1_I3_J,axiom,
hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,e),produc899768717on_val(ha,la))) ).
fof(fact_11_ty_Osimps_I13_J,axiom,
nt != boolean ).
fof(fact_12_ty_Osimps_I12_J,axiom,
boolean != nt ).
fof(fact_13_red__reds_OFAccRed,axiom,
! [Fa,Da,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Eb,Fa,Da),S_1),produc1259058957on_val(fAcc_list_char(E_b,Fa,Da),S)),red(Pa))) ) ).
fof(fact_14_red__reds_OFAssRed1,axiom,
! [Fa,Da,E_2,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Eb,Fa,Da,E_2),S_1),produc1259058957on_val(fAss_list_char(E_b,Fa,Da,E_2),S)),red(Pa))) ) ).
fof(fact_15_void,axiom,
t = void ).
fof(fact_16_widen__refl,axiom,
! [P_2,T_1] : hBOOL(widen_2090681816t_char(P_2,T_1,T_1)) ).
fof(fact_17_red__preserves__hconf,axiom,
! [Ea,Ta,Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hconf_97414254t_char(Pa,Hb))
=> hBOOL(hconf_97414254t_char(Pa,H_b)) ) ) ) ).
fof(fact_18_red__preserves__lconf,axiom,
! [Ea,Ta,Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(lconf_496643946t_char(Pa,Hb,Lb,Ea))
=> hBOOL(lconf_496643946t_char(Pa,H_b,L_b,Ea)) ) ) ) ).
fof(fact_19_exp_Osimps_I154_J,axiom,
! [Exp_16,List1_17,List2_17,Exp1_16,List1_16,List2_16,Exp2_16] : fAcc_list_char(Exp_16,List1_17,List2_17) != fAss_list_char(Exp1_16,List1_16,List2_16,Exp2_16) ).
fof(fact_20_exp_Osimps_I155_J,axiom,
! [Exp1_15,List1_15,List2_15,Exp2_15,Exp_15,List1_14,List2_14] : fAss_list_char(Exp1_15,List1_15,List2_15,Exp2_15) != fAcc_list_char(Exp_15,List1_14,List2_14) ).
fof(fact_21_red__preserves__sconf,axiom,
! [Ea,Ta,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> ( hBOOL(wTrt(Pa,hp(S_1),Ea,Eb,Ta))
=> ( hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S_1))
=> hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S)) ) ) ) ).
fof(fact_22_ty_Osimps_I7_J,axiom,
nt != void ).
fof(fact_23_ty_Osimps_I6_J,axiom,
void != nt ).
fof(fact_24_ty_Osimps_I3_J,axiom,
boolean != void ).
fof(fact_25_ty_Osimps_I2_J,axiom,
void != boolean ).
fof(fact_26_widen__trans,axiom,
! [T,P_1,S_4,U] :
( hBOOL(widen_2090681816t_char(P_1,S_4,U))
=> ( hBOOL(widen_2090681816t_char(P_1,U,T))
=> hBOOL(widen_2090681816t_char(P_1,S_4,T)) ) ) ).
fof(fact_27_exp_Osimps_I8_J,axiom,
! [Exp1_2,List1_13,List2_13,Exp2_2,Exp1_1,List1_12,List2_12,Exp2_1] :
( fAss_list_char(Exp1_2,List1_13,List2_13,Exp2_2) = fAss_list_char(Exp1_1,List1_12,List2_12,Exp2_1)
<=> ( Exp1_2 = Exp1_1
& List1_13 = List1_12
& List2_13 = List2_12
& Exp2_2 = Exp2_1 ) ) ).
fof(fact_28_exp_Osimps_I7_J,axiom,
! [Exp_2,List1_13,List2_13,Exp_1,List1_12,List2_12] :
( fAcc_list_char(Exp_2,List1_13,List2_13) = fAcc_list_char(Exp_1,List1_12,List2_12)
<=> ( Exp_2 = Exp_1
& List1_13 = List1_12
& List2_13 = List2_12 ) ) ).
fof(fact_29_WTrtFAssNT,axiom,
! [Fa,Da,E_2,T_2,Pa,Hb,Ea,E_1] :
( hBOOL(wTrt(Pa,Hb,Ea,E_1,nt))
=> ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2))
=> hBOOL(wTrt(Pa,Hb,Ea,fAss_list_char(E_1,Fa,Da,E_2),void)) ) ) ).
fof(fact_30_red__hext__incr,axiom,
! [Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> hBOOL(hext(Hb,H_b)) ) ).
fof(fact_31_prod__cases4,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2,D] : Y_1 != produc1441475159on_val(A_10,produc1259058957on_val(B_1,produc899768717on_val(C_2,D))) ).
fof(fact_32_prod__cases4,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2,D] : Y_1 != produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,D))) ).
fof(fact_33_prod__induct4,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2,D] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,produc1259058957on_val(B_1,produc899768717on_val(C_2,D)))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X)) ) ).
fof(fact_34_prod__induct4,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2,D] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,D)))))
=> hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).
fof(fact_35_prod__cases5,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2,D,E] : Y_1 != produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,produc899768717on_val(D,E)))) ).
fof(fact_36_prod__induct5,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2,D,E] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,produc1441475159on_val(B_1,produc1259058957on_val(C_2,produc899768717on_val(D,E))))))
=> hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).
fof(fact_37_WTrt__hext__mono,axiom,
! [H_b,Pa,Hb,Ea,Eb,Ta] :
( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
=> ( hBOOL(hext(Hb,H_b))
=> hBOOL(wTrt(Pa,H_b,Ea,Eb,Ta)) ) ) ).
fof(fact_38_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
<=> ! [A_10,B_1] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,B_1))) ) ).
fof(fact_39_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
<=> ! [A_10,B_1] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_10,B_1))) ) ).
fof(fact_40_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ! [A_10,B_1] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_10,B_1))) ) ).
fof(fact_41_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ! [A_10,B_1] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,B_1))) ) ).
fof(fact_42_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ! [A_10,B_1] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_10,B_1))) ) ).
fof(fact_43_Pair__eq,axiom,
! [A_2,B,A_1,B_2] :
( produc1564932627on_val(A_2,B) = produc1564932627on_val(A_1,B_2)
<=> ( A_2 = A_1
& B = B_2 ) ) ).
fof(fact_44_Pair__eq,axiom,
! [A_2,B,A_1,B_2] :
( produc870913623on_val(A_2,B) = produc870913623on_val(A_1,B_2)
<=> ( A_2 = A_1
& B = B_2 ) ) ).
fof(fact_45_Pair__eq,axiom,
! [A_2,B,A_1,B_2] :
( produc899768717on_val(A_2,B) = produc899768717on_val(A_1,B_2)
<=> ( A_2 = A_1
& B = B_2 ) ) ).
fof(fact_46_Pair__eq,axiom,
! [A_2,B,A_1,B_2] :
( produc1441475159on_val(A_2,B) = produc1441475159on_val(A_1,B_2)
<=> ( A_2 = A_1
& B = B_2 ) ) ).
fof(fact_47_Pair__eq,axiom,
! [A_2,B,A_1,B_2] :
( produc1259058957on_val(A_2,B) = produc1259058957on_val(A_1,B_2)
<=> ( A_2 = A_1
& B = B_2 ) ) ).
fof(fact_48_Pair__inject,axiom,
! [A_2,B,A_1,B_2] :
( produc1564932627on_val(A_2,B) = produc1564932627on_val(A_1,B_2)
=> ~ ( A_2 = A_1
=> B != B_2 ) ) ).
fof(fact_49_Pair__inject,axiom,
! [A_2,B,A_1,B_2] :
( produc870913623on_val(A_2,B) = produc870913623on_val(A_1,B_2)
=> ~ ( A_2 = A_1
=> B != B_2 ) ) ).
fof(fact_50_Pair__inject,axiom,
! [A_2,B,A_1,B_2] :
( produc899768717on_val(A_2,B) = produc899768717on_val(A_1,B_2)
=> ~ ( A_2 = A_1
=> B != B_2 ) ) ).
fof(fact_51_Pair__inject,axiom,
! [A_2,B,A_1,B_2] :
( produc1441475159on_val(A_2,B) = produc1441475159on_val(A_1,B_2)
=> ~ ( A_2 = A_1
=> B != B_2 ) ) ).
fof(fact_52_Pair__inject,axiom,
! [A_2,B,A_1,B_2] :
( produc1259058957on_val(A_2,B) = produc1259058957on_val(A_1,B_2)
=> ~ ( A_2 = A_1
=> B != B_2 ) ) ).
fof(fact_53_hext__refl,axiom,
! [Hb] : hBOOL(hext(Hb,Hb)) ).
fof(fact_54_lconf__hext,axiom,
! [H_b,Pa,Hb,Lb,Ea] :
( hBOOL(lconf_496643946t_char(Pa,Hb,Lb,Ea))
=> ( hBOOL(hext(Hb,H_b))
=> hBOOL(lconf_496643946t_char(Pa,H_b,Lb,Ea)) ) ) ).
fof(fact_55_prod__induct3,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,produc1259058957on_val(B_1,C_2))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X)) ) ).
fof(fact_56_prod__induct3,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_10,produc899768717on_val(B_1,C_2))))
=> hBOOL(hAPP_P1708370145l_bool(Pa,X)) ) ).
fof(fact_57_prod__induct3,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_10,produc899768717on_val(B_1,C_2))))
=> hBOOL(hAPP_P1221872711l_bool(Pa,X)) ) ).
fof(fact_58_prod__induct3,axiom,
! [X,Pa] :
( ! [A_10,B_1,C_2] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,produc1441475159on_val(B_1,C_2))))
=> hBOOL(hAPP_P378063101l_bool(Pa,X)) ) ).
fof(fact_59_prod__cases3,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2] : Y_1 != produc1441475159on_val(A_10,produc1259058957on_val(B_1,C_2)) ).
fof(fact_60_prod__cases3,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2] : Y_1 != produc1259058957on_val(A_10,produc899768717on_val(B_1,C_2)) ).
fof(fact_61_prod__cases3,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2] : Y_1 != produc870913623on_val(A_10,produc899768717on_val(B_1,C_2)) ).
fof(fact_62_prod__cases3,axiom,
! [Y_1] :
~ ! [A_10,B_1,C_2] : Y_1 != produc1564932627on_val(A_10,produc1441475159on_val(B_1,C_2)) ).
fof(fact_63_hext__trans,axiom,
! [H,Hb,H_b] :
( hBOOL(hext(Hb,H_b))
=> ( hBOOL(hext(H_b,H))
=> hBOOL(hext(Hb,H)) ) ) ).
fof(fact_64_red__lcl__add,axiom,
! [L_0,Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,map_ad325961431ar_val(L_0,Lb))),produc1259058957on_val(E_b,produc899768717on_val(H_b,map_ad325961431ar_val(L_0,L_b)))),red(Pa))) ) ).
fof(fact_65_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X_1,Xa_1] :
( hBOOL(member808015754on_val(produc1564932627on_val(X_1,Xa_1),R_1))
<=> hBOOL(member808015754on_val(produc1564932627on_val(X_1,Xa_1),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_66_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X_1,Xa_1] :
( hBOOL(member563141460on_val(produc870913623on_val(X_1,Xa_1),R_1))
<=> hBOOL(member563141460on_val(produc870913623on_val(X_1,Xa_1),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_67_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X_1,Xa_1] :
( hBOOL(member763590124on_val(produc899768717on_val(X_1,Xa_1),R_1))
<=> hBOOL(member763590124on_val(produc899768717on_val(X_1,Xa_1),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_68_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X_1,Xa_1] :
( hBOOL(member840932460on_val(produc1259058957on_val(X_1,Xa_1),R_1))
<=> hBOOL(member840932460on_val(produc1259058957on_val(X_1,Xa_1),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_69_pred__equals__eq2,axiom,
! [S_3,R_1] :
( ! [X_1,Xa_1] :
( hBOOL(member773094996on_val(produc1441475159on_val(X_1,Xa_1),R_1))
<=> hBOOL(member773094996on_val(produc1441475159on_val(X_1,Xa_1),S_3)) )
<=> R_1 = S_3 ) ).
fof(fact_70_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_10,B_1] : Y_1 != produc1564932627on_val(A_10,B_1) ).
fof(fact_71_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_10,B_1] : Y_1 != produc870913623on_val(A_10,B_1) ).
fof(fact_72_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_10,B_1] : Y_1 != produc899768717on_val(A_10,B_1) ).
fof(fact_73_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_10,B_1] : Y_1 != produc1441475159on_val(A_10,B_1) ).
fof(fact_74_prod_Oexhaust,axiom,
! [Y_1] :
~ ! [A_10,B_1] : Y_1 != produc1259058957on_val(A_10,B_1) ).
fof(fact_75_PairE,axiom,
! [P] :
~ ! [X_1,Y] : P != produc1564932627on_val(X_1,Y) ).
fof(fact_76_PairE,axiom,
! [P] :
~ ! [X_1,Y] : P != produc870913623on_val(X_1,Y) ).
fof(fact_77_PairE,axiom,
! [P] :
~ ! [X_1,Y] : P != produc899768717on_val(X_1,Y) ).
fof(fact_78_PairE,axiom,
! [P] :
~ ! [X_1,Y] : P != produc1441475159on_val(X_1,Y) ).
fof(fact_79_PairE,axiom,
! [P] :
~ ! [X_1,Y] : P != produc1259058957on_val(X_1,Y) ).
fof(fact_80_Red__lcl__add,axiom,
! [L_0,Eb,Hb,Lb,E_b,H_b,L_b,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,Lb)),produc1259058957on_val(E_b,produc899768717on_val(H_b,L_b))),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,produc899768717on_val(Hb,map_ad325961431ar_val(L_0,Lb))),produc1259058957on_val(E_b,produc899768717on_val(H_b,map_ad325961431ar_val(L_0,L_b)))),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_81_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
<=> ? [A_10,B_1] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_10,B_1))) ) ).
fof(fact_82_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
<=> ? [A_10,B_1] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_10,B_1))) ) ).
fof(fact_83_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ? [A_10,B_1] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_10,B_1))) ) ).
fof(fact_84_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ? [A_10,B_1] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_10,B_1))) ) ).
fof(fact_85_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ? [A_10,B_1] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_10,B_1))) ) ).
fof(fact_86_FAccReds,axiom,
! [Fa,Da,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Eb,Fa,Da),S_1),produc1259058957on_val(fAcc_list_char(E_b,Fa,Da),S)),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_87_FAssReds1,axiom,
! [Fa,Da,E_2,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Eb,Fa,Da,E_2),S_1),produc1259058957on_val(fAss_list_char(E_b,Fa,Da,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_88_rtrancl_Ortrancl__refl,axiom,
! [A_2,R] : hBOOL(member808015754on_val(produc1564932627on_val(A_2,A_2),transi910771962on_val(R))) ).
fof(fact_89_rtrancl_Ortrancl__refl,axiom,
! [A_2,R] : hBOOL(member563141460on_val(produc870913623on_val(A_2,A_2),transi921647814on_val(R))) ).
fof(fact_90_rtrancl_Ortrancl__refl,axiom,
! [A_2,R] : hBOOL(member773094996on_val(produc1441475159on_val(A_2,A_2),transi2024712006on_val(R))) ).
fof(fact_91_r__into__rtrancl,axiom,
! [P,R] :
( hBOOL(member808015754on_val(P,R))
=> hBOOL(member808015754on_val(P,transi910771962on_val(R))) ) ).
fof(fact_92_r__into__rtrancl,axiom,
! [P,R] :
( hBOOL(member563141460on_val(P,R))
=> hBOOL(member563141460on_val(P,transi921647814on_val(R))) ) ).
fof(fact_93_r__into__rtrancl,axiom,
! [P,R] :
( hBOOL(member773094996on_val(P,R))
=> hBOOL(member773094996on_val(P,transi2024712006on_val(R))) ) ).
fof(fact_94_rtrancl__idemp,axiom,
! [R] : transi910771962on_val(transi910771962on_val(R)) = transi910771962on_val(R) ).
fof(fact_95_rtrancl__idemp,axiom,
! [R] : transi921647814on_val(transi921647814on_val(R)) = transi921647814on_val(R) ).
fof(fact_96_rtrancl__idemp,axiom,
! [R] : transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R) ).
fof(fact_97_converse__rtrancl__into__rtrancl,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R)))
=> hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).
fof(fact_98_converse__rtrancl__into__rtrancl,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R)))
=> hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).
fof(fact_99_converse__rtrancl__into__rtrancl,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).
fof(fact_100_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),R))
=> hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).
fof(fact_101_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),R))
=> hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).
fof(fact_102_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),R))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).
fof(fact_103_rtrancl__trans,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R)))
=> hBOOL(member808015754on_val(produc1564932627on_val(A_2,C_1),transi910771962on_val(R))) ) ) ).
fof(fact_104_rtrancl__trans,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R)))
=> hBOOL(member563141460on_val(produc870913623on_val(A_2,C_1),transi921647814on_val(R))) ) ) ).
fof(fact_105_rtrancl__trans,axiom,
! [C_1,A_2,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_2,C_1),transi2024712006on_val(R))) ) ) ).
fof(fact_106_converse__rtranclE2,axiom,
! [Xa,Xb,Za,Zb,R] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa,Xb),produc1564932627on_val(Za,Zb)),transi678815536on_val(R)))
=> ( produc1564932627on_val(Xa,Xb) != produc1564932627on_val(Za,Zb)
=> ~ ! [A_10,B_1] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa,Xb),produc1564932627on_val(A_10,B_1)),R))
=> ~ hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_10,B_1),produc1564932627on_val(Za,Zb)),transi678815536on_val(R))) ) ) ) ).
fof(fact_107_converse__rtranclE2,axiom,
! [Xa,Xb,Za,Zb,R] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa,Xb),produc870913623on_val(Za,Zb)),transi594096122on_val(R)))
=> ( produc870913623on_val(Xa,Xb) != produc870913623on_val(Za,Zb)
=> ~ ! [A_10,B_1] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa,Xb),produc870913623on_val(A_10,B_1)),R))
=> ~ hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_10,B_1),produc870913623on_val(Za,Zb)),transi594096122on_val(R))) ) ) ) ).
fof(fact_108_converse__rtranclE2,axiom,
! [Xa,Xb,Za,Zb,R] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa,Xb),produc899768717on_val(Za,Zb)),transi921647814on_val(R)))
=> ( produc899768717on_val(Xa,Xb) != produc899768717on_val(Za,Zb)
=> ~ ! [A_10,B_1] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa,Xb),produc899768717on_val(A_10,B_1)),R))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_10,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R))) ) ) ) ).
fof(fact_109_converse__rtranclE2,axiom,
! [Xa,Xb,Za,Zb,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa,Xb),produc1441475159on_val(Za,Zb)),transi910771962on_val(R)))
=> ( produc1441475159on_val(Xa,Xb) != produc1441475159on_val(Za,Zb)
=> ~ ! [A_10,B_1] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa,Xb),produc1441475159on_val(A_10,B_1)),R))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_10,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R))) ) ) ) ).
fof(fact_110_converse__rtranclE2,axiom,
! [Xa,Xb,Za,Zb,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa,Xb),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R)))
=> ( produc1259058957on_val(Xa,Xb) != produc1259058957on_val(Za,Zb)
=> ~ ! [A_10,B_1] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa,Xb),produc1259058957on_val(A_10,B_1)),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_10,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R))) ) ) ) ).
fof(fact_111_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By))
=> ( ! [A_10,B_1,Aa,Ba] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_10,B_1),produc1564932627on_val(Aa,Ba)),R))
=> ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Aa,Ba),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_112_converse__rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By))
=> ( ! [A_10,B_1,Aa,Ba] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_10,B_1),produc870913623on_val(Aa,Ba)),R))
=> ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Aa,Ba),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_10),B_1)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_113_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_10,B_1,Aa,Ba] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_10,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_10),B_1)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_114_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_10,B_1,Aa,Ba] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_10,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_10),B_1)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_115_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_10,B_1,Aa,Ba] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_10,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_10),B_1)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).
fof(fact_116_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay))
=> ( ! [A_10,B_1,Aa,Ba] :
( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(A_10,B_1)),transi678815536on_val(R)))
=> ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_10,B_1),produc1564932627on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_117_rtrancl__induct2,axiom,
! [Pa,Ax,Ay,Bx,By,R] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay))
=> ( ! [A_10,B_1,Aa,Ba] :
( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(A_10,B_1)),transi594096122on_val(R)))
=> ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_10,B_1),produc870913623on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_118_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_10,B_1,Aa,Ba] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A_10,B_1)),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_10,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_119_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_10,B_1,Aa,Ba] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A_10,B_1)),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_10,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_120_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_10,B_1,Aa,Ba] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A_10,B_1)),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_10,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_10),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).
fof(fact_121_rtranclE,axiom,
! [A_2,B,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( A_2 != B
=> ~ ! [Y] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,Y),transi910771962on_val(R)))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(Y,B),R)) ) ) ) ).
fof(fact_122_rtranclE,axiom,
! [A_2,B,R] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( A_2 != B
=> ~ ! [Y] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,Y),transi921647814on_val(R)))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(Y,B),R)) ) ) ) ).
fof(fact_123_rtranclE,axiom,
! [A_2,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( A_2 != B
=> ~ ! [Y] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,Y),transi2024712006on_val(R)))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y,B),R)) ) ) ) ).
fof(fact_124_converse__rtranclE,axiom,
! [X,Z_1,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(X,Z_1),transi910771962on_val(R)))
=> ( X != Z_1
=> ~ ! [Y] :
( hBOOL(member808015754on_val(produc1564932627on_val(X,Y),R))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(Y,Z_1),transi910771962on_val(R))) ) ) ) ).
fof(fact_125_converse__rtranclE,axiom,
! [X,Z_1,R] :
( hBOOL(member563141460on_val(produc870913623on_val(X,Z_1),transi921647814on_val(R)))
=> ( X != Z_1
=> ~ ! [Y] :
( hBOOL(member563141460on_val(produc870913623on_val(X,Y),R))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(Y,Z_1),transi921647814on_val(R))) ) ) ) ).
fof(fact_126_converse__rtranclE,axiom,
! [X,Z_1,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(X,Z_1),transi2024712006on_val(R)))
=> ( X != Z_1
=> ~ ! [Y] :
( hBOOL(member773094996on_val(produc1441475159on_val(X,Y),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y,Z_1),transi2024712006on_val(R))) ) ) ) ).
fof(fact_127_converse__rtrancl__induct,axiom,
! [Pa,A_2,B,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,B))
=> ( ! [Y,Z] :
( hBOOL(member808015754on_val(produc1564932627on_val(Y,Z),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(Z,B),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,Z))
=> hBOOL(hAPP_P282169671l_bool(Pa,Y)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(Pa,A_2)) ) ) ) ).
fof(fact_128_converse__rtrancl__induct,axiom,
! [Pa,A_2,B,R] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,B))
=> ( ! [Y,Z] :
( hBOOL(member563141460on_val(produc870913623on_val(Y,Z),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(Z,B),transi921647814on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,Z))
=> hBOOL(hAPP_P159683425l_bool(Pa,Y)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(Pa,A_2)) ) ) ) ).
fof(fact_129_converse__rtrancl__induct,axiom,
! [Pa,A_2,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
=> ( ! [Y,Z] :
( hBOOL(member773094996on_val(produc1441475159on_val(Y,Z),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Y)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,A_2)) ) ) ) ).
fof(fact_130_rtrancl__induct,axiom,
! [Pa,A_2,B,R] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,B),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,A_2))
=> ( ! [Y,Z] :
( hBOOL(member808015754on_val(produc1564932627on_val(A_2,Y),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(Y,Z),R))
=> ( hBOOL(hAPP_P282169671l_bool(Pa,Y))
=> hBOOL(hAPP_P282169671l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P282169671l_bool(Pa,B)) ) ) ) ).
fof(fact_131_rtrancl__induct,axiom,
! [Pa,A_2,B,R] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,B),transi921647814on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,A_2))
=> ( ! [Y,Z] :
( hBOOL(member563141460on_val(produc870913623on_val(A_2,Y),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(Y,Z),R))
=> ( hBOOL(hAPP_P159683425l_bool(Pa,Y))
=> hBOOL(hAPP_P159683425l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(Pa,B)) ) ) ) ).
fof(fact_132_rtrancl__induct,axiom,
! [Pa,A_2,B,R] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,A_2))
=> ( ! [Y,Z] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_2,Y),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Y,Z),R))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Y))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).
fof(fact_133_mem__def,axiom,
! [X,A_9] :
( hBOOL(member808015754on_val(X,A_9))
<=> hBOOL(hAPP_P378063101l_bool(A_9,X)) ) ).
fof(fact_134_mem__def,axiom,
! [X,A_9] :
( hBOOL(member563141460on_val(X,A_9))
<=> hBOOL(hAPP_P1221872711l_bool(A_9,X)) ) ).
fof(fact_135_mem__def,axiom,
! [X,A_9] :
( hBOOL(member840932460on_val(X,A_9))
<=> hBOOL(hAPP_P1708370145l_bool(A_9,X)) ) ).
fof(fact_136_mem__def,axiom,
! [X,A_9] :
( hBOOL(member763590124on_val(X,A_9))
<=> hBOOL(hAPP_P159683425l_bool(A_9,X)) ) ).
fof(fact_137_mem__def,axiom,
! [X,A_9] :
( hBOOL(member773094996on_val(X,A_9))
<=> hBOOL(hAPP_P282169671l_bool(A_9,X)) ) ).
fof(fact_138_FAssReds2,axiom,
! [V,Fa,Da,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,Eb),S_1),produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,E_b),S)),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_139_exp_Osimps_I3_J,axiom,
! [Val_9,Val_8] :
( val_list_char(Val_9) = val_list_char(Val_8)
<=> Val_9 = Val_8 ) ).
fof(fact_140_exp_Osimps_I76_J,axiom,
! [Val_7,Exp_14,List1_11,List2_11] : val_list_char(Val_7) != fAcc_list_char(Exp_14,List1_11,List2_11) ).
fof(fact_141_exp_Osimps_I77_J,axiom,
! [Exp_13,List1_10,List2_10,Val_6] : fAcc_list_char(Exp_13,List1_10,List2_10) != val_list_char(Val_6) ).
fof(fact_142_exp_Osimps_I78_J,axiom,
! [Val_5,Exp1_14,List1_9,List2_9,Exp2_14] : val_list_char(Val_5) != fAss_list_char(Exp1_14,List1_9,List2_9,Exp2_14) ).
fof(fact_143_exp_Osimps_I79_J,axiom,
! [Exp1_13,List1_8,List2_8,Exp2_13,Val_4] : fAss_list_char(Exp1_13,List1_8,List2_8,Exp2_13) != val_list_char(Val_4) ).
fof(fact_144_red__reds_OFAssRed2,axiom,
! [V,Fa,Da,Eb,S_1,E_b,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(E_b,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,Eb),S_1),produc1259058957on_val(fAss_list_char(val_list_char(V),Fa,Da,E_b),S)),red(Pa))) ) ).
fof(fact_145_FAssRedsThrow2,axiom,
! [Fa,Da,E_2,Eb,S_2,E_1,S_0,V,S_1_1,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1,S_0),produc1259058957on_val(val_list_char(V),S_1_1)),transi2024712006on_val(red(Pa))))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(throw_list_char(Eb),S_2)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(E_1,Fa,Da,E_2),S_0),produc1259058957on_val(throw_list_char(Eb),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).
fof(fact_146_TryRedsVal,axiom,
! [C,V_1,E_2,Eb,S_1,V,S,Pa] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Eb,S_1),produc1259058957on_val(val_list_char(V),S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Eb,C,V_1,E_2),S_1),produc1259058957on_val(val_list_char(V),S)),transi2024712006on_val(red(Pa)))) ) ).
fof(fact_147_exp_Osimps_I90_J,axiom,
! [Val_3,Exp_12] : val_list_char(Val_3) != throw_list_char(Exp_12) ).
fof(fact_148_exp_Osimps_I91_J,axiom,
! [Exp_11,Val_2] : throw_list_char(Exp_11) != val_list_char(Val_2) ).
fof(fact_149_exp_Osimps_I92_J,axiom,
! [Val_1,Exp1_12,List_8,A_8,Exp2_12] : val_list_char(Val_1) != tryCatch_list_char(Exp1_12,List_8,A_8,Exp2_12) ).
fof(fact_150_exp_Osimps_I93_J,axiom,
! [Exp1_11,List_7,A_7,Exp2_11,Val] : tryCatch_list_char(Exp1_11,List_7,A_7,Exp2_11) != val_list_char(Val) ).
fof(fact_151_exp_Osimps_I180_J,axiom,
! [Exp1_10,List1_7,List2_7,Exp2_10,Exp_10] : fAss_list_char(Exp1_10,List1_7,List2_7,Exp2_10) != throw_list_char(Exp_10) ).
fof(fact_152_exp_Osimps_I181_J,axiom,
! [Exp_9,Exp1_9,List1_6,List2_6,Exp2_9] : throw_list_char(Exp_9) != fAss_list_char(Exp1_9,List1_6,List2_6,Exp2_9) ).
fof(fact_153_exp_Osimps_I166_J,axiom,
! [Exp_8,List1_5,List2_5,Exp_7] : fAcc_list_char(Exp_8,List1_5,List2_5) != throw_list_char(Exp_7) ).
fof(fact_154_exp_Osimps_I167_J,axiom,
! [Exp_6,Exp_5,List1_4,List2_4] : throw_list_char(Exp_6) != fAcc_list_char(Exp_5,List1_4,List2_4) ).
fof(fact_155_exp_Osimps_I183_J,axiom,
! [Exp1_8,List_6,A_6,Exp2_8,Exp1_7,List1_3,List2_3,Exp2_7] : tryCatch_list_char(Exp1_8,List_6,A_6,Exp2_8) != fAss_list_char(Exp1_7,List1_3,List2_3,Exp2_7) ).
fof(fact_156_exp_Osimps_I182_J,axiom,
! [Exp1_6,List1_2,List2_2,Exp2_6,Exp1_5,List_5,A_5,Exp2_5] : fAss_list_char(Exp1_6,List1_2,List2_2,Exp2_6) != tryCatch_list_char(Exp1_5,List_5,A_5,Exp2_5) ).
fof(fact_157_exp_Osimps_I169_J,axiom,
! [Exp1_4,List_4,A_4,Exp2_4,Exp_4,List1_1,List2_1] : tryCatch_list_char(Exp1_4,List_4,A_4,Exp2_4) != fAcc_list_char(Exp_4,List1_1,List2_1) ).
fof(fact_158_exp_Osimps_I168_J,axiom,
! [Exp_3,List1,List2,Exp1_3,List_3,A_3,Exp2_3] : fAcc_list_char(Exp_3,List1,List2) != tryCatch_list_char(Exp1_3,List_3,A_3,Exp2_3) ).
fof(fact_159_exp_Osimps_I15_J,axiom,
! [Exp1_2,List_2,A_2,Exp2_2,Exp1_1,List_1,A_1,Exp2_1] :
( tryCatch_list_char(Exp1_2,List_2,A_2,Exp2_2) = tryCatch_list_char(Exp1_1,List_1,A_1,Exp2_1)
<=> ( Exp1_2 = Exp1_1
& List_2 = List_1
& A_2 = A_1
& Exp2_2 = Exp2_1 ) ) ).
fof(fact_160_exp_Osimps_I14_J,axiom,
! [Exp_2,Exp_1] :
( throw_list_char(Exp_2) = throw_list_char(Exp_1)
<=> Exp_2 = Exp_1 ) ).
fof(fact_161_exp_Osimps_I225_J,axiom,
! [Exp1,List,A,Exp2,Exp] : tryCatch_list_char(Exp1,List,A,Exp2) != throw_list_char(Exp) ).
%----Conjectures (1)
fof(conj_0,conjecture,
hBOOL(wTrt(p,h_a,e,e_a,nt)) ).
%------------------------------------------------------------------------------