TPTP Problem File: SWW471+2.p
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%------------------------------------------------------------------------------
% File : SWW471+2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 269, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : hoare_500_fofmg_l269 [Bla11]
% Status : Theorem
% Rating : 1.00 v7.0.0, 0.93 v6.4.0, 1.00 v5.3.0
% Syntax : Number of formulae : 856 ( 378 unt; 0 def)
% Number of atoms : 1938 ( 739 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1352 ( 270 ~; 53 |; 130 &)
% ( 150 <=>; 749 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% Number of functors : 396 ( 396 usr; 117 con; 0-4 aty)
% Number of variables : 2252 (2217 !; 35 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:25:50
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (55)
fof(gsy_c_Big__Operators_Olattice__class_OInf__fin_000tc__HOL__Obool,axiom,
! [B_1_1] :
( is_fun_bool_bool(B_1_1)
=> is_bool(big_la472677547n_bool(B_1_1)) ) ).
fof(gsy_c_Big__Operators_Olattice__class_OInf__fin_000tc__fun_Itc__Com__Opname_Mtc__,axiom,
! [B_1_1] :
( is_fun1661590463l_bool(B_1_1)
=> is_fun_pname_bool(big_la28065288e_bool(B_1_1)) ) ).
fof(gsy_c_Big__Operators_Olattice__class_OSup__fin_000tc__HOL__Obool,axiom,
! [B_1_1] :
( is_fun_bool_bool(B_1_1)
=> is_bool(big_la1480321694n_bool(B_1_1)) ) ).
fof(gsy_c_Big__Operators_Olattice__class_OSup__fin_000tc__fun_Itc__Com__Opname_Mtc__,axiom,
! [B_1_1] :
( is_fun1661590463l_bool(B_1_1)
=> is_fun_pname_bool(big_la841148155e_bool(B_1_1)) ) ).
fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,axiom,
is_fun1661590463l_bool(finite_finite_pname) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] : is_bool(finite1282449217_pname(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple,axiom,
! [B_1_1,B_2_1] : is_bool(finite1669978781iple_a(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_001,axiom,
! [B_1_1,B_2_1] : is_bool(finite774711482_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] : is_bool(finite89670078_pname(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O,axiom,
! [B_1_1,B_2_1] : is_bool(finite950012314iple_a(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O_002,axiom,
! [B_1_1,B_2_1] : is_bool(finite506823037_state(B_1_1,B_2_1)) ).
fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
is_pname(undefined_pname(pname)) ).
fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
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_Lattices_Osemilattice__inf__class_Oinf_000tc__HOL__Obool,axiom,
! [B_1_1] :
( is_bool(B_1_1)
=> is_fun_bool_bool(semila310582991f_bool(B_1_1)) ) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool) ).
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_Orderings_Obot__class_Obot_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
is_fun_bool_bool(bot_bo806936373l_bool) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__,axiom,
is_fun1661590463l_bool(bot_bo1649642514l_bool) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fNot,axiom,
is_fun_bool_bool(fNot) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_pname(hAPP_pname_pname(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( ( is_fun_pname_bool(B_1_1)
& is_pname(B_2_1) )
=> is_bool(hAPP_pname_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_fun_bool_bool(hAPP_p393069232l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_state_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Com__Ostate_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_s58564346l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( ( is_fun_bool_bool(B_1_1)
& is_bool(B_2_1) )
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun_pname_bool(hAPP_b76515610e_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun_bool_bool(hAPP_b589554111l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__Com__,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_H676960377_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__HOL__,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_H1421470952a_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__fun_I,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H1991058245e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_000tc__fun_I_003,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_H1017515220l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_004,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H1632039476e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_005,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_H226398757l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] :
( is_fun_pname_bool(B_2_1)
=> is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( ( is_fun1661590463l_bool(B_1_1)
& is_fun_pname_bool(B_2_1) )
=> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,axiom,
! [B_1_1,B_2_1] :
( is_fun_pname_bool(B_2_1)
=> is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,axiom,
! [B_1_1,B_2_1] :
( is_fun_pname_bool(B_2_1)
=> is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__fun_Itc__Com__Opname_Mtc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f42430548e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_fun_bool_bool(B_2_1)
=> is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__HOL__Obo,axiom,
! [B_1_1,B_2_1] :
( is_fun_bool_bool(B_2_1)
=> is_fun_bool_bool(hAPP_f961197973l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_Mtc,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_f540970102l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_Mtc_006,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f1126670547e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
! [B_1_1,B_2_1] :
( is_fun1661590463l_bool(B_2_1)
=> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_007,axiom,
! [B_1_1,B_2_1] :
( is_fun1661590463l_bool(B_2_1)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1557928608l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It_008,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f239102607l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_Procs,hypothesis,
is_fun_pname_bool(procs) ).
%----Relevant facts (698)
fof(fact_0_triple_Oinject,axiom,
! [Fun1,Com,Fun2,Fun1_2,Com_1,Fun2_2] :
( hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1),Com),Fun2) = hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1_2),Com_1),Fun2_2)
<=> ( Fun1 = Fun1_2
& Com = Com_1
& Fun2 = Fun2_2 ) ) ).
fof(fact_1_triple_Oinject,axiom,
! [Fun1,Com,Fun2,Fun1_2,Com_1,Fun2_2] :
( hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_2),Com_1),Fun2_2)
<=> ( Fun1 = Fun1_2
& Com = Com_1
& Fun2 = Fun2_2 ) ) ).
fof(fact_2_hoare__valids__def,axiom,
! [Ga,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(Ga),Ts))
<=> ! [N] :
( ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ga))
=> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N),X)) )
=> ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ts))
=> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N),X)) ) ) ) ).
fof(fact_3_hoare__valids__def,axiom,
! [Ga,Ts] :
( hBOOL(hAPP_f540970102l_bool(hoare_943851888lids_a(Ga),Ts))
<=> ! [N] :
( ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ga))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)) )
=> ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ts))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)) ) ) ) ).
fof(fact_4_hoare__derivs_OBody,axiom,
! [Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),body)),Qa)),Procsa))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),body)),Qa)),Procsa))) ) ).
fof(fact_5_hoare__derivs_OBody,axiom,
! [Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa)))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),body)),Qa)),Procsa))) ) ).
fof(fact_6_UnE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1)) ) ) ).
fof(fact_7_UnE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)))
=> ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ) ).
fof(fact_8_UnE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(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_9_sup1E,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2))
=> ( ~ hBOOL(hAPP_H513860823e_bool(A,X_2))
=> hBOOL(hAPP_H513860823e_bool(B_1,X_2)) ) ) ).
fof(fact_10_sup1E,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_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_11_sup1E,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2))
=> ( ~ hBOOL(hAPP_H1421470952a_bool(A,X_2))
=> hBOOL(hAPP_H1421470952a_bool(B_1,X_2)) ) ) ).
fof(fact_12_sup1CI,axiom,
! [A,B_1,X_2] :
( ( ~ hBOOL(hAPP_H513860823e_bool(B_1,X_2))
=> hBOOL(hAPP_H513860823e_bool(A,X_2)) )
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)) ) ).
fof(fact_13_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(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)) ) ).
fof(fact_14_sup1CI,axiom,
! [A,B_1,X_2] :
( ( ~ hBOOL(hAPP_H1421470952a_bool(B_1,X_2))
=> hBOOL(hAPP_H1421470952a_bool(A,X_2)) )
=> hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)) ) ).
fof(fact_15_UnCI,axiom,
! [A,C,B_1] :
( ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) ) ).
fof(fact_16_UnCI,axiom,
! [A,C,B_1] :
( ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) )
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) ) ).
fof(fact_17_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),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) ) ).
fof(fact_18_image__eqI,axiom,
! [A,B,F_1,X_2] :
( B = hAPP_p1842370726_state(F_1,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f631639356e_bool(image_275883510_state(F_1),A))) ) ) ).
fof(fact_19_image__eqI,axiom,
! [A,B,F_1,X_2] :
( B = hAPP_H676960377_pname(F_1,X_2)
=> ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A))) ) ) ).
fof(fact_20_image__eqI,axiom,
! [A,B,F_1,X_2] :
( B = hAPP_p263283121iple_a(F_1,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) ) ) ).
fof(fact_21_image__Un,axiom,
! [F_1,A,B_1] : hAPP_f631639356e_bool(image_275883510_state(F_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F_1),A)),hAPP_f631639356e_bool(image_275883510_state(F_1),B_1)) ).
fof(fact_22_image__Un,axiom,
! [F_1,A,B_1] : hAPP_f1182387808e_bool(image_1604514514_state(F_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f1182387808e_bool(image_1604514514_state(F_1),A)),hAPP_f1182387808e_bool(image_1604514514_state(F_1),B_1)) ).
fof(fact_23_image__Un,axiom,
! [F_1,A,B_1] : hAPP_f1126670547e_bool(image_2068426537_pname(F_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A)),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),B_1)) ).
fof(fact_24_image__Un,axiom,
! [F_1,A,B_1] : hAPP_f75870650a_bool(image_129517430iple_a(F_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f75870650a_bool(image_129517430iple_a(F_1),A)),hAPP_f75870650a_bool(image_129517430iple_a(F_1),B_1)) ).
fof(fact_25_image__Un,axiom,
! [F_1,A,B_1] : hAPP_f271130963a_bool(image_1654749281iple_a(F_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),B_1)) ).
fof(fact_26_sup__fun__def,axiom,
! [F_1,G,X] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F_1),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F_1,X)),hAPP_H513860823e_bool(G,X))) ) ).
fof(fact_27_sup__fun__def,axiom,
! [F_1,G,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F_1,X)),hAPP_pname_bool(G,X))) ) ).
fof(fact_28_sup__fun__def,axiom,
! [F_1,G,X] :
( hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F_1),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1421470952a_bool(F_1,X)),hAPP_H1421470952a_bool(G,X))) ) ).
fof(fact_29_sup__apply,axiom,
! [F_1,G,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F_1),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F_1,X_2)),hAPP_H513860823e_bool(G,X_2))) ) ).
fof(fact_30_sup__apply,axiom,
! [F_1,G,X_2] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F_1,X_2)),hAPP_pname_bool(G,X_2))) ) ).
fof(fact_31_sup__apply,axiom,
! [F_1,G,X_2] :
( hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F_1),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1421470952a_bool(F_1,X_2)),hAPP_H1421470952a_bool(G,X_2))) ) ).
fof(fact_32_cut,axiom,
! [Ga,G_1,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),G_1))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts)) ) ) ).
fof(fact_33_cut,axiom,
! [Ga,G_1,Ts] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(G_1),Ts))
=> ( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),G_1))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts)) ) ) ).
fof(fact_34_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),Z_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) ).
fof(fact_35_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),Z_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) ).
fof(fact_36_sup__assoc,axiom,
! [X_2,Y_1,Z_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),Z_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))) ) ).
fof(fact_37_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),Z_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) ).
fof(fact_38_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),Z_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) ).
fof(fact_39_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),Z_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) ).
fof(fact_40_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),Z_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1))) ) ).
fof(fact_41_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),Z_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) ).
fof(fact_42_sup_Oassoc,axiom,
! [A_1,B,C] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C)) ).
fof(fact_43_sup_Oassoc,axiom,
! [A_1,B,C] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),C) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C)) ).
fof(fact_44_sup_Oassoc,axiom,
! [A_1,B,C] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B)),C))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),C))) ) ).
fof(fact_45_sup_Oassoc,axiom,
! [A_1,B,C] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B)),C) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),C)) ).
fof(fact_46_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1)) ).
fof(fact_47_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)) ).
fof(fact_48_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))) ) ).
fof(fact_49_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1)) ).
fof(fact_50_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1)) ).
fof(fact_51_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)) ).
fof(fact_52_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))) ) ).
fof(fact_53_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1)) ).
fof(fact_54_sup_Oleft__commute,axiom,
! [B,A_1,C] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C)) ).
fof(fact_55_sup_Oleft__commute,axiom,
! [B,A_1,C] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),C)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C)) ).
fof(fact_56_sup_Oleft__commute,axiom,
! [B,A_1,C] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),C)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),C))) ) ).
fof(fact_57_sup_Oleft__commute,axiom,
! [B,A_1,C] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),C)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),C)) ).
fof(fact_58_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) ).
fof(fact_59_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) ).
fof(fact_60_sup__left__idem,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)) ) ).
fof(fact_61_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) ).
fof(fact_62_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) ).
fof(fact_63_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) ).
fof(fact_64_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)) ) ).
fof(fact_65_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) ).
fof(fact_66_sup_Oleft__idem,axiom,
! [A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) ).
fof(fact_67_sup_Oleft__idem,axiom,
! [A_1,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) ).
fof(fact_68_sup_Oleft__idem,axiom,
! [A_1,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B)) ) ).
fof(fact_69_sup_Oleft__idem,axiom,
! [A_1,B] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B) ).
fof(fact_70_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_2) ).
fof(fact_71_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),X_2) ).
fof(fact_72_sup__commute,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),X_2)) ) ).
fof(fact_73_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),X_2) ).
fof(fact_74_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_2) ).
fof(fact_75_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),X_2) ).
fof(fact_76_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),X_2)) ) ).
fof(fact_77_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),X_2) ).
fof(fact_78_sup_Ocommute,axiom,
! [A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1) ).
fof(fact_79_sup_Ocommute,axiom,
! [A_1,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A_1) ).
fof(fact_80_sup_Ocommute,axiom,
! [A_1,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),B))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B),A_1)) ) ).
fof(fact_81_sup_Ocommute,axiom,
! [A_1,B] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),B) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B),A_1) ).
fof(fact_82_sup__idem,axiom,
! [X_2] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),X_2) = X_2 ).
fof(fact_83_sup__idem,axiom,
! [X_2] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),X_2) = X_2 ) ).
fof(fact_84_sup__idem,axiom,
! [X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2))
<=> hBOOL(X_2) ) ).
fof(fact_85_sup__idem,axiom,
! [X_2] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),X_2) = X_2 ).
fof(fact_86_sup_Oidem,axiom,
! [A_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),A_1) = A_1 ).
fof(fact_87_sup_Oidem,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),A_1) = A_1 ) ).
fof(fact_88_sup_Oidem,axiom,
! [A_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),A_1))
<=> hBOOL(A_1) ) ).
fof(fact_89_sup_Oidem,axiom,
! [A_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),A_1) = A_1 ).
fof(fact_90_rev__image__eqI,axiom,
! [B,F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( B = hAPP_p1842370726_state(F_1,X_2)
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f631639356e_bool(image_275883510_state(F_1),A))) ) ) ).
fof(fact_91_rev__image__eqI,axiom,
! [B,F_1,X_2,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> ( B = hAPP_H676960377_pname(F_1,X_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A))) ) ) ).
fof(fact_92_rev__image__eqI,axiom,
! [B,F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( B = hAPP_p263283121iple_a(F_1,X_2)
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) ) ) ).
fof(fact_93_imageI,axiom,
! [F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F_1,X_2)),hAPP_f631639356e_bool(image_275883510_state(F_1),A))) ) ).
fof(fact_94_imageI,axiom,
! [F_1,X_2,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H676960377_pname(F_1,X_2)),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A))) ) ).
fof(fact_95_imageI,axiom,
! [F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_p263283121iple_a(F_1,X_2)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A))) ) ).
fof(fact_96_image__iff,axiom,
! [Z_1,F_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z_1),hAPP_f631639356e_bool(image_275883510_state(F_1),A)))
<=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
& Z_1 = hAPP_p1842370726_state(F_1,X) ) ) ).
fof(fact_97_image__iff,axiom,
! [Z_1,F_1,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Z_1),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)))
<=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
& Z_1 = hAPP_p263283121iple_a(F_1,X) ) ) ).
fof(fact_98_UnI2,axiom,
! [A,C,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) ) ).
fof(fact_99_UnI2,axiom,
! [A,C,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) ) ).
fof(fact_100_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),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) ) ).
fof(fact_101_UnI1,axiom,
! [B_1,C,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) ) ).
fof(fact_102_UnI1,axiom,
! [B_1,C,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))) ) ).
fof(fact_103_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),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) ) ).
fof(fact_104_sup1I2,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_H513860823e_bool(B_1,X_2))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)) ) ).
fof(fact_105_sup1I2,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_pname_bool(B_1,X_2))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)) ) ).
fof(fact_106_sup1I2,axiom,
! [A,B_1,X_2] :
( hBOOL(hAPP_H1421470952a_bool(B_1,X_2))
=> hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)) ) ).
fof(fact_107_sup1I1,axiom,
! [B_1,A,X_2] :
( hBOOL(hAPP_H513860823e_bool(A,X_2))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1),X_2)) ) ).
fof(fact_108_sup1I1,axiom,
! [B_1,A,X_2] :
( hBOOL(hAPP_pname_bool(A,X_2))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1),X_2)) ) ).
fof(fact_109_sup1I1,axiom,
! [B_1,A,X_2] :
( hBOOL(hAPP_H1421470952a_bool(A,X_2))
=> hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1),X_2)) ) ).
fof(fact_110_ball__Un,axiom,
! [Pa,A,B_1] :
( ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)))
=> hBOOL(hAPP_H513860823e_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))
=> hBOOL(hAPP_H513860823e_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),B_1))
=> hBOOL(hAPP_H513860823e_bool(Pa,X)) ) ) ) ).
fof(fact_111_ball__Un,axiom,
! [Pa,A,B_1] :
( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(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_112_ball__Un,axiom,
! [Pa,A,B_1] :
( ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)))
=> hBOOL(hAPP_H1421470952a_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))
=> hBOOL(hAPP_H1421470952a_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),B_1))
=> hBOOL(hAPP_H1421470952a_bool(Pa,X)) ) ) ) ).
fof(fact_113_bex__Un,axiom,
! [Pa,A,B_1] :
( ? [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)))
& hBOOL(hAPP_H513860823e_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))
& hBOOL(hAPP_H513860823e_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),B_1))
& hBOOL(hAPP_H513860823e_bool(Pa,X)) ) ) ) ).
fof(fact_114_bex__Un,axiom,
! [Pa,A,B_1] :
( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(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_115_bex__Un,axiom,
! [Pa,A,B_1] :
( ? [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)))
& hBOOL(hAPP_H1421470952a_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))
& hBOOL(hAPP_H1421470952a_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),B_1))
& hBOOL(hAPP_H1421470952a_bool(Pa,X)) ) ) ) ).
fof(fact_116_Un__assoc,axiom,
! [A,B_1,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)) ).
fof(fact_117_Un__assoc,axiom,
! [A,B_1,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)) ).
fof(fact_118_Un__assoc,axiom,
! [A,B_1,C_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)) ).
fof(fact_119_Un__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A))
| hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B_1)) ) ) ).
fof(fact_120_Un__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)))
<=> ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
| hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ) ).
fof(fact_121_Un__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(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_122_Un__left__commute,axiom,
! [A,B_1,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C_1)) ).
fof(fact_123_Un__left__commute,axiom,
! [A,B_1,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1)) ).
fof(fact_124_Un__left__commute,axiom,
! [A,B_1,C_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),C_1)) ).
fof(fact_125_Un__left__absorb,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) ).
fof(fact_126_Un__left__absorb,axiom,
! [A,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) ).
fof(fact_127_Un__left__absorb,axiom,
! [A,B_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) ).
fof(fact_128_Un__commute,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A) ).
fof(fact_129_Un__commute,axiom,
! [A,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A) ).
fof(fact_130_Un__commute,axiom,
! [A,B_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),A) ).
fof(fact_131_Un__def,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B_1))) ).
fof(fact_132_Un__def,axiom,
! [A,B_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B_1))) ).
fof(fact_133_Un__def,axiom,
! [A,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_1))) ).
fof(fact_134_Un__absorb,axiom,
! [A] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),A) = A ).
fof(fact_135_Un__absorb,axiom,
! [A] :
( is_fun_pname_bool(A)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),A) = A ) ).
fof(fact_136_Un__absorb,axiom,
! [A] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),A) = A ).
fof(fact_137_image__image,axiom,
! [F_1,G,A] : hAPP_f1182387808e_bool(image_1604514514_state(F_1),hAPP_f271130963a_bool(image_1654749281iple_a(G),A)) = hAPP_f631639356e_bool(image_275883510_state(hAPP_f1026488024_state(cOMBB_2118237115_pname(F_1),G)),A) ).
fof(fact_138_image__image,axiom,
! [F_1,G,A] : hAPP_f75870650a_bool(image_129517430iple_a(F_1),hAPP_f631639356e_bool(image_275883510_state(G),A)) = hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f113652738iple_a(cOMBB_2015474199_pname(F_1),G)),A) ).
fof(fact_139_sup__Un__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S_1)),X))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,R_1),S_1))) ) ).
fof(fact_140_sup__Un__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S_1)),X))
<=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,R_1),S_1))) ) ).
fof(fact_141_sup__Un__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S_1)),X))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S_1))) ) ).
fof(fact_142_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),Pa)),Qa)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,Pa)),hAPP_f759274231e_bool(collect_pname,Qa)) ).
fof(fact_143_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),Pa)),Qa)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,Pa)),hAPP_f921536533e_bool(collec727977250_state,Qa)) ).
fof(fact_144_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),Pa)),Qa)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(collec268032053iple_a,Pa)),hAPP_f1591852335a_bool(collec268032053iple_a,Qa)) ).
fof(fact_145_imageE,axiom,
! [B,F_1,A] :
( is_pname(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f1126670547e_bool(image_2068426537_pname(F_1),A)))
=> ~ ! [X] :
( B = hAPP_H676960377_pname(F_1,X)
=> ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A)) ) ) ) ).
fof(fact_146_imageE,axiom,
! [B,F_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f631639356e_bool(image_275883510_state(F_1),A)))
=> ~ ! [X] :
( is_pname(X)
=> ( B = hAPP_p1842370726_state(F_1,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) ) ) ) ).
fof(fact_147_imageE,axiom,
! [B,F_1,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)))
=> ~ ! [X] :
( is_pname(X)
=> ( B = hAPP_p263283121iple_a(F_1,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) ) ) ) ).
fof(fact_148_Body__triple__valid__Suc,axiom,
! [N_1,Pa,Pn_1,Qa] :
( hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_1),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)))
<=> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(suc(N_1)),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ) ).
fof(fact_149_Body__triple__valid__Suc,axiom,
! [N_1,Pa,Pn_1,Qa] :
( hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_1),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)))
<=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(suc(N_1)),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ) ).
fof(fact_150_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1_1,Com_2,Fun2_1] : Y_1 != hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1_1),Com_2),Fun2_1) ).
fof(fact_151_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1_1,Com_2,Fun2_1] : Y_1 != hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_1),Com_2),Fun2_1) ).
fof(fact_152_Body1,axiom,
! [Pn_1,Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),body)),Qa)),Procsa))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa)))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procsa))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p1637813682e_bool(Qa,Pn_1))),bot_bo1055319631e_bool))) ) ) ).
fof(fact_153_Body1,axiom,
! [Pn_1,Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa)))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procsa))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_p635540397e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p635540397e_bool(Qa,Pn_1))),bot_bo1181479936a_bool))) ) ) ).
fof(fact_154_image__cong,axiom,
! [F_1,G,M_3,N_3] :
( M_3 = N_3
=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3))
=> hAPP_p1842370726_state(F_1,X) = hAPP_p1842370726_state(G,X) ) )
=> hAPP_f631639356e_bool(image_275883510_state(F_1),M_3) = hAPP_f631639356e_bool(image_275883510_state(G),N_3) ) ) ).
fof(fact_155_image__cong,axiom,
! [F_1,G,M_3,N_3] :
( M_3 = N_3
=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3))
=> hAPP_p263283121iple_a(F_1,X) = hAPP_p263283121iple_a(G,X) ) )
=> hAPP_f271130963a_bool(image_1654749281iple_a(F_1),M_3) = hAPP_f271130963a_bool(image_1654749281iple_a(G),N_3) ) ) ).
fof(fact_156_Body__triple__valid__0,axiom,
! [Pa,Pn_1,Qa] : hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(zero_zero_nat),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ).
fof(fact_157_Body__triple__valid__0,axiom,
! [Pa,Pn_1,Qa] : hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(zero_zero_nat),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ).
fof(fact_158_com_Osimps_I6_J,axiom,
! [Pname_3,Pname_2] :
( ( is_pname(Pname_3)
& is_pname(Pname_2) )
=> ( hAPP_pname_com(body,Pname_3) = hAPP_pname_com(body,Pname_2)
<=> Pname_3 = Pname_2 ) ) ).
fof(fact_159_evalc_OBody,axiom,
! [Pn,S0,S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn))),S0),S1_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,Pn)),S0),S1_1)) ) ).
fof(fact_160_evalc__elim__cases_I6_J,axiom,
! [P,S_2,S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,P)),S_2),S1_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P))),S_2),S1_1)) ) ).
fof(fact_161_Sup__fin_Oidem,axiom,
! [X_2] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),X_2) = X_2 ).
fof(fact_162_Sup__fin_Oidem,axiom,
! [X_2] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),X_2) = X_2 ) ).
fof(fact_163_Sup__fin_Oidem,axiom,
! [X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2))
<=> hBOOL(X_2) ) ).
fof(fact_164_Sup__fin_Oidem,axiom,
! [X_2] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),X_2) = X_2 ).
fof(fact_165_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),bot_bo1181479936a_bool)) ).
fof(fact_166_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),bot_bo1055319631e_bool)) ).
fof(fact_167_emptyE,axiom,
! [A_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),bot_bo844097828e_bool)) ).
fof(fact_168_insertE,axiom,
! [A_1,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A)))
=> ( A_1 != B
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) ) ) ).
fof(fact_169_insertE,axiom,
! [A_1,B,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),A)))
=> ( A_1 != B
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) ) ) ).
fof(fact_170_insertE,axiom,
! [A_1,B,A] :
( ( is_pname(A_1)
& is_pname(B) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),A)))
=> ( A_1 != B
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ) ).
fof(fact_171_insertCI,axiom,
! [B,A_1,B_1] :
( ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_1))
=> A_1 = B )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))) ) ).
fof(fact_172_insertCI,axiom,
! [B,A_1,B_1] :
( ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_1))
=> A_1 = B )
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),B_1))) ) ).
fof(fact_173_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),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),B_1))) ) ).
fof(fact_174_empty__not__insert,axiom,
! [A_1,A] : bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) ).
fof(fact_175_empty__not__insert,axiom,
! [A_1,A] : bot_bo1181479936a_bool != hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) ).
fof(fact_176_empty__not__insert,axiom,
! [A_1,A] : bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) ).
fof(fact_177_insert__not__empty,axiom,
! [A_1,A] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) != bot_bo1055319631e_bool ).
fof(fact_178_insert__not__empty,axiom,
! [A_1,A] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) != bot_bo1181479936a_bool ).
fof(fact_179_insert__not__empty,axiom,
! [A_1,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) != bot_bo844097828e_bool ).
fof(fact_180_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X))
<=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),bot_bo1181479936a_bool)) ) ).
fof(fact_181_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),bot_bo1055319631e_bool)) ) ).
fof(fact_182_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_183_empty__def,axiom,
bot_bo1181479936a_bool = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_b119575286a_bool(cOMBK_151824839iple_a,fFalse)) ).
fof(fact_184_empty__def,axiom,
bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,hAPP_b76515610e_bool(cOMBK_bool_pname,fFalse)) ).
fof(fact_185_empty__def,axiom,
bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,hAPP_b1245957081e_bool(cOMBK_1079618832_state,fFalse)) ).
fof(fact_186_insertI1,axiom,
! [A_1,B_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1))) ).
fof(fact_187_insertI1,axiom,
! [A_1,B_1] : hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1))) ).
fof(fact_188_insertI1,axiom,
! [A_1,B_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1))) ).
fof(fact_189_all__not__in__conv,axiom,
! [A] :
( ! [X] : ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))
<=> A = bot_bo1181479936a_bool ) ).
fof(fact_190_all__not__in__conv,axiom,
! [A] :
( ! [X] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))
<=> A = bot_bo1055319631e_bool ) ).
fof(fact_191_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_192_singleton__conv2,axiom,
! [A_1] : hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) ).
fof(fact_193_singleton__conv2,axiom,
! [A_1] : hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_H1190454433a_bool(fequal879838495iple_a,A_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) ).
fof(fact_194_singleton__conv2,axiom,
! [A_1] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool) ).
fof(fact_195_ex__in__conv,axiom,
! [A] :
( ? [X] : hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))
<=> A != bot_bo1181479936a_bool ) ).
fof(fact_196_ex__in__conv,axiom,
! [A] :
( ? [X] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))
<=> A != bot_bo1055319631e_bool ) ).
fof(fact_197_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_198_singleton__conv,axiom,
! [A_1] : hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) ).
fof(fact_199_singleton__conv,axiom,
! [A_1] : hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) ).
fof(fact_200_singleton__conv,axiom,
! [A_1] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool) ).
fof(fact_201_Collect__conv__if2,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_H513860823e_bool(Pa,A_1))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A_1))),Pa)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) )
& ( ~ hBOOL(hAPP_H513860823e_bool(Pa,A_1))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A_1))),Pa)) = bot_bo1055319631e_bool ) ) ).
fof(fact_202_Collect__conv__if2,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_H1421470952a_bool(Pa,A_1))
=> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(fequal879838495iple_a,A_1))),Pa)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) )
& ( ~ hBOOL(hAPP_H1421470952a_bool(Pa,A_1))
=> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(fequal879838495iple_a,A_1))),Pa)) = bot_bo1181479936a_bool ) ) ).
fof(fact_203_Collect__conv__if2,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_pname_bool(Pa,A_1))
=> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A_1))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(Pa,A_1))
=> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A_1))),Pa)) = bot_bo844097828e_bool ) ) ).
fof(fact_204_Collect__conv__if,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_H513860823e_bool(Pa,A_1))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),Pa)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) )
& ( ~ hBOOL(hAPP_H513860823e_bool(Pa,A_1))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),Pa)) = bot_bo1055319631e_bool ) ) ).
fof(fact_205_Collect__conv__if,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_H1421470952a_bool(Pa,A_1))
=> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),Pa)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) )
& ( ~ hBOOL(hAPP_H1421470952a_bool(Pa,A_1))
=> hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),Pa)) = bot_bo1181479936a_bool ) ) ).
fof(fact_206_Collect__conv__if,axiom,
! [Pa,A_1] :
( ( hBOOL(hAPP_pname_bool(Pa,A_1))
=> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(Pa,A_1))
=> hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),Pa)) = bot_bo844097828e_bool ) ) ).
fof(fact_207_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo1181479936a_bool = hAPP_f1591852335a_bool(collec268032053iple_a,Pa)
<=> ! [X] : ~ hBOOL(hAPP_H1421470952a_bool(Pa,X)) ) ).
fof(fact_208_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,Pa)
<=> ! [X] :
( is_pname(X)
=> ~ hBOOL(hAPP_pname_bool(Pa,X)) ) ) ).
fof(fact_209_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,Pa)
<=> ! [X] : ~ hBOOL(hAPP_H513860823e_bool(Pa,X)) ) ).
fof(fact_210_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
<=> hBOOL(hAPP_H1421470952a_bool(A,X_2)) ) ).
fof(fact_211_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_212_Collect__def,axiom,
! [Pa] : hAPP_f1591852335a_bool(collec268032053iple_a,Pa) = Pa ).
fof(fact_213_Collect__def,axiom,
! [Pa] :
( is_fun_pname_bool(Pa)
=> hAPP_f759274231e_bool(collect_pname,Pa) = Pa ) ).
fof(fact_214_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),bot_bo1181479936a_bool)) ).
fof(fact_215_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),bot_bo1055319631e_bool)) ).
fof(fact_216_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool)) ).
fof(fact_217_insert__compr,axiom,
! [A_1,B_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B_1))) ).
fof(fact_218_insert__compr,axiom,
! [A_1,B_1] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B_1))) ).
fof(fact_219_insert__compr,axiom,
! [A_1,B_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_1))) ).
fof(fact_220_insert__Collect,axiom,
! [A_1,Pa] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(collec727977250_state,Pa)) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1)))),Pa)) ).
fof(fact_221_insert__Collect,axiom,
! [A_1,Pa] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(collec268032053iple_a,Pa)) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fimplies),hAPP_f1591852335a_bool(cOMBB_1799513916iple_a(fNot),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1)))),Pa)) ).
fof(fact_222_insert__Collect,axiom,
! [A_1,Pa] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(collect_pname,Pa)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fimplies),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1)))),Pa)) ).
fof(fact_223_singleton__iff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)))
<=> B = A_1 ) ).
fof(fact_224_singleton__iff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)))
<=> B = A_1 ) ).
fof(fact_225_singleton__iff,axiom,
! [B,A_1] :
( ( is_pname(B)
& is_pname(A_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)))
<=> B = A_1 ) ) ).
fof(fact_226_insert__absorb2,axiom,
! [X_2,A] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A) ).
fof(fact_227_insert__absorb2,axiom,
! [X_2,A] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A) ).
fof(fact_228_insert__absorb2,axiom,
! [X_2,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A) ).
fof(fact_229_insert__commute,axiom,
! [X_2,Y_1,A] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) ).
fof(fact_230_insert__commute,axiom,
! [X_2,Y_1,A] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_1),A)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) ).
fof(fact_231_insert__commute,axiom,
! [X_2,Y_1,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) ).
fof(fact_232_insert__iff,axiom,
! [A_1,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A)))
<=> ( A_1 = B
| hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) ) ) ).
fof(fact_233_insert__iff,axiom,
! [A_1,B,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),A)))
<=> ( A_1 = B
| hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) ) ) ).
fof(fact_234_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),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),A)))
<=> ( A_1 = B
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ) ).
fof(fact_235_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f1591852335a_bool(collec268032053iple_a,Pa) = bot_bo1181479936a_bool
<=> ! [X] : ~ hBOOL(hAPP_H1421470952a_bool(Pa,X)) ) ).
fof(fact_236_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f759274231e_bool(collect_pname,Pa) = bot_bo844097828e_bool
<=> ! [X] :
( is_pname(X)
=> ~ hBOOL(hAPP_pname_bool(Pa,X)) ) ) ).
fof(fact_237_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f921536533e_bool(collec727977250_state,Pa) = bot_bo1055319631e_bool
<=> ! [X] : ~ hBOOL(hAPP_H513860823e_bool(Pa,X)) ) ).
fof(fact_238_doubleton__eq__iff,axiom,
! [A_1,B,C,D] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D),bot_bo1055319631e_bool))
<=> ( ( A_1 = C
& B = D )
| ( A_1 = D
& B = C ) ) ) ).
fof(fact_239_doubleton__eq__iff,axiom,
! [A_1,B,C,D] :
( hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),bot_bo1181479936a_bool)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,C),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,D),bot_bo1181479936a_bool))
<=> ( ( A_1 = C
& B = D )
| ( A_1 = D
& B = C ) ) ) ).
fof(fact_240_doubleton__eq__iff,axiom,
! [A_1,B,C,D] :
( ( is_pname(A_1)
& is_pname(B)
& is_pname(C)
& is_pname(D) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool))
<=> ( ( A_1 = C
& B = D )
| ( A_1 = D
& B = C ) ) ) ) ).
fof(fact_241_insert__code,axiom,
! [Y_1,A,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_H513860823e_bool(A,X_2)) ) ) ).
fof(fact_242_insert__code,axiom,
! [Y_1,A,X_2] :
( hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_1),A),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_H1421470952a_bool(A,X_2)) ) ) ).
fof(fact_243_insert__code,axiom,
! [Y_1,A,X_2] :
( ( is_pname(Y_1)
& is_pname(X_2) )
=> ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_pname_bool(A,X_2)) ) ) ) ).
fof(fact_244_insert__ident,axiom,
! [B_1,X_2,A] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
=> ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1)
<=> A = B_1 ) ) ) ).
fof(fact_245_insert__ident,axiom,
! [B_1,X_2,A] :
( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),B_1))
=> ( hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),B_1)
<=> A = B_1 ) ) ) ).
fof(fact_246_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))
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_1)
<=> A = B_1 ) ) ) ) ).
fof(fact_247_equals0D,axiom,
! [A_1,A] :
( A = bot_bo1181479936a_bool
=> ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A)) ) ).
fof(fact_248_equals0D,axiom,
! [A_1,A] :
( A = bot_bo1055319631e_bool
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A)) ) ).
fof(fact_249_equals0D,axiom,
! [A_1,A] :
( A = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ).
fof(fact_250_insertI2,axiom,
! [B,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))) ) ).
fof(fact_251_insertI2,axiom,
! [B,A_1,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_1))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),B_1))) ) ).
fof(fact_252_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),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),B_1))) ) ).
fof(fact_253_insert__absorb,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))
=> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) = A ) ).
fof(fact_254_insert__absorb,axiom,
! [A_1,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))
=> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) = A ) ).
fof(fact_255_insert__absorb,axiom,
! [A_1,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) = A ) ) ).
fof(fact_256_singletonE,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)))
=> B = A_1 ) ).
fof(fact_257_singletonE,axiom,
! [B,A_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,B),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)))
=> B = A_1 ) ).
fof(fact_258_singletonE,axiom,
! [B,A_1] :
( ( is_pname(B)
& is_pname(A_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)))
=> B = A_1 ) ) ).
fof(fact_259_singleton__inject,axiom,
! [A_1,B] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool)
=> A_1 = B ) ).
fof(fact_260_singleton__inject,axiom,
! [A_1,B] :
( hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,B),bot_bo1181479936a_bool)
=> A_1 = B ) ).
fof(fact_261_singleton__inject,axiom,
! [A_1,B] :
( ( is_pname(A_1)
& is_pname(B) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B),bot_bo844097828e_bool)
=> A_1 = B ) ) ).
fof(fact_262_com__det,axiom,
! [U_1,C_2,S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),U_1))
=> U_1 = T_1 ) ) ).
fof(fact_263_insert__is__Un,axiom,
! [A_1,A] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),bot_bo1055319631e_bool)),A) ).
fof(fact_264_insert__is__Un,axiom,
! [A_1,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),bot_bo844097828e_bool)),A) ).
fof(fact_265_insert__is__Un,axiom,
! [A_1,A] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),bot_bo1181479936a_bool)),A) ).
fof(fact_266_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),Xa) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),X))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),Xa))) ).
fof(fact_267_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),Xa) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),X))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),Xa))) ).
fof(fact_268_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),Xa) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),X))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa))) ).
fof(fact_269_derivs__insertD,axiom,
! [Ga,T,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool)))
& hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts)) ) ) ).
fof(fact_270_derivs__insertD,axiom,
! [Ga,T,Ts] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),Ts)))
=> ( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),bot_bo1181479936a_bool)))
& hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts)) ) ) ).
fof(fact_271_hoare__derivs_Oinsert,axiom,
! [Ts,Ga,T] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),Ts))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) ) ) ).
fof(fact_272_hoare__derivs_Oinsert,axiom,
! [Ts,Ga,T] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),bot_bo1181479936a_bool)))
=> ( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),Ts))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,T),Ts))) ) ) ).
fof(fact_273_image__constant__conv,axiom,
! [C,A] :
( is_fun_pname_bool(A)
=> ( ( A = bot_bo844097828e_bool
=> hAPP_f631639356e_bool(image_275883510_state(hAPP_H1797237070_state(cOMBK_90103121_pname,C)),A) = bot_bo1055319631e_bool )
& ( A != bot_bo844097828e_bool
=> hAPP_f631639356e_bool(image_275883510_state(hAPP_H1797237070_state(cOMBK_90103121_pname,C)),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool) ) ) ) ).
fof(fact_274_image__constant__conv,axiom,
! [C,A] :
( is_fun_pname_bool(A)
=> ( ( A = bot_bo844097828e_bool
=> hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,C)),A) = bot_bo1181479936a_bool )
& ( A != bot_bo844097828e_bool
=> hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,C)),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,C),bot_bo1181479936a_bool) ) ) ) ).
fof(fact_275_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_f631639356e_bool(image_275883510_state(hAPP_H1797237070_state(cOMBK_90103121_pname,C)),A) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool) ) ).
fof(fact_276_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ).
fof(fact_277_image__constant,axiom,
! [C,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_pname,C)),A) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,C),bot_bo1181479936a_bool) ) ).
fof(fact_278_image__insert,axiom,
! [F_1,A_1,B_1] : hAPP_f631639356e_bool(image_275883510_state(F_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F_1,A_1)),hAPP_f631639356e_bool(image_275883510_state(F_1),B_1)) ).
fof(fact_279_image__insert,axiom,
! [F_1,A_1,B_1] : hAPP_f271130963a_bool(image_1654749281iple_a(F_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_p263283121iple_a(F_1,A_1)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),B_1)) ).
fof(fact_280_insert__image,axiom,
! [F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F_1,X_2)),hAPP_f631639356e_bool(image_275883510_state(F_1),A)) = hAPP_f631639356e_bool(image_275883510_state(F_1),A) ) ).
fof(fact_281_insert__image,axiom,
! [F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F_1,X_2)),hAPP_f759274231e_bool(image_pname_pname(F_1),A)) = hAPP_f759274231e_bool(image_pname_pname(F_1),A) ) ).
fof(fact_282_insert__image,axiom,
! [F_1,X_2,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_p263283121iple_a(F_1,X_2)),hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)) = hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A) ) ).
fof(fact_283_Un__insert__right,axiom,
! [A,A_1,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) ).
fof(fact_284_Un__insert__right,axiom,
! [A,A_1,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) ).
fof(fact_285_Un__insert__right,axiom,
! [A,A_1,B_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) ).
fof(fact_286_Un__insert__left,axiom,
! [A_1,B_1,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)) ).
fof(fact_287_Un__insert__left,axiom,
! [A_1,B_1,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)) ).
fof(fact_288_Un__insert__left,axiom,
! [A_1,B_1,C_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)) ).
fof(fact_289_empty__is__image,axiom,
! [F_1,A] :
( is_fun_pname_bool(A)
=> ( bot_bo1055319631e_bool = hAPP_f631639356e_bool(image_275883510_state(F_1),A)
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_290_empty__is__image,axiom,
! [F_1,A] :
( is_fun_pname_bool(A)
=> ( bot_bo1181479936a_bool = hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_291_image__empty,axiom,
! [F_1] : hAPP_f631639356e_bool(image_275883510_state(F_1),bot_bo844097828e_bool) = bot_bo1055319631e_bool ).
fof(fact_292_image__empty,axiom,
! [F_1] : hAPP_f271130963a_bool(image_1654749281iple_a(F_1),bot_bo844097828e_bool) = bot_bo1181479936a_bool ).
fof(fact_293_image__is__empty,axiom,
! [F_1,A] :
( is_fun_pname_bool(A)
=> ( hAPP_f631639356e_bool(image_275883510_state(F_1),A) = bot_bo1055319631e_bool
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_294_image__is__empty,axiom,
! [F_1,A] :
( is_fun_pname_bool(A)
=> ( hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A) = bot_bo1181479936a_bool
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_295_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),bot_bo1055319631e_bool))
=> hBOOL(hAPP_H513860823e_bool(Pa,X)) ) ).
fof(fact_296_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),bot_bo1181479936a_bool))
=> hBOOL(hAPP_H1421470952a_bool(Pa,X)) ) ).
fof(fact_297_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),bot_bo844097828e_bool))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) ).
fof(fact_298_Un__empty__left,axiom,
! [B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),B_1) = B_1 ).
fof(fact_299_Un__empty__left,axiom,
! [B_1] :
( is_fun_pname_bool(B_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B_1) = B_1 ) ).
fof(fact_300_Un__empty__left,axiom,
! [B_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,bot_bo1181479936a_bool),B_1) = B_1 ).
fof(fact_301_Un__empty__right,axiom,
! [A] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),bot_bo1055319631e_bool) = A ).
fof(fact_302_Un__empty__right,axiom,
! [A] :
( is_fun_pname_bool(A)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),bot_bo844097828e_bool) = A ) ).
fof(fact_303_Un__empty__right,axiom,
! [A] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),bot_bo1181479936a_bool) = A ).
fof(fact_304_Un__empty,axiom,
! [A,B_1] :
( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = bot_bo1055319631e_bool
<=> ( A = bot_bo1055319631e_bool
& B_1 = bot_bo1055319631e_bool ) ) ).
fof(fact_305_Un__empty,axiom,
! [A,B_1] :
( ( is_fun_pname_bool(A)
& is_fun_pname_bool(B_1) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) = bot_bo844097828e_bool
<=> ( A = bot_bo844097828e_bool
& B_1 = bot_bo844097828e_bool ) ) ) ).
fof(fact_306_Un__empty,axiom,
! [A,B_1] :
( hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) = bot_bo1181479936a_bool
<=> ( A = bot_bo1181479936a_bool
& B_1 = bot_bo1181479936a_bool ) ) ).
fof(fact_307_constant,axiom,
! [Ga,Pa,C,Qa,C_1] :
( ( hBOOL(C_1)
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))) )
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),Pa))),C_1)),C),Qa)),bot_bo1181479936a_bool))) ) ).
fof(fact_308_constant,axiom,
! [Ga,Pa,C,Qa,C_1] :
( ( hBOOL(C_1)
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),Pa))),C_1)),C),Qa)),bot_bo1055319631e_bool))) ) ).
fof(fact_309_empty,axiom,
! [Ga] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),bot_bo1055319631e_bool)) ).
fof(fact_310_empty,axiom,
! [Ga] : hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),bot_bo1181479936a_bool)) ).
fof(fact_311_sup__bot__left,axiom,
! [X_2] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),X_2) = X_2 ).
fof(fact_312_sup__bot__left,axiom,
! [X_2] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_2) = X_2 ) ).
fof(fact_313_sup__bot__left,axiom,
! [X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_2))
<=> hBOOL(X_2) ) ).
fof(fact_314_sup__bot__left,axiom,
! [X_2] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,bot_bo1181479936a_bool),X_2) = X_2 ).
fof(fact_315_sup__bot__right,axiom,
! [X_2] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),bot_bo1055319631e_bool) = X_2 ).
fof(fact_316_sup__bot__right,axiom,
! [X_2] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),bot_bo844097828e_bool) = X_2 ) ).
fof(fact_317_sup__bot__right,axiom,
! [X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),bot_bot_bool))
<=> hBOOL(X_2) ) ).
fof(fact_318_sup__bot__right,axiom,
! [X_2] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),bot_bo1181479936a_bool) = X_2 ).
fof(fact_319_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1) = bot_bo1055319631e_bool
<=> ( X_2 = bot_bo1055319631e_bool
& Y_1 = bot_bo1055319631e_bool ) ) ).
fof(fact_320_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_1) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1) = bot_bo844097828e_bool
<=> ( X_2 = bot_bo844097828e_bool
& Y_1 = bot_bo844097828e_bool ) ) ) ).
fof(fact_321_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1))
<=> hBOOL(bot_bot_bool) )
<=> ( ( hBOOL(X_2)
<=> hBOOL(bot_bot_bool) )
& ( hBOOL(Y_1)
<=> hBOOL(bot_bot_bool) ) ) ) ).
fof(fact_322_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1) = bot_bo1181479936a_bool
<=> ( X_2 = bot_bo1181479936a_bool
& Y_1 = bot_bo1181479936a_bool ) ) ).
fof(fact_323_triple__valid__Suc,axiom,
! [N_4,T_2] :
( hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(suc(N_4)),T_2))
=> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_4),T_2)) ) ).
fof(fact_324_triple__valid__Suc,axiom,
! [N_4,T_2] :
( hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(suc(N_4)),T_2))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_4),T_2)) ) ).
fof(fact_325_insert__def,axiom,
! [A_1,B_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A_1))),B_1) ).
fof(fact_326_insert__def,axiom,
! [A_1,B_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_1))),B_1) ).
fof(fact_327_insert__def,axiom,
! [A_1,B_1] : hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,fequal879838495iple_a),A_1))),B_1) ).
fof(fact_328_weak__Body,axiom,
! [Ga,Pa,Pn_1,Qa] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1181479936a_bool)))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1181479936a_bool))) ) ).
fof(fact_329_weak__Body,axiom,
! [Ga,Pa,Pn_1,Qa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1055319631e_bool))) ) ).
fof(fact_330_BodyN,axiom,
! [Pa,Pn_1,Qa,Ga] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1181479936a_bool)))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1181479936a_bool))) ) ).
fof(fact_331_BodyN,axiom,
! [Pa,Pn_1,Qa,Ga] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo1055319631e_bool))) ) ).
fof(fact_332_triples__valid__Suc,axiom,
! [N_1,Ts] :
( ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ts))
=> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(suc(N_1)),X)) )
=> ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),Ts))
=> hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_1),X)) ) ) ).
fof(fact_333_triples__valid__Suc,axiom,
! [N_1,Ts] :
( ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ts))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(suc(N_1)),X)) )
=> ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),Ts))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_1),X)) ) ) ).
fof(fact_334_escape,axiom,
! [Ga,C,Qa,Pa] :
( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(Qa,Z_3)))),bot_bo1181479936a_bool))) )
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))) ) ).
fof(fact_335_escape,axiom,
! [Ga,C,Qa,Pa] :
( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Qa,Z_3)))),bot_bo1055319631e_bool))) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))) ) ).
fof(fact_336_conseq1,axiom,
! [Pa,Ga,P_1,C,Qa] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,P_1),C),Qa)),bot_bo1181479936a_bool)))
=> ( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_3),S_3)) )
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))) ) ) ).
fof(fact_337_conseq1,axiom,
! [Pa,Ga,P_1,C,Qa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Qa)),bot_bo1055319631e_bool)))
=> ( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_3),S_3)) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_338_conseq2,axiom,
! [Qa,Ga,Pa,C,Q_1] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Q_1)),bot_bo1181479936a_bool)))
=> ( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_3),S_3))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_3),S_3)) )
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))) ) ) ).
fof(fact_339_conseq2,axiom,
! [Qa,Ga,Pa,C,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Q_1)),bot_bo1055319631e_bool)))
=> ( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_3),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_3),S_3)) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_340_triple_Osize_I1_J,axiom,
! [Fa,Fun1,Com,Fun2] : hoare_1674107620_state(Fa,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2)) = zero_zero_nat ).
fof(fact_341_triple_Osize_I1_J,axiom,
! [Fa,Fun1,Com,Fun2] : hoare_953425885size_a(Fa,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1),Com),Fun2)) = zero_zero_nat ).
fof(fact_342_MGT__def,axiom,
! [C] : hoare_Mirabelle_MGT(C) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,fequal_state),C),evalc(C)) ).
fof(fact_343_triple_Osize_I2_J,axiom,
! [Fun1,Com,Fun2] : size_s346246881_state(hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2)) = zero_zero_nat ).
fof(fact_344_triple_Osize_I2_J,axiom,
! [Fun1,Com,Fun2] : size_s315943222iple_a(hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Fun1),Com),Fun2)) = zero_zero_nat ).
fof(fact_345_conseq12,axiom,
! [Qa,Pa,Ga,P_1,C,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))
=> ( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3))
=> ! [S_4] :
( ! [Z_4] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_4),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_4),S_4)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_3),S_4)) ) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_346_conseq12,axiom,
! [Qa,Pa,Ga,P_1,C,Q_1] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,P_1),C),Q_1)),bot_bo1181479936a_bool)))
=> ( ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3))
=> ! [S_4] :
( ! [Z_4] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_4),S_3))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_4),S_4)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_3),S_4)) ) )
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool))) ) ) ).
fof(fact_347_the__elem__eq,axiom,
! [X_2] : hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2 ).
fof(fact_348_the__elem__eq,axiom,
! [X_2] : hAPP_f124283079iple_a(the_el1436340927iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),bot_bo1181479936a_bool)) = X_2 ).
fof(fact_349_the__elem__eq,axiom,
! [X_2] :
( is_pname(X_2)
=> hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = X_2 ) ).
fof(fact_350_Zero__not__Suc,axiom,
! [M] : zero_zero_nat != suc(M) ).
fof(fact_351_nat_Osimps_I2_J,axiom,
! [Nat_4] : zero_zero_nat != suc(Nat_4) ).
fof(fact_352_Suc__not__Zero,axiom,
! [M] : suc(M) != zero_zero_nat ).
fof(fact_353_nat_Osimps_I3_J,axiom,
! [Nat_3] : suc(Nat_3) != zero_zero_nat ).
fof(fact_354_Zero__neq__Suc,axiom,
! [M] : zero_zero_nat != suc(M) ).
fof(fact_355_Suc__neq__Zero,axiom,
! [M] : suc(M) != zero_zero_nat ).
fof(fact_356_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_357_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_358_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_359_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat ).
fof(fact_360_Suc__inject,axiom,
! [X_1,Y] :
( suc(X_1) = suc(Y)
=> X_1 = Y ) ).
fof(fact_361_nat_Oinject,axiom,
! [Nat_2,Nat_1] :
( suc(Nat_2) = suc(Nat_1)
<=> Nat_2 = Nat_1 ) ).
fof(fact_362_Suc__n__not__n,axiom,
! [N_2] : suc(N_2) != N_2 ).
fof(fact_363_n__not__Suc__n,axiom,
! [N_2] : N_2 != suc(N_2) ).
fof(fact_364_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_365_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_H1421470952a_bool(bot_bo1181479936a_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_366_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_367_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero_nat
=> ~ ! [Nat] : Y != suc(Nat) ) ).
fof(fact_368_zero__induct,axiom,
! [Pa,K] :
( hBOOL(hAPP_nat_bool(Pa,K))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,suc(N)))
=> hBOOL(hAPP_nat_bool(Pa,N)) )
=> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).
fof(fact_369_nat__induct,axiom,
! [N_1,Pa] :
( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,N))
=> hBOOL(hAPP_nat_bool(Pa,suc(N))) )
=> hBOOL(hAPP_nat_bool(Pa,N_1)) ) ) ).
fof(fact_370_not0__implies__Suc,axiom,
! [N_2] :
( N_2 != zero_zero_nat
=> ? [M_2] : N_2 = suc(M_2) ) ).
fof(fact_371_evaln_OBody,axiom,
! [Pn,S0,N_2,S1_1] :
( hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn)),S0,N_2),S1_1))
=> hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,Pn),S0,suc(N_2)),S1_1)) ) ).
fof(fact_372_hoare__derivs_OSkip,axiom,
! [Ga,Pa] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),skip),Pa)),bot_bo1055319631e_bool))) ).
fof(fact_373_hoare__derivs_OSkip,axiom,
! [Ga,Pa] : hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),skip),Pa)),bot_bo1181479936a_bool))) ).
fof(fact_374_evaln__elim__cases_I1_J,axiom,
! [S_2,N_2,T_1] :
( hBOOL(hAPP_state_bool(evaln(skip,S_2,N_2),T_1))
=> T_1 = S_2 ) ).
fof(fact_375_evaln_OSkip,axiom,
! [S_2,N_2] : hBOOL(hAPP_state_bool(evaln(skip,S_2,N_2),S_2)) ).
fof(fact_376_evalc_OSkip,axiom,
! [S_2] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),S_2)) ).
fof(fact_377_evalc__elim__cases_I1_J,axiom,
! [S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),T_1))
=> T_1 = S_2 ) ).
fof(fact_378_evaln__Suc,axiom,
! [C_2,S_2,N_2,S_5] :
( hBOOL(hAPP_state_bool(evaln(C_2,S_2,N_2),S_5))
=> hBOOL(hAPP_state_bool(evaln(C_2,S_2,suc(N_2)),S_5)) ) ).
fof(fact_379_eval__eq,axiom,
! [C,S,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),T))
<=> ? [N] : hBOOL(hAPP_state_bool(evaln(C,S,N),T)) ) ).
fof(fact_380_evaln__evalc,axiom,
! [C_2,S_2,N_2,T_1] :
( hBOOL(hAPP_state_bool(evaln(C_2,S_2,N_2),T_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1)) ) ).
fof(fact_381_com_Osimps_I19_J,axiom,
! [Pname_1] : hAPP_pname_com(body,Pname_1) != skip ).
fof(fact_382_com_Osimps_I18_J,axiom,
! [Pname_1] : skip != hAPP_pname_com(body,Pname_1) ).
fof(fact_383_triple__valid__def2,axiom,
! [N_1,Pa,C,Qa] :
( hBOOL(hAPP_H513860823e_bool(hoare_592710359_state(N_1),hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)))
<=> ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_3),S_3))
=> ! [S_4] :
( hBOOL(hAPP_state_bool(evaln(C,S_3,N_1),S_4))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_3),S_4)) ) ) ) ).
fof(fact_384_triple__valid__def2,axiom,
! [N_1,Pa,C,Qa] :
( hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N_1),hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)))
<=> ! [Z_3,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_3),S_3))
=> ! [S_4] :
( hBOOL(hAPP_state_bool(evaln(C,S_3,N_1),S_4))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_3),S_4)) ) ) ) ).
fof(fact_385_evaln__elim__cases_I6_J,axiom,
! [P,S_2,N_2,S1_1] :
( hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,P),S_2,N_2),S1_1))
=> ~ ! [N] :
( N_2 = suc(N)
=> ~ hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P)),S_2,N),S1_1)) ) ) ).
fof(fact_386_evalc__evaln,axiom,
! [C_2,S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1))
=> ? [N] : hBOOL(hAPP_state_bool(evaln(C_2,S_2,N),T_1)) ) ).
fof(fact_387_LoopF,axiom,
! [Ga,Pa,B,C] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),Pa))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B))),while(B,C)),Pa)),bot_bo1055319631e_bool))) ).
fof(fact_388_LoopF,axiom,
! [Ga,Pa,B,C] : hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),Pa))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B))),while(B,C)),Pa)),bot_bo1181479936a_bool))) ).
fof(fact_389_Comp,axiom,
! [D,R_1,Ga,Pa,C,Qa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),C),Qa)),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Qa),D),R_1)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Pa),semi(C,D)),R_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_390_Comp,axiom,
! [D,R_1,Ga,Pa,C,Qa] :
( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),C),Qa)),bot_bo1181479936a_bool)))
=> ( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Qa),D),R_1)),bot_bo1181479936a_bool)))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,Pa),semi(C,D)),R_1)),bot_bo1181479936a_bool))) ) ) ).
fof(fact_391_the__elem__def,axiom,
! [X_3] : hAPP_f2143211163_state(the_el23965208_state,X_3) = hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f1456107715e_bool(cOMBB_1653402815_state(hAPP_f854625363l_bool(fequal1746921144e_bool,X_3)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool))) ).
fof(fact_392_the__elem__def,axiom,
! [X_3] : hAPP_f124283079iple_a(the_el1436340927iple_a,X_3) = hAPP_f124283079iple_a(the_Ho746640593iple_a,hAPP_f772297704a_bool(cOMBB_1501709507iple_a(hAPP_f430043647l_bool(fequal1258664663a_bool,X_3)),hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,insert873085594iple_a),bot_bo1181479936a_bool))) ).
fof(fact_393_the__elem__def,axiom,
! [X_3] : hAPP_f1297739591_pname(the_elem_pname,X_3) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_3)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))) ).
fof(fact_394_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U))
=> ( ! [P_2] :
( is_pname(P_2)
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Q_1,P_2))),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Qa,P_2))),bot_bo1055319631e_bool))) ) )
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),C0)),Q_1)),U)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(Ga),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),Pa)),C0)),Qa)),U))) ) ) ) ).
fof(fact_395_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U))
=> ( ! [P_2] :
( is_pname(P_2)
=> ( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_p635540397e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Q_1,P_2))),bot_bo1181479936a_bool)))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,hAPP_f150255961iple_a(hAPP_c1407587404iple_a(hAPP_f1807945453iple_a(hoare_1760757500iple_a,hAPP_p635540397e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Qa,P_2))),bot_bo1181479936a_bool))) ) )
=> ( hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),P_1)),C0)),Q_1)),U)))
=> hBOOL(hAPP_f540970102l_bool(hoare_606018542rivs_a(Ga),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),Pa)),C0)),Qa)),U))) ) ) ) ).
fof(fact_396_evaln_OWhileFalse,axiom,
! [C,N_1,B,S] :
( ~ hBOOL(hAPP_state_bool(B,S))
=> hBOOL(hAPP_state_bool(evaln(while(B,C),S,N_1),S)) ) ).
fof(fact_397_evaln_OWhileTrue,axiom,
! [S2_1,C,N_1,S1,B,S0_1] :
( hBOOL(hAPP_state_bool(B,S0_1))
=> ( hBOOL(hAPP_state_bool(evaln(C,S0_1,N_1),S1))
=> ( hBOOL(hAPP_state_bool(evaln(while(B,C),S1,N_1),S2_1))
=> hBOOL(hAPP_state_bool(evaln(while(B,C),S0_1,N_1),S2_1)) ) ) ) ).
fof(fact_398_evalc_OWhileTrue,axiom,
! [S2_1,C,S1,B,S0_1] :
( hBOOL(hAPP_state_bool(B,S0_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0_1),S1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S1),S2_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S0_1),S2_1)) ) ) ) ).
fof(fact_399_evalc_OWhileFalse,axiom,
! [C,B,S] :
( ~ hBOOL(hAPP_state_bool(B,S))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S),S)) ) ).
fof(fact_400_evaln_OSemi,axiom,
! [C1_1,S2,C0_1,S0,N_2,S1_1] :
( hBOOL(hAPP_state_bool(evaln(C0_1,S0,N_2),S1_1))
=> ( hBOOL(hAPP_state_bool(evaln(C1_1,S1_1,N_2),S2))
=> hBOOL(hAPP_state_bool(evaln(semi(C0_1,C1_1),S0,N_2),S2)) ) ) ).
fof(fact_401_evalc_OSemi,axiom,
! [C1_1,S2,C0_1,S0,S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0_1),S0),S1_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S1_1),S2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0_1,C1_1)),S0),S2)) ) ) ).
fof(fact_402_com_Osimps_I46_J,axiom,
! [Com1,Com2,Fun_1,Com_1] : semi(Com1,Com2) != while(Fun_1,Com_1) ).
fof(fact_403_com_Osimps_I47_J,axiom,
! [Fun_1,Com_1,Com1,Com2] : while(Fun_1,Com_1) != semi(Com1,Com2) ).
fof(fact_404_com_Osimps_I3_J,axiom,
! [Com1,Com2,Com1_3,Com2_3] :
( semi(Com1,Com2) = semi(Com1_3,Com2_3)
<=> ( Com1 = Com1_3
& Com2 = Com2_3 ) ) ).
fof(fact_405_com_Osimps_I5_J,axiom,
! [Fun,Com,Fun_1,Com_1] :
( while(Fun,Com) = while(Fun_1,Com_1)
<=> ( Fun = Fun_1
& Com = Com_1 ) ) ).
fof(fact_406_com_Osimps_I59_J,axiom,
! [Pname_2,Fun,Com] : hAPP_pname_com(body,Pname_2) != while(Fun,Com) ).
fof(fact_407_com_Osimps_I58_J,axiom,
! [Fun,Com,Pname_2] : while(Fun,Com) != hAPP_pname_com(body,Pname_2) ).
fof(fact_408_com_Osimps_I16_J,axiom,
! [Fun_1,Com_1] : skip != while(Fun_1,Com_1) ).
fof(fact_409_com_Osimps_I17_J,axiom,
! [Fun_1,Com_1] : while(Fun_1,Com_1) != skip ).
fof(fact_410_com_Osimps_I49_J,axiom,
! [Pname_1,Com1_1,Com2_1] : hAPP_pname_com(body,Pname_1) != semi(Com1_1,Com2_1) ).
fof(fact_411_com_Osimps_I48_J,axiom,
! [Com1_1,Com2_1,Pname_1] : semi(Com1_1,Com2_1) != hAPP_pname_com(body,Pname_1) ).
fof(fact_412_com_Osimps_I12_J,axiom,
! [Com1_2,Com2_2] : skip != semi(Com1_2,Com2_2) ).
fof(fact_413_com_Osimps_I13_J,axiom,
! [Com1_2,Com2_2] : semi(Com1_2,Com2_2) != skip ).
fof(fact_414_evalc__elim__cases_I4_J,axiom,
! [C1_1,C2_1,S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1_1,C2_1)),S_2),T_1))
=> ~ ! [S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S_2),S1_2))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2_1),S1_2),T_1)) ) ) ).
fof(fact_415_evaln__elim__cases_I4_J,axiom,
! [C1_1,C2_1,S_2,N_2,T_1] :
( hBOOL(hAPP_state_bool(evaln(semi(C1_1,C2_1),S_2,N_2),T_1))
=> ~ ! [S1_2] :
( hBOOL(hAPP_state_bool(evaln(C1_1,S_2,N_2),S1_2))
=> ~ hBOOL(hAPP_state_bool(evaln(C2_1,S1_2,N_2),T_1)) ) ) ).
fof(fact_416_finite__imageI,axiom,
! [H,F] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(H),F))) ) ).
fof(fact_417_finite__imageI,axiom,
! [H,F] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F))
=> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f271130963a_bool(image_1654749281iple_a(H),F))) ) ).
fof(fact_418_finite_OinsertI,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A))) ) ).
fof(fact_419_finite_OinsertI,axiom,
! [A_1,A] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A))) ) ).
fof(fact_420_finite_OinsertI,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A))) ) ).
fof(fact_421_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).
fof(fact_422_finite_OemptyI,axiom,
hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,bot_bo1181479936a_bool)) ).
fof(fact_423_finite_OemptyI,axiom,
hBOOL(hAPP_f1760790145l_bool(finite784854244_state,bot_bo1055319631e_bool)) ).
fof(fact_424_finite__Collect__conjI,axiom,
! [Qa,Pa] :
( ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Pa)))
| hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Qa))) )
=> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),Pa)),Qa)))) ) ).
fof(fact_425_finite__Collect__conjI,axiom,
! [Qa,Pa] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Pa)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Qa))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),Pa)),Qa)))) ) ).
fof(fact_426_finite__Collect__disjI,axiom,
! [Pa,Qa] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fdisj),Pa)),Qa))))
<=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Pa)))
& hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(collec268032053iple_a,Qa))) ) ) ).
fof(fact_427_finite__Collect__disjI,axiom,
! [Pa,Qa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),Pa)),Qa))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Pa)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Qa))) ) ) ).
fof(fact_428_finite__insert,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)))
<=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) ) ).
fof(fact_429_finite__insert,axiom,
! [A_1,A] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)))
<=> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A)) ) ).
fof(fact_430_finite__insert,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ).
fof(fact_431_finite__Un,axiom,
! [F,Ga] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),Ga)))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)) ) ) ).
fof(fact_432_finite__Un,axiom,
! [F,Ga] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),Ga)))
<=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F))
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Ga)) ) ) ).
fof(fact_433_finite__Un,axiom,
! [F,Ga] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F),Ga)))
<=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F))
& hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,Ga)) ) ) ).
fof(fact_434_finite__UnI,axiom,
! [Ga,F] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),Ga))) ) ) ).
fof(fact_435_finite__UnI,axiom,
! [Ga,F] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Ga))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),Ga))) ) ) ).
fof(fact_436_finite__UnI,axiom,
! [Ga,F] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,Ga))
=> hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,F),Ga))) ) ) ).
fof(fact_437_finite_Osimps,axiom,
! [A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
<=> ( A_1 = bot_bo1055319631e_bool
| ? [A_3,A_2] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_2),A_3)
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_3)) ) ) ) ).
fof(fact_438_finite_Osimps,axiom,
! [A_1] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_1))
<=> ( A_1 = bot_bo1181479936a_bool
| ? [A_3,A_2] :
( A_1 = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_2),A_3)
& hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A_3)) ) ) ) ).
fof(fact_439_finite_Osimps,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
<=> ( A_1 = bot_bo844097828e_bool
| ? [A_3,A_2] :
( is_fun_pname_bool(A_3)
& is_pname(A_2)
& A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_3)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_3)) ) ) ) ) ).
fof(fact_440_finite__induct,axiom,
! [Pa,F] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),F_2))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,F_2))
=> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),F_2))) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(Pa,F)) ) ) ) ).
fof(fact_441_finite__induct,axiom,
! [Pa,F] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F))
=> ( hBOOL(hAPP_f540970102l_bool(Pa,bot_bo1181479936a_bool))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2))
=> ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),F_2))
=> ( hBOOL(hAPP_f540970102l_bool(Pa,F_2))
=> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),F_2))) ) ) )
=> hBOOL(hAPP_f540970102l_bool(Pa,F)) ) ) ) ).
fof(fact_442_finite__induct,axiom,
! [Pa,F] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F))
=> ( hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
=> ( ! [X,F_2] :
( ( is_pname(X)
& is_fun_pname_bool(F_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),F_2))
=> ( hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
=> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(Pa,F)) ) ) ) ).
fof(fact_443_pigeonhole__infinite,axiom,
! [F_1,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(F_1),A)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,hAPP_f998786331e_bool(cOMBB_799949246_pname(fequal1531560888_state),F_1)),hAPP_p1842370726_state(F_1,X)))))) ) ) ) ).
fof(fact_444_pigeonhole__infinite,axiom,
! [F_1,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_H1991058245e_bool(hAPP_f687460073e_bool(cOMBC_1693967286a_bool,hAPP_f1311175287a_bool(cOMBB_858699740_pname(fequal879838495iple_a),F_1)),hAPP_p263283121iple_a(F_1,X)))))) ) ) ) ).
fof(fact_445_evalc__WHILE__case,axiom,
! [B,C,S,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S),T))
=> ( ( T = S
=> hBOOL(hAPP_state_bool(B,S)) )
=> ~ ( hBOOL(hAPP_state_bool(B,S))
=> ! [S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),S1_2))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B,C)),S1_2),T)) ) ) ) ) ).
fof(fact_446_evaln__WHILE__case,axiom,
! [B,C,S,N_1,T] :
( hBOOL(hAPP_state_bool(evaln(while(B,C),S,N_1),T))
=> ( ( T = S
=> hBOOL(hAPP_state_bool(B,S)) )
=> ~ ( hBOOL(hAPP_state_bool(B,S))
=> ! [S1_2] :
( hBOOL(hAPP_state_bool(evaln(C,S,N_1),S1_2))
=> ~ hBOOL(hAPP_state_bool(evaln(while(B,C),S1_2,N_1),T)) ) ) ) ) ).
fof(fact_447_nonempty__iff,axiom,
! [A] :
( A != bot_bo1055319631e_bool
<=> ? [X,B_2] :
( A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),B_2)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),B_2)) ) ) ).
fof(fact_448_nonempty__iff,axiom,
! [A] :
( A != bot_bo1181479936a_bool
<=> ? [X,B_2] :
( A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),B_2)
& ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),B_2)) ) ) ).
fof(fact_449_nonempty__iff,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( A != bot_bo844097828e_bool
<=> ? [X,B_2] :
( is_pname(X)
& is_fun_pname_bool(B_2)
& A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),B_2)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_2)) ) ) ) ).
fof(fact_450_folding__one__idem_Ounion__idem,axiom,
! [B_1,A,F_1,F] :
( ( is_fun_pname_bool(B_1)
& is_fun_pname_bool(A) )
=> ( hBOOL(finite89670078_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_1))
=> ( B_1 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,A)),hAPP_f1297739591_pname(F,B_1)) ) ) ) ) ) ) ).
fof(fact_451_folding__one__idem_Ounion__idem,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite950012314iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( A != bot_bo1181479936a_bool
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B_1))
=> ( B_1 != bot_bo1181479936a_bool
=> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B_1)) ) ) ) ) ) ).
fof(fact_452_folding__one__idem_Ounion__idem,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite506823037_state(F_1,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> ( A != bot_bo1055319631e_bool
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> ( B_1 != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B_1)) ) ) ) ) ) ).
fof(fact_453_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A,F_1,F] :
( hBOOL(finite506823037_state(F_1,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> ( A != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_2),hAPP_f2143211163_state(F,A)) ) ) ) ).
fof(fact_454_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A,F_1,F] :
( hBOOL(finite950012314iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( A != bot_bo1181479936a_bool
=> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),hAPP_f124283079iple_a(F,A)) ) ) ) ).
fof(fact_455_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A,F_1,F] :
( is_fun_pname_bool(A)
=> ( hBOOL(finite89670078_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X_2),hAPP_f1297739591_pname(F,A)) ) ) ) ) ).
fof(fact_456_image__eq__fold__image,axiom,
! [F_1,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hAPP_f631639356e_bool(image_275883510_state(F_1),A) = finite216774046_pname(semila447562797e_bool,hAPP_f621094798e_bool(hAPP_f1505732693e_bool(cOMBC_173904839e_bool,hAPP_f1191449183e_bool(cOMBB_557071226_pname(insert1835143293_state),F_1)),bot_bo1055319631e_bool),bot_bo1055319631e_bool,A) ) ).
fof(fact_457_image__eq__fold__image,axiom,
! [F_1,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hAPP_f271130963a_bool(image_1654749281iple_a(F_1),A) = finite979333485_pname(semila1498788770a_bool,hAPP_f1646799884a_bool(hAPP_f2022238777a_bool(cOMBC_1527561185a_bool,hAPP_f1728520198a_bool(cOMBB_1191710871_pname(insert873085594iple_a),F_1)),bot_bo1181479936a_bool),bot_bo1181479936a_bool,A) ) ).
fof(fact_458_finite__ne__induct,axiom,
! [Pa,F] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F))
=> ( F != bot_bo1055319631e_bool
=> ( ! [X] : hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),bot_bo1055319631e_bool)))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2))
=> ( F_2 != bot_bo1055319631e_bool
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),F_2))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,F_2))
=> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(Pa,F)) ) ) ) ) ).
fof(fact_459_finite__ne__induct,axiom,
! [Pa,F] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F))
=> ( F != bot_bo1181479936a_bool
=> ( ! [X] : hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),bot_bo1181479936a_bool)))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,F_2))
=> ( F_2 != bot_bo1181479936a_bool
=> ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),F_2))
=> ( hBOOL(hAPP_f540970102l_bool(Pa,F_2))
=> hBOOL(hAPP_f540970102l_bool(Pa,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f540970102l_bool(Pa,F)) ) ) ) ) ).
fof(fact_460_finite__ne__induct,axiom,
! [Pa,F] :
( is_fun_pname_bool(F)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F))
=> ( F != bot_bo844097828e_bool
=> ( ! [X] :
( is_pname(X)
=> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),bot_bo844097828e_bool))) )
=> ( ! [X,F_2] :
( ( is_pname(X)
& is_fun_pname_bool(F_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
=> ( F_2 != bot_bo844097828e_bool
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),F_2))
=> ( hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
=> hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),F_2))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(Pa,F)) ) ) ) ) ) ).
fof(fact_461_folding__one__idem_Oin__idem,axiom,
! [X_2,A,F_1,F] :
( hBOOL(finite950012314iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),hAPP_f124283079iple_a(F,A)) = hAPP_f124283079iple_a(F,A) ) ) ) ).
fof(fact_462_folding__one__idem_Oin__idem,axiom,
! [X_2,A,F_1,F] :
( hBOOL(finite89670078_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X_2),hAPP_f1297739591_pname(F,A)) = hAPP_f1297739591_pname(F,A) ) ) ) ).
fof(fact_463_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F_1,F] :
( is_fun_pname_bool(N_3)
=> ( hBOOL(finite89670078_pname(F_1,F))
=> ( ! [X,Y_2] :
( ( is_pname(X)
& is_pname(Y_2) )
=> hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X),Y_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_pname_pname(H,X)),hAPP_pname_pname(H,Y_2)) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N_3))
=> ( N_3 != bot_bo844097828e_bool
=> hAPP_pname_pname(H,hAPP_f1297739591_pname(F,N_3)) = hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(image_pname_pname(H),N_3)) ) ) ) ) ) ).
fof(fact_464_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F_1,F] :
( hBOOL(finite950012314iple_a(F_1,F))
=> ( ! [X,Y_2] : hAPP_H678412245iple_a(H,hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X),Y_2)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_H678412245iple_a(H,X)),hAPP_H678412245iple_a(H,Y_2))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,N_3))
=> ( N_3 != bot_bo1181479936a_bool
=> hAPP_H678412245iple_a(H,hAPP_f124283079iple_a(F,N_3)) = hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(image_306007685iple_a(H),N_3)) ) ) ) ) ).
fof(fact_465_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F_1,F] :
( hBOOL(finite506823037_state(F_1,F))
=> ( ! [X,Y_2] : hAPP_H563960305_state(H,hAPP_H563960305_state(hAPP_H521649881_state(F_1,X),Y_2)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_H563960305_state(H,X)),hAPP_H563960305_state(H,Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,N_3))
=> ( N_3 != bot_bo1055319631e_bool
=> hAPP_H563960305_state(H,hAPP_f2143211163_state(F,N_3)) = hAPP_f2143211163_state(F,hAPP_f921536533e_bool(image_650584225_state(H),N_3)) ) ) ) ) ).
fof(fact_466_folding__one_Oinsert,axiom,
! [X_2,A,F_1,F] :
( hBOOL(finite774711482_state(F_1,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A))
=> ( A != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,X_2),hAPP_f2143211163_state(F,A)) ) ) ) ) ).
fof(fact_467_folding__one_Oinsert,axiom,
! [X_2,A,F_1,F] :
( hBOOL(finite1669978781iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> ( A != bot_bo1181479936a_bool
=> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),A)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X_2),hAPP_f124283079iple_a(F,A)) ) ) ) ) ).
fof(fact_468_folding__one_Oinsert,axiom,
! [X_2,A,F_1,F] :
( is_fun_pname_bool(A)
=> ( hBOOL(finite1282449217_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( A != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X_2),hAPP_f1297739591_pname(F,A)) ) ) ) ) ) ).
fof(fact_469_folding__one_Osingleton,axiom,
! [X_2,F_1,F] :
( hBOOL(finite774711482_state(F_1,F))
=> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2 ) ).
fof(fact_470_folding__one_Osingleton,axiom,
! [X_2,F_1,F] :
( hBOOL(finite1669978781iple_a(F_1,F))
=> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),bot_bo1181479936a_bool)) = X_2 ) ).
fof(fact_471_folding__one_Osingleton,axiom,
! [X_2,F_1,F] :
( is_pname(X_2)
=> ( hBOOL(finite1282449217_pname(F_1,F))
=> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = X_2 ) ) ).
fof(fact_472_folding__one_Oclosed,axiom,
! [A,F_1,F] :
( hBOOL(finite774711482_state(F_1,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> ( A != bot_bo1055319631e_bool
=> ( ! [X,Y_2] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F_1,X),Y_2)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),bot_bo1055319631e_bool))))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(F,A)),A)) ) ) ) ) ).
fof(fact_473_folding__one_Oclosed,axiom,
! [A,F_1,F] :
( hBOOL(finite1669978781iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( A != bot_bo1181479936a_bool
=> ( ! [X,Y_2] : hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,X),Y_2)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,Y_2),bot_bo1181479936a_bool))))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,hAPP_f124283079iple_a(F,A)),A)) ) ) ) ) ).
fof(fact_474_folding__one_Oclosed,axiom,
! [A,F_1,F] :
( is_fun_pname_bool(A)
=> ( hBOOL(finite1282449217_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> ( ! [X,Y_2] :
( ( is_pname(X)
& is_pname(Y_2) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F_1,X),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F,A)),A)) ) ) ) ) ) ).
fof(fact_475_evaln__max2,axiom,
! [C2_1,S2,N2,T2,C1_1,S1_1,N1,T1] :
( hBOOL(hAPP_state_bool(evaln(C1_1,S1_1,N1),T1))
=> ( hBOOL(hAPP_state_bool(evaln(C2_1,S2,N2),T2))
=> ? [N] :
( hBOOL(hAPP_state_bool(evaln(C1_1,S1_1,N),T1))
& hBOOL(hAPP_state_bool(evaln(C2_1,S2,N),T2)) ) ) ) ).
fof(fact_476_mk__disjoint__insert,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))
=> ? [B_2] :
( A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_2)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),B_2)) ) ) ).
fof(fact_477_mk__disjoint__insert,axiom,
! [A_1,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))
=> ? [B_2] :
( A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_2)
& ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),B_2)) ) ) ).
fof(fact_478_mk__disjoint__insert,axiom,
! [A_1,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> ? [B_2] :
( is_fun_pname_bool(B_2)
& A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_2)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_2)) ) ) ) ).
fof(fact_479_Set_Oset__insert,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A))
=> ~ ! [B_2] :
( A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_2)
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_2)) ) ) ).
fof(fact_480_Set_Oset__insert,axiom,
! [X_2,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
=> ~ ! [B_2] :
( A = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,X_2),B_2)
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),B_2)) ) ) ).
fof(fact_481_Set_Oset__insert,axiom,
! [X_2,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ~ ! [B_2] :
( is_fun_pname_bool(B_2)
=> ( A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2)) ) ) ) ) ).
fof(fact_482_equals0I,axiom,
! [A] :
( ! [Y_2] : ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Y_2),A))
=> A = bot_bo1181479936a_bool ) ).
fof(fact_483_equals0I,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( ! [Y_2] :
( is_pname(Y_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_2),A)) )
=> A = bot_bo844097828e_bool ) ) ).
fof(fact_484_equals0I,axiom,
! [A] :
( ! [Y_2] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_2),A))
=> A = bot_bo1055319631e_bool ) ).
fof(fact_485_Sup__fin_Ounion__idem,axiom,
! [B_1,A] :
( ( is_fun_bool_bool(B_1)
& is_fun_bool_bool(A) )
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( A != bot_bo806936373l_bool
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_1))
=> ( B_1 != bot_bo806936373l_bool
=> ( hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A),B_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(A)),big_la1480321694n_bool(B_1))) ) ) ) ) ) ) ).
fof(fact_486_Sup__fin_Ounion__idem,axiom,
! [B_1,A] :
( ( is_fun1661590463l_bool(B_1)
& is_fun1661590463l_bool(A) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_1))
=> ( B_1 != bot_bo1649642514l_bool
=> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(A)),big_la841148155e_bool(B_1)) ) ) ) ) ) ).
fof(fact_487_Sup__fin_Ounion__idem,axiom,
! [B_1,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( A != bot_bo1325454745l_bool
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B_1))
=> ( B_1 != bot_bo1325454745l_bool
=> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(A)),big_la1640362552e_bool(B_1)) ) ) ) ) ).
fof(fact_488_Sup__fin_Ounion__idem,axiom,
! [B_1,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( A != bot_bo1325387246l_bool
=> ( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,B_1))
=> ( B_1 != bot_bo1325387246l_bool
=> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f997688506l_bool(semila1827648460l_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(A)),big_la1993344855a_bool(B_1)) ) ) ) ) ).
fof(fact_489_Sup__fin_Oin__idem,axiom,
! [X_2,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),big_la1480321694n_bool(A)))
<=> hBOOL(big_la1480321694n_bool(A)) ) ) ) ).
fof(fact_490_Sup__fin_Oin__idem,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),big_la841148155e_bool(A)) = big_la841148155e_bool(A) ) ) ).
fof(fact_491_Sup__fin_Oin__idem,axiom,
! [X_2,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),big_la1640362552e_bool(A)) = big_la1640362552e_bool(A) ) ) ).
fof(fact_492_Sup__fin_Oin__idem,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,X_2),A))
=> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),big_la1993344855a_bool(A)) = big_la1993344855a_bool(A) ) ) ).
fof(fact_493_Sup__fin_Oinsert,axiom,
! [X_2,A] :
( is_fun_bool_bool(A)
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> ( A != bot_bo806936373l_bool
=> ( hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),big_la1480321694n_bool(A))) ) ) ) ) ) ).
fof(fact_494_Sup__fin_Oinsert,axiom,
! [X_2,A] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> ( A != bot_bo1649642514l_bool
=> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),big_la841148155e_bool(A)) ) ) ) ) ).
fof(fact_495_Sup__fin_Oinsert,axiom,
! [X_2,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( ~ hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A))
=> ( A != bot_bo1325454745l_bool
=> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),A)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),big_la1640362552e_bool(A)) ) ) ) ).
fof(fact_496_Sup__fin_Oinsert,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( ~ hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,X_2),A))
=> ( A != bot_bo1325387246l_bool
=> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,X_2),A)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),big_la1993344855a_bool(A)) ) ) ) ).
fof(fact_497_Sup__fin_Oinsert__idem,axiom,
! [X_2,A] :
( is_fun_bool_bool(A)
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( A != bot_bo806936373l_bool
=> ( hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),big_la1480321694n_bool(A))) ) ) ) ) ).
fof(fact_498_Sup__fin_Oinsert__idem,axiom,
! [X_2,A] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),big_la841148155e_bool(A)) ) ) ) ).
fof(fact_499_Sup__fin_Oinsert__idem,axiom,
! [X_2,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( A != bot_bo1325454745l_bool
=> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),A)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),big_la1640362552e_bool(A)) ) ) ).
fof(fact_500_Sup__fin_Oinsert__idem,axiom,
! [X_2,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( A != bot_bo1325387246l_bool
=> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,X_2),A)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),big_la1993344855a_bool(A)) ) ) ).
fof(fact_501_Sup__fin_Ohom__commute,axiom,
! [N_3,H] :
( is_fun_bool_bool(N_3)
=> ( ! [X,Y_2] :
( ( is_bool(X)
& is_bool(Y_2) )
=> ( hBOOL(hAPP_bool_bool(H,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Y_2)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(H,X)),hAPP_bool_bool(H,Y_2))) ) )
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,N_3))
=> ( N_3 != bot_bo806936373l_bool
=> ( hBOOL(hAPP_bool_bool(H,big_la1480321694n_bool(N_3)))
<=> hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(image_bool_bool(H),N_3))) ) ) ) ) ) ).
fof(fact_502_Sup__fin_Ohom__commute,axiom,
! [N_3,H] :
( is_fun1661590463l_bool(N_3)
=> ( ! [X,Y_2] :
( ( is_fun_pname_bool(X)
& is_fun_pname_bool(Y_2) )
=> hAPP_f759274231e_bool(H,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(H,X)),hAPP_f759274231e_bool(H,Y_2)) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N_3))
=> ( N_3 != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(H,big_la841148155e_bool(N_3)) = big_la841148155e_bool(hAPP_f559147733l_bool(image_2063528359e_bool(H),N_3)) ) ) ) ) ).
fof(fact_503_Sup__fin_Ohom__commute,axiom,
! [N_3,H] :
( ! [X,Y_2] : hAPP_f921536533e_bool(H,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Y_2)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(H,X)),hAPP_f921536533e_bool(H,Y_2))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,N_3))
=> ( N_3 != bot_bo1325454745l_bool
=> hAPP_f921536533e_bool(H,big_la1640362552e_bool(N_3)) = big_la1640362552e_bool(hAPP_f1970439265l_bool(image_505022149e_bool(H),N_3)) ) ) ) ).
fof(fact_504_Sup__fin_Ohom__commute,axiom,
! [N_3,H] :
( ! [X,Y_2] : hAPP_f1591852335a_bool(H,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Y_2)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(H,X)),hAPP_f1591852335a_bool(H,Y_2))
=> ( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,N_3))
=> ( N_3 != bot_bo1325387246l_bool
=> hAPP_f1591852335a_bool(H,big_la1993344855a_bool(N_3)) = big_la1993344855a_bool(hAPP_f960623701l_bool(image_119931871a_bool(H),N_3)) ) ) ) ).
fof(fact_505_Sup__fin_Oclosed,axiom,
! [A] :
( is_fun_bool_bool(A)
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( A != bot_bo806936373l_bool
=> ( ! [X,Y_2] :
( ( is_bool(X)
& is_bool(Y_2) )
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Y_2)),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,Y_2),bot_bo806936373l_bool)))) )
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,big_la1480321694n_bool(A)),A)) ) ) ) ) ).
fof(fact_506_Sup__fin_Oclosed,axiom,
! [A] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( ! [X,Y_2] :
( ( is_fun_pname_bool(X)
& is_fun_pname_bool(Y_2) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Y_2)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_2),bot_bo1649642514l_bool)))) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,big_la841148155e_bool(A)),A)) ) ) ) ) ).
fof(fact_507_Sup__fin_Oclosed,axiom,
! [A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( A != bot_bo1325454745l_bool
=> ( ! [X,Y_2] : hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Y_2)),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,Y_2),bot_bo1325454745l_bool))))
=> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,big_la1640362552e_bool(A)),A)) ) ) ) ).
fof(fact_508_Sup__fin_Oclosed,axiom,
! [A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( A != bot_bo1325387246l_bool
=> ( ! [X,Y_2] : hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Y_2)),hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,X),hAPP_f960623701l_bool(hAPP_f1556354660l_bool(insert1805675420a_bool,Y_2),bot_bo1325387246l_bool))))
=> hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,big_la1993344855a_bool(A)),A)) ) ) ) ).
fof(fact_509_Sup__fin_Ounion__inter,axiom,
! [B_1,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_1))
=> ( hAPP_f961197973l_bool(semila1551573549l_bool(A),B_1) != bot_bo806936373l_bool
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A),B_1))),big_la1480321694n_bool(hAPP_f961197973l_bool(semila1551573549l_bool(A),B_1))))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(A)),big_la1480321694n_bool(B_1))) ) ) ) ) ).
fof(fact_510_Sup__fin_Ounion__inter,axiom,
! [B_1,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_1))
=> ( hAPP_f559147733l_bool(semila1130628874l_bool(A),B_1) != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B_1))),big_la841148155e_bool(hAPP_f559147733l_bool(semila1130628874l_bool(A),B_1))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(A)),big_la841148155e_bool(B_1)) ) ) ) ).
fof(fact_511_Sup__fin_Ounion__inter,axiom,
! [B_1,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B_1))
=> ( hAPP_f1970439265l_bool(semila1410775201l_bool(A),B_1) != bot_bo1325454745l_bool
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A),B_1))),big_la1640362552e_bool(hAPP_f1970439265l_bool(semila1410775201l_bool(A),B_1))) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(A)),big_la1640362552e_bool(B_1)) ) ) ) ).
fof(fact_512_Sup__fin_Ounion__inter,axiom,
! [B_1,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,B_1))
=> ( hAPP_f960623701l_bool(semila1746965734l_bool(A),B_1) != bot_bo1325387246l_bool
=> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f997688506l_bool(semila1827648460l_bool,A),B_1))),big_la1993344855a_bool(hAPP_f960623701l_bool(semila1746965734l_bool(A),B_1))) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(A)),big_la1993344855a_bool(B_1)) ) ) ) ).
fof(fact_513_Sup__fin_Ounion__disjoint,axiom,
! [B_1,A] :
( ( is_fun_bool_bool(B_1)
& is_fun_bool_bool(A) )
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( A != bot_bo806936373l_bool
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_1))
=> ( B_1 != bot_bo806936373l_bool
=> ( hAPP_f961197973l_bool(semila1551573549l_bool(A),B_1) = bot_bo806936373l_bool
=> ( hBOOL(big_la1480321694n_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A),B_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,big_la1480321694n_bool(A)),big_la1480321694n_bool(B_1))) ) ) ) ) ) ) ) ).
fof(fact_514_Sup__fin_Ounion__disjoint,axiom,
! [B_1,A] :
( ( is_fun1661590463l_bool(B_1)
& is_fun1661590463l_bool(A) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_1))
=> ( B_1 != bot_bo1649642514l_bool
=> ( hAPP_f559147733l_bool(semila1130628874l_bool(A),B_1) = bot_bo1649642514l_bool
=> big_la841148155e_bool(hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,big_la841148155e_bool(A)),big_la841148155e_bool(B_1)) ) ) ) ) ) ) ).
fof(fact_515_Sup__fin_Ounion__disjoint,axiom,
! [B_1,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( A != bot_bo1325454745l_bool
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B_1))
=> ( B_1 != bot_bo1325454745l_bool
=> ( hAPP_f1970439265l_bool(semila1410775201l_bool(A),B_1) = bot_bo1325454745l_bool
=> big_la1640362552e_bool(hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,big_la1640362552e_bool(A)),big_la1640362552e_bool(B_1)) ) ) ) ) ) ).
fof(fact_516_Sup__fin_Ounion__disjoint,axiom,
! [B_1,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( A != bot_bo1325387246l_bool
=> ( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,B_1))
=> ( B_1 != bot_bo1325387246l_bool
=> ( hAPP_f960623701l_bool(semila1746965734l_bool(A),B_1) = bot_bo1325387246l_bool
=> big_la1993344855a_bool(hAPP_f960623701l_bool(hAPP_f997688506l_bool(semila1827648460l_bool,A),B_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,big_la1993344855a_bool(A)),big_la1993344855a_bool(B_1)) ) ) ) ) ) ).
fof(fact_517_IntI,axiom,
! [B_1,C,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
=> ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) ) ) ).
fof(fact_518_IntI,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),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) ) ) ).
fof(fact_519_IntE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))
=> ~ ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
=> ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ) ).
fof(fact_520_IntE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_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_521_inf__bot__right,axiom,
! [X_2] : hAPP_f759274231e_bool(semila1635148844e_bool(X_2),bot_bo844097828e_bool) = bot_bo844097828e_bool ).
fof(fact_522_inf__bot__right,axiom,
! [X_2] : hAPP_f1591852335a_bool(semila671163144a_bool(X_2),bot_bo1181479936a_bool) = bot_bo1181479936a_bool ).
fof(fact_523_inf__bot__right,axiom,
! [X_2] : hAPP_f921536533e_bool(semila2145357127e_bool(X_2),bot_bo1055319631e_bool) = bot_bo1055319631e_bool ).
fof(fact_524_inf__bot__left,axiom,
! [X_2] : hAPP_f759274231e_bool(semila1635148844e_bool(bot_bo844097828e_bool),X_2) = bot_bo844097828e_bool ).
fof(fact_525_inf__bot__left,axiom,
! [X_2] : hAPP_f1591852335a_bool(semila671163144a_bool(bot_bo1181479936a_bool),X_2) = bot_bo1181479936a_bool ).
fof(fact_526_inf__bot__left,axiom,
! [X_2] : hAPP_f921536533e_bool(semila2145357127e_bool(bot_bo1055319631e_bool),X_2) = bot_bo1055319631e_bool ).
fof(fact_527_sup__inf__distrib2,axiom,
! [Y_1,Z_1,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(Y_1),Z_1)),X_2))
<=> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),X_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Z_1),X_2))) ) ).
fof(fact_528_sup__inf__distrib2,axiom,
! [Y_1,Z_1,X_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),Z_1)),X_2) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),X_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Z_1),X_2)) ).
fof(fact_529_sup__inf__distrib2,axiom,
! [Y_1,Z_1,X_2] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),Z_1)),X_2) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Z_1),X_2)) ).
fof(fact_530_sup__inf__distrib2,axiom,
! [Y_1,Z_1,X_2] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),Z_1)),X_2) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),X_2)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Z_1),X_2)) ).
fof(fact_531_inf__sup__distrib2,axiom,
! [Y_1,Z_1,X_2] :
( hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1)),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(Y_1),X_2)),hAPP_bool_bool(semila310582991f_bool(Z_1),X_2))) ) ).
fof(fact_532_inf__sup__distrib2,axiom,
! [Y_1,Z_1,X_2] : hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)),X_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),X_2)),hAPP_f759274231e_bool(semila1635148844e_bool(Z_1),X_2)) ).
fof(fact_533_inf__sup__distrib2,axiom,
! [Y_1,Z_1,X_2] : hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)),X_2) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),X_2)),hAPP_f921536533e_bool(semila2145357127e_bool(Z_1),X_2)) ).
fof(fact_534_inf__sup__distrib2,axiom,
! [Y_1,Z_1,X_2] : hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)),X_2) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),X_2)),hAPP_f1591852335a_bool(semila671163144a_bool(Z_1),X_2)) ).
fof(fact_535_sup__inf__distrib1,axiom,
! [X_2,Y_1,Z_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(semila310582991f_bool(Y_1),Z_1)))
<=> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))) ) ).
fof(fact_536_sup__inf__distrib1,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),Z_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)) ).
fof(fact_537_sup__inf__distrib1,axiom,
! [X_2,Y_1,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),Z_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1)) ).
fof(fact_538_sup__inf__distrib1,axiom,
! [X_2,Y_1,Z_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),Z_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1)) ).
fof(fact_539_inf__sup__distrib1,axiom,
! [X_2,Y_1,Z_1] :
( hBOOL(hAPP_bool_bool(semila310582991f_bool(X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(X_2),Y_1)),hAPP_bool_bool(semila310582991f_bool(X_2),Z_1))) ) ).
fof(fact_540_inf__sup__distrib1,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(semila1635148844e_bool(X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Y_1)),hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Z_1)) ).
fof(fact_541_inf__sup__distrib1,axiom,
! [X_2,Y_1,Z_1] : hAPP_f921536533e_bool(semila2145357127e_bool(X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Y_1)),hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Z_1)) ).
fof(fact_542_inf__sup__distrib1,axiom,
! [X_2,Y_1,Z_1] : hAPP_f1591852335a_bool(semila671163144a_bool(X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Y_1)),hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Z_1)) ).
fof(fact_543_sup__inf__absorb,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(semila310582991f_bool(X_2),Y_1)))
<=> hBOOL(X_2) ) ).
fof(fact_544_sup__inf__absorb,axiom,
! [X_2,Y_1] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Y_1)) = X_2 ) ).
fof(fact_545_sup__inf__absorb,axiom,
! [X_2,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Y_1)) = X_2 ).
fof(fact_546_sup__inf__absorb,axiom,
! [X_2,Y_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Y_1)) = X_2 ).
fof(fact_547_inf__sup__absorb,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_bool_bool(semila310582991f_bool(X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)))
<=> hBOOL(X_2) ) ).
fof(fact_548_inf__sup__absorb,axiom,
! [X_2,Y_1] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(semila1635148844e_bool(X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)) = X_2 ) ).
fof(fact_549_inf__sup__absorb,axiom,
! [X_2,Y_1] : hAPP_f921536533e_bool(semila2145357127e_bool(X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)) = X_2 ).
fof(fact_550_inf__sup__absorb,axiom,
! [X_2,Y_1] : hAPP_f1591852335a_bool(semila671163144a_bool(X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)) = X_2 ).
fof(fact_551_disjoint__iff__not__equal,axiom,
! [A,B_1] :
( hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) = bot_bo844097828e_bool
<=> ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))
=> ! [Xa] :
( is_pname(Xa)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B_1))
=> X != Xa ) ) ) ) ) ).
fof(fact_552_disjoint__iff__not__equal,axiom,
! [A,B_1] :
( hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) = bot_bo1181479936a_bool
<=> ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),A))
=> ! [Xa] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,Xa),B_1))
=> X != Xa ) ) ) ).
fof(fact_553_disjoint__iff__not__equal,axiom,
! [A,B_1] :
( hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) = bot_bo1055319631e_bool
<=> ! [X] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X),A))
=> ! [Xa] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Xa),B_1))
=> X != Xa ) ) ) ).
fof(fact_554_Int__empty__right,axiom,
! [A] : hAPP_f759274231e_bool(semila1635148844e_bool(A),bot_bo844097828e_bool) = bot_bo844097828e_bool ).
fof(fact_555_Int__empty__right,axiom,
! [A] : hAPP_f1591852335a_bool(semila671163144a_bool(A),bot_bo1181479936a_bool) = bot_bo1181479936a_bool ).
fof(fact_556_Int__empty__right,axiom,
! [A] : hAPP_f921536533e_bool(semila2145357127e_bool(A),bot_bo1055319631e_bool) = bot_bo1055319631e_bool ).
fof(fact_557_Int__empty__left,axiom,
! [B_1] : hAPP_f759274231e_bool(semila1635148844e_bool(bot_bo844097828e_bool),B_1) = bot_bo844097828e_bool ).
fof(fact_558_Int__empty__left,axiom,
! [B_1] : hAPP_f1591852335a_bool(semila671163144a_bool(bot_bo1181479936a_bool),B_1) = bot_bo1181479936a_bool ).
fof(fact_559_Int__empty__left,axiom,
! [B_1] : hAPP_f921536533e_bool(semila2145357127e_bool(bot_bo1055319631e_bool),B_1) = bot_bo1055319631e_bool ).
fof(fact_560_Int__def,axiom,
! [A,B_1] : hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) = hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),A))),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),B_1))) ).
fof(fact_561_Int__def,axiom,
! [A,B_1] : hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_1))) ).
fof(fact_562_Int__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))
<=> ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
& hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ) ).
fof(fact_563_Int__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_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_564_IntD1,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) ) ).
fof(fact_565_IntD1,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) ) ).
fof(fact_566_IntD2,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ).
fof(fact_567_IntD2,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) ) ).
fof(fact_568_Collect__conj__eq,axiom,
! [Pa,Qa] : hAPP_f1591852335a_bool(collec268032053iple_a,hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,hAPP_f997599971l_bool(cOMBB_1782929690iple_a(fconj),Pa)),Qa)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(collec268032053iple_a,Pa)),hAPP_f1591852335a_bool(collec268032053iple_a,Qa)) ).
fof(fact_569_Collect__conj__eq,axiom,
! [Pa,Qa] : hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),Pa)),Qa)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(collect_pname,Pa)),hAPP_f759274231e_bool(collect_pname,Qa)) ).
fof(fact_570_Int__Collect,axiom,
! [X_2,A,Pa] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(collec268032053iple_a,Pa))))
<=> ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X_2),A))
& hBOOL(hAPP_H1421470952a_bool(Pa,X_2)) ) ) ).
fof(fact_571_Int__Collect,axiom,
! [X_2,A,Pa] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(collect_pname,Pa))))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& hBOOL(hAPP_pname_bool(Pa,X_2)) ) ) ).
fof(fact_572_inf__Int__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),R_1)),hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,member1713797107iple_a),S_1)),X))
<=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(semila671163144a_bool(R_1),S_1))) ) ).
fof(fact_573_inf__Int__eq,axiom,
! [R_1,S_1,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S_1)),X))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(semila1635148844e_bool(R_1),S_1))) ) ).
fof(fact_574_Un__Int__crazy,axiom,
! [A,B_1,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1))),hAPP_f759274231e_bool(semila1635148844e_bool(C_1),A)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A)) ).
fof(fact_575_Un__Int__crazy,axiom,
! [A,B_1,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1))),hAPP_f921536533e_bool(semila2145357127e_bool(C_1),A)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A)) ).
fof(fact_576_Un__Int__crazy,axiom,
! [A,B_1,C_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1))),hAPP_f1591852335a_bool(semila671163144a_bool(C_1),A)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1))),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,C_1),A)) ).
fof(fact_577_Un__Int__distrib2,axiom,
! [B_1,C_1,A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)),A) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A)) ).
fof(fact_578_Un__Int__distrib2,axiom,
! [B_1,C_1,A] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)),A) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A)) ).
fof(fact_579_Un__Int__distrib2,axiom,
! [B_1,C_1,A] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)),A) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),A)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,C_1),A)) ).
fof(fact_580_Int__Un__distrib2,axiom,
! [B_1,C_1,A] : hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(B_1),A)),hAPP_f759274231e_bool(semila1635148844e_bool(C_1),A)) ).
fof(fact_581_Int__Un__distrib2,axiom,
! [B_1,C_1,A] : hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(B_1),A)),hAPP_f921536533e_bool(semila2145357127e_bool(C_1),A)) ).
fof(fact_582_Int__Un__distrib2,axiom,
! [B_1,C_1,A] : hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(B_1),A)),hAPP_f1591852335a_bool(semila671163144a_bool(C_1),A)) ).
fof(fact_583_Un__Int__distrib,axiom,
! [A,B_1,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1)) ).
fof(fact_584_Un__Int__distrib,axiom,
! [A,B_1,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C_1)) ).
fof(fact_585_Un__Int__distrib,axiom,
! [A,B_1,C_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),C_1)) ).
fof(fact_586_Int__Un__distrib,axiom,
! [A,B_1,C_1] : hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)),hAPP_f759274231e_bool(semila1635148844e_bool(A),C_1)) ).
fof(fact_587_Int__Un__distrib,axiom,
! [A,B_1,C_1] : hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)),hAPP_f921536533e_bool(semila2145357127e_bool(A),C_1)) ).
fof(fact_588_Int__Un__distrib,axiom,
! [A,B_1,C_1] : hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),C_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)),hAPP_f1591852335a_bool(semila671163144a_bool(A),C_1)) ).
fof(fact_589_Int__insert__left__if1,axiom,
! [B_1,A_1,C_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1))
=> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)) ) ).
fof(fact_590_Int__insert__left__if1,axiom,
! [B_1,A_1,C_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1))
=> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)) ) ).
fof(fact_591_Int__insert__left__if1,axiom,
! [B_1,A_1,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1))
=> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)) ) ).
fof(fact_592_Int__insert__right__if1,axiom,
! [B_1,A_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))
=> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)) ) ).
fof(fact_593_Int__insert__right__if1,axiom,
! [B_1,A_1,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))
=> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)) ) ).
fof(fact_594_Int__insert__right__if1,axiom,
! [B_1,A_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)) ) ).
fof(fact_595_Int__insert__left__if0,axiom,
! [B_1,A_1,C_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1))
=> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1) ) ).
fof(fact_596_Int__insert__left__if0,axiom,
! [B_1,A_1,C_1] :
( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1))
=> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1) ) ).
fof(fact_597_Int__insert__left__if0,axiom,
! [B_1,A_1,C_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1))
=> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1) ) ).
fof(fact_598_Int__insert__right__if0,axiom,
! [B_1,A_1,A] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))
=> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) ) ).
fof(fact_599_Int__insert__right__if0,axiom,
! [B_1,A_1,A] :
( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))
=> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) ) ).
fof(fact_600_Int__insert__right__if0,axiom,
! [B_1,A_1,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) ) ).
fof(fact_601_insert__inter__insert,axiom,
! [A_1,A,B_1] : hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),A)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)) ).
fof(fact_602_insert__inter__insert,axiom,
! [A_1,A,B_1] : hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),A)),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)) ).
fof(fact_603_insert__inter__insert,axiom,
! [A_1,A,B_1] : hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)) ).
fof(fact_604_Int__insert__left,axiom,
! [B_1,A_1,C_1] :
( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1))
=> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),C_1))
=> hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)),C_1) = hAPP_f921536533e_bool(semila2145357127e_bool(B_1),C_1) ) ) ).
fof(fact_605_Int__insert__left,axiom,
! [B_1,A_1,C_1] :
( ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1))
=> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1)) )
& ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),C_1))
=> hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)),C_1) = hAPP_f1591852335a_bool(semila671163144a_bool(B_1),C_1) ) ) ).
fof(fact_606_Int__insert__left,axiom,
! [B_1,A_1,C_1] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1))
=> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),C_1))
=> hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)),C_1) = hAPP_f759274231e_bool(semila1635148844e_bool(B_1),C_1) ) ) ).
fof(fact_607_Int__insert__right,axiom,
! [B_1,A_1,A] :
( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))
=> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_1),A))
=> hAPP_f921536533e_bool(semila2145357127e_bool(A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_1),B_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) ) ) ).
fof(fact_608_Int__insert__right,axiom,
! [B_1,A_1,A] :
( ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))
=> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1)) )
& ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,A_1),A))
=> hAPP_f1591852335a_bool(semila671163144a_bool(A),hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(insert873085594iple_a,A_1),B_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) ) ) ).
fof(fact_609_Int__insert__right,axiom,
! [B_1,A_1,A] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> hAPP_f759274231e_bool(semila1635148844e_bool(A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_1),B_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) ) ) ).
fof(fact_610_if__image__distrib,axiom,
! [Pa,F_1,G,S_1] : hAPP_f631639356e_bool(image_275883510_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,hAPP_f1405979047_state(cOMBB_707293872_pname(if_Hoa533980679_state),Pa)),F_1)),G)),S_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F_1),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,Pa)))),hAPP_f631639356e_bool(image_275883510_state(G),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),Pa))))) ).
fof(fact_611_if__image__distrib,axiom,
! [Pa,F_1,G,S_1] : hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f1044063253iple_a(hAPP_f1401255196iple_a(cOMBS_1128650103iple_a,hAPP_f866544818iple_a(hAPP_f428084316iple_a(cOMBS_546756116iple_a,hAPP_f653022294iple_a(cOMBB_1916528323_pname(if_Hoa638970256iple_a),Pa)),F_1)),G)),S_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f271130963a_bool(image_1654749281iple_a(F_1),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,Pa)))),hAPP_f271130963a_bool(image_1654749281iple_a(G),hAPP_f759274231e_bool(semila1635148844e_bool(S_1),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),Pa))))) ).
fof(fact_612_folding__one_Ounion__inter,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite1282449217_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_1))
=> ( hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) != bot_bo844097828e_bool
=> hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))),hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1))) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,A)),hAPP_f1297739591_pname(F,B_1)) ) ) ) ) ).
fof(fact_613_folding__one_Ounion__inter,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite1669978781iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B_1))
=> ( hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) != bot_bo1181479936a_bool
=> hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1))),hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1))) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B_1)) ) ) ) ) ).
fof(fact_614_folding__one_Ounion__inter,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite774711482_state(F_1,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> ( hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) != bot_bo1055319631e_bool
=> hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))),hAPP_f2143211163_state(F,hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1))) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B_1)) ) ) ) ) ).
fof(fact_615_folding__one_Ounion__disjoint,axiom,
! [B_1,A,F_1,F] :
( ( is_fun_pname_bool(B_1)
& is_fun_pname_bool(A) )
=> ( hBOOL(finite1282449217_pname(F_1,F))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_1))
=> ( B_1 != bot_bo844097828e_bool
=> ( hAPP_f759274231e_bool(semila1635148844e_bool(A),B_1) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F_1,hAPP_f1297739591_pname(F,A)),hAPP_f1297739591_pname(F,B_1)) ) ) ) ) ) ) ) ).
fof(fact_616_folding__one_Ounion__disjoint,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite1669978781iple_a(F_1,F))
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,A))
=> ( A != bot_bo1181479936a_bool
=> ( hBOOL(hAPP_f540970102l_bool(finite1655202547iple_a,B_1))
=> ( B_1 != bot_bo1181479936a_bool
=> ( hAPP_f1591852335a_bool(semila671163144a_bool(A),B_1) = bot_bo1181479936a_bool
=> hAPP_f124283079iple_a(F,hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)) = hAPP_H678412245iple_a(hAPP_H1455657330iple_a(F_1,hAPP_f124283079iple_a(F,A)),hAPP_f124283079iple_a(F,B_1)) ) ) ) ) ) ) ).
fof(fact_617_folding__one_Ounion__disjoint,axiom,
! [B_1,A,F_1,F] :
( hBOOL(finite774711482_state(F_1,F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
=> ( A != bot_bo1055319631e_bool
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> ( B_1 != bot_bo1055319631e_bool
=> ( hAPP_f921536533e_bool(semila2145357127e_bool(A),B_1) = bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F_1,hAPP_f2143211163_state(F,A)),hAPP_f2143211163_state(F,B_1)) ) ) ) ) ) ) ).
fof(fact_618_distrib__imp2,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] :
( ( is_bool(X)
& is_bool(Y_2)
& is_bool(Z_2) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),hAPP_bool_bool(semila310582991f_bool(Y_2),Z_2)))
<=> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X),Z_2))) ) )
=> ( hBOOL(hAPP_bool_bool(semila310582991f_bool(X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_1),Z_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(X_2),Y_1)),hAPP_bool_bool(semila310582991f_bool(X_2),Z_1))) ) ) ).
fof(fact_619_distrib__imp2,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] :
( ( is_fun_pname_bool(X)
& is_fun_pname_bool(Y_2)
& is_fun_pname_bool(Z_2) )
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),hAPP_f759274231e_bool(semila1635148844e_bool(Y_2),Z_2)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X),Z_2)) )
=> hAPP_f759274231e_bool(semila1635148844e_bool(X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Y_1)),hAPP_f759274231e_bool(semila1635148844e_bool(X_2),Z_1)) ) ).
fof(fact_620_distrib__imp2,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),hAPP_f921536533e_bool(semila2145357127e_bool(Y_2),Z_2)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X),Z_2))
=> hAPP_f921536533e_bool(semila2145357127e_bool(X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Y_1)),hAPP_f921536533e_bool(semila2145357127e_bool(X_2),Z_1)) ) ).
fof(fact_621_distrib__imp2,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),hAPP_f1591852335a_bool(semila671163144a_bool(Y_2),Z_2)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Y_2)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X),Z_2))
=> hAPP_f1591852335a_bool(semila671163144a_bool(X_2),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_1),Z_1)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Y_1)),hAPP_f1591852335a_bool(semila671163144a_bool(X_2),Z_1)) ) ).
fof(fact_622_distrib__imp1,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] :
( ( is_bool(X)
& is_bool(Y_2)
& is_bool(Z_2) )
=> ( hBOOL(hAPP_bool_bool(semila310582991f_bool(X),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z_2)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(semila310582991f_bool(X),Y_2)),hAPP_bool_bool(semila310582991f_bool(X),Z_2))) ) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(semila310582991f_bool(Y_1),Z_1)))
<=> hBOOL(hAPP_bool_bool(semila310582991f_bool(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))) ) ) ).
fof(fact_623_distrib__imp1,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] :
( ( is_fun_pname_bool(X)
& is_fun_pname_bool(Y_2)
& is_fun_pname_bool(Z_2) )
=> hAPP_f759274231e_bool(semila1635148844e_bool(X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(semila1635148844e_bool(X),Y_2)),hAPP_f759274231e_bool(semila1635148844e_bool(X),Z_2)) )
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(semila1635148844e_bool(Y_1),Z_1)) = hAPP_f759274231e_bool(semila1635148844e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)) ) ).
fof(fact_624_distrib__imp1,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] : hAPP_f921536533e_bool(semila2145357127e_bool(X),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_2),Z_2)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(semila2145357127e_bool(X),Y_2)),hAPP_f921536533e_bool(semila2145357127e_bool(X),Z_2))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(semila2145357127e_bool(Y_1),Z_1)) = hAPP_f921536533e_bool(semila2145357127e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1)) ) ).
fof(fact_625_distrib__imp1,axiom,
! [X_2,Y_1,Z_1] :
( ! [X,Y_2,Z_2] : hAPP_f1591852335a_bool(semila671163144a_bool(X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,Y_2),Z_2)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(semila671163144a_bool(X),Y_2)),hAPP_f1591852335a_bool(semila671163144a_bool(X),Z_2))
=> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),hAPP_f1591852335a_bool(semila671163144a_bool(Y_1),Z_1)) = hAPP_f1591852335a_bool(semila671163144a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Y_1)),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,X_2),Z_1)) ) ).
fof(fact_626_sup__Inf__absorb,axiom,
! [A_1,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_1),A))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_1),big_la472677547n_bool(A)))
<=> hBOOL(A_1) ) ) ) ).
fof(fact_627_sup__Inf__absorb,axiom,
! [A_1,A] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),big_la28065288e_bool(A)) = A_1 ) ) ) ).
fof(fact_628_sup__Inf__absorb,axiom,
! [A_1,A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_1),A))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),big_la508066411e_bool(A)) = A_1 ) ) ).
fof(fact_629_sup__Inf__absorb,axiom,
! [A_1,A] :
( hBOOL(hAPP_f1557928608l_bool(finite652815363a_bool,A))
=> ( hBOOL(hAPP_f1557928608l_bool(hAPP_f1849264231l_bool(member1154012931a_bool,A_1),A))
=> hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A_1),big_la1164677860a_bool(A)) = A_1 ) ) ).
fof(fact_630_DiffE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1)))
=> ~ ( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ) ).
fof(fact_631_DiffE,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_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_632_DiffI,axiom,
! [B_1,C,A] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A))
=> ( ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1))) ) ) ).
fof(fact_633_DiffI,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),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1))) ) ) ).
fof(fact_634_Un__Diff__cancel,axiom,
! [A,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(minus_1015773161e_bool(B_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1) ).
fof(fact_635_Un__Diff__cancel,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),A)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) ).
fof(fact_636_Un__Diff__cancel,axiom,
! [A,B_1] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),hAPP_f1591852335a_bool(minus_469558085a_bool(B_1),A)) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1) ).
fof(fact_637_Un__Diff__cancel2,axiom,
! [B_1,A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(minus_1015773161e_bool(B_1),A)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A) ).
fof(fact_638_Un__Diff__cancel2,axiom,
! [B_1,A] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),A)),A) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A) ).
fof(fact_639_Un__Diff__cancel2,axiom,
! [B_1,A] : hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(minus_469558085a_bool(B_1),A)),A) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,B_1),A) ).
fof(fact_640_Un__Diff,axiom,
! [A,B_1,C_1] : hAPP_f759274231e_bool(minus_1015773161e_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(minus_1015773161e_bool(A),C_1)),hAPP_f759274231e_bool(minus_1015773161e_bool(B_1),C_1)) ).
fof(fact_641_Un__Diff,axiom,
! [A,B_1,C_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A),C_1)),hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),C_1)) ).
fof(fact_642_Un__Diff,axiom,
! [A,B_1,C_1] : hAPP_f1591852335a_bool(minus_469558085a_bool(hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,A),B_1)),C_1) = hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,hAPP_f1591852335a_bool(minus_469558085a_bool(A),C_1)),hAPP_f1591852335a_bool(minus_469558085a_bool(B_1),C_1)) ).
fof(fact_643_DiffD2,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1)))
=> ~ hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),B_1)) ) ).
fof(fact_644_DiffD2,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1)))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) ) ).
fof(fact_645_DiffD1,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),hAPP_f1591852335a_bool(minus_469558085a_bool(A),B_1)))
=> hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,C),A)) ) ).
fof(fact_646_DiffD1,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_bool(A),B_1)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) ) ).
fof(fact_647_Diff__iff,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(minus_1015773161e_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_648_diff__Suc__Suc,axiom,
! [M,N_2] : hAPP_nat_nat(minus_minus_nat(suc(M)),suc(N_2)) = hAPP_nat_nat(minus_minus_nat(M),N_2) ).
fof(fact_649_Suc__diff__diff,axiom,
! [M,N_2,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(suc(M)),N_2)),suc(K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N_2)),K_1) ).
fof(fact_650_diff__0__eq__0,axiom,
! [N_2] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N_2) = zero_zero_nat ).
fof(fact_651_minus__nat_Odiff__0,axiom,
! [M] : hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M ).
fof(fact_652_diff__self__eq__0,axiom,
! [M] : hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat ).
fof(fact_653_diffs0__imp__equal,axiom,
! [M,N_2] :
( hAPP_nat_nat(minus_minus_nat(M),N_2) = zero_zero_nat
=> ( hAPP_nat_nat(minus_minus_nat(N_2),M) = zero_zero_nat
=> M = N_2 ) ) ).
fof(fact_654_zero__induct__lemma,axiom,
! [I_1,Pa,K] :
( hBOOL(hAPP_nat_bool(Pa,K))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,suc(N)))
=> hBOOL(hAPP_nat_bool(Pa,N)) )
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I_1))) ) ) ).
fof(fact_655_diff__commute,axiom,
! [I,J,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K_1)),J) ).
fof(fact_656_diff__Suc,axiom,
! [M_1,N_1] : hAPP_nat_nat(minus_minus_nat(M_1),suc(N_1)) = nat_case_nat(zero_zero_nat,cOMBI_nat,hAPP_nat_nat(minus_minus_nat(M_1),N_1)) ).
fof(fact_657_diff__Suc__1,axiom,
! [N_2] : hAPP_nat_nat(minus_minus_nat(suc(N_2)),one_one_nat) = N_2 ).
fof(fact_658_diff__Suc__eq__diff__pred,axiom,
! [M,N_2] : hAPP_nat_nat(minus_minus_nat(M),suc(N_2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_2) ).
fof(fact_659_One__nat__def,axiom,
one_one_nat = suc(zero_zero_nat) ).
fof(fact_660_Suc__eq__plus1,axiom,
! [N_2] : suc(N_2) = plus_plus_nat(N_2,one_one_nat) ).
fof(fact_661_Suc__eq__plus1__left,axiom,
! [N_2] : suc(N_2) = plus_plus_nat(one_one_nat,N_2) ).
fof(fact_662_diff__cancel2,axiom,
! [M,K_1,N_2] : hAPP_nat_nat(minus_minus_nat(plus_plus_nat(M,K_1)),plus_plus_nat(N_2,K_1)) = hAPP_nat_nat(minus_minus_nat(M),N_2) ).
fof(fact_663_diff__cancel,axiom,
! [K_1,M,N_2] : hAPP_nat_nat(minus_minus_nat(plus_plus_nat(K_1,M)),plus_plus_nat(K_1,N_2)) = hAPP_nat_nat(minus_minus_nat(M),N_2) ).
fof(fact_664_diff__diff__left,axiom,
! [I,J,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J)),K_1) = hAPP_nat_nat(minus_minus_nat(I),plus_plus_nat(J,K_1)) ).
fof(fact_665_diff__add__inverse,axiom,
! [N_2,M] : hAPP_nat_nat(minus_minus_nat(plus_plus_nat(N_2,M)),N_2) = M ).
fof(fact_666_diff__add__inverse2,axiom,
! [M,N_2] : hAPP_nat_nat(minus_minus_nat(plus_plus_nat(M,N_2)),N_2) = M ).
fof(fact_667_diff__add__0,axiom,
! [N_2,M] : hAPP_nat_nat(minus_minus_nat(N_2),plus_plus_nat(N_2,M)) = zero_zero_nat ).
fof(fact_668_nat__add__commute,axiom,
! [M,N_2] : plus_plus_nat(M,N_2) = plus_plus_nat(N_2,M) ).
fof(fact_669_nat__add__left__commute,axiom,
! [X_1,Y,Z] : plus_plus_nat(X_1,plus_plus_nat(Y,Z)) = plus_plus_nat(Y,plus_plus_nat(X_1,Z)) ).
fof(fact_670_nat__add__assoc,axiom,
! [M,N_2,K_1] : plus_plus_nat(plus_plus_nat(M,N_2),K_1) = plus_plus_nat(M,plus_plus_nat(N_2,K_1)) ).
fof(fact_671_nat__add__left__cancel,axiom,
! [K,M_1,N_1] :
( plus_plus_nat(K,M_1) = plus_plus_nat(K,N_1)
<=> M_1 = N_1 ) ).
fof(fact_672_nat__add__right__cancel,axiom,
! [M_1,K,N_1] :
( plus_plus_nat(M_1,K) = plus_plus_nat(N_1,K)
<=> M_1 = N_1 ) ).
fof(fact_673_add__Suc__shift,axiom,
! [M,N_2] : plus_plus_nat(suc(M),N_2) = plus_plus_nat(M,suc(N_2)) ).
fof(fact_674_add__Suc,axiom,
! [M,N_2] : plus_plus_nat(suc(M),N_2) = suc(plus_plus_nat(M,N_2)) ).
fof(fact_675_add__Suc__right,axiom,
! [M,N_2] : plus_plus_nat(M,suc(N_2)) = suc(plus_plus_nat(M,N_2)) ).
fof(fact_676_one__is__add,axiom,
! [M_1,N_1] :
( suc(zero_zero_nat) = plus_plus_nat(M_1,N_1)
<=> ( ( M_1 = suc(zero_zero_nat)
& N_1 = zero_zero_nat )
| ( M_1 = zero_zero_nat
& N_1 = suc(zero_zero_nat) ) ) ) ).
fof(fact_677_add__is__1,axiom,
! [M_1,N_1] :
( plus_plus_nat(M_1,N_1) = suc(zero_zero_nat)
<=> ( ( M_1 = suc(zero_zero_nat)
& N_1 = zero_zero_nat )
| ( M_1 = zero_zero_nat
& N_1 = suc(zero_zero_nat) ) ) ) ).
fof(fact_678_plus__nat_Oadd__0,axiom,
! [N_2] : plus_plus_nat(zero_zero_nat,N_2) = N_2 ).
fof(fact_679_Nat_Oadd__0__right,axiom,
! [M] : plus_plus_nat(M,zero_zero_nat) = M ).
fof(fact_680_add__is__0,axiom,
! [M_1,N_1] :
( plus_plus_nat(M_1,N_1) = zero_zero_nat
<=> ( M_1 = zero_zero_nat
& N_1 = zero_zero_nat ) ) ).
fof(fact_681_add__eq__self__zero,axiom,
! [M,N_2] :
( plus_plus_nat(M,N_2) = M
=> N_2 = zero_zero_nat ) ).
fof(fact_682_add__eq__if,axiom,
! [N_2,M] :
( ( M = zero_zero_nat
=> plus_plus_nat(M,N_2) = N_2 )
& ( M != zero_zero_nat
=> plus_plus_nat(M,N_2) = suc(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat),N_2)) ) ) ).
fof(fact_683_com_Osize_I4_J,axiom,
! [Com1_1,Com2_1] : com_size(semi(Com1_1,Com2_1)) = plus_plus_nat(plus_plus_nat(com_size(Com1_1),com_size(Com2_1)),suc(zero_zero_nat)) ).
fof(fact_684_com_Osize_I7_J,axiom,
! [Pname] : com_size(hAPP_pname_com(body,Pname)) = zero_zero_nat ).
fof(fact_685_com_Osize_I1_J,axiom,
com_size(skip) = zero_zero_nat ).
fof(fact_686_com_Osize_I6_J,axiom,
! [Fun,Com] : com_size(while(Fun,Com)) = plus_plus_nat(com_size(Com),suc(zero_zero_nat)) ).
fof(fact_687_com_Osize_I12_J,axiom,
! [Com1_1,Com2_1] : size_size_com(semi(Com1_1,Com2_1)) = plus_plus_nat(plus_plus_nat(size_size_com(Com1_1),size_size_com(Com2_1)),suc(zero_zero_nat)) ).
fof(fact_688_com_Osize_I15_J,axiom,
! [Pname] : size_size_com(hAPP_pname_com(body,Pname)) = zero_zero_nat ).
fof(fact_689_com_Osize_I9_J,axiom,
size_size_com(skip) = zero_zero_nat ).
fof(fact_690_com_Osize_I14_J,axiom,
! [Fun,Com] : size_size_com(while(Fun,Com)) = plus_plus_nat(size_size_com(Com),suc(zero_zero_nat)) ).
fof(fact_691_com_Osize_I13_J,axiom,
! [Fun,Com1,Com2] : size_size_com(cond(Fun,Com1,Com2)) = plus_plus_nat(plus_plus_nat(size_size_com(Com1),size_size_com(Com2)),suc(zero_zero_nat)) ).
fof(fact_692_evaln_OIfFalse,axiom,
! [C0,C1,N_1,S1,B,S] :
( ~ hBOOL(hAPP_state_bool(B,S))
=> ( hBOOL(hAPP_state_bool(evaln(C1,S,N_1),S1))
=> hBOOL(hAPP_state_bool(evaln(cond(B,C0,C1),S,N_1),S1)) ) ) ).
fof(fact_693_evaln_OIfTrue,axiom,
! [C1,C0,N_1,S1,B,S] :
( hBOOL(hAPP_state_bool(B,S))
=> ( hBOOL(hAPP_state_bool(evaln(C0,S,N_1),S1))
=> hBOOL(hAPP_state_bool(evaln(cond(B,C0,C1),S,N_1),S1)) ) ) ).
fof(fact_694_evaln__elim__cases_I5_J,axiom,
! [B,C1,C2,S,N_1,T] :
( hBOOL(hAPP_state_bool(evaln(cond(B,C1,C2),S,N_1),T))
=> ( ( hBOOL(hAPP_state_bool(B,S))
=> ~ hBOOL(hAPP_state_bool(evaln(C1,S,N_1),T)) )
=> ~ ( ~ hBOOL(hAPP_state_bool(B,S))
=> ~ hBOOL(hAPP_state_bool(evaln(C2,S,N_1),T)) ) ) ) ).
fof(fact_695_evalc__elim__cases_I5_J,axiom,
! [B,C1,C2,S,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B,C1,C2)),S),T))
=> ( ( hBOOL(hAPP_state_bool(B,S))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S),T)) )
=> ~ ( ~ hBOOL(hAPP_state_bool(B,S))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S),T)) ) ) ) ).
fof(fact_696_evalc_OIfTrue,axiom,
! [C1,C0,S1,B,S] :
( hBOOL(hAPP_state_bool(B,S))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S),S1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B,C0,C1)),S),S1)) ) ) ).
fof(fact_697_evalc_OIfFalse,axiom,
! [C0,C1,S1,B,S] :
( ~ hBOOL(hAPP_state_bool(B,S))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S),S1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B,C0,C1)),S),S1)) ) ) ).
%----Helper facts (101)
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_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
! [P] : hAPP_nat_nat(cOMBI_nat,P) = P ).
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_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,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(hAPP_b76515610e_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(hAPP_p1170154830_pname(cOMBK_pname_pname,P),Q) = P ) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X_1,Y] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X_1),Y))
| X_1 = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X_1),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U,axiom,
! [P,Q] : hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ).
fof(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_T,axiom,
! [X_1,Y] : hAPP_H678412245iple_a(hAPP_H1455657330iple_a(hAPP_b385840250iple_a(if_Hoa638970256iple_a,fTrue),X_1),Y) = X_1 ).
fof(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_T,axiom,
! [X_1,Y] : hAPP_H678412245iple_a(hAPP_H1455657330iple_a(hAPP_b385840250iple_a(if_Hoa638970256iple_a,fFalse),X_1),Y) = Y ).
fof(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBB_647938656_pname(P),Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U,axiom,
! [P,Q,R] : hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,P),Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_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(hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(fequal879838495iple_a,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(fequal879838495iple_a,X_1),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
! [P,Q] : hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(cOMBK_631994958_state,P),Q) = P ).
fof(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate,axiom,
! [X_1,Y] : hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fTrue),X_1),Y) = X_1 ).
fof(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate,axiom,
! [X_1,Y] : hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fFalse),X_1),Y) = Y ).
fof(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X_1),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__,axiom,
! [P,Q,R] : hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H1421470952a_bool(hAPP_b119575286a_bool(cOMBK_151824839iple_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(hAPP_f96342628me_com(cOMBB_923936821_pname(P),Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00,axiom,
! [P,Q] : hAPP_p263283121iple_a(hAPP_H1578029518iple_a(cOMBK_1347789874_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(hAPP_f1402196763l_bool(cOMBB_675860798_pname(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,axiom,
! [P,Q,R] : hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_f42430548e_bool(cOMBB_530759491_pname(P),Q),R) = hAPP_f1664156314l_bool(P,hAPP_p61793385e_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(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O,axiom,
! [P,Q,R] : hAPP_s1806633685e_bool(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_s1874344717e_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(fequal1258664663a_bool,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f540970102l_bool(hAPP_f430043647l_bool(fequal1258664663a_bool,X_1),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg___010,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H513860823e_bool(hAPP_b1245957081e_bool(cOMBK_1079618832_state,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q] : hAPP_p1842370726_state(hAPP_H1797237070_state(cOMBK_90103121_pname,P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
! [P,Q,R] : hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(cOMBB_1799513916iple_a(P),Q),R) = hAPP_bool_bool(P,hAPP_H1421470952a_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f1203760810a_bool(cOMBS_1148211387l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1017515220l_bool(P,R),hAPP_H1421470952a_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_H1991058245e_bool(hAPP_f687460073e_bool(cOMBC_1693967286a_bool,P),Q),R) = hAPP_H1421470952a_bool(hAPP_p2127663045a_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_011,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_012,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X_1),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc,axiom,
! [P,Q,R] : hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel_013,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBB_416661851_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__014,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_p877885514e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015,axiom,
! [P,Q,R] : hAPP_p61793385e_bool(hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob,axiom,
! [P,Q,R] : hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_s1226857760e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016,axiom,
! [P,Q,R] : hAPP_H1017515220l_bool(hAPP_f997599971l_bool(cOMBB_1782929690iple_a(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1421470952a_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [P,Q,R] : hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_a2036067514e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_017,axiom,
! [P,Q,R] : hAPP_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(hAPP_f1371755681a_bool(cOMBC_839220826a_bool,P),Q),R) = hAPP_H1421470952a_bool(hAPP_H1190454433a_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_,axiom,
! [P,Q,R] : hAPP_p263283121iple_a(hAPP_f1044063253iple_a(hAPP_f1401255196iple_a(cOMBS_1128650103iple_a,P),Q),R) = hAPP_H678412245iple_a(hAPP_p363087182iple_a(P,R),hAPP_p263283121iple_a(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_018,axiom,
! [P,Q,R] : hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(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_p263283121iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,P),Q),R) = hAPP_f150255961iple_a(hAPP_p344936018iple_a(P,R),hAPP_p635540397e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_p1842370726_state(hAPP_f1026488024_state(cOMBB_2118237115_pname(P),Q),R) = hAPP_H928324994_state(P,hAPP_p263283121iple_a(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_p263283121iple_a(hAPP_f113652738iple_a(cOMBB_2015474199_pname(P),Q),R) = hAPP_H1600811558iple_a(P,hAPP_p1842370726_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H,axiom,
! [P,Q,R] : hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_a849909144l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__019,axiom,
! [P,Q,R] : hAPP_p1842370726_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,P),Q),R) = hAPP_H563960305_state(hAPP_p80247908_state(P,R),hAPP_p1842370726_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I,axiom,
! [P,Q,R] : hAPP_H1421470952a_bool(hAPP_f772297704a_bool(cOMBB_1501709507iple_a(P),Q),R) = hAPP_f540970102l_bool(P,hAPP_H1190454433a_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_020,axiom,
! [P,Q,R] : hAPP_H1421470952a_bool(hAPP_f1591852335a_bool(hAPP_f672239281a_bool(cOMBC_1552014468l_bool,P),Q),R) = hAPP_f540970102l_bool(hAPP_H1840393229l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_021,axiom,
! [P,Q,R] : hAPP_p2127663045a_bool(hAPP_f1311175287a_bool(cOMBB_858699740_pname(P),Q),R) = hAPP_H1190454433a_bool(P,hAPP_p263283121iple_a(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc,axiom,
! [P,Q,R] : hAPP_p1842370726_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,P),Q),R) = hAPP_f588507005_state(hAPP_p1712839024_state(P,R),hAPP_p1637813682e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_022,axiom,
! [P,Q,R] : hAPP_s1874344717e_bool(hAPP_f873506917e_bool(cOMBB_1757942702_state(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_s2001034685l_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_It_,axiom,
! [P,Q,R] : hAPP_p344936018iple_a(hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,P),Q),R) = hAPP_c1407587404iple_a(hAPP_p1263586117iple_a(P,R),hAPP_pname_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_023,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f1456107715e_bool(cOMBB_1653402815_state(P),Q),R) = hAPP_f1760790145l_bool(P,hAPP_H1645666623e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___024,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___025,axiom,
! [P,Q,R] : hAPP_p877885514e_bool(hAPP_f998786331e_bool(cOMBB_799949246_pname(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_p1842370726_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_026,axiom,
! [P,Q,R] : hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_a849909144l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd,axiom,
! [P,Q,R] : hAPP_p2127663045a_bool(hAPP_f1646799884a_bool(hAPP_f2022238777a_bool(cOMBC_1527561185a_bool,P),Q),R) = hAPP_f1591852335a_bool(hAPP_p54391842a_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc,axiom,
! [P,Q,R] : hAPP_p1712839024_state(hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,P),Q),R) = hAPP_c408625258_state(hAPP_p2032835427_state(P,R),hAPP_pname_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_027,axiom,
! [P,Q,R] : hAPP_s1226857760e_bool(hAPP_f1138284024e_bool(cOMBB_20296667_state(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_s2001034685l_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__028,axiom,
! [P,Q,R] : hAPP_p363087182iple_a(hAPP_f866544818iple_a(hAPP_f428084316iple_a(cOMBS_546756116iple_a,P),Q),R) = hAPP_H1455657330iple_a(hAPP_p321057131iple_a(P,R),hAPP_p263283121iple_a(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd_029,axiom,
! [P,Q,R] : hAPP_p877885514e_bool(hAPP_f621094798e_bool(hAPP_f1505732693e_bool(cOMBC_173904839e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_p1682965390e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_030,axiom,
! [P,Q,R] : hAPP_H1190454433a_bool(hAPP_f1665407592a_bool(hAPP_f549683569a_bool(cOMBC_708118077a_bool,P),Q),R) = hAPP_f1591852335a_bool(hAPP_H1641355846a_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp,axiom,
! [P,Q,R] : hAPP_p321057131iple_a(hAPP_f653022294iple_a(cOMBB_1916528323_pname(P),Q),R) = hAPP_b385840250iple_a(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__031,axiom,
! [P,Q,R] : hAPP_p80247908_state(hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,P),Q),R) = hAPP_H521649881_state(hAPP_p964374716_state(P,R),hAPP_p1842370726_state(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_p1263586117iple_a(hAPP_f1504849325iple_a(cOMBB_109684016_pname(P),Q),R) = hAPP_f1807945453iple_a(P,hAPP_p635540397e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It__a_J_00_032,axiom,
! [P,Q,R] : hAPP_p54391842a_bool(hAPP_f1728520198a_bool(cOMBB_1191710871_pname(P),Q),R) = hAPP_H1641355846a_bool(P,hAPP_p263283121iple_a(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___033,axiom,
! [P,Q,R] : hAPP_H1645666623e_bool(hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp_034,axiom,
! [P,Q,R] : hAPP_p964374716_state(hAPP_f1405979047_state(cOMBB_707293872_pname(P),Q),R) = hAPP_b798484845_state(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__,axiom,
! [P,Q,R] : hAPP_p2032835427_state(hAPP_f950918952_state(cOMBB_2123334001_pname(P),Q),R) = hAPP_f1949912908_state(P,hAPP_p1637813682e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___035,axiom,
! [P,Q,R] : hAPP_p1682965390e_bool(hAPP_f1191449183e_bool(cOMBB_557071226_pname(P),Q),R) = hAPP_H727730819e_bool(P,hAPP_p1842370726_state(Q,R)) ).
%----Conjectures (2)
fof(conj_0,hypothesis,
! [N] :
( ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f1591852335a_bool(hAPP_f1026156344a_bool(semila1498788770a_bool,g),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),p)),body)),q)),procs))))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)) )
=> ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),p)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),q)),procs)))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(N),X)) ) ) ).
fof(conj_1,conjecture,
( ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),g))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(n),X)) )
=> ! [X] :
( hBOOL(hAPP_f540970102l_bool(hAPP_H1840393229l_bool(member1713797107iple_a,X),hAPP_f271130963a_bool(image_1654749281iple_a(hAPP_f79369369iple_a(hAPP_f1821846428iple_a(cOMBS_260455419iple_a,hAPP_f773999884iple_a(hAPP_f1139368540iple_a(cOMBS_2104302062iple_a,hAPP_f1504849325iple_a(cOMBB_109684016_pname(hoare_1760757500iple_a),p)),body)),q)),procs)))
=> hBOOL(hAPP_H1421470952a_bool(hoare_560051114alid_a(n),X)) ) ) ).
%------------------------------------------------------------------------------