TPTP Problem File: SWW471+1.p
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%------------------------------------------------------------------------------
% File : SWW471+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 269, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : hoare_100_fofmg_l269 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 259 ( 106 unt; 0 def)
% Number of atoms : 543 ( 182 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 347 ( 63 ~; 29 |; 44 &)
% ( 54 <=>; 157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 0 prp; 1-2 aty)
% Number of functors : 90 ( 90 usr; 24 con; 0-3 aty)
% Number of variables : 629 ( 619 !; 10 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:39:44
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (28)
fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,axiom,
! [B_1_1,B_2] :
( is_fun_pname_bool(B_2)
=> is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2)) ) ).
fof(gsy_c_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool,axiom,
! [B_1_1,B_2] :
( is_pname(B_2)
=> is_fun_pname_bool(cOMBC_1149511130e_bool(B_1_1,B_2)) ) ).
fof(gsy_c_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000,axiom,
! [B_1_1,B_2] :
( is_fun_pname_bool(B_2)
=> is_fun_pname_bool(cOMBC_1058051404l_bool(B_1_1,B_2)) ) ).
fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname,axiom,
! [B_1_1] :
( is_bool(B_1_1)
=> is_fun_pname_bool(cOMBK_bool_pname(B_1_1)) ) ).
fof(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2] :
( is_fun_pname_bool(B_2)
=> is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2)) ) ).
fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
is_pname(undefined_pname(pname)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ).
fof(gsy_c_Hoare__Mirabelle__jfehddehev_Ohoare__derivs_000t__a,axiom,
! [B_1_1,B_2] : is_bool(hoare_472868247rivs_a(B_1_1,B_2)) ).
fof(gsy_c_Hoare__Mirabelle__jfehddehev_Ohoare__valids_000t__a,axiom,
! [B_1_1,B_2] : is_bool(hoare_810701593lids_a(B_1_1,B_2)) ).
fof(gsy_c_Lattices_Osemilattice__sup__class_Osup_000tc__HOL__Obool,axiom,
! [B_1_1,B_2] :
( ( is_bool(B_1_1)
& is_bool(B_2) )
=> is_bool(semila1168014441p_bool(B_1_1,B_2)) ) ).
fof(gsy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__Com__Opname_Mtc__HO,axiom,
! [B_1_1,B_2] :
( ( is_fun_pname_bool(B_1_1)
& is_fun_pname_bool(B_2) )
=> is_fun_pname_bool(semila278973382e_bool(B_1_1,B_2)) ) ).
fof(gsy_c_Natural_Oevalc,axiom,
! [B_1_1,B_2,B_3] : is_bool(evalc(B_1_1,B_2,B_3)) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(bot_bo844097828e_bool) ).
fof(gsy_c_Set_OCollect_000tc__Com__Opname,axiom,
! [B_1_1] :
( is_fun_pname_bool(B_1_1)
=> is_fun_pname_bool(collect_pname(B_1_1)) ) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [B_1_1,B_2] :
( is_fun_pname_bool(B_2)
=> is_fun_pname_bool(image_pname_pname(B_1_1,B_2)) ) ).
fof(gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc_,axiom,
! [B_1_1,B_2] : is_fun_pname_bool(image_1474161344_pname(B_1_1,B_2)) ).
fof(gsy_c_Set_Oinsert_000tc__Com__Opname,axiom,
! [B_1_1,B_2] :
( ( is_pname(B_1_1)
& is_fun_pname_bool(B_2) )
=> is_fun_pname_bool(insert_pname(B_1_1,B_2)) ) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [B_1_1,B_2] :
( is_pname(B_2)
=> is_pname(hAPP_pname_pname(B_1_1,B_2)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
! [B_1_1,B_2] :
( ( is_fun_pname_bool(B_1_1)
& is_pname(B_2) )
=> is_bool(hAPP_pname_bool(B_1_1,B_2)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2] :
( is_pname(B_2)
=> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2] :
( is_bool(B_2)
=> is_bool(hAPP_bool_bool(B_1_1,B_2)) ) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__Com__,axiom,
! [B_1_1,B_2] : is_pname(hAPP_H82695184_pname(B_1_1,B_2)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__HOL__,hypothesis,
! [B_1_1,B_2] : is_bool(hAPP_H1927961489a_bool(B_1_1,B_2)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2] :
( is_fun_pname_bool(B_2)
=> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc,hypothesis,
! [B_1_1,B_2] : is_bool(hAPP_f1753944735l_bool(B_1_1,B_2)) ).
fof(gsy_v_Procs,hypothesis,
is_fun_pname_bool(procs) ).
%----Relevant facts (190)
fof(fact_0_triple_Oinject,axiom,
! [Fun1_2,Com_2,Fun2_2,Fun1_1,Com_1,Fun2_1] :
( hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Fun1_2),Com_2),Fun2_2) = hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Fun1_1),Com_1),Fun2_1)
<=> ( Fun1_2 = Fun1_1
& Com_2 = Com_1
& Fun2_2 = Fun2_1 ) ) ).
fof(fact_1_hoare__valids__def,axiom,
! [Ga,Ts] :
( hBOOL(hoare_810701593lids_a(Ga,Ts))
<=> ! [N] :
( ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),Ga))
=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)) )
=> ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),Ts))
=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)) ) ) ) ).
fof(fact_2_hoare__derivs_OBody,axiom,
! [Ga,Pa,Qa,Procsa] :
( hBOOL(hoare_472868247rivs_a(semila2005279307a_bool(Ga,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),body),Qa),Procsa)),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),cOMBB_923936821_pname(the_com,body_1)),Qa),Procsa)))
=> hBOOL(hoare_472868247rivs_a(Ga,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),body),Qa),Procsa))) ) ).
fof(fact_3_UnE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1)) ) ) ).
fof(fact_4_UnE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) ) ) ).
fof(fact_5_sup1E,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2))
=> ( ~ hBOOL(hAPP_H1927961489a_bool(A,X_2))
=> hBOOL(hAPP_H1927961489a_bool(B_1,X_2)) ) ) ).
fof(fact_6_sup1E,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2))
=> ( ~ hBOOL(hAPP_pname_bool(A,X_2))
=> hBOOL(hAPP_pname_bool(B_1,X_2)) ) ) ).
fof(fact_7_sup1CI,axiom,
! [A,B_1,X_2] :
( ( ~ hBOOL(hAPP_H1927961489a_bool(B_1,X_2))
=> hBOOL(hAPP_H1927961489a_bool(A,X_2)) )
=> hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)) ) ).
fof(fact_8_sup1CI,axiom,
! [A,B_1,X_2] :
( ( ~ hBOOL(hAPP_pname_bool(B_1,X_2))
=> hBOOL(hAPP_pname_bool(A,X_2)) )
=> hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)) ) ).
fof(fact_9_UnCI,axiom,
! [A,C,B_1] :
( ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A)) )
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))) ) ).
fof(fact_10_UnCI,axiom,
! [A,C,B_1] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))) ) ).
fof(fact_11_image__eqI,axiom,
! [A,B,F,X_2] :
( B = hAPP_p1261697242iple_a(F,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),image_505679754iple_a(F,A))) ) ) ).
fof(fact_12_image__eqI,axiom,
! [A,B,F,X_2] :
( B = hAPP_H82695184_pname(F,X_2)
=> ( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),image_1474161344_pname(F,A))) ) ) ).
fof(fact_13_image__Un,axiom,
! [F,A,B_1] : image_505679754iple_a(F,semila278973382e_bool(A,B_1)) = semila2005279307a_bool(image_505679754iple_a(F,A),image_505679754iple_a(F,B_1)) ).
fof(fact_14_image__Un,axiom,
! [F,A,B_1] : image_1474161344_pname(F,semila2005279307a_bool(A,B_1)) = semila278973382e_bool(image_1474161344_pname(F,A),image_1474161344_pname(F,B_1)) ).
fof(fact_15_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(F,G),X))
<=> hBOOL(semila1168014441p_bool(hAPP_H1927961489a_bool(F,X),hAPP_H1927961489a_bool(G,X))) ) ).
fof(fact_16_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_pname_bool(semila278973382e_bool(F,G),X))
<=> hBOOL(semila1168014441p_bool(hAPP_pname_bool(F,X),hAPP_pname_bool(G,X))) ) ).
fof(fact_17_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(F,G),X_2))
<=> hBOOL(semila1168014441p_bool(hAPP_H1927961489a_bool(F,X_2),hAPP_H1927961489a_bool(G,X_2))) ) ).
fof(fact_18_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_pname_bool(semila278973382e_bool(F,G),X_2))
<=> hBOOL(semila1168014441p_bool(hAPP_pname_bool(F,X_2),hAPP_pname_bool(G,X_2))) ) ).
fof(fact_19_cut,axiom,
! [Ga,G_1,Ts] :
( hBOOL(hoare_472868247rivs_a(G_1,Ts))
=> ( hBOOL(hoare_472868247rivs_a(Ga,G_1))
=> hBOOL(hoare_472868247rivs_a(Ga,Ts)) ) ) ).
fof(fact_20_sup__assoc,axiom,
! [X_2,Y_1,Z] : semila2005279307a_bool(semila2005279307a_bool(X_2,Y_1),Z) = semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z)) ).
fof(fact_21_sup__assoc,axiom,
! [X_2,Y_1,Z] : semila278973382e_bool(semila278973382e_bool(X_2,Y_1),Z) = semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z)) ).
fof(fact_22_sup__assoc,axiom,
! [X_2,Y_1,Z] :
( hBOOL(semila1168014441p_bool(semila1168014441p_bool(X_2,Y_1),Z))
<=> hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z))) ) ).
fof(fact_23_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z] : semila2005279307a_bool(semila2005279307a_bool(X_2,Y_1),Z) = semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z)) ).
fof(fact_24_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z] : semila278973382e_bool(semila278973382e_bool(X_2,Y_1),Z) = semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z)) ).
fof(fact_25_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z] :
( hBOOL(semila1168014441p_bool(semila1168014441p_bool(X_2,Y_1),Z))
<=> hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z))) ) ).
fof(fact_26_sup_Oassoc,axiom,
! [A_1,B,C] : semila2005279307a_bool(semila2005279307a_bool(A_1,B),C) = semila2005279307a_bool(A_1,semila2005279307a_bool(B,C)) ).
fof(fact_27_sup_Oassoc,axiom,
! [A_1,B,C] : semila278973382e_bool(semila278973382e_bool(A_1,B),C) = semila278973382e_bool(A_1,semila278973382e_bool(B,C)) ).
fof(fact_28_sup_Oassoc,axiom,
! [A_1,B,C] :
( hBOOL(semila1168014441p_bool(semila1168014441p_bool(A_1,B),C))
<=> hBOOL(semila1168014441p_bool(A_1,semila1168014441p_bool(B,C))) ) ).
fof(fact_29_sup__left__commute,axiom,
! [X_2,Y_1,Z] : semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z)) = semila2005279307a_bool(Y_1,semila2005279307a_bool(X_2,Z)) ).
fof(fact_30_sup__left__commute,axiom,
! [X_2,Y_1,Z] : semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z)) = semila278973382e_bool(Y_1,semila278973382e_bool(X_2,Z)) ).
fof(fact_31_sup__left__commute,axiom,
! [X_2,Y_1,Z] :
( hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z)))
<=> hBOOL(semila1168014441p_bool(Y_1,semila1168014441p_bool(X_2,Z))) ) ).
fof(fact_32_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z] : semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z)) = semila2005279307a_bool(Y_1,semila2005279307a_bool(X_2,Z)) ).
fof(fact_33_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z] : semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z)) = semila278973382e_bool(Y_1,semila278973382e_bool(X_2,Z)) ).
fof(fact_34_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z] :
( hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z)))
<=> hBOOL(semila1168014441p_bool(Y_1,semila1168014441p_bool(X_2,Z))) ) ).
fof(fact_35_sup_Oleft__commute,axiom,
! [B,A_1,C] : semila2005279307a_bool(B,semila2005279307a_bool(A_1,C)) = semila2005279307a_bool(A_1,semila2005279307a_bool(B,C)) ).
fof(fact_36_sup_Oleft__commute,axiom,
! [B,A_1,C] : semila278973382e_bool(B,semila278973382e_bool(A_1,C)) = semila278973382e_bool(A_1,semila278973382e_bool(B,C)) ).
fof(fact_37_sup_Oleft__commute,axiom,
! [B,A_1,C] :
( hBOOL(semila1168014441p_bool(B,semila1168014441p_bool(A_1,C)))
<=> hBOOL(semila1168014441p_bool(A_1,semila1168014441p_bool(B,C))) ) ).
fof(fact_38_sup__left__idem,axiom,
! [X_2,Y_1] : semila2005279307a_bool(X_2,semila2005279307a_bool(X_2,Y_1)) = semila2005279307a_bool(X_2,Y_1) ).
fof(fact_39_sup__left__idem,axiom,
! [X_2,Y_1] : semila278973382e_bool(X_2,semila278973382e_bool(X_2,Y_1)) = semila278973382e_bool(X_2,Y_1) ).
fof(fact_40_sup__left__idem,axiom,
! [X_2,Y_1] :
( hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(X_2,Y_1)))
<=> hBOOL(semila1168014441p_bool(X_2,Y_1)) ) ).
fof(fact_41_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : semila2005279307a_bool(X_2,semila2005279307a_bool(X_2,Y_1)) = semila2005279307a_bool(X_2,Y_1) ).
fof(fact_42_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : semila278973382e_bool(X_2,semila278973382e_bool(X_2,Y_1)) = semila278973382e_bool(X_2,Y_1) ).
fof(fact_43_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] :
( hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(X_2,Y_1)))
<=> hBOOL(semila1168014441p_bool(X_2,Y_1)) ) ).
fof(fact_44_sup_Oleft__idem,axiom,
! [A_1,B] : semila2005279307a_bool(A_1,semila2005279307a_bool(A_1,B)) = semila2005279307a_bool(A_1,B) ).
fof(fact_45_sup_Oleft__idem,axiom,
! [A_1,B] : semila278973382e_bool(A_1,semila278973382e_bool(A_1,B)) = semila278973382e_bool(A_1,B) ).
fof(fact_46_sup_Oleft__idem,axiom,
! [A_1,B] :
( hBOOL(semila1168014441p_bool(A_1,semila1168014441p_bool(A_1,B)))
<=> hBOOL(semila1168014441p_bool(A_1,B)) ) ).
fof(fact_47_sup__commute,axiom,
! [X_2,Y_1] : semila2005279307a_bool(X_2,Y_1) = semila2005279307a_bool(Y_1,X_2) ).
fof(fact_48_sup__commute,axiom,
! [X_2,Y_1] : semila278973382e_bool(X_2,Y_1) = semila278973382e_bool(Y_1,X_2) ).
fof(fact_49_sup__commute,axiom,
! [X_2,Y_1] :
( hBOOL(semila1168014441p_bool(X_2,Y_1))
<=> hBOOL(semila1168014441p_bool(Y_1,X_2)) ) ).
fof(fact_50_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : semila2005279307a_bool(X_2,Y_1) = semila2005279307a_bool(Y_1,X_2) ).
fof(fact_51_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : semila278973382e_bool(X_2,Y_1) = semila278973382e_bool(Y_1,X_2) ).
fof(fact_52_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] :
( hBOOL(semila1168014441p_bool(X_2,Y_1))
<=> hBOOL(semila1168014441p_bool(Y_1,X_2)) ) ).
fof(fact_53_sup_Ocommute,axiom,
! [A_1,B] : semila2005279307a_bool(A_1,B) = semila2005279307a_bool(B,A_1) ).
fof(fact_54_sup_Ocommute,axiom,
! [A_1,B] : semila278973382e_bool(A_1,B) = semila278973382e_bool(B,A_1) ).
fof(fact_55_sup_Ocommute,axiom,
! [A_1,B] :
( hBOOL(semila1168014441p_bool(A_1,B))
<=> hBOOL(semila1168014441p_bool(B,A_1)) ) ).
fof(fact_56_sup__idem,axiom,
! [X_2] : semila2005279307a_bool(X_2,X_2) = X_2 ).
fof(fact_57_sup__idem,axiom,
! [X_2] :
( is_fun_pname_bool(X_2)
=> semila278973382e_bool(X_2,X_2) = X_2 ) ).
fof(fact_58_sup__idem,axiom,
! [X_2] :
( hBOOL(semila1168014441p_bool(X_2,X_2))
<=> hBOOL(X_2) ) ).
fof(fact_59_sup_Oidem,axiom,
! [A_1] : semila2005279307a_bool(A_1,A_1) = A_1 ).
fof(fact_60_sup_Oidem,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> semila278973382e_bool(A_1,A_1) = A_1 ) ).
fof(fact_61_sup_Oidem,axiom,
! [A_1] :
( hBOOL(semila1168014441p_bool(A_1,A_1))
<=> hBOOL(A_1) ) ).
fof(fact_62_rev__image__eqI,axiom,
! [B,F,X_2,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
=> ( B = hAPP_H82695184_pname(F,X_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),image_1474161344_pname(F,A))) ) ) ).
fof(fact_63_rev__image__eqI,axiom,
! [B,F,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( B = hAPP_p1261697242iple_a(F,X_2)
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),image_505679754iple_a(F,A))) ) ) ).
fof(fact_64_imageI,axiom,
! [F,X_2,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H82695184_pname(F,X_2)),image_1474161344_pname(F,A))) ) ).
fof(fact_65_imageI,axiom,
! [F,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hAPP_p1261697242iple_a(F,X_2)),image_505679754iple_a(F,A))) ) ).
fof(fact_66_image__iff,axiom,
! [Z,F,A] :
( is_pname(Z)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Z),image_1474161344_pname(F,A)))
<=> ? [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))
& Z = hAPP_H82695184_pname(F,X) ) ) ) ).
fof(fact_67_image__iff,axiom,
! [Z,F,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,Z),image_505679754iple_a(F,A)))
<=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
& Z = hAPP_p1261697242iple_a(F,X) ) ) ).
fof(fact_68_UnI2,axiom,
! [A,C,B_1] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))) ) ).
fof(fact_69_UnI2,axiom,
! [A,C,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))) ) ).
fof(fact_70_UnI1,axiom,
! [B_1,C,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))) ) ).
fof(fact_71_UnI1,axiom,
! [B_1,C,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))) ) ).
fof(fact_72_sup1I2,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_H1927961489a_bool(B_1,X_2))
=> hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)) ) ).
fof(fact_73_sup1I2,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_pname_bool(B_1,X_2))
=> hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)) ) ).
fof(fact_74_sup1I1,axiom,
! [B_1,A,X_2] :
( hBOOL(hAPP_H1927961489a_bool(A,X_2))
=> hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)) ) ).
fof(fact_75_sup1I1,axiom,
! [B_1,A,X_2] :
( hBOOL(hAPP_pname_bool(A,X_2))
=> hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)) ) ).
fof(fact_76_ball__Un,axiom,
! [Pa,A,B_1] :
( ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(A,B_1)))
=> hBOOL(hAPP_H1927961489a_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))
=> hBOOL(hAPP_H1927961489a_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),B_1))
=> hBOOL(hAPP_H1927961489a_bool(Pa,X)) ) ) ) ).
fof(fact_77_ball__Un,axiom,
! [Pa,A,B_1] :
( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),semila278973382e_bool(A,B_1)))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) )
<=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) )
& ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_1))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) ) ) ) ).
fof(fact_78_bex__Un,axiom,
! [Pa,A,B_1] :
( ? [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(A,B_1)))
& hBOOL(hAPP_H1927961489a_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))
& hBOOL(hAPP_H1927961489a_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),B_1))
& hBOOL(hAPP_H1927961489a_bool(Pa,X)) ) ) ) ).
fof(fact_79_bex__Un,axiom,
! [Pa,A,B_1] :
( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),semila278973382e_bool(A,B_1)))
& hBOOL(hAPP_pname_bool(Pa,X)) )
<=> ( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
& hBOOL(hAPP_pname_bool(Pa,X)) )
| ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_1))
& hBOOL(hAPP_pname_bool(Pa,X)) ) ) ) ).
fof(fact_80_Un__assoc,axiom,
! [A,B_1,C_2] : semila2005279307a_bool(semila2005279307a_bool(A,B_1),C_2) = semila2005279307a_bool(A,semila2005279307a_bool(B_1,C_2)) ).
fof(fact_81_Un__assoc,axiom,
! [A,B_1,C_2] : semila278973382e_bool(semila278973382e_bool(A,B_1),C_2) = semila278973382e_bool(A,semila278973382e_bool(B_1,C_2)) ).
fof(fact_82_Un__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1)))
<=> ( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A))
| hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1)) ) ) ).
fof(fact_83_Un__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) ) ) ).
fof(fact_84_Un__left__commute,axiom,
! [A,B_1,C_2] : semila2005279307a_bool(A,semila2005279307a_bool(B_1,C_2)) = semila2005279307a_bool(B_1,semila2005279307a_bool(A,C_2)) ).
fof(fact_85_Un__left__commute,axiom,
! [A,B_1,C_2] : semila278973382e_bool(A,semila278973382e_bool(B_1,C_2)) = semila278973382e_bool(B_1,semila278973382e_bool(A,C_2)) ).
fof(fact_86_Un__left__absorb,axiom,
! [A,B_1] : semila2005279307a_bool(A,semila2005279307a_bool(A,B_1)) = semila2005279307a_bool(A,B_1) ).
fof(fact_87_Un__left__absorb,axiom,
! [A,B_1] : semila278973382e_bool(A,semila278973382e_bool(A,B_1)) = semila278973382e_bool(A,B_1) ).
fof(fact_88_Un__commute,axiom,
! [A,B_1] : semila2005279307a_bool(A,B_1) = semila2005279307a_bool(B_1,A) ).
fof(fact_89_Un__commute,axiom,
! [A,B_1] : semila278973382e_bool(A,B_1) = semila278973382e_bool(B_1,A) ).
fof(fact_90_Un__def,axiom,
! [A,B_1] : semila2005279307a_bool(A,B_1) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,cOMBC_2067518550l_bool(member564727580iple_a,A)),cOMBC_2067518550l_bool(member564727580iple_a,B_1))) ).
fof(fact_91_Un__def,axiom,
! [A,B_1] : semila278973382e_bool(A,B_1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,cOMBC_1058051404l_bool(member_pname,A)),cOMBC_1058051404l_bool(member_pname,B_1))) ).
fof(fact_92_Un__absorb,axiom,
! [A] : semila2005279307a_bool(A,A) = A ).
fof(fact_93_Un__absorb,axiom,
! [A] :
( is_fun_pname_bool(A)
=> semila278973382e_bool(A,A) = A ) ).
fof(fact_94_image__image,axiom,
! [F,G,A] : image_505679754iple_a(F,image_1474161344_pname(G,A)) = image_29267653iple_a(cOMBB_548833416iple_a(F,G),A) ).
fof(fact_95_image__image,axiom,
! [F,G,A] : image_1474161344_pname(F,image_505679754iple_a(G,A)) = image_pname_pname(cOMBB_1314377293_pname(F,G),A) ).
fof(fact_96_sup__Un__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(cOMBC_2067518550l_bool(member564727580iple_a,R_1),cOMBC_2067518550l_bool(member564727580iple_a,S_1)),X))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(R_1,S_1))) ) ).
fof(fact_97_sup__Un__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_pname_bool(semila278973382e_bool(cOMBC_1058051404l_bool(member_pname,R_1),cOMBC_1058051404l_bool(member_pname,S_1)),X))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),semila278973382e_bool(R_1,S_1))) ) ).
fof(fact_98_Collect__disj__eq,axiom,
! [Pa,Qa] : collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,Pa),Qa)) = semila2005279307a_bool(collec1266446174iple_a(Pa),collec1266446174iple_a(Qa)) ).
fof(fact_99_Collect__disj__eq,axiom,
! [Pa,Qa] : collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Qa)) = semila278973382e_bool(collect_pname(Pa),collect_pname(Qa)) ).
fof(fact_100_imageE,axiom,
! [B,F,A] :
( is_pname(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),image_1474161344_pname(F,A)))
=> ~ ! [X] :
( B = hAPP_H82695184_pname(F,X)
=> ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A)) ) ) ) ).
fof(fact_101_imageE,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),image_505679754iple_a(F,A)))
=> ~ ! [X] :
( is_pname(X)
=> ( B = hAPP_p1261697242iple_a(F,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) ) ) ) ).
fof(fact_102_Body__triple__valid__Suc,axiom,
! [N_2,Pa,Pn_1,Qa] :
( hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N_2),hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)))
<=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(suc(N_2)),hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ) ).
fof(fact_103_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1,Com,Fun2] : Y_1 != hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Fun1),Com),Fun2) ).
fof(fact_104_Body1,axiom,
! [Pn_1,Ga,Pa,Qa,Procsa] :
( hBOOL(hoare_472868247rivs_a(semila2005279307a_bool(Ga,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),body),Qa),Procsa)),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),cOMBB_923936821_pname(the_com,body_1)),Qa),Procsa)))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procsa))
=> hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,hAPP_p635540397e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p635540397e_bool(Qa,Pn_1)),bot_bo1687970473a_bool))) ) ) ).
fof(fact_105_image__cong,axiom,
! [F,G,M,N_1] :
( M = N_1
=> ( ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),N_1))
=> hAPP_H82695184_pname(F,X) = hAPP_H82695184_pname(G,X) )
=> image_1474161344_pname(F,M) = image_1474161344_pname(G,N_1) ) ) ).
fof(fact_106_image__cong,axiom,
! [F,G,M,N_1] :
( M = N_1
=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_1))
=> hAPP_p1261697242iple_a(F,X) = hAPP_p1261697242iple_a(G,X) ) )
=> image_505679754iple_a(F,M) = image_505679754iple_a(G,N_1) ) ) ).
fof(fact_107_Body__triple__valid__0,axiom,
! [Pa,Pn_1,Qa] : hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(zero_zero_nat),hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ).
fof(fact_108_com_Osimps_I6_J,axiom,
! [Pname_1,Pname] :
( ( is_pname(Pname_1)
& is_pname(Pname) )
=> ( hAPP_pname_com(body,Pname_1) = hAPP_pname_com(body,Pname)
<=> Pname_1 = Pname ) ) ).
fof(fact_109_evalc_OBody,axiom,
! [Pn,S0,S1] :
( hBOOL(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn)),S0,S1))
=> hBOOL(evalc(hAPP_pname_com(body,Pn),S0,S1)) ) ).
fof(fact_110_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),bot_bo1687970473a_bool)) ).
fof(fact_111_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),bot_bo844097828e_bool)) ).
fof(fact_112_insertE,axiom,
! [A_1,B,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,A)))
=> ( A_1 != B
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A)) ) ) ).
fof(fact_113_insertE,axiom,
! [A_1,B,A] :
( ( is_pname(A_1)
& is_pname(B) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,A)))
=> ( A_1 != B
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ) ).
fof(fact_114_insertCI,axiom,
! [B,A_1,B_1] :
( ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),B_1))
=> A_1 = B )
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,B_1))) ) ).
fof(fact_115_insertCI,axiom,
! [B,A_1,B_1] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_1))
=> A_1 = B )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,B_1))) ) ).
fof(fact_116_evalc__elim__cases_I6_J,axiom,
! [P,S,S1] :
( hBOOL(evalc(hAPP_pname_com(body,P),S,S1))
=> hBOOL(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P)),S,S1)) ) ).
fof(fact_117_empty__not__insert,axiom,
! [A_1,A] : bot_bo1687970473a_bool != insert1871499715iple_a(A_1,A) ).
fof(fact_118_empty__not__insert,axiom,
! [A_1,A] : bot_bo844097828e_bool != insert_pname(A_1,A) ).
fof(fact_119_insert__not__empty,axiom,
! [A_1,A] : insert1871499715iple_a(A_1,A) != bot_bo1687970473a_bool ).
fof(fact_120_insert__not__empty,axiom,
! [A_1,A] : insert_pname(A_1,A) != bot_bo844097828e_bool ).
fof(fact_121_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X))
<=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),bot_bo1687970473a_bool)) ) ).
fof(fact_122_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),bot_bo844097828e_bool)) ) ).
fof(fact_123_empty__def,axiom,
bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)) ).
fof(fact_124_empty__def,axiom,
bot_bo1687970473a_bool = collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) ).
fof(fact_125_insertI1,axiom,
! [A_1,B_1] : hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(A_1,B_1))) ).
fof(fact_126_insertI1,axiom,
! [A_1,B_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(A_1,B_1))) ).
fof(fact_127_all__not__in__conv,axiom,
! [A] :
( ! [X] : ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))
<=> A = bot_bo1687970473a_bool ) ).
fof(fact_128_all__not__in__conv,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( ! [X] :
( is_pname(X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) )
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_129_singleton__conv2,axiom,
! [A_1] : collec1266446174iple_a(hAPP_H562195827a_bool(fequal1878252616iple_a,A_1)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool) ).
fof(fact_130_singleton__conv2,axiom,
! [A_1] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_1)) = insert_pname(A_1,bot_bo844097828e_bool) ).
fof(fact_131_ex__in__conv,axiom,
! [A] :
( ? [X] : hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))
<=> A != bot_bo1687970473a_bool ) ).
fof(fact_132_ex__in__conv,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) )
<=> A != bot_bo844097828e_bool ) ) ).
fof(fact_133_singleton__conv,axiom,
! [A_1] : collec1266446174iple_a(cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool) ).
fof(fact_134_singleton__conv,axiom,
! [A_1] : collect_pname(cOMBC_1149511130e_bool(fequal_pname,A_1)) = insert_pname(A_1,bot_bo844097828e_bool) ).
fof(fact_135_Collect__conv__if2,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_H1927961489a_bool(Pa,A_1))
=> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,hAPP_H562195827a_bool(fequal1878252616iple_a,A_1)),Pa)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool) )
& ( ~ hBOOL(hAPP_H1927961489a_bool(Pa,A_1))
=> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,hAPP_H562195827a_bool(fequal1878252616iple_a,A_1)),Pa)) = bot_bo1687970473a_bool ) ) ).
fof(fact_136_Collect__conv__if2,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_pname_bool(Pa,A_1))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_1)),Pa)) = insert_pname(A_1,bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(Pa,A_1))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_1)),Pa)) = bot_bo844097828e_bool ) ) ).
fof(fact_137_Collect__conv__if,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_H1927961489a_bool(Pa,A_1))
=> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)),Pa)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool) )
& ( ~ hBOOL(hAPP_H1927961489a_bool(Pa,A_1))
=> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)),Pa)) = bot_bo1687970473a_bool ) ) ).
fof(fact_138_Collect__conv__if,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_pname_bool(Pa,A_1))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,cOMBC_1149511130e_bool(fequal_pname,A_1)),Pa)) = insert_pname(A_1,bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(Pa,A_1))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,cOMBC_1149511130e_bool(fequal_pname,A_1)),Pa)) = bot_bo844097828e_bool ) ) ).
fof(fact_139_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo844097828e_bool = collect_pname(Pa)
<=> ! [X] :
( is_pname(X)
=> ~ hBOOL(hAPP_pname_bool(Pa,X)) ) ) ).
fof(fact_140_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo1687970473a_bool = collec1266446174iple_a(Pa)
<=> ! [X] : ~ hBOOL(hAPP_H1927961489a_bool(Pa,X)) ) ).
fof(fact_141_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),bot_bo1687970473a_bool)) ).
fof(fact_142_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool)) ).
fof(fact_143_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
<=> hBOOL(hAPP_H1927961489a_bool(A,X_2)) ) ).
fof(fact_144_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
<=> hBOOL(hAPP_pname_bool(A,X_2)) ) ).
fof(fact_145_Collect__def,axiom,
! [Pa] :
( is_fun_pname_bool(Pa)
=> collect_pname(Pa) = Pa ) ).
fof(fact_146_Collect__def,axiom,
! [Pa] : collec1266446174iple_a(Pa) = Pa ).
fof(fact_147_insert__compr,axiom,
! [A_1,B_1] : insert1871499715iple_a(A_1,B_1) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)),cOMBC_2067518550l_bool(member564727580iple_a,B_1))) ).
fof(fact_148_insert__compr,axiom,
! [A_1,B_1] : insert_pname(A_1,B_1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,cOMBC_1149511130e_bool(fequal_pname,A_1)),cOMBC_1058051404l_bool(member_pname,B_1))) ).
fof(fact_149_insert__is__Un,axiom,
! [A_1,A] : insert1871499715iple_a(A_1,A) = semila2005279307a_bool(insert1871499715iple_a(A_1,bot_bo1687970473a_bool),A) ).
fof(fact_150_insert__is__Un,axiom,
! [A_1,A] : insert_pname(A_1,A) = semila278973382e_bool(insert_pname(A_1,bot_bo844097828e_bool),A) ).
fof(fact_151_insert__Collect,axiom,
! [A_1,Pa] : insert1871499715iple_a(A_1,collec1266446174iple_a(Pa)) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fimplies,cOMBB_650444389iple_a(fNot,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1))),Pa)) ).
fof(fact_152_insert__Collect,axiom,
! [A_1,Pa] : insert_pname(A_1,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,cOMBC_1149511130e_bool(fequal_pname,A_1))),Pa)) ).
fof(fact_153_singleton__iff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),insert1871499715iple_a(A_1,bot_bo1687970473a_bool)))
<=> B = A_1 ) ).
fof(fact_154_singleton__iff,axiom,
! [B,A_1] :
( ( is_pname(B)
& is_pname(A_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),insert_pname(A_1,bot_bo844097828e_bool)))
<=> B = A_1 ) ) ).
fof(fact_155_insert__absorb2,axiom,
! [X_2,A] : insert1871499715iple_a(X_2,insert1871499715iple_a(X_2,A)) = insert1871499715iple_a(X_2,A) ).
fof(fact_156_insert__absorb2,axiom,
! [X_2,A] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A) ).
fof(fact_157_insert__commute,axiom,
! [X_2,Y_1,A] : insert1871499715iple_a(X_2,insert1871499715iple_a(Y_1,A)) = insert1871499715iple_a(Y_1,insert1871499715iple_a(X_2,A)) ).
fof(fact_158_insert__commute,axiom,
! [X_2,Y_1,A] : insert_pname(X_2,insert_pname(Y_1,A)) = insert_pname(Y_1,insert_pname(X_2,A)) ).
fof(fact_159_insert__iff,axiom,
! [A_1,B,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,A)))
<=> ( A_1 = B
| hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A)) ) ) ).
fof(fact_160_insert__iff,axiom,
! [A_1,B,A] :
( ( is_pname(A_1)
& is_pname(B) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,A)))
<=> ( A_1 = B
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ) ).
fof(fact_161_Collect__empty__eq,axiom,
! [Pa] :
( collect_pname(Pa) = bot_bo844097828e_bool
<=> ! [X] :
( is_pname(X)
=> ~ hBOOL(hAPP_pname_bool(Pa,X)) ) ) ).
fof(fact_162_Collect__empty__eq,axiom,
! [Pa] :
( collec1266446174iple_a(Pa) = bot_bo1687970473a_bool
<=> ! [X] : ~ hBOOL(hAPP_H1927961489a_bool(Pa,X)) ) ).
fof(fact_163_doubleton__eq__iff,axiom,
! [A_1,B,C,D] :
( insert1871499715iple_a(A_1,insert1871499715iple_a(B,bot_bo1687970473a_bool)) = insert1871499715iple_a(C,insert1871499715iple_a(D,bot_bo1687970473a_bool))
<=> ( ( A_1 = C
& B = D )
| ( A_1 = D
& B = C ) ) ) ).
fof(fact_164_doubleton__eq__iff,axiom,
! [A_1,B,C,D] :
( ( is_pname(A_1)
& is_pname(B)
& is_pname(C)
& is_pname(D) )
=> ( insert_pname(A_1,insert_pname(B,bot_bo844097828e_bool)) = insert_pname(C,insert_pname(D,bot_bo844097828e_bool))
<=> ( ( A_1 = C
& B = D )
| ( A_1 = D
& B = C ) ) ) ) ).
fof(fact_165_insert__code,axiom,
! [Y_1,A,X_2] :
( hBOOL(hAPP_H1927961489a_bool(insert1871499715iple_a(Y_1,A),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_H1927961489a_bool(A,X_2)) ) ) ).
fof(fact_166_insert__code,axiom,
! [Y_1,A,X_2] :
( ( is_pname(Y_1)
& is_pname(X_2) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_pname_bool(A,X_2)) ) ) ) ).
fof(fact_167_insert__compr__raw,axiom,
! [X,Xa] : insert1871499715iple_a(X,Xa) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,cOMBC_2049287834a_bool(fequal1878252616iple_a,X)),cOMBC_2067518550l_bool(member564727580iple_a,Xa))) ).
fof(fact_168_insert__compr__raw,axiom,
! [X,Xa] : insert_pname(X,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,cOMBC_1149511130e_bool(fequal_pname,X)),cOMBC_1058051404l_bool(member_pname,Xa))) ).
fof(fact_169_insert__ident,axiom,
! [B_1,X_2,A] :
( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
=> ( ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),B_1))
=> ( insert1871499715iple_a(X_2,A) = insert1871499715iple_a(X_2,B_1)
<=> A = B_1 ) ) ) ).
fof(fact_170_insert__ident,axiom,
! [B_1,X_2,A] :
( ( is_fun_pname_bool(B_1)
& is_fun_pname_bool(A) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_1))
=> ( insert_pname(X_2,A) = insert_pname(X_2,B_1)
<=> A = B_1 ) ) ) ) ).
fof(fact_171_equals0D,axiom,
! [A_1,A] :
( A = bot_bo1687970473a_bool
=> ~ hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A)) ) ).
fof(fact_172_equals0D,axiom,
! [A_1,A] :
( A = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ).
fof(fact_173_insertI2,axiom,
! [B,A_1,B_1] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),B_1))
=> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,B_1))) ) ).
fof(fact_174_insertI2,axiom,
! [B,A_1,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,B_1))) ) ).
fof(fact_175_insert__absorb,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A))
=> insert1871499715iple_a(A_1,A) = A ) ).
fof(fact_176_insert__absorb,axiom,
! [A_1,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> insert_pname(A_1,A) = A ) ) ).
fof(fact_177_hoare__derivs_Oinsert,axiom,
! [Ts,Ga,T_1] :
( hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,bot_bo1687970473a_bool)))
=> ( hBOOL(hoare_472868247rivs_a(Ga,Ts))
=> hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,Ts))) ) ) ).
fof(fact_178_singletonE,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),insert1871499715iple_a(A_1,bot_bo1687970473a_bool)))
=> B = A_1 ) ).
fof(fact_179_singletonE,axiom,
! [B,A_1] :
( ( is_pname(B)
& is_pname(A_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),insert_pname(A_1,bot_bo844097828e_bool)))
=> B = A_1 ) ) ).
fof(fact_180_derivs__insertD,axiom,
! [Ga,T_1,Ts] :
( hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,Ts)))
=> ( hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,bot_bo1687970473a_bool)))
& hBOOL(hoare_472868247rivs_a(Ga,Ts)) ) ) ).
fof(fact_181_singleton__inject,axiom,
! [A_1,B] :
( insert1871499715iple_a(A_1,bot_bo1687970473a_bool) = insert1871499715iple_a(B,bot_bo1687970473a_bool)
=> A_1 = B ) ).
fof(fact_182_singleton__inject,axiom,
! [A_1,B] :
( ( is_pname(A_1)
& is_pname(B) )
=> ( insert_pname(A_1,bot_bo844097828e_bool) = insert_pname(B,bot_bo844097828e_bool)
=> A_1 = B ) ) ).
fof(fact_183_com__det,axiom,
! [U,C_1,S,T] :
( hBOOL(evalc(C_1,S,T))
=> ( hBOOL(evalc(C_1,S,U))
=> U = T ) ) ).
fof(fact_184_image__constant__conv,axiom,
! [C,A] :
( ( A = bot_bo1687970473a_bool
=> image_1474161344_pname(cOMBK_1932526739iple_a(C),A) = bot_bo844097828e_bool )
& ( A != bot_bo1687970473a_bool
=> image_1474161344_pname(cOMBK_1932526739iple_a(C),A) = insert_pname(C,bot_bo844097828e_bool) ) ) ).
fof(fact_185_image__constant__conv,axiom,
! [C,A] :
( is_fun_pname_bool(A)
=> ( ( A = bot_bo844097828e_bool
=> image_505679754iple_a(cOMBK_753524681_pname(C),A) = bot_bo1687970473a_bool )
& ( A != bot_bo844097828e_bool
=> image_505679754iple_a(cOMBK_753524681_pname(C),A) = insert1871499715iple_a(C,bot_bo1687970473a_bool) ) ) ) ).
fof(fact_186_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
=> image_1474161344_pname(cOMBK_1932526739iple_a(C),A) = insert_pname(C,bot_bo844097828e_bool) ) ).
fof(fact_187_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))
=> image_29267653iple_a(cOMBK_1548232270iple_a(C),A) = insert1871499715iple_a(C,bot_bo1687970473a_bool) ) ).
fof(fact_188_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> image_pname_pname(cOMBK_pname_pname(C),A) = insert_pname(C,bot_bo844097828e_bool) ) ).
fof(fact_189_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> image_505679754iple_a(cOMBK_753524681_pname(C),A) = insert1871499715iple_a(C,bot_bo1687970473a_bool) ) ).
%----Helper facts (39)
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(hAPP_bool_bool(fNot,P))
| ~ hBOOL(P) ) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(fNot,P)) ) ).
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_fdisj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
fof(help_fdisj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
fof(help_fdisj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
| hBOOL(P)
| hBOOL(Q) ) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse) ).
fof(help_fFalse_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fimplies_1_1_U,axiom,
! [Q,P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
fof(help_fimplies_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
fof(help_fimplies_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
| ~ hBOOL(P)
| hBOOL(Q) ) ).
fof(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
! [X_1,Y] :
( ( is_pname(X_1)
& is_pname(Y) )
=> ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X_1),Y))
| X_1 = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X_1),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U,axiom,
! [P,Q] :
( is_pname(P)
=> hAPP_pname_pname(cOMBK_pname_pname(P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
! [P,Q,R] : hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_pname_bool(cOMBC_1149511130e_bool(P,Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_H1927961489a_bool(hAPP_H562195827a_bool(fequal1878252616iple_a,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_H1927961489a_bool(hAPP_H562195827a_bool(fequal1878252616iple_a,X_1),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00,axiom,
! [P,Q,R] : hAPP_pname_com(cOMBB_923936821_pname(P,Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_,axiom,
! [P,Q] :
( is_pname(P)
=> hAPP_H82695184_pname(cOMBK_1932526739iple_a(P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00,axiom,
! [P,Q] : hAPP_p1261697242iple_a(cOMBK_753524681_pname(P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [P,Q,R] : hAPP_pname_bool(cOMBC_1058051404l_bool(P,Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
! [P,Q,R] : hAPP_H1927961489a_bool(cOMBB_650444389iple_a(P,Q),R) = hAPP_bool_bool(P,hAPP_H1927961489a_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_H1927961489a_bool(cOMBS_213702372l_bool(P,Q),R) = hAPP_bool_bool(hAPP_H1877746411l_bool(P,R),hAPP_H1927961489a_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_pname_pname(cOMBB_1314377293_pname(P,Q),R) = hAPP_H82695184_pname(P,hAPP_p1261697242iple_a(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_001,axiom,
! [P,Q] : hAPP_H401672213iple_a(cOMBK_1548232270iple_a(P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_002,axiom,
! [P,Q,R] : hAPP_H1877746411l_bool(cOMBB_633860163iple_a(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_H1927961489a_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_H1927961489a_bool(cOMBC_2049287834a_bool(P,Q),R) = hAPP_H1927961489a_bool(hAPP_H562195827a_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_,axiom,
! [P,Q,R] : hAPP_H401672213iple_a(cOMBB_548833416iple_a(P,Q),R) = hAPP_p1261697242iple_a(P,hAPP_H82695184_pname(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_It__a_Mtc__fun_Itc__Com__Osta,axiom,
! [P,Q,R] : hAPP_p1261697242iple_a(cOMBS_1258869540iple_a(P,Q),R) = hAPP_f1148670082iple_a(hAPP_p510058747iple_a(P,R),hAPP_p635540397e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_003,axiom,
! [P,Q,R] : hAPP_H1927961489a_bool(cOMBC_2067518550l_bool(P,Q),R) = hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_It_,axiom,
! [P,Q,R] : hAPP_p510058747iple_a(cOMBS_121941143iple_a(P,Q),R) = hAPP_c1572710133iple_a(hAPP_p297245038iple_a(P,R),hAPP_pname_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_p297245038iple_a(cOMBB_1500441031_pname(P,Q),R) = hAPP_f841604374iple_a(P,hAPP_p635540397e_bool(Q,R)) ).
%----Conjectures (2)
fof(conj_0,hypothesis,
! [N] :
( ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(g,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,p),body),q),procs))))
=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)) )
=> ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,p),cOMBB_923936821_pname(the_com,body_1)),q),procs)))
=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)) ) ) ).
fof(conj_1,conjecture,
( ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),g))
=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(n),X)) )
=> ! [X] :
( hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,p),body),q),procs)))
=> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(n),X)) ) ) ).
%------------------------------------------------------------------------------