TPTP Problem File: SWW471+3.p
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%------------------------------------------------------------------------------
% File : SWW471+3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 269, 1000 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : hoare_1000_fofmg_l269 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 1423 ( 631 unt; 0 def)
% Number of atoms : 3065 (1168 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 2061 ( 419 ~; 88 |; 179 &)
% ( 258 <=>;1117 =>; 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 : 655 ( 655 usr; 205 con; 0-3 aty)
% Number of variables : 3695 (3625 !; 70 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 17:39:34
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (65)
fof(gsy_c_Big__Operators_Ocomm__monoid__big_000tc__fun_Itc__Hoare____Mirabelle____uw,axiom,
! [B_1_1,B_2_1,B_3_1] : is_bool(big_co2022808324_pname(B_1_1,B_2_1,B_3_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____uwgpyvfjxg__Otriple,axiom,
! [B_1_1,B_2_1] : is_bool(finite1753440478iple_a(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_001,axiom,
! [B_1_1,B_2_1] : is_bool(finite683959609_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,axiom,
! [B_1_1,B_2_1] : is_bool(finite988810631ne_nat(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg,axiom,
! [B_1_1,B_2_1] : is_bool(finite2103247258a_bool(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____uwgpyvfjxg__O,axiom,
! [B_1_1,B_2_1] : is_bool(finite1033474011iple_a(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__O_002,axiom,
! [B_1_1,B_2_1] : is_bool(finite416071164_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,axiom,
! [B_1_1,B_2_1] : is_bool(finite795500164em_nat(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Hoare____Mirabelle____uwgp,axiom,
! [B_1_1,B_2_1] : is_bool(finite927518301a_bool(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__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ).
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____uwgpyvfjxg__Otriple_It__a_J_000tc__Com__,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_H2000557816_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__HOL__,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_H1037229737a_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__fun_I,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H1078816262e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_000tc__fun_I_003,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_H2130837971l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_H242767318e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_004,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H1776011827e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_005,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_H1270401638l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_nat_pname(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__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_n1006566506l_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____uwgpyvfjxg__Otriple_It__a_J_Mtc,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_f1764134762_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc_006,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_f1695230391l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc_007,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f1216026388e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_Mtc_008,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_f244528453l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1378282496l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f654413245e_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_009,axiom,
! [B_1_1,B_2_1] :
( is_fun1661590463l_bool(B_2_1)
=> is_fun_pname_bool(hAPP_f674760225e_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_010,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____uwgpyvfjxg__Otriple_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2110825313l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It_011,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f147139262e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It_012,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1410040974l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f670355311l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_Procs,hypothesis,
is_fun_pname_bool(procs) ).
%----Relevant facts (1196)
fof(fact_0_triple_Oinject,axiom,
! [Fun1,Com_1,Fun2,Fun1_2,Com,Fun2_2] :
( hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1),Com_1),Fun2) = hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1_2),Com),Fun2_2)
<=> ( Fun1 = Fun1_2
& Com_1 = Com
& Fun2 = Fun2_2 ) ) ).
fof(fact_1_triple_Oinject,axiom,
! [Fun1,Com_1,Fun2,Fun1_2,Com,Fun2_2] :
( hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com_1),Fun2) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_2),Com),Fun2_2)
<=> ( Fun1 = Fun1_2
& Com_1 = Com
& Fun2 = Fun2_2 ) ) ).
fof(fact_2_hoare__valids__def,axiom,
! [Ga,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(Ga),Ts))
<=> ! [N] :
( ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ga))
=> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N),X)) )
=> ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ts))
=> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N),X)) ) ) ) ).
fof(fact_3_hoare__valids__def,axiom,
! [Ga,Ts] :
( hBOOL(hAPP_f1695230391l_bool(hoare_293150257lids_a(Ga),Ts))
<=> ! [N] :
( ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ga))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)) )
=> ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ts))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)) ) ) ) ).
fof(fact_4_hoare__derivs_OBody,axiom,
! [Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),body)),Qa)),Procsa))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),body)),Qa)),Procsa))) ) ).
fof(fact_5_hoare__derivs_OBody,axiom,
! [Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),Qa)),Procsa)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),body)),Qa)),Procsa))) ) ).
fof(fact_6_UnE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) ) ) ).
fof(fact_7_UnE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)))
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) ) ) ).
fof(fact_8_UnE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2)) ) ) ).
fof(fact_9_UnE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)))
=> ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) ) ) ).
fof(fact_10_UnE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) ) ) ).
fof(fact_11_sup1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2))
=> ( ~ hBOOL(hAPP_nat_bool(A_1,X_2))
=> hBOOL(hAPP_nat_bool(B_2,X_2)) ) ) ).
fof(fact_12_sup1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2))
=> ( ~ hBOOL(hAPP_f1695230391l_bool(A_1,X_2))
=> hBOOL(hAPP_f1695230391l_bool(B_2,X_2)) ) ) ).
fof(fact_13_sup1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2))
=> ( ~ hBOOL(hAPP_H242767318e_bool(A_1,X_2))
=> hBOOL(hAPP_H242767318e_bool(B_2,X_2)) ) ) ).
fof(fact_14_sup1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2))
=> ( ~ hBOOL(hAPP_pname_bool(A_1,X_2))
=> hBOOL(hAPP_pname_bool(B_2,X_2)) ) ) ).
fof(fact_15_sup1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2))
=> ( ~ hBOOL(hAPP_H1037229737a_bool(A_1,X_2))
=> hBOOL(hAPP_H1037229737a_bool(B_2,X_2)) ) ) ).
fof(fact_16_sup1CI,axiom,
! [A_1,B_2,X_2] :
( ( ~ hBOOL(hAPP_nat_bool(B_2,X_2))
=> hBOOL(hAPP_nat_bool(A_1,X_2)) )
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)) ) ).
fof(fact_17_sup1CI,axiom,
! [A_1,B_2,X_2] :
( ( ~ hBOOL(hAPP_f1695230391l_bool(B_2,X_2))
=> hBOOL(hAPP_f1695230391l_bool(A_1,X_2)) )
=> hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)) ) ).
fof(fact_18_sup1CI,axiom,
! [A_1,B_2,X_2] :
( ( ~ hBOOL(hAPP_H242767318e_bool(B_2,X_2))
=> hBOOL(hAPP_H242767318e_bool(A_1,X_2)) )
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)) ) ).
fof(fact_19_sup1CI,axiom,
! [A_1,B_2,X_2] :
( ( ~ hBOOL(hAPP_pname_bool(B_2,X_2))
=> hBOOL(hAPP_pname_bool(A_1,X_2)) )
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)) ) ).
fof(fact_20_sup1CI,axiom,
! [A_1,B_2,X_2] :
( ( ~ hBOOL(hAPP_H1037229737a_bool(B_2,X_2))
=> hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) )
=> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)) ) ).
fof(fact_21_UnCI,axiom,
! [A_1,C_2,B_2] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) ) ).
fof(fact_22_UnCI,axiom,
! [A_1,C_2,B_2] :
( ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1)) )
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) ) ).
fof(fact_23_UnCI,axiom,
! [A_1,C_2,B_2] :
( ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) ) ).
fof(fact_24_UnCI,axiom,
! [A_1,C_2,B_2] :
( ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1)) )
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) ) ).
fof(fact_25_UnCI,axiom,
! [A_1,C_2,B_2] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) ) ).
fof(fact_26_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_nat_nat(F,X_2)
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1))) ) ) ).
fof(fact_27_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_p1751618853_state(F,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1))) ) ) ).
fof(fact_28_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_pname_nat(F,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f1066163005t_bool(image_pname_nat(F),A_1))) ) ) ).
fof(fact_29_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_p1743421830a_bool(F,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))) ) ) ).
fof(fact_30_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_nat_pname(F,X_2)
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f654413245e_bool(image_nat_pname(F),A_1))) ) ) ).
fof(fact_31_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_f1764134762_pname(F,X_2)
=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1))) ) ) ).
fof(fact_32_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_H2000557816_pname(F,X_2)
=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1))) ) ) ).
fof(fact_33_image__eqI,axiom,
! [A_1,B_1,F,X_2] :
( B_1 = hAPP_p346744818iple_a(F,X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) ) ) ).
fof(fact_34_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f800510211t_bool(image_nat_nat(F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(image_nat_nat(F),A_1)),hAPP_f800510211t_bool(image_nat_nat(F),B_2)) ).
fof(fact_35_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A_1)),hAPP_f360545851e_bool(image_185131637_state(F),B_2)) ).
fof(fact_36_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f1968395738t_bool(image_48635758_a_nat(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f1968395738t_bool(image_48635758_a_nat(F),A_1)),hAPP_f1968395738t_bool(image_48635758_a_nat(F),B_2)) ).
fof(fact_37_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f1767618879l_bool(image_2034400499a_bool(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f1767618879l_bool(image_2034400499a_bool(F),A_1)),hAPP_f1767618879l_bool(image_2034400499a_bool(F),B_2)) ).
fof(fact_38_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f101573982e_bool(image_1599849618_state(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f101573982e_bool(image_1599849618_state(F),A_1)),hAPP_f101573982e_bool(image_1599849618_state(F),B_2)) ).
fof(fact_39_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f1216026388e_bool(image_1244540328_pname(F),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1)),hAPP_f1216026388e_bool(image_1244540328_pname(F),B_2)) ).
fof(fact_40_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f420957402a_bool(image_1865589340iple_a(F),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f420957402a_bool(image_1865589340iple_a(F),A_1)),hAPP_f420957402a_bool(image_1865589340iple_a(F),B_2)) ).
fof(fact_41_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f258822235a_bool(image_1153683671iple_a(F),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f258822235a_bool(image_1153683671iple_a(F),A_1)),hAPP_f258822235a_bool(image_1153683671iple_a(F),B_2)) ).
fof(fact_42_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f1029392762a_bool(image_299066104iple_a(F),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f1029392762a_bool(image_299066104iple_a(F),A_1)),hAPP_f1029392762a_bool(image_299066104iple_a(F),B_2)) ).
fof(fact_43_image__Un,axiom,
! [F,A_1,B_2] : hAPP_f2034373396a_bool(image_1738210978iple_a(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),B_2)) ).
fof(fact_44_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_nat_bool(F,X)),hAPP_nat_bool(G,X))) ) ).
fof(fact_45_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_f1695230391l_bool(F,X)),hAPP_f1695230391l_bool(G,X))) ) ).
fof(fact_46_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X)),hAPP_H242767318e_bool(G,X))) ) ).
fof(fact_47_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X)),hAPP_pname_bool(G,X))) ) ).
fof(fact_48_sup__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1037229737a_bool(F,X)),hAPP_H1037229737a_bool(G,X))) ) ).
fof(fact_49_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).
fof(fact_50_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_f1695230391l_bool(F,X_2)),hAPP_f1695230391l_bool(G,X_2))) ) ).
fof(fact_51_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2))) ) ).
fof(fact_52_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))) ) ).
fof(fact_53_sup__apply,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1037229737a_bool(F,X_2)),hAPP_H1037229737a_bool(G,X_2))) ) ).
fof(fact_54_cut,axiom,
! [Ga,G_1,Ts] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(G_1),Ts))
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),G_1))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts)) ) ) ).
fof(fact_55_cut,axiom,
! [Ga,G_1,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_1),Ts))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),G_1))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),Ts)) ) ) ).
fof(fact_56_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)),Z_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1)) ).
fof(fact_57_sup__assoc,axiom,
! [X_20,Y_17,Z_9] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_20),Y_17)),Z_9) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_17),Z_9)) ).
fof(fact_58_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)),Z_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1)) ).
fof(fact_59_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)),Z_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1)) ).
fof(fact_60_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_61_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_62_sup__assoc,axiom,
! [X_2,Y_1,Z_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)),Z_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1)) ).
fof(fact_63_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)),Z_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1)) ).
fof(fact_64_inf__sup__aci_I6_J,axiom,
! [X_19,Y_16,Z_8] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_19),Y_16)),Z_8) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_16),Z_8)) ).
fof(fact_65_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)),Z_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1)) ).
fof(fact_66_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)),Z_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1)) ).
fof(fact_67_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_68_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_69_inf__sup__aci_I6_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)),Z_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1)) ).
fof(fact_70_sup_Oassoc,axiom,
! [A_2,B_1,C_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1)),C_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),C_2)) ).
fof(fact_71_sup_Oassoc,axiom,
! [A_13,B_10,C_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_13),B_10)),C_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_10),C_5)) ).
fof(fact_72_sup_Oassoc,axiom,
! [A_2,B_1,C_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1)),C_2) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),C_2)) ).
fof(fact_73_sup_Oassoc,axiom,
! [A_2,B_1,C_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1)),C_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C_2)) ).
fof(fact_74_sup_Oassoc,axiom,
! [A_2,B_1,C_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1)),C_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_2)) ).
fof(fact_75_sup_Oassoc,axiom,
! [A_2,B_1,C_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1)),C_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C_2))) ) ).
fof(fact_76_sup_Oassoc,axiom,
! [A_2,B_1,C_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1)),C_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),C_2)) ).
fof(fact_77_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Z_1)) ).
fof(fact_78_sup__left__commute,axiom,
! [X_18,Y_15,Z_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_15),Z_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_18),Z_7)) ).
fof(fact_79_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Z_1)) ).
fof(fact_80_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Z_1)) ).
fof(fact_81_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_82_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_83_sup__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Z_1)) ).
fof(fact_84_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Z_1)) ).
fof(fact_85_inf__sup__aci_I7_J,axiom,
! [X_17,Y_14,Z_6] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_17),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_14),Z_6)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_17),Z_6)) ).
fof(fact_86_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),Z_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Z_1)) ).
fof(fact_87_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Z_1)) ).
fof(fact_88_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_89_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_90_inf__sup__aci_I7_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Z_1)) ).
fof(fact_91_sup_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),C_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),C_2)) ).
fof(fact_92_sup_Oleft__commute,axiom,
! [B_9,A_12,C_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_12),C_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_9),C_4)) ).
fof(fact_93_sup_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),C_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),C_2)) ).
fof(fact_94_sup_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),C_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C_2)) ).
fof(fact_95_sup_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),C_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C_2)) ).
fof(fact_96_sup_Oleft__commute,axiom,
! [B_1,A_2,C_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),C_2)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C_2))) ) ).
fof(fact_97_sup_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),C_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),C_2)) ).
fof(fact_98_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) ).
fof(fact_99_sup__left__idem,axiom,
! [X_16,Y_13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_16),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_16),Y_13)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_16),Y_13) ).
fof(fact_100_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) ).
fof(fact_101_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) ).
fof(fact_102_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_103_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_104_sup__left__idem,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) ).
fof(fact_105_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) ).
fof(fact_106_inf__sup__aci_I8_J,axiom,
! [X_15,Y_12] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_15),Y_12)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_15),Y_12) ).
fof(fact_107_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) ).
fof(fact_108_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) ).
fof(fact_109_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_110_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_111_inf__sup__aci_I8_J,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) ).
fof(fact_112_sup_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1) ).
fof(fact_113_sup_Oleft__idem,axiom,
! [A_11,B_8] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_11),B_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_11),B_8) ).
fof(fact_114_sup_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1) ).
fof(fact_115_sup_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1) ).
fof(fact_116_sup_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1) ).
fof(fact_117_sup_Oleft__idem,axiom,
! [A_2,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1)) ) ).
fof(fact_118_sup_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1) ).
fof(fact_119_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),X_2) ).
fof(fact_120_sup__commute,axiom,
! [X_14,Y_11] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_14),Y_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_11),X_14) ).
fof(fact_121_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),X_2) ).
fof(fact_122_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),X_2) ).
fof(fact_123_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_124_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_125_sup__commute,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),X_2) ).
fof(fact_126_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,Y_1),X_2) ).
fof(fact_127_inf__sup__aci_I5_J,axiom,
! [X_13,Y_10] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_13),Y_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,Y_10),X_13) ).
fof(fact_128_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,Y_1),X_2) ).
fof(fact_129_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_1),X_2) ).
fof(fact_130_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_131_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_132_inf__sup__aci_I5_J,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Y_1),X_2) ).
fof(fact_133_sup_Ocommute,axiom,
! [A_2,B_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),B_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_1),A_2) ).
fof(fact_134_sup_Ocommute,axiom,
! [A_10,B_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_10),B_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,B_7),A_10) ).
fof(fact_135_sup_Ocommute,axiom,
! [A_2,B_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),B_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_1),A_2) ).
fof(fact_136_sup_Ocommute,axiom,
! [A_2,B_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),B_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),A_2) ).
fof(fact_137_sup_Ocommute,axiom,
! [A_2,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A_2) ).
fof(fact_138_sup_Ocommute,axiom,
! [A_2,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),B_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),A_2)) ) ).
fof(fact_139_sup_Ocommute,axiom,
! [A_2,B_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),B_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_1),A_2) ).
fof(fact_140_sup__idem,axiom,
! [X_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),X_2) = X_2 ).
fof(fact_141_sup__idem,axiom,
! [X_12] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_12),X_12) = X_12 ).
fof(fact_142_sup__idem,axiom,
! [X_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),X_2) = X_2 ).
fof(fact_143_sup__idem,axiom,
! [X_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),X_2) = X_2 ).
fof(fact_144_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_145_sup__idem,axiom,
! [X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2))
<=> hBOOL(X_2) ) ).
fof(fact_146_sup__idem,axiom,
! [X_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),X_2) = X_2 ).
fof(fact_147_sup_Oidem,axiom,
! [A_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_2),A_2) = A_2 ).
fof(fact_148_sup_Oidem,axiom,
! [A_9] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,A_9),A_9) = A_9 ).
fof(fact_149_sup_Oidem,axiom,
! [A_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_2),A_2) = A_2 ).
fof(fact_150_sup_Oidem,axiom,
! [A_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_2),A_2) = A_2 ).
fof(fact_151_sup_Oidem,axiom,
! [A_2] :
( is_fun_pname_bool(A_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_2),A_2) = A_2 ) ).
fof(fact_152_sup_Oidem,axiom,
! [A_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_2),A_2))
<=> hBOOL(A_2) ) ).
fof(fact_153_sup_Oidem,axiom,
! [A_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_2),A_2) = A_2 ).
fof(fact_154_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> ( B_1 = hAPP_nat_nat(F,X_2)
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1))) ) ) ).
fof(fact_155_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( B_1 = hAPP_p1751618853_state(F,X_2)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1))) ) ) ).
fof(fact_156_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( B_1 = hAPP_pname_nat(F,X_2)
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f1066163005t_bool(image_pname_nat(F),A_1))) ) ) ).
fof(fact_157_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( B_1 = hAPP_p1743421830a_bool(F,X_2)
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))) ) ) ).
fof(fact_158_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> ( B_1 = hAPP_nat_pname(F,X_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f654413245e_bool(image_nat_pname(F),A_1))) ) ) ).
fof(fact_159_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> ( B_1 = hAPP_f1764134762_pname(F,X_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1))) ) ) ).
fof(fact_160_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> ( B_1 = hAPP_H2000557816_pname(F,X_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1))) ) ) ).
fof(fact_161_rev__image__eqI,axiom,
! [B_1,F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( B_1 = hAPP_p346744818iple_a(F,X_2)
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) ) ) ).
fof(fact_162_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(F,X_2)),hAPP_f800510211t_bool(image_nat_nat(F),A_1))) ) ).
fof(fact_163_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_2)),hAPP_f360545851e_bool(image_185131637_state(F),A_1))) ) ).
fof(fact_164_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_2)),hAPP_f1066163005t_bool(image_pname_nat(F),A_1))) ) ).
fof(fact_165_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,hAPP_p1743421830a_bool(F,X_2)),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1))) ) ).
fof(fact_166_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_2)),hAPP_f654413245e_bool(image_nat_pname(F),A_1))) ) ).
fof(fact_167_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1764134762_pname(F,X_2)),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1))) ) ).
fof(fact_168_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H2000557816_pname(F,X_2)),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1))) ) ).
fof(fact_169_imageI,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_p346744818iple_a(F,X_2)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1))) ) ).
fof(fact_170_image__iff,axiom,
! [Z_1,F,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Z_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1)))
<=> ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
& Z_1 = hAPP_nat_nat(F,X) ) ) ).
fof(fact_171_image__iff,axiom,
! [Z_1,F,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Z_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1)))
<=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& Z_1 = hAPP_p1751618853_state(F,X) ) ) ).
fof(fact_172_image__iff,axiom,
! [Z_1,F,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Z_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)))
<=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& Z_1 = hAPP_p346744818iple_a(F,X) ) ) ).
fof(fact_173_UnI2,axiom,
! [A_1,C_2,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) ) ).
fof(fact_174_UnI2,axiom,
! [A_1,C_2,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) ) ).
fof(fact_175_UnI2,axiom,
! [A_1,C_2,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) ) ).
fof(fact_176_UnI2,axiom,
! [A_1,C_2,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) ) ).
fof(fact_177_UnI2,axiom,
! [A_1,C_2,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) ) ).
fof(fact_178_UnI1,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))) ) ).
fof(fact_179_UnI1,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))) ) ).
fof(fact_180_UnI1,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))) ) ).
fof(fact_181_UnI1,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))) ) ).
fof(fact_182_UnI1,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))) ) ).
fof(fact_183_sup1I2,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_nat_bool(B_2,X_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)) ) ).
fof(fact_184_sup1I2,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_f1695230391l_bool(B_2,X_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)) ) ).
fof(fact_185_sup1I2,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_H242767318e_bool(B_2,X_2))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)) ) ).
fof(fact_186_sup1I2,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_pname_bool(B_2,X_2))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)) ) ).
fof(fact_187_sup1I2,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_H1037229737a_bool(B_2,X_2))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)) ) ).
fof(fact_188_sup1I1,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_nat_bool(A_1,X_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2),X_2)) ) ).
fof(fact_189_sup1I1,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_f1695230391l_bool(A_1,X_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2),X_2)) ) ).
fof(fact_190_sup1I1,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_H242767318e_bool(A_1,X_2))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2),X_2)) ) ).
fof(fact_191_sup1I1,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_pname_bool(A_1,X_2))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2),X_2)) ) ).
fof(fact_192_sup1I1,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_H1037229737a_bool(A_1,X_2))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2),X_2)) ) ).
fof(fact_193_ball__Un,axiom,
! [Pa,A_1,B_2] :
( ! [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)))
=> hBOOL(hAPP_nat_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
=> hBOOL(hAPP_nat_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),B_2))
=> hBOOL(hAPP_nat_bool(Pa,X)) ) ) ) ).
fof(fact_194_ball__Un,axiom,
! [Pa,A_1,B_2] :
( ! [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)))
=> hBOOL(hAPP_f1695230391l_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))
=> hBOOL(hAPP_f1695230391l_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),B_2))
=> hBOOL(hAPP_f1695230391l_bool(Pa,X)) ) ) ) ).
fof(fact_195_ball__Un,axiom,
! [Pa,A_1,B_2] :
( ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)))
=> hBOOL(hAPP_H242767318e_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1))
=> hBOOL(hAPP_H242767318e_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),B_2))
=> hBOOL(hAPP_H242767318e_bool(Pa,X)) ) ) ) ).
fof(fact_196_ball__Un,axiom,
! [Pa,A_1,B_2] :
( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) )
<=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) )
& ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_2))
=> hBOOL(hAPP_pname_bool(Pa,X)) ) ) ) ) ).
fof(fact_197_ball__Un,axiom,
! [Pa,A_1,B_2] :
( ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)))
=> hBOOL(hAPP_H1037229737a_bool(Pa,X)) )
<=> ( ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))
=> hBOOL(hAPP_H1037229737a_bool(Pa,X)) )
& ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),B_2))
=> hBOOL(hAPP_H1037229737a_bool(Pa,X)) ) ) ) ).
fof(fact_198_bex__Un,axiom,
! [Pa,A_1,B_2] :
( ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)))
& hBOOL(hAPP_nat_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
& hBOOL(hAPP_nat_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),B_2))
& hBOOL(hAPP_nat_bool(Pa,X)) ) ) ) ).
fof(fact_199_bex__Un,axiom,
! [Pa,A_1,B_2] :
( ? [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)))
& hBOOL(hAPP_f1695230391l_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))
& hBOOL(hAPP_f1695230391l_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),B_2))
& hBOOL(hAPP_f1695230391l_bool(Pa,X)) ) ) ) ).
fof(fact_200_bex__Un,axiom,
! [Pa,A_1,B_2] :
( ? [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)))
& hBOOL(hAPP_H242767318e_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1))
& hBOOL(hAPP_H242767318e_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),B_2))
& hBOOL(hAPP_H242767318e_bool(Pa,X)) ) ) ) ).
fof(fact_201_bex__Un,axiom,
! [Pa,A_1,B_2] :
( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)))
& hBOOL(hAPP_pname_bool(Pa,X)) )
<=> ( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& hBOOL(hAPP_pname_bool(Pa,X)) )
| ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_2))
& hBOOL(hAPP_pname_bool(Pa,X)) ) ) ) ).
fof(fact_202_bex__Un,axiom,
! [Pa,A_1,B_2] :
( ? [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)))
& hBOOL(hAPP_H1037229737a_bool(Pa,X)) )
<=> ( ? [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))
& hBOOL(hAPP_H1037229737a_bool(Pa,X)) )
| ? [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),B_2))
& hBOOL(hAPP_H1037229737a_bool(Pa,X)) ) ) ) ).
fof(fact_203_Un__assoc,axiom,
! [A_1,B_2,C_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)),C_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1)) ).
fof(fact_204_Un__assoc,axiom,
! [A_1,B_2,C_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)),C_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1)) ).
fof(fact_205_Un__assoc,axiom,
! [A_1,B_2,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1)) ).
fof(fact_206_Un__assoc,axiom,
! [A_1,B_2,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1)) ).
fof(fact_207_Un__assoc,axiom,
! [A_1,B_2,C_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)),C_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1)) ).
fof(fact_208_Un__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) ) ) ).
fof(fact_209_Un__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
| hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) ) ) ).
fof(fact_210_Un__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),A_1))
| hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),B_2)) ) ) ).
fof(fact_211_Un__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
| hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) ) ) ).
fof(fact_212_Un__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) ) ) ).
fof(fact_213_Un__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),C_1)) ).
fof(fact_214_Un__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),C_1)) ).
fof(fact_215_Un__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),C_1)) ).
fof(fact_216_Un__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),C_1)) ).
fof(fact_217_Un__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),C_1)) ).
fof(fact_218_Un__left__absorb,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) ).
fof(fact_219_Un__left__absorb,axiom,
! [A_1,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) ).
fof(fact_220_Un__left__absorb,axiom,
! [A_1,B_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) ).
fof(fact_221_Un__left__absorb,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) ).
fof(fact_222_Un__left__absorb,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) ).
fof(fact_223_Un__commute,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),A_1) ).
fof(fact_224_Un__commute,axiom,
! [A_1,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),A_1) ).
fof(fact_225_Un__commute,axiom,
! [A_1,B_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),A_1) ).
fof(fact_226_Un__commute,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),A_1) ).
fof(fact_227_Un__commute,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),A_1) ).
fof(fact_228_Un__def,axiom,
! [A_1,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2))) ).
fof(fact_229_Un__def,axiom,
! [A_1,B_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A_1))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B_2))) ).
fof(fact_230_Un__def,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2))) ).
fof(fact_231_Un__def,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2))) ).
fof(fact_232_Un__def,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) = 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_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2))) ).
fof(fact_233_Un__absorb,axiom,
! [A_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),A_1) = A_1 ).
fof(fact_234_Un__absorb,axiom,
! [A_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),A_1) = A_1 ).
fof(fact_235_Un__absorb,axiom,
! [A_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),A_1) = A_1 ).
fof(fact_236_Un__absorb,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_237_Un__absorb,axiom,
! [A_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),A_1) = A_1 ).
fof(fact_238_image__ident,axiom,
! [Y_9] : hAPP_f800510211t_bool(image_nat_nat(cOMBI_nat),Y_9) = Y_9 ).
fof(fact_239_image__image,axiom,
! [F,G,A_1] : hAPP_f101573982e_bool(image_1599849618_state(F),hAPP_f2034373396a_bool(image_1738210978iple_a(G),A_1)) = hAPP_f360545851e_bool(image_185131637_state(hAPP_f922567064_state(cOMBB_452540923_pname(F),G)),A_1) ).
fof(fact_240_image__image,axiom,
! [F,G,A_1] : hAPP_f1029392762a_bool(image_299066104iple_a(F),hAPP_f360545851e_bool(image_185131637_state(G),A_1)) = hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f1273628548iple_a(cOMBB_1824120853_pname(F),G)),A_1) ).
fof(fact_241_sup__Un__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_2)),X))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,R_1),S_2))) ) ).
fof(fact_242_sup__Un__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),R_1)),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),S_2)),X))
<=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,R_1),S_2))) ) ).
fof(fact_243_sup__Un__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),R_1)),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),S_2)),X))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,R_1),S_2))) ) ).
fof(fact_244_sup__Un__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),R_1)),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_2)),X))
<=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,R_1),S_2))) ) ).
fof(fact_245_sup__Un__eq,axiom,
! [R_1,S_2,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_2)),X))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S_2))) ) ).
fof(fact_246_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_247_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),Pa)),Qa)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(collec999179778a_bool,Pa)),hAPP_f396832789l_bool(collec999179778a_bool,Qa)) ).
fof(fact_248_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),Pa)),Qa)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,Pa)),hAPP_f806699093e_bool(collec637225377_state,Qa)) ).
fof(fact_249_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),Pa)),Qa)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(collec351493750iple_a,Pa)),hAPP_f20753329a_bool(collec351493750iple_a,Qa)) ).
fof(fact_250_Collect__disj__eq,axiom,
! [Pa,Qa] : hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),Pa)),Qa)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(collect_nat,Pa)),hAPP_f800510211t_bool(collect_nat,Qa)) ).
fof(fact_251_imageE,axiom,
! [B_1,F,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(image_nat_nat(F),A_1)))
=> ~ ! [X] :
( B_1 = hAPP_nat_nat(F,X)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) ) ) ).
fof(fact_252_imageE,axiom,
! [B_1,F,A_1] :
( is_pname(B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f654413245e_bool(image_nat_pname(F),A_1)))
=> ~ ! [X] :
( B_1 = hAPP_nat_pname(F,X)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1)) ) ) ) ).
fof(fact_253_imageE,axiom,
! [B_1,F,A_1] :
( is_pname(B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f147139262e_bool(image_2037030074_pname(F),A_1)))
=> ~ ! [X] :
( B_1 = hAPP_f1764134762_pname(F,X)
=> ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1)) ) ) ) ).
fof(fact_254_imageE,axiom,
! [B_1,F,A_1] :
( is_pname(B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1216026388e_bool(image_1244540328_pname(F),A_1)))
=> ~ ! [X] :
( B_1 = hAPP_H2000557816_pname(F,X)
=> ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1)) ) ) ) ).
fof(fact_255_imageE,axiom,
! [B_1,F,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A_1)))
=> ~ ! [X] :
( is_pname(X)
=> ( B_1 = hAPP_p1751618853_state(F,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) ) ) ) ).
fof(fact_256_imageE,axiom,
! [B_1,F,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f1066163005t_bool(image_pname_nat(F),A_1)))
=> ~ ! [X] :
( is_pname(X)
=> ( B_1 = hAPP_pname_nat(F,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) ) ) ) ).
fof(fact_257_imageE,axiom,
! [B_1,F,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1)))
=> ~ ! [X] :
( is_pname(X)
=> ( B_1 = hAPP_p1743421830a_bool(F,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) ) ) ) ).
fof(fact_258_imageE,axiom,
! [B_1,F,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)))
=> ~ ! [X] :
( is_pname(X)
=> ( B_1 = hAPP_p346744818iple_a(F,X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) ) ) ) ).
fof(fact_259_Body__triple__valid__Suc,axiom,
! [N_1,Pa,Pn_1,Qa] :
( hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_1),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)))
<=> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,hAPP_nat_nat(suc,N_1)),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ) ).
fof(fact_260_Body__triple__valid__Suc,axiom,
! [N_1,Pa,Pn_1,Qa] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_1),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)))
<=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,hAPP_nat_nat(suc,N_1)),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ) ).
fof(fact_261_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1_1,Com_2,Fun2_1] : Y_1 != hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1_1),Com_2),Fun2_1) ).
fof(fact_262_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1_1,Com_2,Fun2_1] : Y_1 != hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_1),Com_2),Fun2_1) ).
fof(fact_263_Body1,axiom,
! [Pn_1,Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),body)),Qa)),Procsa))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_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_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p1637813682e_bool(Qa,Pn_1))),bot_bo784226126e_bool))) ) ) ).
fof(fact_264_Body1,axiom,
! [Pn_1,Ga,Pa,Qa,Procsa] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),body)),Qa)),Procsa))),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_p635540397e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p635540397e_bool(Qa,Pn_1))),bot_bo797238721a_bool))) ) ) ).
fof(fact_265_image__cong,axiom,
! [F,G,M_5,N_3] :
( M_5 = N_3
=> ( ! [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),N_3))
=> hAPP_nat_nat(F,X) = hAPP_nat_nat(G,X) )
=> hAPP_f800510211t_bool(image_nat_nat(F),M_5) = hAPP_f800510211t_bool(image_nat_nat(G),N_3) ) ) ).
fof(fact_266_image__cong,axiom,
! [F,G,M_5,N_3] :
( M_5 = N_3
=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3))
=> hAPP_p1751618853_state(F,X) = hAPP_p1751618853_state(G,X) ) )
=> hAPP_f360545851e_bool(image_185131637_state(F),M_5) = hAPP_f360545851e_bool(image_185131637_state(G),N_3) ) ) ).
fof(fact_267_image__cong,axiom,
! [F,G,M_5,N_3] :
( M_5 = N_3
=> ( ! [X] :
( is_pname(X)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_3))
=> hAPP_p346744818iple_a(F,X) = hAPP_p346744818iple_a(G,X) ) )
=> hAPP_f2034373396a_bool(image_1738210978iple_a(F),M_5) = hAPP_f2034373396a_bool(image_1738210978iple_a(G),N_3) ) ) ).
fof(fact_268_Body__triple__valid__0,axiom,
! [Pa,Pn_1,Qa] : hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,zero_zero_nat),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ).
fof(fact_269_Body__triple__valid__0,axiom,
! [Pa,Pn_1,Qa] : hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,zero_zero_nat),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))) ).
fof(fact_270_com_Osimps_I6_J,axiom,
! [Pname_3,Pname] :
( ( is_pname(Pname_3)
& is_pname(Pname) )
=> ( hAPP_pname_com(body,Pname_3) = hAPP_pname_com(body,Pname)
<=> Pname_3 = Pname ) ) ).
fof(fact_271_evalc_OBody,axiom,
! [Pn,S0,S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn))),S0),S1_2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,Pn)),S0),S1_2)) ) ).
fof(fact_272_evalc__elim__cases_I6_J,axiom,
! [P,S,S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body,P)),S),S1_2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P))),S),S1_2)) ) ).
fof(fact_273_Sup__fin_Oidem,axiom,
! [X_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),X_2) = X_2 ).
fof(fact_274_Sup__fin_Oidem,axiom,
! [X_11] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_11),X_11) = X_11 ).
fof(fact_275_Sup__fin_Oidem,axiom,
! [X_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),X_2) = X_2 ).
fof(fact_276_Sup__fin_Oidem,axiom,
! [X_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),X_2) = X_2 ).
fof(fact_277_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_278_Sup__fin_Oidem,axiom,
! [X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),X_2))
<=> hBOOL(X_2) ) ).
fof(fact_279_Sup__fin_Oidem,axiom,
! [X_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),X_2) = X_2 ).
fof(fact_280_triples__valid__Suc,axiom,
! [N_1,Ts] :
( ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ts))
=> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,hAPP_nat_nat(suc,N_1)),X)) )
=> ! [X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),Ts))
=> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_1),X)) ) ) ).
fof(fact_281_triples__valid__Suc,axiom,
! [N_1,Ts] :
( ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ts))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,hAPP_nat_nat(suc,N_1)),X)) )
=> ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),Ts))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_1),X)) ) ) ).
fof(fact_282_emptyE,axiom,
! [A_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),bot_bot_fun_nat_bool)) ).
fof(fact_283_emptyE,axiom,
! [A_2] : ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),bot_bo332163887l_bool)) ).
fof(fact_284_emptyE,axiom,
! [A_2] : ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),bot_bo797238721a_bool)) ).
fof(fact_285_emptyE,axiom,
! [A_2] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),bot_bo784226126e_bool)) ).
fof(fact_286_emptyE,axiom,
! [A_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool)) ).
fof(fact_287_insertE,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),A_1)))
=> ( A_2 != B_1
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) ) ) ).
fof(fact_288_insertE,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),A_1)))
=> ( A_2 != B_1
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)) ) ) ).
fof(fact_289_insertE,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),A_1)))
=> ( A_2 != B_1
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)) ) ) ).
fof(fact_290_insertE,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A_1)))
=> ( A_2 != B_1
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)) ) ) ).
fof(fact_291_insertE,axiom,
! [A_2,B_1,A_1] :
( ( is_pname(A_2)
& is_pname(B_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))
=> ( A_2 != B_1
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)) ) ) ) ).
fof(fact_292_insertCI,axiom,
! [B_1,A_2,B_2] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B_2))
=> A_2 = B_1 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),B_2))) ) ).
fof(fact_293_insertCI,axiom,
! [B_1,A_2,B_2] :
( ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),B_2))
=> A_2 = B_1 )
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),B_2))) ) ).
fof(fact_294_insertCI,axiom,
! [B_1,A_2,B_2] :
( ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),B_2))
=> A_2 = B_1 )
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),B_2))) ) ).
fof(fact_295_insertCI,axiom,
! [B_1,A_2,B_2] :
( ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),B_2))
=> A_2 = B_1 )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B_2))) ) ).
fof(fact_296_insertCI,axiom,
! [B_1,A_2,B_2] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B_2))
=> A_2 = B_1 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B_2))) ) ).
fof(fact_297_empty__not__insert,axiom,
! [A_2,A_1] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) ).
fof(fact_298_empty__not__insert,axiom,
! [A_2,A_1] : bot_bo332163887l_bool != hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) ).
fof(fact_299_empty__not__insert,axiom,
! [A_2,A_1] : bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) ).
fof(fact_300_empty__not__insert,axiom,
! [A_2,A_1] : bot_bo797238721a_bool != hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) ).
fof(fact_301_empty__not__insert,axiom,
! [A_2,A_1] : bot_bo784226126e_bool != hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) ).
fof(fact_302_insert__not__empty,axiom,
! [A_2,A_1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) != bot_bot_fun_nat_bool ).
fof(fact_303_insert__not__empty,axiom,
! [A_2,A_1] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) != bot_bo332163887l_bool ).
fof(fact_304_insert__not__empty,axiom,
! [A_2,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) != bot_bo844097828e_bool ).
fof(fact_305_insert__not__empty,axiom,
! [A_2,A_1] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) != bot_bo797238721a_bool ).
fof(fact_306_insert__not__empty,axiom,
! [A_2,A_1] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) != bot_bo784226126e_bool ).
fof(fact_307_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),bot_bot_fun_nat_bool)) ) ).
fof(fact_308_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_f1695230391l_bool(bot_bo332163887l_bool,X))
<=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),bot_bo332163887l_bool)) ) ).
fof(fact_309_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X))
<=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),bot_bo797238721a_bool)) ) ).
fof(fact_310_bot__empty__eq,axiom,
! [X] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),bot_bo784226126e_bool)) ) ).
fof(fact_311_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_312_empty__def,axiom,
bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,hAPP_b76515610e_bool(cOMBK_bool_pname,fFalse)) ).
fof(fact_313_empty__def,axiom,
bot_bo797238721a_bool = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_b1882817719a_bool(cOMBK_235286536iple_a,fFalse)) ).
fof(fact_314_empty__def,axiom,
bot_bo332163887l_bool = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_b83765433l_bool(cOMBK_404565488a_bool,fFalse)) ).
fof(fact_315_empty__def,axiom,
bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,hAPP_b974863576e_bool(cOMBK_988866959_state,fFalse)) ).
fof(fact_316_empty__def,axiom,
bot_bot_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fFalse)) ).
fof(fact_317_insertI1,axiom,
! [A_2,B_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2))) ).
fof(fact_318_insertI1,axiom,
! [A_2,B_2] : hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2))) ).
fof(fact_319_insertI1,axiom,
! [A_2,B_2] : hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2))) ).
fof(fact_320_insertI1,axiom,
! [A_2,B_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2))) ).
fof(fact_321_insertI1,axiom,
! [A_2,B_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2))) ).
fof(fact_322_all__not__in__conv,axiom,
! [A_1] :
( ! [X] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
<=> A_1 = bot_bot_fun_nat_bool ) ).
fof(fact_323_all__not__in__conv,axiom,
! [A_1] :
( ! [X] : ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))
<=> A_1 = bot_bo332163887l_bool ) ).
fof(fact_324_all__not__in__conv,axiom,
! [A_1] :
( ! [X] : ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))
<=> A_1 = bot_bo797238721a_bool ) ).
fof(fact_325_all__not__in__conv,axiom,
! [A_1] :
( ! [X] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1))
<=> A_1 = bot_bo784226126e_bool ) ).
fof(fact_326_all__not__in__conv,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( ! [X] :
( is_pname(X)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) )
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_327_singleton__conv2,axiom,
! [A_2] : hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(fequal874423448a_bool,A_2)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool) ).
fof(fact_328_singleton__conv2,axiom,
! [A_2] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool) ).
fof(fact_329_singleton__conv2,axiom,
! [A_2] : hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(fequal963300192iple_a,A_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool) ).
fof(fact_330_singleton__conv2,axiom,
! [A_2] : hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(fequal1440809015_state,A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool) ).
fof(fact_331_singleton__conv2,axiom,
! [A_2] : hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(fequal_nat,A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) ).
fof(fact_332_ex__in__conv,axiom,
! [A_1] :
( ? [X] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
<=> A_1 != bot_bot_fun_nat_bool ) ).
fof(fact_333_ex__in__conv,axiom,
! [A_1] :
( ? [X] : hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))
<=> A_1 != bot_bo332163887l_bool ) ).
fof(fact_334_ex__in__conv,axiom,
! [A_1] :
( ? [X] : hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))
<=> A_1 != bot_bo797238721a_bool ) ).
fof(fact_335_ex__in__conv,axiom,
! [A_1] :
( ? [X] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),A_1))
<=> A_1 != bot_bo784226126e_bool ) ).
fof(fact_336_ex__in__conv,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1)) )
<=> A_1 != bot_bo844097828e_bool ) ) ).
fof(fact_337_singleton__conv,axiom,
! [A_2] : hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool) ).
fof(fact_338_singleton__conv,axiom,
! [A_2] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool) ).
fof(fact_339_singleton__conv,axiom,
! [A_2] : hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool) ).
fof(fact_340_singleton__conv,axiom,
! [A_2] : hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool) ).
fof(fact_341_singleton__conv,axiom,
! [A_2] : hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) ).
fof(fact_342_Collect__conv__if2,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_f1695230391l_bool(Pa,A_2))
=> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(fequal874423448a_bool,A_2))),Pa)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool) )
& ( ~ hBOOL(hAPP_f1695230391l_bool(Pa,A_2))
=> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(fequal874423448a_bool,A_2))),Pa)) = bot_bo332163887l_bool ) ) ).
fof(fact_343_Collect__conv__if2,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_pname_bool(Pa,A_2))
=> 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_2))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(Pa,A_2))
=> 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_2))),Pa)) = bot_bo844097828e_bool ) ) ).
fof(fact_344_Collect__conv__if2,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_H1037229737a_bool(Pa,A_2))
=> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(fequal963300192iple_a,A_2))),Pa)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool) )
& ( ~ hBOOL(hAPP_H1037229737a_bool(Pa,A_2))
=> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(fequal963300192iple_a,A_2))),Pa)) = bot_bo797238721a_bool ) ) ).
fof(fact_345_Collect__conv__if2,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_H242767318e_bool(Pa,A_2))
=> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(fequal1440809015_state,A_2))),Pa)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool) )
& ( ~ hBOOL(hAPP_H242767318e_bool(Pa,A_2))
=> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(fequal1440809015_state,A_2))),Pa)) = bot_bo784226126e_bool ) ) ).
fof(fact_346_Collect__conv__if2,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_nat_bool(Pa,A_2))
=> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(fequal_nat,A_2))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) )
& ( ~ hBOOL(hAPP_nat_bool(Pa,A_2))
=> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(fequal_nat,A_2))),Pa)) = bot_bot_fun_nat_bool ) ) ).
fof(fact_347_Collect__conv__if,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_f1695230391l_bool(Pa,A_2))
=> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),Pa)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool) )
& ( ~ hBOOL(hAPP_f1695230391l_bool(Pa,A_2))
=> hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),Pa)) = bot_bo332163887l_bool ) ) ).
fof(fact_348_Collect__conv__if,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_pname_bool(Pa,A_2))
=> 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_2))),Pa)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(Pa,A_2))
=> 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_2))),Pa)) = bot_bo844097828e_bool ) ) ).
fof(fact_349_Collect__conv__if,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_H1037229737a_bool(Pa,A_2))
=> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),Pa)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool) )
& ( ~ hBOOL(hAPP_H1037229737a_bool(Pa,A_2))
=> hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),Pa)) = bot_bo797238721a_bool ) ) ).
fof(fact_350_Collect__conv__if,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_H242767318e_bool(Pa,A_2))
=> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),Pa)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool) )
& ( ~ hBOOL(hAPP_H242767318e_bool(Pa,A_2))
=> hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),Pa)) = bot_bo784226126e_bool ) ) ).
fof(fact_351_Collect__conv__if,axiom,
! [Pa,A_2] :
( ( hBOOL(hAPP_nat_bool(Pa,A_2))
=> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) )
& ( ~ hBOOL(hAPP_nat_bool(Pa,A_2))
=> hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),Pa)) = bot_bot_fun_nat_bool ) ) ).
fof(fact_352_mem__def,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
<=> hBOOL(hAPP_nat_bool(A_1,X_2)) ) ).
fof(fact_353_mem__def,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
<=> hBOOL(hAPP_f1695230391l_bool(A_1,X_2)) ) ).
fof(fact_354_mem__def,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
<=> hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) ) ).
fof(fact_355_mem__def,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
<=> hBOOL(hAPP_pname_bool(A_1,X_2)) ) ).
fof(fact_356_Collect__def,axiom,
! [Pa] :
( is_fun_pname_bool(Pa)
=> hAPP_f759274231e_bool(collect_pname,Pa) = Pa ) ).
fof(fact_357_Collect__def,axiom,
! [Pa] : hAPP_f20753329a_bool(collec351493750iple_a,Pa) = Pa ).
fof(fact_358_Collect__def,axiom,
! [Pa] : hAPP_f800510211t_bool(collect_nat,Pa) = Pa ).
fof(fact_359_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_360_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo797238721a_bool = hAPP_f20753329a_bool(collec351493750iple_a,Pa)
<=> ! [X] : ~ hBOOL(hAPP_H1037229737a_bool(Pa,X)) ) ).
fof(fact_361_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo332163887l_bool = hAPP_f396832789l_bool(collec999179778a_bool,Pa)
<=> ! [X] : ~ hBOOL(hAPP_f1695230391l_bool(Pa,X)) ) ).
fof(fact_362_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,Pa)
<=> ! [X] : ~ hBOOL(hAPP_H242767318e_bool(Pa,X)) ) ).
fof(fact_363_empty__Collect__eq,axiom,
! [Pa] :
( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,Pa)
<=> ! [X] : ~ hBOOL(hAPP_nat_bool(Pa,X)) ) ).
fof(fact_364_empty__iff,axiom,
! [C_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),bot_bot_fun_nat_bool)) ).
fof(fact_365_empty__iff,axiom,
! [C_2] : ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),bot_bo332163887l_bool)) ).
fof(fact_366_empty__iff,axiom,
! [C_2] : ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),bot_bo797238721a_bool)) ).
fof(fact_367_empty__iff,axiom,
! [C_2] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C_2),bot_bo784226126e_bool)) ).
fof(fact_368_empty__iff,axiom,
! [C_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),bot_bo844097828e_bool)) ).
fof(fact_369_insert__compr,axiom,
! [A_2,B_2] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2))) ).
fof(fact_370_insert__compr,axiom,
! [A_2,B_2] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2))) ).
fof(fact_371_insert__compr,axiom,
! [A_2,B_2] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B_2))) ).
fof(fact_372_insert__compr,axiom,
! [A_2,B_2] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2))) ).
fof(fact_373_insert__compr,axiom,
! [A_2,B_2] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2) = 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_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2))) ).
fof(fact_374_insert__Collect,axiom,
! [A_2,Pa] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(collec999179778a_bool,Pa)) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fimplies),hAPP_f396832789l_bool(cOMBB_193631803a_bool(fNot),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2)))),Pa)) ).
fof(fact_375_insert__Collect,axiom,
! [A_2,Pa] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),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_2)))),Pa)) ).
fof(fact_376_insert__Collect,axiom,
! [A_2,Pa] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(collec351493750iple_a,Pa)) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fimplies),hAPP_f20753329a_bool(cOMBB_1882975613iple_a(fNot),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2)))),Pa)) ).
fof(fact_377_insert__Collect,axiom,
! [A_2,Pa] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(collec637225377_state,Pa)) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fimplies),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2)))),Pa)) ).
fof(fact_378_insert__Collect,axiom,
! [A_2,Pa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(collect_nat,Pa)) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fimplies),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2)))),Pa)) ).
fof(fact_379_singleton__iff,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)))
<=> B_1 = A_2 ) ).
fof(fact_380_singleton__iff,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)))
<=> B_1 = A_2 ) ).
fof(fact_381_singleton__iff,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)))
<=> B_1 = A_2 ) ).
fof(fact_382_singleton__iff,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)))
<=> B_1 = A_2 ) ).
fof(fact_383_singleton__iff,axiom,
! [B_1,A_2] :
( ( is_pname(B_1)
& is_pname(A_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))
<=> B_1 = A_2 ) ) ).
fof(fact_384_insert__absorb2,axiom,
! [X_2,A_1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1) ).
fof(fact_385_insert__absorb2,axiom,
! [X_2,A_1] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1) ).
fof(fact_386_insert__absorb2,axiom,
! [X_2,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1) ).
fof(fact_387_insert__absorb2,axiom,
! [X_2,A_1] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1) ).
fof(fact_388_insert__absorb2,axiom,
! [X_2,A_1] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1) ).
fof(fact_389_insert__commute,axiom,
! [X_2,Y_1,A_1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) ).
fof(fact_390_insert__commute,axiom,
! [X_2,Y_1,A_1] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_1),A_1)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) ).
fof(fact_391_insert__commute,axiom,
! [X_2,Y_1,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) ).
fof(fact_392_insert__commute,axiom,
! [X_2,Y_1,A_1] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),A_1)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) ).
fof(fact_393_insert__commute,axiom,
! [X_2,Y_1,A_1] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) ).
fof(fact_394_insert__iff,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),A_1)))
<=> ( A_2 = B_1
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) ) ) ).
fof(fact_395_insert__iff,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),A_1)))
<=> ( A_2 = B_1
| hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)) ) ) ).
fof(fact_396_insert__iff,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),A_1)))
<=> ( A_2 = B_1
| hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)) ) ) ).
fof(fact_397_insert__iff,axiom,
! [A_2,B_1,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A_1)))
<=> ( A_2 = B_1
| hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)) ) ) ).
fof(fact_398_insert__iff,axiom,
! [A_2,B_1,A_1] :
( ( is_pname(A_2)
& is_pname(B_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))
<=> ( A_2 = B_1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)) ) ) ) ).
fof(fact_399_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_400_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f20753329a_bool(collec351493750iple_a,Pa) = bot_bo797238721a_bool
<=> ! [X] : ~ hBOOL(hAPP_H1037229737a_bool(Pa,X)) ) ).
fof(fact_401_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f396832789l_bool(collec999179778a_bool,Pa) = bot_bo332163887l_bool
<=> ! [X] : ~ hBOOL(hAPP_f1695230391l_bool(Pa,X)) ) ).
fof(fact_402_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f806699093e_bool(collec637225377_state,Pa) = bot_bo784226126e_bool
<=> ! [X] : ~ hBOOL(hAPP_H242767318e_bool(Pa,X)) ) ).
fof(fact_403_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f800510211t_bool(collect_nat,Pa) = bot_bot_fun_nat_bool
<=> ! [X] : ~ hBOOL(hAPP_nat_bool(Pa,X)) ) ).
fof(fact_404_doubleton__eq__iff,axiom,
! [A_2,B_1,C_2,D] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D),bot_bot_fun_nat_bool))
<=> ( ( A_2 = C_2
& B_1 = D )
| ( A_2 = D
& B_1 = C_2 ) ) ) ).
fof(fact_405_doubleton__eq__iff,axiom,
! [A_2,B_1,C_2,D] :
( hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),bot_bo332163887l_bool)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,D),bot_bo332163887l_bool))
<=> ( ( A_2 = C_2
& B_1 = D )
| ( A_2 = D
& B_1 = C_2 ) ) ) ).
fof(fact_406_doubleton__eq__iff,axiom,
! [A_2,B_1,C_2,D] :
( ( is_pname(A_2)
& is_pname(B_1)
& is_pname(C_2)
& is_pname(D) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool))
<=> ( ( A_2 = C_2
& B_1 = D )
| ( A_2 = D
& B_1 = C_2 ) ) ) ) ).
fof(fact_407_doubleton__eq__iff,axiom,
! [A_2,B_1,C_2,D] :
( hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),bot_bo797238721a_bool)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,C_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,D),bot_bo797238721a_bool))
<=> ( ( A_2 = C_2
& B_1 = D )
| ( A_2 = D
& B_1 = C_2 ) ) ) ).
fof(fact_408_doubleton__eq__iff,axiom,
! [A_2,B_1,C_2,D] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,D),bot_bo784226126e_bool))
<=> ( ( A_2 = C_2
& B_1 = D )
| ( A_2 = D
& B_1 = C_2 ) ) ) ).
fof(fact_409_insert__code,axiom,
! [Y_1,A_1,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_1),A_1),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_nat_bool(A_1,X_2)) ) ) ).
fof(fact_410_insert__code,axiom,
! [Y_1,A_1,X_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_1),A_1),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_f1695230391l_bool(A_1,X_2)) ) ) ).
fof(fact_411_insert__code,axiom,
! [Y_1,A_1,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_1),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_pname_bool(A_1,X_2)) ) ) ) ).
fof(fact_412_insert__code,axiom,
! [Y_1,A_1,X_2] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_1),A_1),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_H1037229737a_bool(A_1,X_2)) ) ) ).
fof(fact_413_insert__code,axiom,
! [Y_1,A_1,X_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_1),A_1),X_2))
<=> ( Y_1 = X_2
| hBOOL(hAPP_H242767318e_bool(A_1,X_2)) ) ) ).
fof(fact_414_insert__ident,axiom,
! [B_2,X_2,A_1] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_2))
=> ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_2)
<=> A_1 = B_2 ) ) ) ).
fof(fact_415_insert__ident,axiom,
! [B_2,X_2,A_1] :
( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),B_2))
=> ( hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),B_2)
<=> A_1 = B_2 ) ) ) ).
fof(fact_416_insert__ident,axiom,
! [B_2,X_2,A_1] :
( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B_2))
=> ( hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),B_2)
<=> A_1 = B_2 ) ) ) ).
fof(fact_417_insert__ident,axiom,
! [B_2,X_2,A_1] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_2))
=> ( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_2)
<=> A_1 = B_2 ) ) ) ).
fof(fact_418_insert__ident,axiom,
! [B_2,X_2,A_1] :
( ( is_fun_pname_bool(B_2)
& is_fun_pname_bool(A_1) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2))
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2)
<=> A_1 = B_2 ) ) ) ) ).
fof(fact_419_equals0D,axiom,
! [A_2,A_1] :
( A_1 = bot_bot_fun_nat_bool
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1)) ) ).
fof(fact_420_equals0D,axiom,
! [A_2,A_1] :
( A_1 = bot_bo332163887l_bool
=> ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1)) ) ).
fof(fact_421_equals0D,axiom,
! [A_2,A_1] :
( A_1 = bot_bo797238721a_bool
=> ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1)) ) ).
fof(fact_422_equals0D,axiom,
! [A_2,A_1] :
( A_1 = bot_bo784226126e_bool
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1)) ) ).
fof(fact_423_equals0D,axiom,
! [A_2,A_1] :
( A_1 = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1)) ) ).
fof(fact_424_insertI2,axiom,
! [B_1,A_2,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),B_2))) ) ).
fof(fact_425_insertI2,axiom,
! [B_1,A_2,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),B_2))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),B_2))) ) ).
fof(fact_426_insertI2,axiom,
! [B_1,A_2,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),B_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),B_2))) ) ).
fof(fact_427_insertI2,axiom,
! [B_1,A_2,B_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),B_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B_2))) ) ).
fof(fact_428_insertI2,axiom,
! [B_1,A_2,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B_2))) ) ).
fof(fact_429_insert__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) = A_1 ) ).
fof(fact_430_insert__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1))
=> hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) = A_1 ) ).
fof(fact_431_insert__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1))
=> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) = A_1 ) ).
fof(fact_432_insert__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) = A_1 ) ).
fof(fact_433_insert__absorb,axiom,
! [A_2,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) = A_1 ) ) ).
fof(fact_434_singletonE,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)))
=> B_1 = A_2 ) ).
fof(fact_435_singletonE,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,B_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)))
=> B_1 = A_2 ) ).
fof(fact_436_singletonE,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,B_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)))
=> B_1 = A_2 ) ).
fof(fact_437_singletonE,axiom,
! [B_1,A_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)))
=> B_1 = A_2 ) ).
fof(fact_438_singletonE,axiom,
! [B_1,A_2] :
( ( is_pname(B_1)
& is_pname(A_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))
=> B_1 = A_2 ) ) ).
fof(fact_439_singleton__inject,axiom,
! [A_2,B_1] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_1),bot_bot_fun_nat_bool)
=> A_2 = B_1 ) ).
fof(fact_440_singleton__inject,axiom,
! [A_2,B_1] :
( hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,B_1),bot_bo332163887l_bool)
=> A_2 = B_1 ) ).
fof(fact_441_singleton__inject,axiom,
! [A_2,B_1] :
( ( is_pname(A_2)
& is_pname(B_1) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)
=> A_2 = B_1 ) ) ).
fof(fact_442_singleton__inject,axiom,
! [A_2,B_1] :
( hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,B_1),bot_bo797238721a_bool)
=> A_2 = B_1 ) ).
fof(fact_443_singleton__inject,axiom,
! [A_2,B_1] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)
=> A_2 = B_1 ) ).
fof(fact_444_com__det,axiom,
! [U_1,C,S,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),T))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),U_1))
=> U_1 = T ) ) ).
fof(fact_445_insert__is__Un,axiom,
! [A_2,A_1] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)),A_1) ).
fof(fact_446_insert__is__Un,axiom,
! [A_2,A_1] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),bot_bo332163887l_bool)),A_1) ).
fof(fact_447_insert__is__Un,axiom,
! [A_2,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)),A_1) ).
fof(fact_448_insert__is__Un,axiom,
! [A_2,A_1] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)),A_1) ).
fof(fact_449_insert__is__Un,axiom,
! [A_2,A_1] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),bot_bo797238721a_bool)),A_1) ).
fof(fact_450_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),Xa) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),X))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),Xa))) ).
fof(fact_451_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),Xa) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),X))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),Xa))) ).
fof(fact_452_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),Xa) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),X))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),Xa))) ).
fof(fact_453_insert__compr__raw,axiom,
! [X,Xa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),Xa) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),X))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),Xa))) ).
fof(fact_454_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_455_derivs__insertD,axiom,
! [Ga,T_1,Ts] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),Ts)))
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),bot_bo797238721a_bool)))
& hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts)) ) ) ).
fof(fact_456_derivs__insertD,axiom,
! [Ga,T_1,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool)))
& hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),Ts)) ) ) ).
fof(fact_457_hoare__derivs_Oinsert,axiom,
! [Ts,Ga,T_1] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),bot_bo797238721a_bool)))
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),Ts))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,T_1),Ts))) ) ) ).
fof(fact_458_hoare__derivs_Oinsert,axiom,
! [Ts,Ga,T_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),Ts))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T_1),Ts))) ) ) ).
fof(fact_459_image__constant__conv,axiom,
! [C_2,A_1] :
( ( A_1 = bot_bot_fun_nat_bool
=> hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,C_2)),A_1) = bot_bot_fun_nat_bool )
& ( A_1 != bot_bot_fun_nat_bool
=> hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,C_2)),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),bot_bot_fun_nat_bool) ) ) ).
fof(fact_460_image__constant__conv,axiom,
! [C_2,A_1] :
( is_fun_pname_bool(A_1)
=> ( ( A_1 = bot_bo844097828e_bool
=> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C_2)),A_1) = bot_bo784226126e_bool )
& ( A_1 != bot_bo844097828e_bool
=> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C_2)),A_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C_2),bot_bo784226126e_bool) ) ) ) ).
fof(fact_461_image__constant__conv,axiom,
! [C_2,A_1] :
( is_fun_pname_bool(A_1)
=> ( ( A_1 = bot_bo844097828e_bool
=> hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,C_2)),A_1) = bot_bo797238721a_bool )
& ( A_1 != bot_bo844097828e_bool
=> hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,C_2)),A_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,C_2),bot_bo797238721a_bool) ) ) ) ).
fof(fact_462_image__constant,axiom,
! [C_2,X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,C_2)),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),bot_bot_fun_nat_bool) ) ).
fof(fact_463_image__constant,axiom,
! [C_2,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C_2)),A_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C_2),bot_bo784226126e_bool) ) ).
fof(fact_464_image__constant,axiom,
! [C_2,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f1066163005t_bool(image_pname_nat(hAPP_n362732366me_nat(cOMBK_nat_pname,C_2)),A_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_2),bot_bot_fun_nat_bool) ) ).
fof(fact_465_image__constant,axiom,
! [C_2,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f290545180l_bool(image_2016317142a_bool(hAPP_f624861966a_bool(cOMBK_1667642481_pname,C_2)),A_1) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,C_2),bot_bo332163887l_bool) ) ).
fof(fact_466_image__constant,axiom,
! [C_2,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C_2)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C_2),bot_bo844097828e_bool) ) ).
fof(fact_467_image__constant,axiom,
! [C_2,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,C_2)),A_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,C_2),bot_bo797238721a_bool) ) ).
fof(fact_468_image__insert,axiom,
! [F,A_2,B_2] : hAPP_f800510211t_bool(image_nat_nat(F),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_nat_nat(F,A_2)),hAPP_f800510211t_bool(image_nat_nat(F),B_2)) ).
fof(fact_469_image__insert,axiom,
! [F,A_2,B_2] : hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,A_2)),hAPP_f360545851e_bool(image_185131637_state(F),B_2)) ).
fof(fact_470_image__insert,axiom,
! [F,A_2,B_2] : hAPP_f2034373396a_bool(image_1738210978iple_a(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_p346744818iple_a(F,A_2)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),B_2)) ).
fof(fact_471_insert__image,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_nat_nat(F,X_2)),hAPP_f800510211t_bool(image_nat_nat(F),A_1)) = hAPP_f800510211t_bool(image_nat_nat(F),A_1) ) ).
fof(fact_472_insert__image,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,X_2)),hAPP_f360545851e_bool(image_185131637_state(F),A_1)) = hAPP_f360545851e_bool(image_185131637_state(F),A_1) ) ).
fof(fact_473_insert__image,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,hAPP_pname_nat(F,X_2)),hAPP_f1066163005t_bool(image_pname_nat(F),A_1)) = hAPP_f1066163005t_bool(image_pname_nat(F),A_1) ) ).
fof(fact_474_insert__image,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,hAPP_p1743421830a_bool(F,X_2)),hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1)) = hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1) ) ).
fof(fact_475_insert__image,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F,X_2)),hAPP_f759274231e_bool(image_pname_pname(F),A_1)) = hAPP_f759274231e_bool(image_pname_pname(F),A_1) ) ).
fof(fact_476_insert__image,axiom,
! [F,X_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_p346744818iple_a(F,X_2)),hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)) = hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1) ) ).
fof(fact_477_Un__insert__right,axiom,
! [A_1,A_2,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) ).
fof(fact_478_Un__insert__right,axiom,
! [A_1,A_2,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2)) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) ).
fof(fact_479_Un__insert__right,axiom,
! [A_1,A_2,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) ).
fof(fact_480_Un__insert__right,axiom,
! [A_1,A_2,B_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) ).
fof(fact_481_Un__insert__right,axiom,
! [A_1,A_2,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2)) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) ).
fof(fact_482_Un__insert__left,axiom,
! [A_2,B_2,C_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2)),C_1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1)) ).
fof(fact_483_Un__insert__left,axiom,
! [A_2,B_2,C_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2)),C_1) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1)) ).
fof(fact_484_Un__insert__left,axiom,
! [A_2,B_2,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1)) ).
fof(fact_485_Un__insert__left,axiom,
! [A_2,B_2,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1)) ).
fof(fact_486_Un__insert__left,axiom,
! [A_2,B_2,C_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2)),C_1) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1)) ).
fof(fact_487_empty__is__image,axiom,
! [F,A_1] :
( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(image_nat_nat(F),A_1)
<=> A_1 = bot_bot_fun_nat_bool ) ).
fof(fact_488_empty__is__image,axiom,
! [F,A_1] :
( is_fun_pname_bool(A_1)
=> ( bot_bo784226126e_bool = hAPP_f360545851e_bool(image_185131637_state(F),A_1)
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_489_empty__is__image,axiom,
! [F,A_1] :
( is_fun_pname_bool(A_1)
=> ( bot_bo797238721a_bool = hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_490_image__empty,axiom,
! [F] : hAPP_f800510211t_bool(image_nat_nat(F),bot_bot_fun_nat_bool) = bot_bot_fun_nat_bool ).
fof(fact_491_image__empty,axiom,
! [F] : hAPP_f360545851e_bool(image_185131637_state(F),bot_bo844097828e_bool) = bot_bo784226126e_bool ).
fof(fact_492_image__empty,axiom,
! [F] : hAPP_f2034373396a_bool(image_1738210978iple_a(F),bot_bo844097828e_bool) = bot_bo797238721a_bool ).
fof(fact_493_image__is__empty,axiom,
! [F,A_1] :
( hAPP_f800510211t_bool(image_nat_nat(F),A_1) = bot_bot_fun_nat_bool
<=> A_1 = bot_bot_fun_nat_bool ) ).
fof(fact_494_image__is__empty,axiom,
! [F,A_1] :
( is_fun_pname_bool(A_1)
=> ( hAPP_f360545851e_bool(image_185131637_state(F),A_1) = bot_bo784226126e_bool
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_495_image__is__empty,axiom,
! [F,A_1] :
( is_fun_pname_bool(A_1)
=> ( hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1) = bot_bo797238721a_bool
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_496_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),bot_bot_fun_nat_bool))
=> hBOOL(hAPP_nat_bool(Pa,X)) ) ).
fof(fact_497_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),bot_bo797238721a_bool))
=> hBOOL(hAPP_H1037229737a_bool(Pa,X)) ) ).
fof(fact_498_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),bot_bo332163887l_bool))
=> hBOOL(hAPP_f1695230391l_bool(Pa,X)) ) ).
fof(fact_499_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_500_ball__empty,axiom,
! [Pa,X] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),bot_bo784226126e_bool))
=> hBOOL(hAPP_H242767318e_bool(Pa,X)) ) ).
fof(fact_501_Un__empty__left,axiom,
! [B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,bot_bot_fun_nat_bool),B_2) = B_2 ).
fof(fact_502_Un__empty__left,axiom,
! [B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,bot_bo332163887l_bool),B_2) = B_2 ).
fof(fact_503_Un__empty__left,axiom,
! [B_2] :
( is_fun_pname_bool(B_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B_2) = B_2 ) ).
fof(fact_504_Un__empty__left,axiom,
! [B_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),B_2) = B_2 ).
fof(fact_505_Un__empty__left,axiom,
! [B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,bot_bo797238721a_bool),B_2) = B_2 ).
fof(fact_506_Un__empty__right,axiom,
! [A_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),bot_bot_fun_nat_bool) = A_1 ).
fof(fact_507_Un__empty__right,axiom,
! [A_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),bot_bo332163887l_bool) = A_1 ).
fof(fact_508_Un__empty__right,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),bot_bo844097828e_bool) = A_1 ) ).
fof(fact_509_Un__empty__right,axiom,
! [A_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),bot_bo784226126e_bool) = A_1 ).
fof(fact_510_Un__empty__right,axiom,
! [A_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),bot_bo797238721a_bool) = A_1 ).
fof(fact_511_Un__empty,axiom,
! [A_1,B_2] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2) = bot_bot_fun_nat_bool
<=> ( A_1 = bot_bot_fun_nat_bool
& B_2 = bot_bot_fun_nat_bool ) ) ).
fof(fact_512_Un__empty,axiom,
! [A_1,B_2] :
( hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2) = bot_bo332163887l_bool
<=> ( A_1 = bot_bo332163887l_bool
& B_2 = bot_bo332163887l_bool ) ) ).
fof(fact_513_Un__empty,axiom,
! [A_1,B_2] :
( ( is_fun_pname_bool(A_1)
& is_fun_pname_bool(B_2) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2) = bot_bo844097828e_bool
<=> ( A_1 = bot_bo844097828e_bool
& B_2 = bot_bo844097828e_bool ) ) ) ).
fof(fact_514_Un__empty,axiom,
! [A_1,B_2] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2) = bot_bo784226126e_bool
<=> ( A_1 = bot_bo784226126e_bool
& B_2 = bot_bo784226126e_bool ) ) ).
fof(fact_515_Un__empty,axiom,
! [A_1,B_2] :
( hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2) = bot_bo797238721a_bool
<=> ( A_1 = bot_bo797238721a_bool
& B_2 = bot_bo797238721a_bool ) ) ).
fof(fact_516_constant,axiom,
! [Ga,Pa,C_2,Qa,C_1] :
( ( hBOOL(C_1)
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))) )
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_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_2),Qa)),bot_bo797238721a_bool))) ) ).
fof(fact_517_constant,axiom,
! [Ga,Pa,C_2,Qa,C_1] :
( ( hBOOL(C_1)
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_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_2),Qa)),bot_bo784226126e_bool))) ) ).
fof(fact_518_empty,axiom,
! [Ga] : hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),bot_bo797238721a_bool)) ).
fof(fact_519_empty,axiom,
! [Ga] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),bot_bo784226126e_bool)) ).
fof(fact_520_sup__bot__left,axiom,
! [X_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,bot_bot_fun_nat_bool),X_2) = X_2 ).
fof(fact_521_sup__bot__left,axiom,
! [X_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,bot_bo332163887l_bool),X_2) = X_2 ).
fof(fact_522_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_523_sup__bot__left,axiom,
! [X_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),X_2) = X_2 ).
fof(fact_524_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_525_sup__bot__left,axiom,
! [X_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,bot_bo797238721a_bool),X_2) = X_2 ).
fof(fact_526_sup__bot__right,axiom,
! [X_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),bot_bot_fun_nat_bool) = X_2 ).
fof(fact_527_sup__bot__right,axiom,
! [X_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),bot_bo332163887l_bool) = X_2 ).
fof(fact_528_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_529_sup__bot__right,axiom,
! [X_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),bot_bo784226126e_bool) = X_2 ).
fof(fact_530_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_531_sup__bot__right,axiom,
! [X_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),bot_bo797238721a_bool) = X_2 ).
fof(fact_532_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),Y_1) = bot_bot_fun_nat_bool
<=> ( X_2 = bot_bot_fun_nat_bool
& Y_1 = bot_bot_fun_nat_bool ) ) ).
fof(fact_533_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),Y_1) = bot_bo332163887l_bool
<=> ( X_2 = bot_bo332163887l_bool
& Y_1 = bot_bo332163887l_bool ) ) ).
fof(fact_534_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_535_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_1) = bot_bo784226126e_bool
<=> ( X_2 = bot_bo784226126e_bool
& Y_1 = bot_bo784226126e_bool ) ) ).
fof(fact_536_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_537_sup__eq__bot__iff,axiom,
! [X_2,Y_1] :
( hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),Y_1) = bot_bo797238721a_bool
<=> ( X_2 = bot_bo797238721a_bool
& Y_1 = bot_bo797238721a_bool ) ) ).
fof(fact_538_triple__valid__Suc,axiom,
! [N_4,T_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,hAPP_nat_nat(suc,N_4)),T_2))
=> hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_4),T_2)) ) ).
fof(fact_539_triple__valid__Suc,axiom,
! [N_4,T_2] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,hAPP_nat_nat(suc,N_4)),T_2))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_4),T_2)) ) ).
fof(fact_540_insert__def,axiom,
! [A_2,B_2] : hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_2) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,fequal874423448a_bool),A_2))),B_2) ).
fof(fact_541_insert__def,axiom,
! [A_2,B_2] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_2) = 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_2))),B_2) ).
fof(fact_542_insert__def,axiom,
! [A_2,B_2] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_2))),B_2) ).
fof(fact_543_insert__def,axiom,
! [A_2,B_2] : hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,fequal963300192iple_a),A_2))),B_2) ).
fof(fact_544_insert__def,axiom,
! [A_2,B_2] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,fequal_nat),A_2))),B_2) ).
fof(fact_545_weak__Body,axiom,
! [Ga,Pa,Pn_1,Qa] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo797238721a_bool))) ) ).
fof(fact_546_weak__Body,axiom,
! [Ga,Pa,Pn_1,Qa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo784226126e_bool))) ) ).
fof(fact_547_BodyN,axiom,
! [Pa,Pn_1,Qa,Ga] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo797238721a_bool))) ) ).
fof(fact_548_BodyN,axiom,
! [Pa,Pn_1,Qa,Ga] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),Ga)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),hAPP_pname_com(body,Pn_1)),Qa)),bot_bo784226126e_bool))) ) ).
fof(fact_549_escape,axiom,
! [Ga,C_2,Qa,Pa] :
( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C_2),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(Qa,Z_4)))),bot_bo797238721a_bool))) )
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))) ) ).
fof(fact_550_escape,axiom,
! [Ga,C_2,Qa,Pa] :
( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C_2),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Qa,Z_4)))),bot_bo784226126e_bool))) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))) ) ).
fof(fact_551_conseq1,axiom,
! [Pa,Ga,P_1,C_2,Qa] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,P_1),C_2),Qa)),bot_bo797238721a_bool)))
=> ( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_4),S_3)) )
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))) ) ) ).
fof(fact_552_conseq1,axiom,
! [Pa,Ga,P_1,C_2,Qa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C_2),Qa)),bot_bo784226126e_bool)))
=> ( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_4),S_3)) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))) ) ) ).
fof(fact_553_conseq2,axiom,
! [Qa,Ga,Pa,C_2,Q_1] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Q_1)),bot_bo797238721a_bool)))
=> ( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_4),S_3))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_4),S_3)) )
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))) ) ) ).
fof(fact_554_conseq2,axiom,
! [Qa,Ga,Pa,C_2,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Q_1)),bot_bo784226126e_bool)))
=> ( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_4),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_4),S_3)) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))) ) ) ).
fof(fact_555_triple_Osize_I1_J,axiom,
! [Fa,Fun1,Com_1,Fun2] : hAPP_H592031934_a_nat(hoare_571935964size_a(Fa),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1),Com_1),Fun2)) = zero_zero_nat ).
fof(fact_556_triple_Osize_I1_J,axiom,
! [Fa,Fun1,Com_1,Fun2] : hAPP_H175283793te_nat(hoare_163978021_state(Fa),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com_1),Fun2)) = zero_zero_nat ).
fof(fact_557_MGT__def,axiom,
! [C_2] : hoare_Mirabelle_MGT(C_2) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,fequal_state),C_2),evalc(C_2)) ).
fof(fact_558_triple_Osize_I2_J,axiom,
! [Fun1,Com_1,Fun2] : hAPP_H592031934_a_nat(size_s399404919iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Fun1),Com_1),Fun2)) = zero_zero_nat ).
fof(fact_559_triple_Osize_I2_J,axiom,
! [Fun1,Com_1,Fun2] : hAPP_H175283793te_nat(size_s255495008_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com_1),Fun2)) = zero_zero_nat ).
fof(fact_560_conseq12,axiom,
! [Qa,Pa,Ga,P_1,C_2,Q_1] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,P_1),C_2),Q_1)),bot_bo797238721a_bool)))
=> ( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3))
=> ! [S_4] :
( ! [Z_5] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_5),S_3))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_5),S_4)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_4),S_4)) ) )
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool))) ) ) ).
fof(fact_561_conseq12,axiom,
! [Qa,Pa,Ga,P_1,C_2,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C_2),Q_1)),bot_bo784226126e_bool)))
=> ( ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3))
=> ! [S_4] :
( ! [Z_5] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_5),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_5),S_4)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_4),S_4)) ) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool))) ) ) ).
fof(fact_562_the__elem__eq,axiom,
! [X_2] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) = X_2 ).
fof(fact_563_the__elem__eq,axiom,
! [X_2] : hAPP_f258822235a_bool(the_el979963640a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) = X_2 ).
fof(fact_564_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_565_the__elem__eq,axiom,
! [X_2] : hAPP_f1693662087iple_a(the_el1519802624iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) = X_2 ).
fof(fact_566_the__elem__eq,axiom,
! [X_2] : hAPP_f718417177_state(the_el2080696983_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) = X_2 ).
fof(fact_567_Suc__neq__Zero,axiom,
! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).
fof(fact_568_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat ).
fof(fact_569_n__not__Suc__n,axiom,
! [N_2] : N_2 != hAPP_nat_nat(suc,N_2) ).
fof(fact_570_Suc__n__not__n,axiom,
! [N_2] : hAPP_nat_nat(suc,N_2) != N_2 ).
fof(fact_571_nat_Oinject,axiom,
! [Nat_4,Nat_3] :
( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3)
<=> Nat_4 = Nat_3 ) ).
fof(fact_572_Suc__inject,axiom,
! [X_1,Y] :
( hAPP_nat_nat(suc,X_1) = hAPP_nat_nat(suc,Y)
=> X_1 = Y ) ).
fof(fact_573_Zero__not__Suc,axiom,
! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).
fof(fact_574_nat_Osimps_I2_J,axiom,
! [Nat_2] : zero_zero_nat != hAPP_nat_nat(suc,Nat_2) ).
fof(fact_575_Suc__not__Zero,axiom,
! [M_2] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).
fof(fact_576_nat_Osimps_I3_J,axiom,
! [Nat_1] : hAPP_nat_nat(suc,Nat_1) != zero_zero_nat ).
fof(fact_577_Zero__neq__Suc,axiom,
! [M_2] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).
fof(fact_578_not0__implies__Suc,axiom,
! [N_2] :
( N_2 != zero_zero_nat
=> ? [M_1] : N_2 = hAPP_nat_nat(suc,M_1) ) ).
fof(fact_579_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,hAPP_nat_nat(suc,N))) )
=> hBOOL(hAPP_nat_bool(Pa,N_1)) ) ) ).
fof(fact_580_zero__induct,axiom,
! [Pa,K_1] :
( hBOOL(hAPP_nat_bool(Pa,K_1))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N)))
=> hBOOL(hAPP_nat_bool(Pa,N)) )
=> hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).
fof(fact_581_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero_nat
=> ~ ! [Nat] : Y != hAPP_nat_nat(suc,Nat) ) ).
fof(fact_582_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_583_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_584_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_f1695230391l_bool(bot_bo332163887l_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_585_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_586_bot__fun__def,axiom,
! [X] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_587_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_588_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_H1037229737a_bool(bot_bo797238721a_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_589_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f1695230391l_bool(bot_bo332163887l_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_590_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_591_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_592_evaln_OBody,axiom,
! [Pn,S0,N_2,S1_2] :
( hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn)),S0,N_2),S1_2))
=> hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,Pn),S0,hAPP_nat_nat(suc,N_2)),S1_2)) ) ).
fof(fact_593_hoare__derivs_OSkip,axiom,
! [Ga,Pa] : hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),skip),Pa)),bot_bo797238721a_bool))) ).
fof(fact_594_hoare__derivs_OSkip,axiom,
! [Ga,Pa] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),skip),Pa)),bot_bo784226126e_bool))) ).
fof(fact_595_LoopF,axiom,
! [Ga,Pa,B_1,C_2] : hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_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_1))),while(B_1,C_2)),Pa)),bot_bo797238721a_bool))) ).
fof(fact_596_LoopF,axiom,
! [Ga,Pa,B_1,C_2] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_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_1))),while(B_1,C_2)),Pa)),bot_bo784226126e_bool))) ).
fof(fact_597_evaln_OWhileFalse,axiom,
! [C_2,N_1,B_1,S_1] :
( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S_1,N_1),S_1)) ) ).
fof(fact_598_evaln_OWhileTrue,axiom,
! [S2_1,C_2,N_1,S1,B_1,S0_1] :
( hBOOL(hAPP_state_bool(B_1,S0_1))
=> ( hBOOL(hAPP_state_bool(evaln(C_2,S0_1,N_1),S1))
=> ( hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S1,N_1),S2_1))
=> hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S0_1,N_1),S2_1)) ) ) ) ).
fof(fact_599_evalc_OWhileTrue,axiom,
! [S2_1,C_2,S1,B_1,S0_1] :
( hBOOL(hAPP_state_bool(B_1,S0_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S0_1),S1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S1),S2_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S0_1),S2_1)) ) ) ) ).
fof(fact_600_evalc_OWhileFalse,axiom,
! [C_2,B_1,S_1] :
( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S_1),S_1)) ) ).
fof(fact_601_evaln_OSkip,axiom,
! [S,N_2] : hBOOL(hAPP_state_bool(evaln(skip,S,N_2),S)) ).
fof(fact_602_evaln__elim__cases_I1_J,axiom,
! [S,N_2,T] :
( hBOOL(hAPP_state_bool(evaln(skip,S,N_2),T))
=> T = S ) ).
fof(fact_603_evalc__elim__cases_I1_J,axiom,
! [S,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S),T))
=> T = S ) ).
fof(fact_604_evalc_OSkip,axiom,
! [S] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S),S)) ).
fof(fact_605_com_Osimps_I16_J,axiom,
! [Fun,Com] : skip != while(Fun,Com) ).
fof(fact_606_com_Osimps_I17_J,axiom,
! [Fun,Com] : while(Fun,Com) != skip ).
fof(fact_607_com_Osimps_I5_J,axiom,
! [Fun_1,Com_1,Fun,Com] :
( while(Fun_1,Com_1) = while(Fun,Com)
<=> ( Fun_1 = Fun
& Com_1 = Com ) ) ).
fof(fact_608_evaln__Suc,axiom,
! [C,S,N_2,S_5] :
( hBOOL(hAPP_state_bool(evaln(C,S,N_2),S_5))
=> hBOOL(hAPP_state_bool(evaln(C,S,hAPP_nat_nat(suc,N_2)),S_5)) ) ).
fof(fact_609_evaln__evalc,axiom,
! [C,S,N_2,T] :
( hBOOL(hAPP_state_bool(evaln(C,S,N_2),T))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S),T)) ) ).
fof(fact_610_eval__eq,axiom,
! [C_2,S_1,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),T_1))
<=> ? [N] : hBOOL(hAPP_state_bool(evaln(C_2,S_1,N),T_1)) ) ).
fof(fact_611_com_Osimps_I59_J,axiom,
! [Pname,Fun_1,Com_1] : hAPP_pname_com(body,Pname) != while(Fun_1,Com_1) ).
fof(fact_612_com_Osimps_I58_J,axiom,
! [Fun_1,Com_1,Pname] : while(Fun_1,Com_1) != hAPP_pname_com(body,Pname) ).
fof(fact_613_com_Osimps_I18_J,axiom,
! [Pname_2] : skip != hAPP_pname_com(body,Pname_2) ).
fof(fact_614_com_Osimps_I19_J,axiom,
! [Pname_2] : hAPP_pname_com(body,Pname_2) != skip ).
fof(fact_615_triple__valid__def2,axiom,
! [N_1,Pa,C_2,Qa] :
( hBOOL(hAPP_H242767318e_bool(hAPP_n1497837059e_bool(hoare_446535894_state,N_1),hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)))
<=> ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_4),S_3))
=> ! [S_4] :
( hBOOL(hAPP_state_bool(evaln(C_2,S_3,N_1),S_4))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_4),S_4)) ) ) ) ).
fof(fact_616_triple__valid__def2,axiom,
! [N_1,Pa,C_2,Qa] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N_1),hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)))
<=> ! [Z_4,S_3] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_4),S_3))
=> ! [S_4] :
( hBOOL(hAPP_state_bool(evaln(C_2,S_3,N_1),S_4))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Qa,Z_4),S_4)) ) ) ) ).
fof(fact_617_evaln__elim__cases_I6_J,axiom,
! [P,S,N_2,S1_2] :
( hBOOL(hAPP_state_bool(evaln(hAPP_pname_com(body,P),S,N_2),S1_2))
=> ~ ! [N] :
( N_2 = hAPP_nat_nat(suc,N)
=> ~ hBOOL(hAPP_state_bool(evaln(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P)),S,N),S1_2)) ) ) ).
fof(fact_618_evalc__WHILE__case,axiom,
! [B_1,C_2,S_1,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S_1),T_1))
=> ( ( T_1 = S_1
=> hBOOL(hAPP_state_bool(B_1,S_1)) )
=> ~ ( hBOOL(hAPP_state_bool(B_1,S_1))
=> ! [S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_1),S1_1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C_2)),S1_1),T_1)) ) ) ) ) ).
fof(fact_619_evaln__WHILE__case,axiom,
! [B_1,C_2,S_1,N_1,T_1] :
( hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S_1,N_1),T_1))
=> ( ( T_1 = S_1
=> hBOOL(hAPP_state_bool(B_1,S_1)) )
=> ~ ( hBOOL(hAPP_state_bool(B_1,S_1))
=> ! [S1_1] :
( hBOOL(hAPP_state_bool(evaln(C_2,S_1,N_1),S1_1))
=> ~ hBOOL(hAPP_state_bool(evaln(while(B_1,C_2),S1_1,N_1),T_1)) ) ) ) ) ).
fof(fact_620_evalc__evaln,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_621_Comp,axiom,
! [D,R_1,Ga,Pa,C_2,Qa] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),C_2),Qa)),bot_bo797238721a_bool)))
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Qa),D),R_1)),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,Pa),semi(C_2,D)),R_1)),bot_bo797238721a_bool))) ) ) ).
fof(fact_622_Comp,axiom,
! [D,R_1,Ga,Pa,C_2,Qa] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),C_2),Qa)),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Qa),D),R_1)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Pa),semi(C_2,D)),R_1)),bot_bo784226126e_bool))) ) ) ).
fof(fact_623_the__elem__def,axiom,
! [X_10] : hAPP_f22106695ol_nat(the_elem_nat,X_10) = hAPP_f22106695ol_nat(the_nat,hAPP_f158894502t_bool(cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_10)),hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,insert_nat),bot_bot_fun_nat_bool))) ).
fof(fact_624_the__elem__def,axiom,
! [X_10] : hAPP_f258822235a_bool(the_el979963640a_bool,X_10) = hAPP_f258822235a_bool(the_fu1555441254a_bool,hAPP_f536631715l_bool(cOMBB_1575464575a_bool(hAPP_f1303207443l_bool(fequal1455900568l_bool,X_10)),hAPP_f759941367l_bool(hAPP_f254338943l_bool(cOMBC_1324894996l_bool,insert1421434205a_bool),bot_bo332163887l_bool))) ).
fof(fact_625_the__elem__def,axiom,
! [X_10] : hAPP_f1297739591_pname(the_elem_pname,X_10) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_10)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))) ).
fof(fact_626_the__elem__def,axiom,
! [X_10] : hAPP_f1693662087iple_a(the_el1519802624iple_a,X_10) = hAPP_f1693662087iple_a(the_Ho830102290iple_a,hAPP_f1194757675a_bool(cOMBB_1610959875iple_a(hAPP_f1767618879l_bool(fequal874423448a_bool,X_10)),hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,insert956547291iple_a),bot_bo797238721a_bool))) ).
fof(fact_627_the__elem__def,axiom,
! [X_10] : hAPP_f718417177_state(the_el2080696983_state,X_10) = hAPP_f718417177_state(the_Ho2067184133_state,hAPP_f1900156034e_bool(cOMBB_1282391997_state(hAPP_f849457489l_bool(fequal1475827639e_bool,X_10)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool))) ).
fof(fact_628_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,U_2))
=> ( ! [P_2] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_H1893885264e_bool(P_1,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H1893885264e_bool(Q_1,P_2))),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_H1893885264e_bool(Pa,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H1893885264e_bool(Qa,P_2))),bot_bo797238721a_bool))) )
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(image_533441733iple_a(hAPP_f1766326554iple_a(hAPP_f2004506425iple_a(cOMBS_1744968921iple_a,hAPP_f524917645iple_a(hAPP_f51865337iple_a(cOMBS_1597898188iple_a,hAPP_f338450734iple_a(cOMBB_1799328076iple_a(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(image_533441733iple_a(hAPP_f1766326554iple_a(hAPP_f2004506425iple_a(cOMBS_1744968921iple_a,hAPP_f524917645iple_a(hAPP_f51865337iple_a(cOMBS_1597898188iple_a,hAPP_f338450734iple_a(cOMBB_1799328076iple_a(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_629_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,U_2))
=> ( ! [P_2] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_f477771714e_bool(P_1,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f477771714e_bool(Q_1,P_2))),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_f477771714e_bool(Pa,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f477771714e_bool(Qa,P_2))),bot_bo797238721a_bool))) )
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f258822235a_bool(image_1153683671iple_a(hAPP_f1255935540iple_a(hAPP_f410259831iple_a(cOMBS_1097875753iple_a,hAPP_f159541635iple_a(hAPP_f2023640211iple_a(cOMBS_1949899292iple_a,hAPP_f1787234632iple_a(cOMBB_1013749676a_bool(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f258822235a_bool(image_1153683671iple_a(hAPP_f1255935540iple_a(hAPP_f410259831iple_a(cOMBS_1097875753iple_a,hAPP_f159541635iple_a(hAPP_f2023640211iple_a(cOMBS_1949899292iple_a,hAPP_f1787234632iple_a(cOMBB_1013749676a_bool(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_630_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2))
=> ( ! [P_2] :
( is_pname(P_2)
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Q_1,P_2))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p1637813682e_bool(Qa,P_2))),bot_bo784226126e_bool))) ) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f360545851e_bool(image_185131637_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,hAPP_f804744487_state(cOMBB_2084106034_pname(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_631_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,U_2))
=> ( ! [P_2] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_H838560847e_bool(P_1,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H838560847e_bool(Q_1,P_2))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_H838560847e_bool(Pa,P_2)),hAPP_H463278718_a_com(C0,P_2)),hAPP_H838560847e_bool(Qa,P_2))),bot_bo784226126e_bool))) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f101573982e_bool(image_1599849618_state(hAPP_f1551299824_state(hAPP_f461066925_state(cOMBS_1860286139_state,hAPP_f1573424489_state(hAPP_f1527065593_state(cOMBS_1436317352_state,hAPP_f1874377965_state(cOMBB_1269509967iple_a(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f101573982e_bool(image_1599849618_state(hAPP_f1551299824_state(hAPP_f461066925_state(cOMBS_1860286139_state,hAPP_f1573424489_state(hAPP_f1527065593_state(cOMBS_1436317352_state,hAPP_f1874377965_state(cOMBB_1269509967iple_a(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_632_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,U_2))
=> ( ! [P_2] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1246524253e_bool(P_1,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f1246524253e_bool(Q_1,P_2))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1246524253e_bool(Pa,P_2)),hAPP_f1968907248ol_com(C0,P_2)),hAPP_f1246524253e_bool(Qa,P_2))),bot_bo784226126e_bool))) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f1513075764e_bool(image_821490176_state(hAPP_f582141064_state(hAPP_f1784570101_state(cOMBS_988488459_state,hAPP_f1235235423_state(hAPP_f1151038867_state(cOMBS_1113512696_state,hAPP_f868277077_state(cOMBB_989249001a_bool(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f1513075764e_bool(image_821490176_state(hAPP_f582141064_state(hAPP_f1784570101_state(cOMBS_988488459_state,hAPP_f1235235423_state(hAPP_f1151038867_state(cOMBS_1113512696_state,hAPP_f868277077_state(cOMBB_989249001a_bool(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_633_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2))
=> ( ! [P_2] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_n1063102567e_bool(P_1,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1063102567e_bool(Q_1,P_2))),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_n1063102567e_bool(Pa,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1063102567e_bool(Qa,P_2))),bot_bo797238721a_bool))) )
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f420957402a_bool(image_1865589340iple_a(hAPP_f817035994iple_a(hAPP_f311800994iple_a(cOMBS_1417107330iple_a,hAPP_f1857794253iple_a(hAPP_f803745506iple_a(cOMBS_519355893iple_a,hAPP_f1921807086iple_a(cOMBB_1443236341_a_nat(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f420957402a_bool(image_1865589340iple_a(hAPP_f817035994iple_a(hAPP_f311800994iple_a(cOMBS_1417107330iple_a,hAPP_f1857794253iple_a(hAPP_f803745506iple_a(cOMBS_519355893iple_a,hAPP_f1921807086iple_a(cOMBB_1443236341_a_nat(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_634_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2))
=> ( ! [P_2] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_n1252169848e_bool(P_1,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1252169848e_bool(Q_1,P_2))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_n1252169848e_bool(Pa,P_2)),hAPP_nat_com(C0,P_2)),hAPP_n1252169848e_bool(Qa,P_2))),bot_bo784226126e_bool))) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f375948533e_bool(image_1730813499_state(hAPP_f634763074_state(hAPP_f1172439208_state(cOMBS_1390821348_state,hAPP_f1158791849_state(hAPP_f459571426_state(cOMBS_183256401_state,hAPP_f432895259_state(cOMBB_1531938296te_nat(hoare_1191504582_state),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(Ga),hAPP_f375948533e_bool(image_1730813499_state(hAPP_f634763074_state(hAPP_f1172439208_state(cOMBS_1390821348_state,hAPP_f1158791849_state(hAPP_f459571426_state(cOMBS_183256401_state,hAPP_f432895259_state(cOMBB_1531938296te_nat(hoare_1191504582_state),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_635_finite__pointwise,axiom,
! [Pa,Qa,Ga,P_1,C0,Q_1,U_2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2))
=> ( ! [P_2] :
( is_pname(P_2)
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_p635540397e_bool(P_1,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Q_1,P_2))),bot_bo797238721a_bool)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hAPP_f233717658iple_a(hAPP_c142510605iple_a(hAPP_f1350218798iple_a(hoare_1916936827iple_a,hAPP_p635540397e_bool(Pa,P_2)),hAPP_pname_com(C0,P_2)),hAPP_p635540397e_bool(Qa,P_2))),bot_bo797238721a_bool))) ) )
=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),P_1)),C0)),Q_1)),U_2)))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),Pa)),C0)),Qa)),U_2))) ) ) ) ).
fof(fact_636_evaln__max2,axiom,
! [C2_1,S2,N2,T2,C1_1,S1_2,N1,T1] :
( hBOOL(hAPP_state_bool(evaln(C1_1,S1_2,N1),T1))
=> ( hBOOL(hAPP_state_bool(evaln(C2_1,S2,N2),T2))
=> ? [N] :
( hBOOL(hAPP_state_bool(evaln(C1_1,S1_2,N),T1))
& hBOOL(hAPP_state_bool(evaln(C2_1,S2,N),T2)) ) ) ) ).
fof(fact_637_mk__disjoint__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1))
=> ? [B_6] :
( A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B_6)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B_6)) ) ) ).
fof(fact_638_mk__disjoint__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1))
=> ? [B_6] :
( A_1 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),B_6)
& ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),B_6)) ) ) ).
fof(fact_639_mk__disjoint__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),A_1))
=> ? [B_6] :
( A_1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),B_6)
& ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,A_2),B_6)) ) ) ).
fof(fact_640_mk__disjoint__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_1))
=> ? [B_6] :
( A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),B_6)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),B_6)) ) ) ).
fof(fact_641_mk__disjoint__insert,axiom,
! [A_2,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1))
=> ? [B_6] :
( is_fun_pname_bool(B_6)
& A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B_6)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B_6)) ) ) ) ).
fof(fact_642_evaln_OSemi,axiom,
! [C1_1,S2,C0_1,S0,N_2,S1_2] :
( hBOOL(hAPP_state_bool(evaln(C0_1,S0,N_2),S1_2))
=> ( hBOOL(hAPP_state_bool(evaln(C1_1,S1_2,N_2),S2))
=> hBOOL(hAPP_state_bool(evaln(semi(C0_1,C1_1),S0,N_2),S2)) ) ) ).
fof(fact_643_evalc_OSemi,axiom,
! [C1_1,S2,C0_1,S0,S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0_1),S0),S1_2))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S1_2),S2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0_1,C1_1)),S0),S2)) ) ) ).
fof(fact_644_com_Osimps_I3_J,axiom,
! [Com1_1,Com2_1,Com1,Com2] :
( semi(Com1_1,Com2_1) = semi(Com1,Com2)
<=> ( Com1_1 = Com1
& Com2_1 = Com2 ) ) ).
fof(fact_645_com_Osimps_I48_J,axiom,
! [Com1_2,Com2_2,Pname_2] : semi(Com1_2,Com2_2) != hAPP_pname_com(body,Pname_2) ).
fof(fact_646_com_Osimps_I49_J,axiom,
! [Pname_2,Com1_2,Com2_2] : hAPP_pname_com(body,Pname_2) != semi(Com1_2,Com2_2) ).
fof(fact_647_com_Osimps_I47_J,axiom,
! [Fun,Com,Com1_1,Com2_1] : while(Fun,Com) != semi(Com1_1,Com2_1) ).
fof(fact_648_com_Osimps_I46_J,axiom,
! [Com1_1,Com2_1,Fun,Com] : semi(Com1_1,Com2_1) != while(Fun,Com) ).
fof(fact_649_com_Osimps_I13_J,axiom,
! [Com1_3,Com2_3] : semi(Com1_3,Com2_3) != skip ).
fof(fact_650_com_Osimps_I12_J,axiom,
! [Com1_3,Com2_3] : skip != semi(Com1_3,Com2_3) ).
fof(fact_651_evalc__elim__cases_I4_J,axiom,
! [C1_1,C2_1,S,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1_1,C2_1)),S),T))
=> ~ ! [S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1_1),S),S1_1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2_1),S1_1),T)) ) ) ).
fof(fact_652_evaln__elim__cases_I4_J,axiom,
! [C1_1,C2_1,S,N_2,T] :
( hBOOL(hAPP_state_bool(evaln(semi(C1_1,C2_1),S,N_2),T))
=> ~ ! [S1_1] :
( hBOOL(hAPP_state_bool(evaln(C1_1,S,N_2),S1_1))
=> ~ hBOOL(hAPP_state_bool(evaln(C2_1,S1_1,N_2),T)) ) ) ).
fof(fact_653_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(H),F_1))) ) ).
fof(fact_654_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f420957402a_bool(image_1865589340iple_a(H),F_1))) ) ).
fof(fact_655_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f1098153174l_bool(image_1590538908a_bool(H),F_1))) ) ).
fof(fact_656_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f654413245e_bool(image_nat_pname(H),F_1))) ) ).
fof(fact_657_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(image_nat_nat(H),F_1))) ) ).
fof(fact_658_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1968395738t_bool(image_48635758_a_nat(H),F_1))) ) ).
fof(fact_659_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1900748420t_bool(image_1769043840ol_nat(H),F_1))) ) ).
fof(fact_660_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1066163005t_bool(image_pname_nat(H),F_1))) ) ).
fof(fact_661_finite__imageI,axiom,
! [H,F_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f2034373396a_bool(image_1738210978iple_a(H),F_1))) ) ).
fof(fact_662_finite_OinsertI,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1))) ) ).
fof(fact_663_finite_OinsertI,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1))) ) ).
fof(fact_664_finite_OinsertI,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1))) ) ).
fof(fact_665_finite_OinsertI,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1))) ) ).
fof(fact_666_finite_OinsertI,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1))) ) ).
fof(fact_667_finite_OemptyI,axiom,
hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,bot_bo797238721a_bool)) ).
fof(fact_668_finite_OemptyI,axiom,
hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,bot_bo332163887l_bool)) ).
fof(fact_669_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).
fof(fact_670_finite_OemptyI,axiom,
hBOOL(hAPP_f1378282496l_bool(finite694102371_state,bot_bo784226126e_bool)) ).
fof(fact_671_finite_OemptyI,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)) ).
fof(fact_672_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_673_finite__Collect__conjI,axiom,
! [Qa,Pa] :
( ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Pa)))
| hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Qa))) )
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),Pa)),Qa)))) ) ).
fof(fact_674_finite__Collect__conjI,axiom,
! [Qa,Pa] :
( ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Pa)))
| hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Qa))) )
=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),Pa)),Qa)))) ) ).
fof(fact_675_finite__Collect__conjI,axiom,
! [Qa,Pa] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Pa)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Qa))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),Qa)))) ) ).
fof(fact_676_finite__Un,axiom,
! [F_1,Ga] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F_1),Ga)))
<=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1))
& hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,Ga)) ) ) ).
fof(fact_677_finite__Un,axiom,
! [F_1,Ga] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),Ga)))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)) ) ) ).
fof(fact_678_finite__Un,axiom,
! [F_1,Ga] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F_1),Ga)))
<=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Ga)) ) ) ).
fof(fact_679_finite__Un,axiom,
! [F_1,Ga] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F_1),Ga)))
<=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1))
& hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,Ga)) ) ) ).
fof(fact_680_finite__Un,axiom,
! [F_1,Ga] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F_1),Ga)))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)) ) ) ).
fof(fact_681_finite__UnI,axiom,
! [Ga,F_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,Ga))
=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,F_1),Ga))) ) ) ).
fof(fact_682_finite__UnI,axiom,
! [Ga,F_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F_1),Ga))) ) ) ).
fof(fact_683_finite__UnI,axiom,
! [Ga,F_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Ga))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F_1),Ga))) ) ) ).
fof(fact_684_finite__UnI,axiom,
! [Ga,F_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,Ga))
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,F_1),Ga))) ) ) ).
fof(fact_685_finite__UnI,axiom,
! [Ga,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,F_1),Ga))) ) ) ).
fof(fact_686_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_687_finite__Collect__disjI,axiom,
! [Pa,Qa] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fdisj),Pa)),Qa))))
<=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Pa)))
& hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,Qa))) ) ) ).
fof(fact_688_finite__Collect__disjI,axiom,
! [Pa,Qa] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fdisj),Pa)),Qa))))
<=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Pa)))
& hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,Qa))) ) ) ).
fof(fact_689_finite__Collect__disjI,axiom,
! [Pa,Qa] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fdisj),Pa)),Qa))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Pa)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,Qa))) ) ) ).
fof(fact_690_finite__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_2),A_1)))
<=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1)) ) ).
fof(fact_691_finite__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ).
fof(fact_692_finite__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_2),A_1)))
<=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1)) ) ).
fof(fact_693_finite__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_1)))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1)) ) ).
fof(fact_694_finite__insert,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A_1)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ).
fof(fact_695_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(Pa,bot_bo332163887l_bool))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_2))
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),F_2))
=> ( hBOOL(hAPP_f2110825313l_bool(Pa,F_2))
=> hBOOL(hAPP_f2110825313l_bool(Pa,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),F_2))) ) ) )
=> hBOOL(hAPP_f2110825313l_bool(Pa,F_1)) ) ) ) ).
fof(fact_696_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(Pa,bot_bo797238721a_bool))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2))
=> ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),F_2))
=> ( hBOOL(hAPP_f1695230391l_bool(Pa,F_2))
=> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),F_2))) ) ) )
=> hBOOL(hAPP_f1695230391l_bool(Pa,F_1)) ) ) ) ).
fof(fact_697_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,bot_bo784226126e_bool))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,F_2))
=> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),F_2))) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)) ) ) ) ).
fof(fact_698_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),F_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),F_2))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ).
fof(fact_699_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( 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_1)) ) ) ) ).
fof(fact_700_finite_Osimps,axiom,
! [A_2] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_2))
<=> ( A_2 = bot_bo332163887l_bool
| ? [A_8,A_7] :
( A_2 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,A_7),A_8)
& hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_8)) ) ) ) ).
fof(fact_701_finite_Osimps,axiom,
! [A_2] :
( is_fun_pname_bool(A_2)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_2))
<=> ( A_2 = bot_bo844097828e_bool
| ? [A_8,A_7] :
( is_fun_pname_bool(A_8)
& is_pname(A_7)
& A_2 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_7),A_8)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_8)) ) ) ) ) ).
fof(fact_702_finite_Osimps,axiom,
! [A_2] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_2))
<=> ( A_2 = bot_bo797238721a_bool
| ? [A_8,A_7] :
( A_2 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,A_7),A_8)
& hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_8)) ) ) ) ).
fof(fact_703_finite_Osimps,axiom,
! [A_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_2))
<=> ( A_2 = bot_bo784226126e_bool
| ? [A_8,A_7] :
( A_2 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_7),A_8)
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_8)) ) ) ) ).
fof(fact_704_finite_Osimps,axiom,
! [A_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
<=> ( A_2 = bot_bot_fun_nat_bool
| ? [A_8,A_7] :
( A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_7),A_8)
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_8)) ) ) ) ).
fof(fact_705_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1900748420t_bool(image_1769043840ol_nat(F),A_1)))
=> ? [X] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),A_1))
& ~ hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_n37219812l_bool(hAPP_f1852971749l_bool(cOMBC_594836627t_bool,hAPP_f1144745493t_bool(cOMBB_85437587a_bool(fequal_nat),F)),hAPP_f2097660464ol_nat(F,X)))))) ) ) ) ).
fof(fact_706_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1968395738t_bool(image_48635758_a_nat(F),A_1)))
=> ? [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),A_1))
& ~ hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_n1919155532a_bool(hAPP_f228417655a_bool(cOMBC_364739t_bool,hAPP_f1872860171t_bool(cOMBB_1391527205iple_a(fequal_nat),F)),hAPP_H592031934_a_nat(F,X)))))) ) ) ) ).
fof(fact_707_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f1066163005t_bool(image_pname_nat(F),A_1)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& ~ 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_1))),hAPP_n1025906991e_bool(hAPP_f1715247037e_bool(cOMBC_pname_nat_bool,hAPP_f1358769483t_bool(cOMBB_523834888_pname(fequal_nat),F)),hAPP_pname_nat(F,X)))))) ) ) ) ).
fof(fact_708_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(image_nat_nat(F),A_1)))
=> ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(fequal_nat),F)),hAPP_nat_nat(F,X)))))) ) ) ) ).
fof(fact_709_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f420957402a_bool(image_1865589340iple_a(F),A_1)))
=> ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_H144868812t_bool(hAPP_f1886543991t_bool(cOMBC_533513393a_bool,hAPP_f260875897a_bool(cOMBB_1063143712ol_nat(fequal963300192iple_a),F)),hAPP_n261501868iple_a(F,X)))))) ) ) ) ).
fof(fact_710_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f1098153174l_bool(image_1590538908a_bool(F),A_1)))
=> ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f1968395738t_bool(hAPP_f2110185157t_bool(cOMBC_805992879l_bool,hAPP_f635381775l_bool(cOMBB_1370228356ol_nat(fequal874423448a_bool),F)),hAPP_n1919155532a_bool(F,X)))))) ) ) ) ).
fof(fact_711_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f654413245e_bool(image_nat_pname(F),A_1)))
=> ? [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),A_1))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_p1499970991t_bool(hAPP_f998021053t_bool(cOMBC_nat_pname_bool,hAPP_f414474559e_bool(cOMBB_1212655066ol_nat(fequal_pname),F)),hAPP_nat_pname(F,X)))))) ) ) ) ).
fof(fact_712_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(F),A_1)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& ~ 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_1))),hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,hAPP_f472107739e_bool(cOMBB_181781758_pname(fequal1440809015_state),F)),hAPP_p1751618853_state(F,X)))))) ) ) ) ).
fof(fact_713_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f290545180l_bool(image_2016317142a_bool(F),A_1)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& ~ 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_1))),hAPP_f1216026388e_bool(hAPP_f1415030585e_bool(cOMBC_173670761l_bool,hAPP_f1577042203l_bool(cOMBB_1363536318_pname(fequal874423448a_bool),F)),hAPP_p1743421830a_bool(F,X)))))) ) ) ) ).
fof(fact_714_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A_1)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& ~ 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_1))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X)))))) ) ) ) ).
fof(fact_715_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1)))
=> ? [X] :
( is_pname(X)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A_1))
& ~ 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_1))),hAPP_H1078816262e_bool(hAPP_f421895915e_bool(cOMBC_1309726071a_bool,hAPP_f2085416313a_bool(cOMBB_1388879450_pname(fequal963300192iple_a),F)),hAPP_p346744818iple_a(F,X)))))) ) ) ) ).
fof(fact_716_nonempty__iff,axiom,
! [A_1] :
( A_1 != bot_bot_fun_nat_bool
<=> ? [X,B_6] :
( A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),B_6)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),B_6)) ) ) ).
fof(fact_717_nonempty__iff,axiom,
! [A_1] :
( A_1 != bot_bo332163887l_bool
<=> ? [X,B_6] :
( A_1 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),B_6)
& ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),B_6)) ) ) ).
fof(fact_718_nonempty__iff,axiom,
! [A_1] :
( A_1 != bot_bo797238721a_bool
<=> ? [X,B_6] :
( A_1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),B_6)
& ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),B_6)) ) ) ).
fof(fact_719_nonempty__iff,axiom,
! [A_1] :
( A_1 != bot_bo784226126e_bool
<=> ? [X,B_6] :
( A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),B_6)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),B_6)) ) ) ).
fof(fact_720_nonempty__iff,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( A_1 != bot_bo844097828e_bool
<=> ? [X,B_6] :
( is_pname(X)
& is_fun_pname_bool(B_6)
& A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),B_6)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_6)) ) ) ) ).
fof(fact_721_folding__one__idem_Ounion__idem,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite927518301a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( A_1 != bot_bo332163887l_bool
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2))
=> ( B_2 != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,A_1)),hAPP_f258822235a_bool(F_1,B_2)) ) ) ) ) ) ).
fof(fact_722_folding__one__idem_Ounion__idem,axiom,
! [B_2,A_1,F,F_1] :
( ( is_fun_pname_bool(B_2)
& is_fun_pname_bool(A_1) )
=> ( hBOOL(finite89670078_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_2))
=> ( B_2 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,A_1)),hAPP_f1297739591_pname(F_1,B_2)) ) ) ) ) ) ) ).
fof(fact_723_folding__one__idem_Ounion__idem,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( A_1 != bot_bo784226126e_bool
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_2))
=> ( B_2 != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,A_1)),hAPP_f718417177_state(F_1,B_2)) ) ) ) ) ) ).
fof(fact_724_folding__one__idem_Ounion__idem,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite1033474011iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( A_1 != bot_bo797238721a_bool
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B_2))
=> ( B_2 != bot_bo797238721a_bool
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,A_1)),hAPP_f1693662087iple_a(F_1,B_2)) ) ) ) ) ) ).
fof(fact_725_folding__one__idem_Ounion__idem,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2))
=> ( B_2 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,A_1)),hAPP_f22106695ol_nat(F_1,B_2)) ) ) ) ) ) ).
fof(fact_726_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite927518301a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( A_1 != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,A_1)) ) ) ) ).
fof(fact_727_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A_1,F,F_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(finite89670078_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,A_1)) ) ) ) ) ).
fof(fact_728_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite1033474011iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( A_1 != bot_bo797238721a_bool
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,A_1)) ) ) ) ).
fof(fact_729_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( A_1 != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),hAPP_f718417177_state(F_1,A_1)) ) ) ) ).
fof(fact_730_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,A_1)) ) ) ) ).
fof(fact_731_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hAPP_f360545851e_bool(image_185131637_state(F),A_1) = hAPP_f360545851e_bool(hAPP_f447027986e_bool(finite1443934175_pname(semila176469292e_bool,hAPP_f103229774e_bool(hAPP_f376349141e_bool(cOMBC_59067399e_bool,hAPP_f2028971360e_bool(cOMBB_667059641_pname(insert1744391420_state),F)),bot_bo784226126e_bool)),bot_bo784226126e_bool),A_1) ) ).
fof(fact_732_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> hAPP_f20753329a_bool(image_533441733iple_a(F),A_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(finite1750867337iple_a(semila1114547555a_bool,hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,hAPP_f181951559a_bool(cOMBB_1722563443iple_a(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1) ) ).
fof(fact_733_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> hAPP_f258822235a_bool(image_1153683671iple_a(F),A_1) = hAPP_f258822235a_bool(hAPP_f1748906467a_bool(finite576419631a_bool(semila1114547555a_bool,hAPP_f1706700729a_bool(hAPP_f957014749a_bool(cOMBC_288844080a_bool,hAPP_f2116512939a_bool(cOMBB_734913733a_bool(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1) ) ).
fof(fact_734_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hAPP_f800510211t_bool(image_nat_nat(F),A_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(finite2098682953ol_nat(semila465093516t_bool,hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,hAPP_f934069744t_bool(cOMBB_1141542387ol_nat(insert_nat),F)),bot_bot_fun_nat_bool)),bot_bot_fun_nat_bool),A_1) ) ).
fof(fact_735_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hAPP_f1098153174l_bool(image_1590538908a_bool(F),A_1) = hAPP_f1098153174l_bool(hAPP_f1659318414l_bool(finite183661956ol_nat(semila834425101l_bool,hAPP_f924569416l_bool(hAPP_f1384990677l_bool(cOMBC_1645572109l_bool,hAPP_f992030835l_bool(cOMBB_1467678496ol_nat(insert1421434205a_bool),F)),bot_bo332163887l_bool)),bot_bo332163887l_bool),A_1) ) ).
fof(fact_736_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hAPP_f654413245e_bool(image_nat_pname(F),A_1) = hAPP_f654413245e_bool(hAPP_f1319825314e_bool(finite491497871ol_nat(semila278973382e_bool,hAPP_f1501416730e_bool(hAPP_f883303749e_bool(cOMBC_1771919087e_bool,hAPP_f446737578e_bool(cOMBB_1209446585ol_nat(insert_pname),F)),bot_bo844097828e_bool)),bot_bo844097828e_bool),A_1) ) ).
fof(fact_737_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hAPP_f420957402a_bool(image_1865589340iple_a(F),A_1) = hAPP_f420957402a_bool(hAPP_f1023496418a_bool(finite658192434ol_nat(semila1114547555a_bool,hAPP_f1938783956a_bool(hAPP_f816688069a_bool(cOMBC_1584660393a_bool,hAPP_f1402630535a_bool(cOMBB_2115959324ol_nat(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1) ) ).
fof(fact_738_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hAPP_f375948533e_bool(image_1730813499_state(F),A_1) = hAPP_f375948533e_bool(hAPP_f1502860876e_bool(finite1171393829ol_nat(semila176469292e_bool,hAPP_f1718442376e_bool(hAPP_f1696618965e_bool(cOMBC_1048264781e_bool,hAPP_f953597140e_bool(cOMBB_1524346879ol_nat(insert1744391420_state),F)),bot_bo784226126e_bool)),bot_bo784226126e_bool),A_1) ) ).
fof(fact_739_image__eq__fold__image,axiom,
! [F,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hAPP_f2034373396a_bool(image_1738210978iple_a(F),A_1) = hAPP_f2034373396a_bool(hAPP_f490436380a_bool(finite1174086764_pname(semila1114547555a_bool,hAPP_f624861966a_bool(hAPP_f843217465a_bool(cOMBC_2103945827a_bool,hAPP_f682420871a_bool(cOMBB_1481150806_pname(insert956547291iple_a),F)),bot_bo797238721a_bool)),bot_bo797238721a_bool),A_1) ) ).
fof(fact_740_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1))
=> ( F_1 != bot_bo332163887l_bool
=> ( ! [X] : hBOOL(hAPP_f2110825313l_bool(Pa,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),bot_bo332163887l_bool)))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_2))
=> ( F_2 != bot_bo332163887l_bool
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),F_2))
=> ( hBOOL(hAPP_f2110825313l_bool(Pa,F_2))
=> hBOOL(hAPP_f2110825313l_bool(Pa,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f2110825313l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_741_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1))
=> ( F_1 != bot_bo797238721a_bool
=> ( ! [X] : hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),bot_bo797238721a_bool)))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_2))
=> ( F_2 != bot_bo797238721a_bool
=> ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),F_2))
=> ( hBOOL(hAPP_f1695230391l_bool(Pa,F_2))
=> hBOOL(hAPP_f1695230391l_bool(Pa,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f1695230391l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_742_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_1))
=> ( F_1 != bot_bo784226126e_bool
=> ( ! [X] : hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),bot_bo784226126e_bool)))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( F_2 != bot_bo784226126e_bool
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(Pa,F_2))
=> hBOOL(hAPP_f1378282496l_bool(Pa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_743_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
=> ( F_1 != bot_bot_fun_nat_bool
=> ( ! [X] : hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),bot_bot_fun_nat_bool)))
=> ( ! [X,F_2] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
=> ( F_2 != bot_bot_fun_nat_bool
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),F_2))
=> ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
=> hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),F_2))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_744_finite__ne__induct,axiom,
! [Pa,F_1] :
( is_fun_pname_bool(F_1)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( F_1 != 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_1)) ) ) ) ) ) ).
fof(fact_745_folding__one__idem_Oidem,axiom,
! [X_2,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),X_2) = X_2 ) ).
fof(fact_746_folding__one__idem_Oidem,axiom,
! [X_2,F,F_1] :
( is_pname(X_2)
=> ( hBOOL(finite89670078_pname(F,F_1))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),X_2) = X_2 ) ) ).
fof(fact_747_folding__one__idem_Oidem,axiom,
! [X_2,F,F_1] :
( hBOOL(finite1033474011iple_a(F,F_1))
=> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),X_2) = X_2 ) ).
fof(fact_748_fold__image__empty,axiom,
! [F,G,Z_1] : hAPP_f2034373396a_bool(hAPP_f490436380a_bool(finite1174086764_pname(F,G),Z_1),bot_bo844097828e_bool) = Z_1 ).
fof(fact_749_folding__one__idem_Oin__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite927518301a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,A_1)) = hAPP_f258822235a_bool(F_1,A_1) ) ) ) ).
fof(fact_750_folding__one__idem_Oin__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite1033474011iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,A_1)) = hAPP_f1693662087iple_a(F_1,A_1) ) ) ) ).
fof(fact_751_folding__one__idem_Oin__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,A_1)) = hAPP_f22106695ol_nat(F_1,A_1) ) ) ) ).
fof(fact_752_folding__one__idem_Oin__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite89670078_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,A_1)) = hAPP_f1297739591_pname(F_1,A_1) ) ) ) ).
fof(fact_753_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F,F_1] :
( hBOOL(finite1033474011iple_a(F,F_1))
=> ( ! [X,Y_8] : hAPP_H905846293iple_a(H,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X),Y_8)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_H905846293iple_a(H,X)),hAPP_H905846293iple_a(H,Y_8))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,N_3))
=> ( N_3 != bot_bo797238721a_bool
=> hAPP_H905846293iple_a(H,hAPP_f1693662087iple_a(F_1,N_3)) = hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(image_533441733iple_a(H),N_3)) ) ) ) ) ).
fof(fact_754_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F,F_1] :
( hBOOL(finite927518301a_bool(F,F_1))
=> ( ! [X,Y_8] : hAPP_f20753329a_bool(H,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X),Y_8)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f20753329a_bool(H,X)),hAPP_f20753329a_bool(H,Y_8))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,N_3))
=> ( N_3 != bot_bo332163887l_bool
=> hAPP_f20753329a_bool(H,hAPP_f258822235a_bool(F_1,N_3)) = hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(image_696316513a_bool(H),N_3)) ) ) ) ) ).
fof(fact_755_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F,F_1] :
( is_fun_pname_bool(N_3)
=> ( hBOOL(finite89670078_pname(F,F_1))
=> ( ! [X,Y_8] :
( ( is_pname(X)
& is_pname(Y_8) )
=> hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F,X),Y_8)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H,X)),hAPP_pname_pname(H,Y_8)) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N_3))
=> ( N_3 != bot_bo844097828e_bool
=> hAPP_pname_pname(H,hAPP_f1297739591_pname(F_1,N_3)) = hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(image_pname_pname(H),N_3)) ) ) ) ) ) ).
fof(fact_756_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F,F_1] :
( hBOOL(finite416071164_state(F,F_1))
=> ( ! [X,Y_8] : hAPP_H574424047_state(H,hAPP_H574424047_state(hAPP_H280516760_state(F,X),Y_8)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_H574424047_state(H,X)),hAPP_H574424047_state(H,Y_8))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,N_3))
=> ( N_3 != bot_bo784226126e_bool
=> hAPP_H574424047_state(H,hAPP_f718417177_state(F_1,N_3)) = hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(image_661047967_state(H),N_3)) ) ) ) ) ).
fof(fact_757_folding__one__idem_Ohom__commute,axiom,
! [N_3,H,F,F_1] :
( hBOOL(finite795500164em_nat(F,F_1))
=> ( ! [X,Y_8] : hAPP_nat_nat(H,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X),Y_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(H,X)),hAPP_nat_nat(H,Y_8))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3))
=> ( N_3 != bot_bot_fun_nat_bool
=> hAPP_nat_nat(H,hAPP_f22106695ol_nat(F_1,N_3)) = hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(image_nat_nat(H),N_3)) ) ) ) ) ).
fof(fact_758_comm__monoid__big_OF__eq,axiom,
! [G,A_1,F,Z_1,F_1] :
( hBOOL(big_co2022808324_pname(F,Z_1,F_1))
=> ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hAPP_f2034373396a_bool(hAPP_f1234324863a_bool(F_1,G),A_1) = hAPP_f2034373396a_bool(hAPP_f490436380a_bool(finite1174086764_pname(F,G),Z_1),A_1) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hAPP_f2034373396a_bool(hAPP_f1234324863a_bool(F_1,G),A_1) = Z_1 ) ) ) ).
fof(fact_759_folding__one_Oinsert,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite2103247258a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> ( A_1 != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,A_1)) ) ) ) ) ).
fof(fact_760_folding__one_Oinsert,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite1753440478iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> ( A_1 != bot_bo797238721a_bool
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,A_1)) ) ) ) ) ).
fof(fact_761_folding__one_Oinsert,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1))
=> ( A_1 != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),hAPP_f718417177_state(F_1,A_1)) ) ) ) ) ).
fof(fact_762_folding__one_Oinsert,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,A_1)) ) ) ) ) ).
fof(fact_763_folding__one_Oinsert,axiom,
! [X_2,A_1,F,F_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(finite1282449217_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( A_1 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,A_1)) ) ) ) ) ) ).
fof(fact_764_folding__one_Osingleton,axiom,
! [X_2,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) = X_2 ) ).
fof(fact_765_folding__one_Osingleton,axiom,
! [X_2,F,F_1] :
( hBOOL(finite2103247258a_bool(F,F_1))
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) = X_2 ) ).
fof(fact_766_folding__one_Osingleton,axiom,
! [X_2,F,F_1] :
( is_pname(X_2)
=> ( hBOOL(finite1282449217_pname(F,F_1))
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = X_2 ) ) ).
fof(fact_767_folding__one_Osingleton,axiom,
! [X_2,F,F_1] :
( hBOOL(finite1753440478iple_a(F,F_1))
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) = X_2 ) ).
fof(fact_768_folding__one_Osingleton,axiom,
! [X_2,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) = X_2 ) ).
fof(fact_769_folding__one_Oclosed,axiom,
! [A_1,F,F_1] :
( hBOOL(finite2103247258a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( A_1 != bot_bo332163887l_bool
=> ( ! [X,Y_8] : hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X),Y_8)),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,Y_8),bot_bo332163887l_bool))))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,hAPP_f258822235a_bool(F_1,A_1)),A_1)) ) ) ) ) ).
fof(fact_770_folding__one_Oclosed,axiom,
! [A_1,F,F_1] :
( hBOOL(finite1753440478iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( A_1 != bot_bo797238721a_bool
=> ( ! [X,Y_8] : hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X),Y_8)),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,Y_8),bot_bo797238721a_bool))))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,hAPP_f1693662087iple_a(F_1,A_1)),A_1)) ) ) ) ) ).
fof(fact_771_folding__one_Oclosed,axiom,
! [A_1,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( A_1 != bot_bo784226126e_bool
=> ( ! [X,Y_8] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_H574424047_state(hAPP_H280516760_state(F,X),Y_8)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_8),bot_bo784226126e_bool))))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_f718417177_state(F_1,A_1)),A_1)) ) ) ) ) ).
fof(fact_772_folding__one_Oclosed,axiom,
! [A_1,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> ( ! [X,Y_8] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X),Y_8)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_8),bot_bot_fun_nat_bool))))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A_1)),A_1)) ) ) ) ) ).
fof(fact_773_folding__one_Oclosed,axiom,
! [A_1,F,F_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(finite1282449217_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> ( ! [X,Y_8] :
( ( is_pname(X)
& is_pname(Y_8) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X),Y_8)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_8),bot_bo844097828e_bool)))) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F_1,A_1)),A_1)) ) ) ) ) ) ).
fof(fact_774_Set_Oset__insert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> ~ ! [B_6] :
( A_1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_6)
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_6)) ) ) ).
fof(fact_775_Set_Oset__insert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> ~ ! [B_6] :
( A_1 = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),B_6)
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),B_6)) ) ) ).
fof(fact_776_Set_Oset__insert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
=> ~ ! [B_6] :
( A_1 = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),B_6)
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),B_6)) ) ) ).
fof(fact_777_Set_Oset__insert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1))
=> ~ ! [B_6] :
( A_1 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_6)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_6)) ) ) ).
fof(fact_778_Set_Oset__insert,axiom,
! [X_2,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ~ ! [B_6] :
( is_fun_pname_bool(B_6)
=> ( A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_6)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_6)) ) ) ) ) ).
fof(fact_779_equals0I,axiom,
! [A_1] :
( ! [Y_8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_8),A_1))
=> A_1 = bot_bot_fun_nat_bool ) ).
fof(fact_780_equals0I,axiom,
! [A_1] :
( ! [Y_8] : ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,Y_8),A_1))
=> A_1 = bot_bo332163887l_bool ) ).
fof(fact_781_equals0I,axiom,
! [A_1] :
( ! [Y_8] : ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,Y_8),A_1))
=> A_1 = bot_bo797238721a_bool ) ).
fof(fact_782_equals0I,axiom,
! [A_1] :
( ! [Y_8] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_8),A_1))
=> A_1 = bot_bo784226126e_bool ) ).
fof(fact_783_equals0I,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( ! [Y_8] :
( is_pname(Y_8)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_8),A_1)) )
=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_784_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
=> ( A_1 != bot_bo1701429464l_bool
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_2))
=> ( B_2 != bot_bo1701429464l_bool
=> hAPP_f582319405t_bool(big_la1704749377t_bool,hAPP_f1246832597l_bool(hAPP_f540020688l_bool(semila653644470l_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)),hAPP_f582319405t_bool(big_la1704749377t_bool,B_2)) ) ) ) ) ).
fof(fact_785_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,A_1))
=> ( A_1 != bot_bo156414585l_bool
=> ( hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,B_2))
=> ( B_2 != bot_bo156414585l_bool
=> hAPP_f2060061063l_bool(big_la914314008l_bool,hAPP_f1841260065l_bool(hAPP_f1120848625l_bool(semila1803437851l_bool,A_1),B_2)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f2060061063l_bool(big_la914314008l_bool,A_1)),hAPP_f2060061063l_bool(big_la914314008l_bool,B_2)) ) ) ) ) ).
fof(fact_786_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_1))
=> ( A_1 != bot_bo942947096l_bool
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B_2))
=> ( B_2 != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(big_la1369269047e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A_1),B_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f1216288071e_bool(big_la1369269047e_bool,A_1)),hAPP_f1216288071e_bool(big_la1369269047e_bool,B_2)) ) ) ) ) ).
fof(fact_787_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( ( is_fun1661590463l_bool(B_2)
& is_fun1661590463l_bool(A_1) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_2))
=> ( B_2 != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(big_la841148155e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f674760225e_bool(big_la841148155e_bool,A_1)),hAPP_f674760225e_bool(big_la841148155e_bool,B_2)) ) ) ) ) ) ).
fof(fact_788_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( ( is_fun_bool_bool(B_2)
& is_fun_bool_bool(A_1) )
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A_1))
=> ( A_1 != bot_bo806936373l_bool
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B_2))
=> ( B_2 != bot_bo806936373l_bool
=> ( hBOOL(hAPP_f387058535l_bool(big_la1480321694n_bool,hAPP_f961197973l_bool(hAPP_f1172769267l_bool(semila1866150931l_bool,A_1),B_2)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_f387058535l_bool(big_la1480321694n_bool,A_1)),hAPP_f387058535l_bool(big_la1480321694n_bool,B_2))) ) ) ) ) ) ) ).
fof(fact_789_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( A_1 != bot_bo332163887l_bool
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2))
=> ( B_2 != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(big_la1609103640a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)),hAPP_f258822235a_bool(big_la1609103640a_bool,B_2)) ) ) ) ) ).
fof(fact_790_Sup__fin_Ounion__idem,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2))
=> ( B_2 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)),hAPP_f22106695ol_nat(big_la43341705in_nat,B_2)) ) ) ) ) ).
fof(fact_791_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A_1))
=> ( A_1 != bot_bo1701429464l_bool
=> hAPP_f582319405t_bool(big_la1704749377t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_2),A_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)) ) ) ) ).
fof(fact_792_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,A_1))
=> ( ~ hBOOL(hAPP_f670355311l_bool(hAPP_f21712077l_bool(member38210668l_bool,X_2),A_1))
=> ( A_1 != bot_bo156414585l_bool
=> hAPP_f2060061063l_bool(big_la914314008l_bool,hAPP_f1841260065l_bool(hAPP_f1499754623l_bool(insert2046103699l_bool,X_2),A_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f2060061063l_bool(big_la914314008l_bool,A_1)) ) ) ) ).
fof(fact_793_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_1))
=> ( ~ hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A_1))
=> ( A_1 != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(big_la1369269047e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),A_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f1216288071e_bool(big_la1369269047e_bool,A_1)) ) ) ) ).
fof(fact_794_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( is_fun1661590463l_bool(A_1)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(big_la841148155e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f674760225e_bool(big_la841148155e_bool,A_1)) ) ) ) ) ).
fof(fact_795_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( is_fun_bool_bool(A_1)
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A_1))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> ( A_1 != bot_bo806936373l_bool
=> ( hBOOL(hAPP_f387058535l_bool(big_la1480321694n_bool,hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_f387058535l_bool(big_la1480321694n_bool,A_1))) ) ) ) ) ) ).
fof(fact_796_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
=> ( A_1 != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(big_la1609103640a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)) ) ) ) ).
fof(fact_797_Sup__fin_Oinsert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_2),hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)) ) ) ) ).
fof(fact_798_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
=> ( A_1 != bot_bo1701429464l_bool
=> hAPP_f582319405t_bool(big_la1704749377t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_2),A_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,X_2),hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)) ) ) ).
fof(fact_799_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f670355311l_bool(finite1823766380l_bool,A_1))
=> ( A_1 != bot_bo156414585l_bool
=> hAPP_f2060061063l_bool(big_la914314008l_bool,hAPP_f1841260065l_bool(hAPP_f1499754623l_bool(insert2046103699l_bool,X_2),A_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,X_2),hAPP_f2060061063l_bool(big_la914314008l_bool,A_1)) ) ) ).
fof(fact_800_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_1))
=> ( A_1 != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(big_la1369269047e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),A_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f1216288071e_bool(big_la1369269047e_bool,A_1)) ) ) ).
fof(fact_801_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( is_fun1661590463l_bool(A_1)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(big_la841148155e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f674760225e_bool(big_la841148155e_bool,A_1)) ) ) ) ).
fof(fact_802_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( is_fun_bool_bool(A_1)
=> ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A_1))
=> ( A_1 != bot_bo806936373l_bool
=> ( hBOOL(hAPP_f387058535l_bool(big_la1480321694n_bool,hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,X_2),A_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_f387058535l_bool(big_la1480321694n_bool,A_1))) ) ) ) ) ).
fof(fact_803_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( A_1 != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(big_la1609103640a_bool,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,X_2),hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)) ) ) ).
fof(fact_804_Sup__fin_Oinsert__idem,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(big_la43341705in_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila972727038up_nat,X_2),hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)) ) ) ).
fof(fact_805_folding__one_Ounion__disjoint,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite2103247258a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( A_1 != bot_bo332163887l_bool
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2))
=> ( B_2 != bot_bo332163887l_bool
=> ( hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2) = bot_bo332163887l_bool
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,A_1)),hAPP_f258822235a_bool(F_1,B_2)) ) ) ) ) ) ) ).
fof(fact_806_folding__one_Ounion__disjoint,axiom,
! [B_2,A_1,F,F_1] :
( ( is_fun_pname_bool(B_2)
& is_fun_pname_bool(A_1) )
=> ( hBOOL(finite1282449217_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_2))
=> ( B_2 != bot_bo844097828e_bool
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,A_1)),hAPP_f1297739591_pname(F_1,B_2)) ) ) ) ) ) ) ) ).
fof(fact_807_folding__one_Ounion__disjoint,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( A_1 != bot_bo784226126e_bool
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_2))
=> ( B_2 != bot_bo784226126e_bool
=> ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2) = bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,A_1)),hAPP_f718417177_state(F_1,B_2)) ) ) ) ) ) ) ).
fof(fact_808_folding__one_Ounion__disjoint,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite1753440478iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( A_1 != bot_bo797238721a_bool
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B_2))
=> ( B_2 != bot_bo797238721a_bool
=> ( hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) = bot_bo797238721a_bool
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,A_1)),hAPP_f1693662087iple_a(F_1,B_2)) ) ) ) ) ) ) ).
fof(fact_809_folding__one_Ounion__disjoint,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( A_1 != bot_bot_fun_nat_bool
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2))
=> ( B_2 != bot_bot_fun_nat_bool
=> ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) = bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,A_1)),hAPP_f22106695ol_nat(F_1,B_2)) ) ) ) ) ) ) ).
fof(fact_810_folding__one_Ounion__inter,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite2103247258a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,B_2))
=> ( hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2) != bot_bo332163887l_bool
=> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,A_1),B_2))),hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2))) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,hAPP_f258822235a_bool(F_1,A_1)),hAPP_f258822235a_bool(F_1,B_2)) ) ) ) ) ).
fof(fact_811_folding__one_Ounion__inter,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite1282449217_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_2))
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) != bot_bo844097828e_bool
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B_2))),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,A_1)),hAPP_f1297739591_pname(F_1,B_2)) ) ) ) ) ).
fof(fact_812_folding__one_Ounion__inter,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B_2))
=> ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2) != bot_bo784226126e_bool
=> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_1),B_2))),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2))) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(F_1,A_1)),hAPP_f718417177_state(F_1,B_2)) ) ) ) ) ).
fof(fact_813_folding__one_Ounion__inter,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite1753440478iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,B_2))
=> ( hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) != bot_bo797238721a_bool
=> hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,A_1),B_2))),hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2))) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,hAPP_f1693662087iple_a(F_1,A_1)),hAPP_f1693662087iple_a(F_1,B_2)) ) ) ) ) ).
fof(fact_814_folding__one_Ounion__inter,axiom,
! [B_2,A_1,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_2))
=> ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) != bot_bot_fun_nat_bool
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,A_1),B_2))),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,A_1)),hAPP_f22106695ol_nat(F_1,B_2)) ) ) ) ) ).
fof(fact_815_folding__one_Oinsert__remove,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite2103247258a_bool(F,F_1))
=> ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( ( hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) = bot_bo332163887l_bool
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = X_2 )
& ( hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)) != bot_bo332163887l_bool
=> hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),A_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(F,X_2),hAPP_f258822235a_bool(F_1,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1376242083l_bool(insert1421434205a_bool,X_2),bot_bo332163887l_bool)))) ) ) ) ) ).
fof(fact_816_folding__one_Oinsert__remove,axiom,
! [X_2,A_1,F,F_1] :
( is_pname(X_2)
=> ( hBOOL(finite1282449217_pname(F,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = X_2 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)) != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)))) ) ) ) ) ) ).
fof(fact_817_folding__one_Oinsert__remove,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite1753440478iple_a(F,F_1))
=> ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> ( ( hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) = bot_bo797238721a_bool
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = X_2 )
& ( hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)) != bot_bo797238721a_bool
=> hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),A_1)) = hAPP_H905846293iple_a(hAPP_H2085992369iple_a(F,X_2),hAPP_f1693662087iple_a(F_1,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,X_2),bot_bo797238721a_bool)))) ) ) ) ) ).
fof(fact_818_folding__one_Oinsert__remove,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite683959609_state(F,F_1))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_1))
=> ( ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) = bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = X_2 )
& ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)) != bot_bo784226126e_bool
=> hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),A_1)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),hAPP_f718417177_state(F_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)))) ) ) ) ) ).
fof(fact_819_folding__one_Oinsert__remove,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite988810631ne_nat(F,F_1))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = X_2 )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),A_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))) ) ) ) ) ).
fof(fact_820_inf1I,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_nat_bool(A_1,X_2))
=> ( hBOOL(hAPP_nat_bool(B_2,X_2))
=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2),X_2)) ) ) ).
fof(fact_821_inf1I,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_H1037229737a_bool(A_1,X_2))
=> ( hBOOL(hAPP_H1037229737a_bool(B_2,X_2))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2),X_2)) ) ) ).
fof(fact_822_inf1I,axiom,
! [B_2,A_1,X_2] :
( hBOOL(hAPP_pname_bool(A_1,X_2))
=> ( hBOOL(hAPP_pname_bool(B_2,X_2))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2),X_2)) ) ) ).
fof(fact_823_IntI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2))) ) ) ).
fof(fact_824_IntI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2))) ) ) ).
fof(fact_825_IntI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2))) ) ) ).
fof(fact_826_IntI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2))) ) ) ).
fof(fact_827_IntE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) ) ) ).
fof(fact_828_IntE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
=> ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) ) ) ).
fof(fact_829_IntE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
=> ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) ) ) ).
fof(fact_830_IntE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) ) ) ).
fof(fact_831_inf1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2),X_2))
=> ~ ( hBOOL(hAPP_nat_bool(A_1,X_2))
=> ~ hBOOL(hAPP_nat_bool(B_2,X_2)) ) ) ).
fof(fact_832_inf1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2),X_2))
=> ~ ( hBOOL(hAPP_H1037229737a_bool(A_1,X_2))
=> ~ hBOOL(hAPP_H1037229737a_bool(B_2,X_2)) ) ) ).
fof(fact_833_inf1E,axiom,
! [A_1,B_2,X_2] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2),X_2))
=> ~ ( hBOOL(hAPP_pname_bool(A_1,X_2))
=> ~ hBOOL(hAPP_pname_bool(B_2,X_2)) ) ) ).
fof(fact_834_DiffI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2))) ) ) ).
fof(fact_835_DiffI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
=> ( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2))) ) ) ).
fof(fact_836_DiffI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
=> ( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2))) ) ) ).
fof(fact_837_DiffI,axiom,
! [B_2,C_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2))) ) ) ).
fof(fact_838_DiffE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) ) ) ).
fof(fact_839_DiffE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) ) ) ).
fof(fact_840_DiffE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) ) ) ).
fof(fact_841_DiffE,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) ) ) ).
fof(fact_842_finite__Int,axiom,
! [Ga,F_1] :
( ( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,F_1))
| hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,Ga)) )
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,F_1),Ga))) ) ).
fof(fact_843_finite__Int,axiom,
! [Ga,F_1] :
( ( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,F_1))
| hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,Ga)) )
=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,F_1),Ga))) ) ).
fof(fact_844_finite__Int,axiom,
! [Ga,F_1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Ga)) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,F_1),Ga))) ) ).
fof(fact_845_finite__Int,axiom,
! [Ga,F_1] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,Ga)) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,F_1),Ga))) ) ).
fof(fact_846_finite__Diff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,A_1))
=> hBOOL(hAPP_f1695230391l_bool(finite1738664244iple_a,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2))) ) ).
fof(fact_847_finite__Diff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2))) ) ).
fof(fact_848_finite__Diff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2))) ) ).
fof(fact_849_finite__Diff,axiom,
! [B_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2))) ) ).
fof(fact_850_inf__Sup__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f2110825313l_bool(finite268574148a_bool,A_1))
=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,A_2),A_1))
=> hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),hAPP_f258822235a_bool(big_la1609103640a_bool,A_1)) = A_2 ) ) ).
fof(fact_851_inf__Sup__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),A_1))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),hAPP_f582319405t_bool(big_la1704749377t_bool,A_1)) = A_2 ) ) ).
fof(fact_852_inf__Sup__absorb,axiom,
! [A_2,A_1] :
( is_fun_pname_bool(A_2)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),hAPP_f674760225e_bool(big_la841148155e_bool,A_1)) = A_2 ) ) ) ).
fof(fact_853_inf__Sup__absorb,axiom,
! [A_2,A_1] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_2),hAPP_f22106695ol_nat(big_la43341705in_nat,A_1)) = A_2 ) ) ).
fof(fact_854_Diff__Int,axiom,
! [A_1,B_2,C_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),C_1)) ).
fof(fact_855_Diff__Int,axiom,
! [A_1,B_2,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),C_1)) ).
fof(fact_856_Diff__Int,axiom,
! [A_1,B_2,C_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,B_2),C_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),C_1)) ).
fof(fact_857_Diff__Int,axiom,
! [A_1,B_2,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B_2),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),B_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),C_1)) ).
fof(fact_858_Diff__Int,axiom,
! [A_1,B_2,C_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),C_1)) ).
fof(fact_859_Diff__Un,axiom,
! [A_1,B_2,C_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),C_1)) ).
fof(fact_860_Diff__Un,axiom,
! [A_1,B_2,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),C_1)) ).
fof(fact_861_Diff__Un,axiom,
! [A_1,B_2,C_1] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,B_2),C_1)) = hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),C_1)) ).
fof(fact_862_Diff__Un,axiom,
! [A_1,B_2,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_2),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),B_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),C_1)) ).
fof(fact_863_Diff__Un,axiom,
! [A_1,B_2,C_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),C_1)) ).
fof(fact_864_Un__Diff__Int,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila465093516t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)) = A_1 ).
fof(fact_865_Un__Diff__Int,axiom,
! [A_1,B_2] :
( is_fun_pname_bool(A_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)) = A_1 ) ).
fof(fact_866_Un__Diff__Int,axiom,
! [A_1,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila834425101l_bool,hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2)) = A_1 ).
fof(fact_867_Un__Diff__Int,axiom,
! [A_1,B_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_1),B_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_1),B_2)) = A_1 ).
fof(fact_868_Un__Diff__Int,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)) = A_1 ).
fof(fact_869_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(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,Pa)),hAPP_f759274231e_bool(collect_pname,Qa)) ).
fof(fact_870_Collect__conj__eq,axiom,
! [Pa,Qa] : hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),Pa)),Qa)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,hAPP_f20753329a_bool(collec351493750iple_a,Pa)),hAPP_f20753329a_bool(collec351493750iple_a,Qa)) ).
fof(fact_871_Collect__conj__eq,axiom,
! [Pa,Qa] : hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),Qa)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(collect_nat,Pa)),hAPP_f800510211t_bool(collect_nat,Qa)) ).
fof(fact_872_Int__Collect,axiom,
! [X_2,A_1,Pa] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),hAPP_f396832789l_bool(collec999179778a_bool,Pa))))
<=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X_2),A_1))
& hBOOL(hAPP_f1695230391l_bool(Pa,X_2)) ) ) ).
fof(fact_873_Int__Collect,axiom,
! [X_2,A_1,Pa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),hAPP_f800510211t_bool(collect_nat,Pa))))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_1))
& hBOOL(hAPP_nat_bool(Pa,X_2)) ) ) ).
fof(fact_874_Int__Collect,axiom,
! [X_2,A_1,Pa] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),hAPP_f20753329a_bool(collec351493750iple_a,Pa))))
<=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X_2),A_1))
& hBOOL(hAPP_H1037229737a_bool(Pa,X_2)) ) ) ).
fof(fact_875_Int__Collect,axiom,
! [X_2,A_1,Pa] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,Pa))))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
& hBOOL(hAPP_pname_bool(Pa,X_2)) ) ) ).
fof(fact_876_inf__Int__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),R_1)),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),S_2)),X))
<=> hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,X),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,R_1),S_2))) ) ).
fof(fact_877_inf__Int__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_2)),X))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,R_1),S_2))) ) ).
fof(fact_878_inf__Int__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),R_1)),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),S_2)),X))
<=> hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,R_1),S_2))) ) ).
fof(fact_879_inf__Int__eq,axiom,
! [R_1,S_2,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_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_2)),X))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S_2))) ) ).
fof(fact_880_Int__absorb,axiom,
! [A_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),A_1) = A_1 ).
fof(fact_881_Int__absorb,axiom,
! [A_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),A_1) = A_1 ).
fof(fact_882_Int__absorb,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),A_1) = A_1 ) ).
fof(fact_883_inf_Oidem,axiom,
! [A_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),A_2) = A_2 ).
fof(fact_884_inf_Oidem,axiom,
! [A_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),A_2) = A_2 ).
fof(fact_885_inf_Oidem,axiom,
! [A_6] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_6),A_6) = A_6 ).
fof(fact_886_inf_Oidem,axiom,
! [A_2] :
( is_fun_pname_bool(A_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),A_2) = A_2 ) ).
fof(fact_887_inf__idem,axiom,
! [X_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),X_2) = X_2 ).
fof(fact_888_inf__idem,axiom,
! [X_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),X_2) = X_2 ).
fof(fact_889_inf__idem,axiom,
! [X_9] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_9),X_9) = X_9 ).
fof(fact_890_inf__idem,axiom,
! [X_2] :
( is_fun_pname_bool(X_2)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),X_2) = X_2 ) ).
fof(fact_891_fun__diff__def,axiom,
! [A_1,B_2,X] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_H1037229737a_bool(A_1,X)),hAPP_H1037229737a_bool(B_2,X))) ) ).
fof(fact_892_fun__diff__def,axiom,
! [A_1,B_2,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_pname_bool(A_1,X)),hAPP_pname_bool(B_2,X))) ) ).
fof(fact_893_fun__diff__def,axiom,
! [A_1,B_2,X] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(minus_minus_bool,hAPP_nat_bool(A_1,X)),hAPP_nat_bool(B_2,X))) ) ).
fof(fact_894_inf__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_nat_bool(F,X)),hAPP_nat_bool(G,X))) ) ).
fof(fact_895_inf__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_H1037229737a_bool(F,X)),hAPP_H1037229737a_bool(G,X))) ) ).
fof(fact_896_inf__fun__def,axiom,
! [F,G,X] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,F),G),X))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_pname_bool(F,X)),hAPP_pname_bool(G,X))) ) ).
fof(fact_897_set__diff__eq,axiom,
! [A_1,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_f396832789l_bool(cOMBB_193631803a_bool(fNot),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2)))) ).
fof(fact_898_set__diff__eq,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f800510211t_bool(cOMBB_bool_bool_nat(fNot),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2)))) ).
fof(fact_899_set__diff__eq,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_f20753329a_bool(cOMBB_1882975613iple_a(fNot),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2)))) ).
fof(fact_900_set__diff__eq,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2) = 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_1))),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2)))) ).
fof(fact_901_Int__def,axiom,
! [A_1,B_2] : hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2) = hAPP_f396832789l_bool(collec999179778a_bool,hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,hAPP_f1675405437l_bool(cOMBB_703864541a_bool(fconj),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),A_1))),hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,member769771716a_bool),B_2))) ).
fof(fact_902_Int__def,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) = hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_1))),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_2))) ).
fof(fact_903_Int__def,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) = hAPP_f20753329a_bool(collec351493750iple_a,hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,hAPP_f146754017l_bool(cOMBB_1866391387iple_a(fconj),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),A_1))),hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,member1797258804iple_a),B_2))) ).
fof(fact_904_Int__def,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) = 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_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B_2))) ).
fof(fact_905_Int__commute,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),A_1) ).
fof(fact_906_Int__commute,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),A_1) ).
fof(fact_907_Int__commute,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),A_1) ).
fof(fact_908_inf_Ocommute,axiom,
! [A_2,B_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),B_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_1),A_2) ).
fof(fact_909_inf_Ocommute,axiom,
! [A_2,B_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),B_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_1),A_2) ).
fof(fact_910_inf_Ocommute,axiom,
! [A_5,B_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_5),B_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,B_5),A_5) ).
fof(fact_911_inf_Ocommute,axiom,
! [A_2,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),A_2) ).
fof(fact_912_inf__sup__aci_I1_J,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),X_2) ).
fof(fact_913_inf__sup__aci_I1_J,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),X_2) ).
fof(fact_914_inf__sup__aci_I1_J,axiom,
! [X_8,Y_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_8),Y_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_7),X_8) ).
fof(fact_915_inf__sup__aci_I1_J,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),X_2) ).
fof(fact_916_inf__commute,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),X_2) ).
fof(fact_917_inf__commute,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),X_2) ).
fof(fact_918_inf__commute,axiom,
! [X_7,Y_6] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_7),Y_6) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_6),X_7) ).
fof(fact_919_inf__commute,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),X_2) ).
fof(fact_920_Int__left__absorb,axiom,
! [A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2) ).
fof(fact_921_Int__left__absorb,axiom,
! [A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2) ).
fof(fact_922_Int__left__absorb,axiom,
! [A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2) ).
fof(fact_923_inf_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),B_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),B_1) ).
fof(fact_924_inf_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),B_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),B_1) ).
fof(fact_925_inf_Oleft__idem,axiom,
! [A_4,B_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),B_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_4),B_4) ).
fof(fact_926_inf_Oleft__idem,axiom,
! [A_2,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),B_1) ).
fof(fact_927_inf__sup__aci_I4_J,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1) ).
fof(fact_928_inf__sup__aci_I4_J,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1) ).
fof(fact_929_inf__sup__aci_I4_J,axiom,
! [X_6,Y_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),Y_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_6),Y_5) ).
fof(fact_930_inf__sup__aci_I4_J,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1) ).
fof(fact_931_inf__left__idem,axiom,
! [X_2,Y_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Y_1) ).
fof(fact_932_inf__left__idem,axiom,
! [X_2,Y_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Y_1) ).
fof(fact_933_inf__left__idem,axiom,
! [X_5,Y_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),Y_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_5),Y_4) ).
fof(fact_934_inf__left__idem,axiom,
! [X_2,Y_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_1) ).
fof(fact_935_Int__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),C_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),C_1)) ).
fof(fact_936_Int__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),C_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),C_1)) ).
fof(fact_937_Int__left__commute,axiom,
! [A_1,B_2,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),C_1)) ).
fof(fact_938_inf_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),C_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,B_1),C_2)) ).
fof(fact_939_inf_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),C_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,B_1),C_2)) ).
fof(fact_940_inf_Oleft__commute,axiom,
! [B_3,A_3,C_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,B_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_3),C_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,A_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,B_3),C_3)) ).
fof(fact_941_inf_Oleft__commute,axiom,
! [B_1,A_2,C_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),C_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),C_2)) ).
fof(fact_942_inf__sup__aci_I3_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Z_1)) ).
fof(fact_943_inf__sup__aci_I3_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Z_1)) ).
fof(fact_944_inf__sup__aci_I3_J,axiom,
! [X_4,Y_3,Z_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_3),Z_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_4),Z_3)) ).
fof(fact_945_inf__sup__aci_I3_J,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1)) ).
fof(fact_946_inf__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),Z_1)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,Y_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,X_2),Z_1)) ).
fof(fact_947_inf__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),Z_1)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,Y_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,X_2),Z_1)) ).
fof(fact_948_inf__left__commute,axiom,
! [X_3,Y_2,Z_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_2),Z_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,Y_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(semila80283416nf_nat,X_3),Z_2)) ).
fof(fact_949_inf__left__commute,axiom,
! [X_2,Y_1,Z_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1)) ).
fof(fact_950_Diff__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(minus_98295210l_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
& ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) ) ) ).
fof(fact_951_Diff__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) ) ) ).
fof(fact_952_Diff__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
& ~ hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) ) ) ).
fof(fact_953_Diff__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) ) ) ).
fof(fact_954_Int__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),hAPP_f396832789l_bool(hAPP_f1340058745l_bool(semila753742375l_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),A_1))
& hBOOL(hAPP_f2110825313l_bool(hAPP_f293818473l_bool(member769771716a_bool,C_2),B_2)) ) ) ).
fof(fact_955_Int__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_1))
& hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_2)) ) ) ).
fof(fact_956_Int__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),A_1))
& hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,C_2),B_2)) ) ) ).
fof(fact_957_Int__iff,axiom,
! [C_2,A_1,B_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B_2)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),A_1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_2),B_2)) ) ) ).
fof(fact_958_Diff__Int__distrib,axiom,
! [C_1,A_1,B_2] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,C_1),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,A_1),B_2)) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(minus_85316870a_bool,hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,C_1),A_1)),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila286921929a_bool,C_1),B_2)) ).
fof(fact_959_Diff__Int__distrib,axiom,
! [C_1,A_1,B_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),B_2)) ).
fof(fact_960_Diff__Int__distrib,axiom,
! [C_1,A_1,B_2] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_1),B_2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,C_1),A_1)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(semila840543986t_bool,C_1),B_2)) ).
fof(fact_961_diff__0__eq__0,axiom,
! [N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N_2) = zero_zero_nat ).
fof(fact_962_minus__nat_Odiff__0,axiom,
! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),zero_zero_nat) = M_2 ).
fof(fact_963_diff__self__eq__0,axiom,
! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),M_2) = zero_zero_nat ).
fof(fact_964_diffs0__imp__equal,axiom,
! [M_2,N_2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) = zero_zero_nat
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),M_2) = zero_zero_nat
=> M_2 = N_2 ) ) ).
fof(fact_965_diff__Suc__Suc,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) ).
fof(fact_966_Suc__diff__diff,axiom,
! [M_2,N_2,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_2)),N_2)),hAPP_nat_nat(suc,K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),K_2) ).
fof(fact_967_diff__commute,axiom,
! [I,J_1,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),K_2)),J_1) ).
fof(fact_968_zero__induct__lemma,axiom,
! [I_1,Pa,K_1] :
( hBOOL(hAPP_nat_bool(Pa,K_1))
=> ( ! [N] :
( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N)))
=> hBOOL(hAPP_nat_bool(Pa,N)) )
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_1),I_1))) ) ) ).
fof(fact_969_diff__Suc,axiom,
! [M,N_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_1)) ).
fof(fact_970_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).
fof(fact_971_diff__Suc__1,axiom,
! [N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N_2)),one_one_nat) = N_2 ).
fof(fact_972_diff__Suc__eq__diff__pred,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),one_one_nat)),N_2) ).
fof(fact_973_plus__nat_Oadd__0,axiom,
! [N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_2) = N_2 ).
fof(fact_974_Nat_Oadd__0__right,axiom,
! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2 ).
fof(fact_975_add__is__0,axiom,
! [M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1) = zero_zero_nat
<=> ( M = zero_zero_nat
& N_1 = zero_zero_nat ) ) ).
fof(fact_976_add__eq__self__zero,axiom,
! [M_2,N_2] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = M_2
=> N_2 = zero_zero_nat ) ).
fof(fact_977_add__Suc__right,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)) ).
fof(fact_978_add__Suc,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)) ).
fof(fact_979_add__Suc__shift,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_2)) ).
fof(fact_980_nat__add__commute,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2) ).
fof(fact_981_nat__add__left__commute,axiom,
! [X_1,Y,Z] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),Z)) ).
fof(fact_982_nat__add__assoc,axiom,
! [M_2,N_2,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),K_2)) ).
fof(fact_983_nat__add__left__cancel,axiom,
! [K_1,M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)
<=> M = N_1 ) ).
fof(fact_984_nat__add__right__cancel,axiom,
! [M,K_1,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)
<=> M = N_1 ) ).
fof(fact_985_diff__add__inverse2,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)),N_2) = M_2 ).
fof(fact_986_diff__add__inverse,axiom,
! [N_2,M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)),N_2) = M_2 ).
fof(fact_987_diff__diff__left,axiom,
! [I,J_1,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2)) ).
fof(fact_988_diff__cancel,axiom,
! [K_2,M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) ).
fof(fact_989_diff__cancel2,axiom,
! [M_2,K_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) ).
fof(fact_990_add__is__1,axiom,
! [M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( M = hAPP_nat_nat(suc,zero_zero_nat)
& N_1 = zero_zero_nat )
| ( M = zero_zero_nat
& N_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_991_one__is__add,axiom,
! [M,N_1] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1)
<=> ( ( M = hAPP_nat_nat(suc,zero_zero_nat)
& N_1 = zero_zero_nat )
| ( M = zero_zero_nat
& N_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_992_diff__add__0,axiom,
! [N_2,M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)) = zero_zero_nat ).
fof(fact_993_Suc__eq__plus1,axiom,
! [N_2] : hAPP_nat_nat(suc,N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),one_one_nat) ).
fof(fact_994_Suc__eq__plus1__left,axiom,
! [N_2] : hAPP_nat_nat(suc,N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_2) ).
fof(fact_995_add__eq__if,axiom,
! [N_2,M_2] :
( ( M_2 = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = N_2 )
& ( M_2 != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),one_one_nat)),N_2)) ) ) ).
fof(fact_996_com_Osize_I4_J,axiom,
! [Com1_2,Com2_2] : com_size(semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1_2)),com_size(Com2_2))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_997_com_Osize_I6_J,axiom,
! [Fun_1,Com_1] : com_size(while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_998_com_Osize_I7_J,axiom,
! [Pname_1] : com_size(hAPP_pname_com(body,Pname_1)) = zero_zero_nat ).
fof(fact_999_com_Osize_I1_J,axiom,
com_size(skip) = zero_zero_nat ).
fof(fact_1000_com_Osize_I12_J,axiom,
! [Com1_2,Com2_2] : hAPP_com_nat(size_size_com,semi(Com1_2,Com2_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_com_nat(size_size_com,Com1_2)),hAPP_com_nat(size_size_com,Com2_2))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1001_com_Osize_I14_J,axiom,
! [Fun_1,Com_1] : hAPP_com_nat(size_size_com,while(Fun_1,Com_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_com_nat(size_size_com,Com_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1002_add__mult__distrib2,axiom,
! [K_2,M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_2)) ).
fof(fact_1003_add__mult__distrib,axiom,
! [M_2,N_2,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),K_2)) ).
fof(fact_1004_nat__mult__eq__1__iff,axiom,
! [M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) = one_one_nat
<=> ( M = one_one_nat
& N_1 = one_one_nat ) ) ).
fof(fact_1005_nat__mult__1__right,axiom,
! [N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),one_one_nat) = N_2 ).
fof(fact_1006_nat__1__eq__mult__iff,axiom,
! [M,N_1] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1)
<=> ( M = one_one_nat
& N_1 = one_one_nat ) ) ).
fof(fact_1007_nat__mult__1,axiom,
! [N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N_2) = N_2 ).
fof(fact_1008_mult__0,axiom,
! [N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N_2) = zero_zero_nat ).
fof(fact_1009_mult__0__right,axiom,
! [M_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),zero_zero_nat) = zero_zero_nat ).
fof(fact_1010_mult__is__0,axiom,
! [M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) = zero_zero_nat
<=> ( M = zero_zero_nat
| N_1 = zero_zero_nat ) ) ).
fof(fact_1011_mult__cancel1,axiom,
! [K_1,M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)
<=> ( M = N_1
| K_1 = zero_zero_nat ) ) ).
fof(fact_1012_mult__cancel2,axiom,
! [M,K_1,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1)
<=> ( M = N_1
| K_1 = zero_zero_nat ) ) ).
fof(fact_1013_Suc__mult__cancel1,axiom,
! [K_1,M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N_1)
<=> M = N_1 ) ).
fof(fact_1014_diff__mult__distrib,axiom,
! [M_2,N_2,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),K_2)) ).
fof(fact_1015_diff__mult__distrib2,axiom,
! [K_2,M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),N_2)) ).
fof(fact_1016_mult__eq__1__iff,axiom,
! [M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( M = hAPP_nat_nat(suc,zero_zero_nat)
& N_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ).
fof(fact_1017_mult__Suc,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2)) ).
fof(fact_1018_mult__Suc__right,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),hAPP_nat_nat(suc,N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2)) ).
fof(fact_1019_mult__eq__self__implies__10,axiom,
! [M_2,N_2] :
( M_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2)
=> ( N_2 = one_one_nat
| M_2 = zero_zero_nat ) ) ).
fof(fact_1020_com_Osize_I15_J,axiom,
! [Pname_1] : hAPP_com_nat(size_size_com,hAPP_pname_com(body,Pname_1)) = zero_zero_nat ).
fof(fact_1021_com_Osize_I9_J,axiom,
hAPP_com_nat(size_size_com,skip) = zero_zero_nat ).
fof(fact_1022_mult__eq__if,axiom,
! [N_2,M_2] :
( ( M_2 = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) = zero_zero_nat )
& ( M_2 != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),one_one_nat)),N_2)) ) ) ).
fof(fact_1023_nat__mult__commute,axiom,
! [M_2,N_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),M_2) ).
fof(fact_1024_nat__mult__assoc,axiom,
! [M_2,N_2,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),N_2)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_2),K_2)) ).
fof(fact_1025_left__add__mult__distrib,axiom,
! [I,U_1,J_1,K_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),U_1)),K_2) ).
fof(fact_1026_nat__mult__eq__cancel__disj,axiom,
! [K_1,M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)
<=> ( K_1 = zero_zero_nat
| M = N_1 ) ) ).
fof(fact_1027_com_Osize_I13_J,axiom,
! [Fun_1,Com1_1,Com2_1] : hAPP_com_nat(size_size_com,cond(Fun_1,Com1_1,Com2_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_com_nat(size_size_com,Com1_1)),hAPP_com_nat(size_size_com,Com2_1))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1028_com_Osize_I5_J,axiom,
! [Fun_1,Com1_1,Com2_1] : com_size(cond(Fun_1,Com1_1,Com2_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,com_size(Com1_1)),com_size(Com2_1))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_1029_finite__Collect__le__nat,axiom,
! [K_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K_1)))) ).
fof(fact_1030_le0,axiom,
! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_2)) ).
fof(fact_1031_evaln__elim__cases_I5_J,axiom,
! [B_1,C1,C2,S_1,N_1,T_1] :
( hBOOL(hAPP_state_bool(evaln(cond(B_1,C1,C2),S_1,N_1),T_1))
=> ( ( hBOOL(hAPP_state_bool(B_1,S_1))
=> ~ hBOOL(hAPP_state_bool(evaln(C1,S_1,N_1),T_1)) )
=> ~ ( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> ~ hBOOL(hAPP_state_bool(evaln(C2,S_1,N_1),T_1)) ) ) ) ).
fof(fact_1032_evaln_OIfTrue,axiom,
! [C1,C0,N_1,S1,B_1,S_1] :
( hBOOL(hAPP_state_bool(B_1,S_1))
=> ( hBOOL(hAPP_state_bool(evaln(C0,S_1,N_1),S1))
=> hBOOL(hAPP_state_bool(evaln(cond(B_1,C0,C1),S_1,N_1),S1)) ) ) ).
fof(fact_1033_evaln_OIfFalse,axiom,
! [C0,C1,N_1,S1,B_1,S_1] :
( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> ( hBOOL(hAPP_state_bool(evaln(C1,S_1,N_1),S1))
=> hBOOL(hAPP_state_bool(evaln(cond(B_1,C0,C1),S_1,N_1),S1)) ) ) ).
fof(fact_1034_evalc_OIfFalse,axiom,
! [C0,C1,S1,B_1,S_1] :
( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_1),S1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B_1,C0,C1)),S_1),S1)) ) ) ).
fof(fact_1035_evalc_OIfTrue,axiom,
! [C1,C0,S1,B_1,S_1] :
( hBOOL(hAPP_state_bool(B_1,S_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S_1),S1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B_1,C0,C1)),S_1),S1)) ) ) ).
fof(fact_1036_evalc__elim__cases_I5_J,axiom,
! [B_1,C1,C2,S_1,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(cond(B_1,C1,C2)),S_1),T_1))
=> ( ( hBOOL(hAPP_state_bool(B_1,S_1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_1),T_1)) )
=> ~ ( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S_1),T_1)) ) ) ) ).
fof(fact_1037_com_Osimps_I55_J,axiom,
! [Pname,Fun_1,Com1_1,Com2_1] : hAPP_pname_com(body,Pname) != cond(Fun_1,Com1_1,Com2_1) ).
fof(fact_1038_com_Osimps_I54_J,axiom,
! [Fun_1,Com1_1,Com2_1,Pname] : cond(Fun_1,Com1_1,Com2_1) != hAPP_pname_com(body,Pname) ).
fof(fact_1039_com_Osimps_I4_J,axiom,
! [Fun_1,Com1_1,Com2_1,Fun,Com1,Com2] :
( cond(Fun_1,Com1_1,Com2_1) = cond(Fun,Com1,Com2)
<=> ( Fun_1 = Fun
& Com1_1 = Com1
& Com2_1 = Com2 ) ) ).
fof(fact_1040_le__antisym,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2))
=> M_2 = N_2 ) ) ).
fof(fact_1041_le__trans,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2)) ) ) ).
fof(fact_1042_eq__imp__le,axiom,
! [M_2,N_2] :
( M_2 = N_2
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).
fof(fact_1043_nat__le__linear,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2)) ) ).
fof(fact_1044_le__refl,axiom,
! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),N_2)) ).
fof(fact_1045_Suc__leD,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).
fof(fact_1046_le__SucE,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_2)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> M_2 = hAPP_nat_nat(suc,N_2) ) ) ).
fof(fact_1047_le__SucI,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_2))) ) ).
fof(fact_1048_Suc__le__mono,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),hAPP_nat_nat(suc,M)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) ) ).
fof(fact_1049_le__Suc__eq,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| M = hAPP_nat_nat(suc,N_1) ) ) ).
fof(fact_1050_not__less__eq__eq,axiom,
! [M,N_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M)) ) ).
fof(fact_1051_Suc__n__not__le__n,axiom,
! [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),N_2)) ).
fof(fact_1052_le__0__eq,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),zero_zero_nat))
<=> N_1 = zero_zero_nat ) ).
fof(fact_1053_less__eq__nat_Osimps_I1_J,axiom,
! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_2)) ).
fof(fact_1054_evaln__nonstrict,axiom,
! [M_2,C,S,N_2,T] :
( hBOOL(hAPP_state_bool(evaln(C,S,N_2),T))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2))
=> hBOOL(hAPP_state_bool(evaln(C,S,M_2),T)) ) ) ).
fof(fact_1055_diff__le__self,axiom,
! [M_2,N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),M_2)) ).
fof(fact_1056_diff__le__mono2,axiom,
! [L,M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M_2))) ) ).
fof(fact_1057_diff__le__mono,axiom,
! [L,M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),L)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),L))) ) ).
fof(fact_1058_diff__diff__cancel,axiom,
! [I,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),I)) = I ) ).
fof(fact_1059_eq__diff__iff,axiom,
! [N_1,K_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1)
<=> M = N_1 ) ) ) ).
fof(fact_1060_Nat_Odiff__diff__eq,axiom,
! [N_2,K_2,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) ) ) ).
fof(fact_1061_le__diff__iff,axiom,
! [N_1,K_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ) ) ).
fof(fact_1062_add__leE,axiom,
! [M_2,K_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N_2))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2)) ) ) ).
fof(fact_1063_add__leD1,axiom,
! [M_2,K_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).
fof(fact_1064_add__leD2,axiom,
! [M_2,K_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2)) ) ).
fof(fact_1065_add__le__mono,axiom,
! [K_2,L,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L))) ) ) ).
fof(fact_1066_add__le__mono1,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ) ).
fof(fact_1067_trans__le__add2,axiom,
! [M_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ) ).
fof(fact_1068_trans__le__add1,axiom,
! [M_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ) ).
fof(fact_1069_nat__add__left__cancel__le,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ).
fof(fact_1070_le__iff__add,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
<=> ? [K] : N_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) ) ).
fof(fact_1071_le__add1,axiom,
! [N_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2))) ).
fof(fact_1072_le__add2,axiom,
! [N_2,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_2))) ).
fof(fact_1073_card__Collect__le__nat,axiom,
! [N_1] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),N_1))) = hAPP_nat_nat(suc,N_1) ).
fof(fact_1074_less__eq__nat_Osimps_I2_J,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1))
<=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),N_1)) ) ).
fof(fact_1075_mult__le__mono,axiom,
! [K_2,L,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),L))) ) ) ).
fof(fact_1076_mult__le__mono2,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),J_1))) ) ).
fof(fact_1077_mult__le__mono1,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),K_2))) ) ).
fof(fact_1078_le__cube,axiom,
! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),M_2)))) ).
fof(fact_1079_le__square,axiom,
! [M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_2),M_2))) ).
fof(fact_1080_com_Osimps_I52_J,axiom,
! [Fun_1,Com1_1,Com2_1,Fun,Com] : cond(Fun_1,Com1_1,Com2_1) != while(Fun,Com) ).
fof(fact_1081_com_Osimps_I53_J,axiom,
! [Fun,Com,Fun_1,Com1_1,Com2_1] : while(Fun,Com) != cond(Fun_1,Com1_1,Com2_1) ).
fof(fact_1082_com_Osimps_I45_J,axiom,
! [Fun,Com1,Com2,Com1_1,Com2_1] : cond(Fun,Com1,Com2) != semi(Com1_1,Com2_1) ).
fof(fact_1083_com_Osimps_I44_J,axiom,
! [Com1_1,Com2_1,Fun,Com1,Com2] : semi(Com1_1,Com2_1) != cond(Fun,Com1,Com2) ).
fof(fact_1084_com_Osimps_I15_J,axiom,
! [Fun,Com1,Com2] : cond(Fun,Com1,Com2) != skip ).
fof(fact_1085_com_Osimps_I14_J,axiom,
! [Fun,Com1,Com2] : skip != cond(Fun,Com1,Com2) ).
fof(fact_1086_diff__is__0__eq_H,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2) = zero_zero_nat ) ).
fof(fact_1087_diff__is__0__eq,axiom,
! [M,N_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_1) = zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ).
fof(fact_1088_Suc__diff__le,axiom,
! [N_2,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_2)),N_2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) ) ).
fof(fact_1089_Suc__mult__le__cancel1,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ).
fof(fact_1090_diff__diff__right,axiom,
! [I,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),J_1) ) ).
fof(fact_1091_le__diff__conv,axiom,
! [J_2,K_1,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_1)),I_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1))) ) ).
fof(fact_1092_le__add__diff,axiom,
! [M_2,K_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),M_2)),K_2))) ) ).
fof(fact_1093_le__add__diff__inverse,axiom,
! [N_2,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) = M_2 ) ).
fof(fact_1094_add__diff__assoc,axiom,
! [I,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),K_2) ) ).
fof(fact_1095_le__diff__conv2,axiom,
! [I_1,K_1,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J_2)) ) ) ).
fof(fact_1096_le__add__diff__inverse2,axiom,
! [N_2,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),M_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),N_2) = M_2 ) ).
fof(fact_1097_le__imp__diff__is__add,axiom,
! [K_1,I_1,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_1) = K_1
<=> J_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),I_1) ) ) ).
fof(fact_1098_diff__add__assoc,axiom,
! [I,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)) ) ).
fof(fact_1099_add__diff__assoc2,axiom,
! [I,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)),I) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I)),K_2) ) ).
fof(fact_1100_diff__add__assoc2,axiom,
! [I,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2)),I) ) ).
fof(fact_1101_one__le__mult__iff,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),N_1)) ) ) ).
fof(fact_1102_diff__Suc__diff__eq2,axiom,
! [M_2,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2))),M_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),M_2)) ) ).
fof(fact_1103_diff__Suc__diff__eq1,axiom,
! [M_2,K_2,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_2))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),hAPP_nat_nat(suc,J_1)) ) ).
fof(fact_1104_nat__le__add__iff1,axiom,
! [U,M,N_1,J_2,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J_2)),U)),M)),N_1)) ) ) ).
fof(fact_1105_nat__diff__add__eq1,axiom,
! [U_1,M_2,N_2,J_1,I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U_1)),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J_1)),U_1)),M_2)),N_2) ) ).
fof(fact_1106_nat__eq__add__iff1,axiom,
! [U,M,N_1,J_2,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_1))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1)
<=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J_2)),U)),M) = N_1 ) ) ).
fof(fact_1107_nat__le__add__iff2,axiom,
! [U,M,N_1,I_1,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_1)),U)),N_1))) ) ) ).
fof(fact_1108_nat__diff__add__eq2,axiom,
! [U_1,M_2,N_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_1))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),U_1)),M_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U_1)),N_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I)),U_1)),N_2)) ) ).
fof(fact_1109_nat__eq__add__iff2,axiom,
! [U,M,N_1,I_1,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_2))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_2),U)),N_1)
<=> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),I_1)),U)),N_1) ) ) ).
fof(fact_1110_Suc__le__D,axiom,
! [N_2,M_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_2)),M_4))
=> ? [M_1] : M_4 = hAPP_nat_nat(suc,M_1) ) ).
fof(fact_1111_Suc__le__D__lemma,axiom,
! [Pa,N_1,M_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_3))
=> ( ! [M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,M_1))) )
=> hBOOL(hAPP_nat_bool(Pa,M_3)) ) ) ).
fof(fact_1112_finite__nat__set__iff__bounded__le,axiom,
! [N_3] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3))
<=> ? [M_1] :
! [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),N_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),M_1)) ) ) ).
fof(fact_1113_finite__less__ub,axiom,
! [U,F] :
( ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))) ) ).
fof(fact_1114_termination__basic__simps_I3_J,axiom,
! [Z,X_1,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1115_termination__basic__simps_I4_J,axiom,
! [Y,X_1,Z] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1116_less__zeroE,axiom,
! [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),zero_zero_nat)) ).
fof(fact_1117_lessI,axiom,
! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,N_2))) ).
fof(fact_1118_Suc__mono,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2))) ) ).
fof(fact_1119_finite__Collect__less__nat,axiom,
! [K_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K_1)))) ).
fof(fact_1120_zero__less__Suc,axiom,
! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_2))) ).
fof(fact_1121_finite__M__bounded__by__nat,axiom,
! [Pa,I_1] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) ).
fof(fact_1122_finite__nat__set__iff__bounded,axiom,
! [N_3] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_3))
<=> ? [M_1] :
! [X] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X),N_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),M_1)) ) ) ).
fof(fact_1123_less__or__eq__imp__le,axiom,
! [M_2,N_2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
| M_2 = N_2 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).
fof(fact_1124_le__neq__implies__less,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> ( M_2 != N_2
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ) ).
fof(fact_1125_less__imp__le__nat,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2)) ) ).
fof(fact_1126_le__eq__less__or__eq,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| M = N_1 ) ) ).
fof(fact_1127_nat__less__le,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
& M != N_1 ) ) ).
fof(fact_1128_Suc__le__lessD,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).
fof(fact_1129_le__less__Suc__eq,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M)))
<=> N_1 = M ) ) ).
fof(fact_1130_Suc__leI,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_2)) ) ).
fof(fact_1131_le__imp__less__Suc,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))) ) ).
fof(fact_1132_Suc__le__eq,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ).
fof(fact_1133_less__Suc__eq__le,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ).
fof(fact_1134_less__eq__Suc__le,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M)) ) ).
fof(fact_1135_less__diff__iff,axiom,
! [N_1,K_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ) ) ).
fof(fact_1136_diff__less__mono,axiom,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B),C))) ) ) ).
fof(fact_1137_not__add__less1,axiom,
! [I,J_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),I)) ).
fof(fact_1138_not__add__less2,axiom,
! [J_1,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I)),I)) ).
fof(fact_1139_nat__add__left__cancel__less,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ).
fof(fact_1140_trans__less__add1,axiom,
! [M_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ) ).
fof(fact_1141_trans__less__add2,axiom,
! [M_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ) ).
fof(fact_1142_add__less__mono1,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ) ).
fof(fact_1143_add__less__mono,axiom,
! [K_2,L,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L))) ) ) ).
fof(fact_1144_less__add__eq__less,axiom,
! [M_2,N_2,K_2,L] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N_2)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ) ).
fof(fact_1145_add__lessD1,axiom,
! [I,J_1,K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_1)),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)) ) ).
fof(fact_1146_diff__less__mono2,axiom,
! [L,M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M_2))) ) ) ).
fof(fact_1147_less__imp__diff__less,axiom,
! [N_2,J_1,K_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),N_2)),K_2)) ) ).
fof(fact_1148_not__less0,axiom,
! [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),zero_zero_nat)) ).
fof(fact_1149_neq0__conv,axiom,
! [N_1] :
( N_1 != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ).
fof(fact_1150_less__nat__zero__code,axiom,
! [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),zero_zero_nat)) ).
fof(fact_1151_gr__implies__not0,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> N_2 != zero_zero_nat ) ).
fof(fact_1152_gr0I,axiom,
! [N_2] :
( N_2 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2)) ) ).
fof(fact_1153_not__less__eq,axiom,
! [M,N_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M))) ) ).
fof(fact_1154_less__Suc__eq,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| M = N_1 ) ) ).
fof(fact_1155_Suc__less__eq,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ).
fof(fact_1156_not__less__less__Suc__eq,axiom,
! [N_1,M] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M)))
<=> N_1 = M ) ) ).
fof(fact_1157_less__antisym,axiom,
! [N_2,M_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),hAPP_nat_nat(suc,M_2)))
=> M_2 = N_2 ) ) ).
fof(fact_1158_less__SucI,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2))) ) ).
fof(fact_1159_Suc__lessI,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> ( hAPP_nat_nat(suc,M_2) != N_2
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_2)) ) ) ).
fof(fact_1160_less__trans__Suc,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_2)) ) ) ).
fof(fact_1161_less__SucE,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_2)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> M_2 = N_2 ) ) ).
fof(fact_1162_Suc__lessD,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).
fof(fact_1163_Suc__less__SucD,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_2)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ).
fof(fact_1164_less__not__refl,axiom,
! [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),N_2)) ).
fof(fact_1165_nat__neq__iff,axiom,
! [M,N_1] :
( M != N_1
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) ) ) ).
fof(fact_1166_linorder__neqE__nat,axiom,
! [X_1,Y] :
( X_1 != Y
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X_1)) ) ) ).
fof(fact_1167_less__irrefl__nat,axiom,
! [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),N_2)) ).
fof(fact_1168_less__not__refl2,axiom,
! [N_2,M_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_2),M_2))
=> M_2 != N_2 ) ).
fof(fact_1169_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ) ).
fof(fact_1170_nat__less__cases,axiom,
! [Pa,M,N_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M)) )
=> ( ( M = N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N_1),M)) ) ) ) ).
fof(fact_1171_less__diff__conv,axiom,
! [I_1,J_2,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_2),K_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J_2)) ) ).
fof(fact_1172_add__diff__inverse,axiom,
! [M_2,N_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)) = M_2 ) ).
fof(fact_1173_Suc__mult__less__cancel1,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K_1)),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ).
fof(fact_1174_diff__less__Suc,axiom,
! [M_2,N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),hAPP_nat_nat(suc,M_2))) ).
fof(fact_1175_nat__0__less__mult__iff,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),N_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ) ).
fof(fact_1176_mult__less__cancel1,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ) ).
fof(fact_1177_mult__less__cancel2,axiom,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N_1),K_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ) ).
fof(fact_1178_mult__less__mono1,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),K_2))) ) ) ).
fof(fact_1179_mult__less__mono2,axiom,
! [K_2,I,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_2),J_1))) ) ) ).
fof(fact_1180_nat__mult__eq__cancel1,axiom,
! [M,N_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)
<=> M = N_1 ) ) ).
fof(fact_1181_nat__mult__less__cancel1,axiom,
! [M,N_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ) ).
fof(fact_1182_diff__less,axiom,
! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_2),N_2)),M_2)) ) ) ).
fof(fact_1183_zero__less__diff,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ).
fof(fact_1184_less__add__Suc1,axiom,
! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2)))) ).
fof(fact_1185_less__add__Suc2,axiom,
! [I,M_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I)))) ).
fof(fact_1186_less__iff__Suc__add,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
<=> ? [K] : N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)) ) ).
fof(fact_1187_add__gr__0,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_1)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ) ).
fof(fact_1188_gr0__conv__Suc,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
<=> ? [M_1] : N_1 = hAPP_nat_nat(suc,M_1) ) ).
fof(fact_1189_less__Suc0,axiom,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,zero_zero_nat)))
<=> N_1 = zero_zero_nat ) ).
fof(fact_1190_less__Suc__eq__0__disj,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_1)))
<=> ( M = zero_zero_nat
| ? [J] :
( M = hAPP_nat_nat(suc,J)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),N_1)) ) ) ) ).
fof(fact_1191_card__Collect__less__nat,axiom,
! [N_1] : hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),N_1))) = N_1 ).
fof(fact_1192_less__eq__Suc__le__raw,axiom,
! [X] : hAPP_n1699378549t_bool(ord_less_nat,X) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X)) ).
fof(fact_1193_termination__basic__simps_I1_J,axiom,
! [Z,X_1,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1194_termination__basic__simps_I2_J,axiom,
! [Y,X_1,Z] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).
fof(fact_1195_termination__basic__simps_I5_J,axiom,
! [X_1,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y)) ) ).
%----Helper facts (160)
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__Nat__Onat_T,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X_1),Y)) ) ).
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__Nat__Onat_000tc__Nat__Onat_U,axiom,
! [P,Q] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(cOMBK_nat_nat,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__Com__Opname_U,axiom,
! [P,Q] : hAPP_pname_nat(hAPP_n362732366me_nat(cOMBK_nat_pname,P),Q) = P ).
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__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_1),Y)) ) ).
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_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBB_bool_bool_nat(P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f561022312t_bool(cOMBS_nat_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_n1025906991e_bool(hAPP_f1715247037e_bool(cOMBC_pname_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_p1499970991t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_p1499970991t_bool(hAPP_f998021053t_bool(cOMBC_nat_pname_bool,P),Q),R) = hAPP_pname_bool(hAPP_n1025906991e_bool(P,R),Q) ).
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_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____uwgpyvfjxg__Otriple_It__a_J_,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_H1037229737a_bool(hAPP_H426895267a_bool(fequal963300192iple_a,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_H1037229737a_bool(hAPP_H426895267a_bool(fequal963300192iple_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_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_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____uwgpyvfjxg__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H1037229737a_bool(hAPP_b1882817719a_bool(cOMBK_235286536iple_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____uwgpyvfjxg__Otriple_It__a_J_00,axiom,
! [P,Q] : hAPP_p346744818iple_a(hAPP_H327714446iple_a(cOMBK_523903665_pname,P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f158894502t_bool(cOMBB_955900739ol_nat(P),Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__013,axiom,
! [P,Q,R] : hAPP_p1499970991t_bool(hAPP_f1358769483t_bool(cOMBB_523834888_pname(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_pname_nat(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [P,Q,R] : hAPP_n1025906991e_bool(hAPP_f414474559e_bool(cOMBB_1212655066ol_nat(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_nat_pname(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_014,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_015,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_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_016,axiom,
! [P,Q,R] : hAPP_p61793385e_bool(hAPP_f1336811455e_bool(cOMBB_542850580_pname(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R)) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(fequal874423448a_bool,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(fequal874423448a_bool,X_1),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg___017,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H242767318e_bool(hAPP_b974863576e_bool(cOMBK_988866959_state,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q] : hAPP_p1751618853_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,P),Q) = P ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hAPP_f228417655a_bool(cOMBC_364739t_bool,P),Q),R) = hAPP_nat_bool(hAPP_H144868812t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_H144868812t_bool(hAPP_f1886543991t_bool(cOMBC_533513393a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
! [P,Q,R] : hAPP_H1037229737a_bool(hAPP_f20753329a_bool(cOMBB_1882975613iple_a(P),Q),R) = hAPP_bool_bool(P,hAPP_H1037229737a_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f607497069a_bool(cOMBS_154988028l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H2130837971l_bool(P,R),hAPP_H1037229737a_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_H1078816262e_bool(hAPP_f421895915e_bool(cOMBC_1309726071a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_p1743421830a_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_018,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_019,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____uwg,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1695230391l_bool(hAPP_b83765433l_bool(cOMBK_404565488a_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,axiom,
! [P,Q] : hAPP_p1743421830a_bool(hAPP_f624861966a_bool(cOMBK_1667642481_pname,P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel_020,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f806699093e_bool(cOMBB_325909978_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H242767318e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1270401638l_bool(P,R),hAPP_H242767318e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__021,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_p606792009e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__022,axiom,
! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(hAPP_f688831301t_bool(cOMBC_178881787t_bool,P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_n1025906991e_bool(hAPP_f1501416730e_bool(hAPP_f883303749e_bool(cOMBC_1771919087e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_n60670500e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_023,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_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg,axiom,
! [X_1,Y] :
( ~ hBOOL(hAPP_f2110825313l_bool(hAPP_f1303207443l_bool(fequal1455900568l_bool,X_1),Y))
| X_1 = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg,axiom,
! [X_1,Y] :
( X_1 != Y
| hBOOL(hAPP_f2110825313l_bool(hAPP_f1303207443l_bool(fequal1455900568l_bool,X_1),Y)) ) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__024,axiom,
! [P,Q,R] : hAPP_H144868812t_bool(hAPP_f1872860171t_bool(cOMBB_1391527205iple_a(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_H592031934_a_nat(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp,axiom,
! [P,Q,R] : hAPP_nat_bool(hAPP_f1968395738t_bool(hAPP_f2110185157t_bool(cOMBC_805992879l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_n37219812l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,axiom,
! [P,Q,R] : hAPP_f1695230391l_bool(hAPP_n37219812l_bool(hAPP_f1852971749l_bool(cOMBC_594836627t_bool,P),Q),R) = hAPP_nat_bool(hAPP_f1968395738t_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
! [P,Q,R] : hAPP_f1695230391l_bool(hAPP_f396832789l_bool(cOMBB_193631803a_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1695230391l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_025,axiom,
! [P,Q,R] : hAPP_H2130837971l_bool(hAPP_f146754017l_bool(cOMBB_1866391387iple_a(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1037229737a_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,axiom,
! [P,Q,R] : hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f288270593l_bool(cOMBS_824156748l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f244528453l_bool(P,R),hAPP_f1695230391l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_f1216026388e_bool(hAPP_f1415030585e_bool(cOMBC_173670761l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_p1910214954l_bool(P,R),Q) ).
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_026,axiom,
! [P,Q,R] : hAPP_H1270401638l_bool(hAPP_f832587837l_bool(cOMBB_1291456124_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H242767318e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
! [P,Q,R] : hAPP_n1512601776t_bool(hAPP_f934069744t_bool(cOMBB_1141542387ol_nat(P),Q),R) = hAPP_n1512601776t_bool(P,hAPP_nat_nat(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_027,axiom,
! [P,Q,R] : hAPP_H1037229737a_bool(hAPP_H426895267a_bool(hAPP_f920293029a_bool(cOMBC_1940896922a_bool,P),Q),R) = hAPP_H1037229737a_bool(hAPP_H426895267a_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc,axiom,
! [P,Q,R] : hAPP_n60670500e_bool(hAPP_f446737578e_bool(cOMBB_1209446585ol_nat(P),Q),R) = hAPP_p905327722e_bool(P,hAPP_nat_pname(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate,axiom,
! [P,Q,R] : hAPP_n261501868iple_a(hAPP_f817035994iple_a(hAPP_f311800994iple_a(cOMBS_1417107330iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_n83983309iple_a(P,R),hAPP_n1063102567e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_028,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_p346744818iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_p1227342867iple_a(P,R),hAPP_p635540397e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00,axiom,
! [P,Q,R] : hAPP_p1751618853_state(hAPP_f922567064_state(cOMBB_452540923_pname(P),Q),R) = hAPP_H923660098_state(P,hAPP_p346744818iple_a(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_p346744818iple_a(hAPP_f1273628548iple_a(cOMBB_1824120853_pname(P),Q),R) = hAPP_H1770360232iple_a(P,hAPP_p1751618853_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__029,axiom,
! [P,Q,R] : hAPP_f1968395738t_bool(hAPP_f1144745493t_bool(cOMBB_85437587a_bool(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_f2097660464ol_nat(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_030,axiom,
! [P,Q,R] : hAPP_f244528453l_bool(hAPP_f1675405437l_bool(cOMBB_703864541a_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1695230391l_bool(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____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_H216526335e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_031,axiom,
! [P,Q,R] : hAPP_n1919155532a_bool(hAPP_f260875897a_bool(cOMBB_1063143712ol_nat(P),Q),R) = hAPP_H426895267a_bool(P,hAPP_n261501868iple_a(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,axiom,
! [P,Q,R] : hAPP_H1037229737a_bool(hAPP_f1194757675a_bool(cOMBB_1610959875iple_a(P),Q),R) = hAPP_f1695230391l_bool(P,hAPP_H426895267a_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_032,axiom,
! [P,Q,R] : hAPP_H1037229737a_bool(hAPP_f20753329a_bool(hAPP_f247708275a_bool(cOMBC_1519416966l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_H622608077l_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__,axiom,
! [P,Q,R] : hAPP_n1036200171_state(hAPP_f634763074_state(hAPP_f1172439208_state(cOMBS_1390821348_state,P),Q),R) = hAPP_f497755132_state(hAPP_n766730025_state(P,R),hAPP_n1252169848e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_033,axiom,
! [P,Q,R] : hAPP_p1743421830a_bool(hAPP_f2085416313a_bool(cOMBB_1388879450_pname(P),Q),R) = hAPP_H426895267a_bool(P,hAPP_p346744818iple_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_p1751618853_state(hAPP_f914896950_state(hAPP_f1811131990_state(cOMBS_1524960158_state,P),Q),R) = hAPP_f497755132_state(hAPP_p1331349103_state(P,R),hAPP_p1637813682e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Com__Ocom_000tc__fun_Itc__fun_It__a,axiom,
! [P,Q,R] : hAPP_n83983309iple_a(hAPP_f1857794253iple_a(hAPP_f803745506iple_a(cOMBS_519355893iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_n1753616192iple_a(P,R),hAPP_nat_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_034,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_p1227342867iple_a(hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_p805859462iple_a(P,R),hAPP_pname_com(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_035,axiom,
! [P,Q,R] : hAPP_H905846293iple_a(hAPP_f1766326554iple_a(hAPP_f2004506425iple_a(cOMBS_1744968921iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_H1401668662iple_a(P,R),hAPP_H1893885264e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_036,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f1900156034e_bool(cOMBB_1282391997_state(P),Q),R) = hAPP_f1378282496l_bool(P,hAPP_H216526335e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___037,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___038,axiom,
! [P,Q,R] : hAPP_p606792009e_bool(hAPP_f472107739e_bool(cOMBB_181781758_pname(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_p1751618853_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_039,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__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp_040,axiom,
! [P,Q,R] : hAPP_n1919155532a_bool(hAPP_f1938783956a_bool(hAPP_f816688069a_bool(cOMBC_1584660393a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_n131076574a_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc__,axiom,
! [P,Q,R] : hAPP_n766730025_state(hAPP_f1158791849_state(hAPP_f459571426_state(cOMBS_183256401_state,P),Q),R) = hAPP_c27135337_state(hAPP_n2011101340_state(P,R),hAPP_nat_com(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_041,axiom,
! [P,Q,R] : hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(hAPP_f2100528361l_bool(cOMBC_627599030l_bool,P),Q),R) = hAPP_f1695230391l_bool(hAPP_f1767618879l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw_042,axiom,
! [P,Q,R] : hAPP_p1743421830a_bool(hAPP_f624861966a_bool(hAPP_f843217465a_bool(cOMBC_2103945827a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_p624562724a_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_p1331349103_state(hAPP_f460309545_state(hAPP_f1922754332_state(cOMBS_1020065803_state,P),Q),R) = hAPP_c27135337_state(hAPP_p357103842_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_043,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__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_044,axiom,
! [P,Q,R] : hAPP_H923660098_state(hAPP_f1551299824_state(hAPP_f461066925_state(cOMBS_1860286139_state,P),Q),R) = hAPP_f497755132_state(hAPP_H1275418130_state(P,R),hAPP_H838560847e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_045,axiom,
! [P,Q,R] : hAPP_H1401668662iple_a(hAPP_f524917645iple_a(hAPP_f51865337iple_a(cOMBS_1597898188iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_H189037865iple_a(P,R),hAPP_H463278718_a_com(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_046,axiom,
! [P,Q,R] : hAPP_f1693662087iple_a(hAPP_f1255935540iple_a(hAPP_f410259831iple_a(cOMBS_1097875753iple_a,P),Q),R) = hAPP_f233717658iple_a(hAPP_f1820482984iple_a(P,R),hAPP_f477771714e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Hoare____Mirabelle____uwgp_047,axiom,
! [P,Q,R] : hAPP_n1497837059e_bool(hAPP_f1718442376e_bool(hAPP_f1696618965e_bool(cOMBC_1048264781e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_n525995272e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw_048,axiom,
! [P,Q,R] : hAPP_p606792009e_bool(hAPP_f103229774e_bool(hAPP_f376349141e_bool(cOMBC_59067399e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_p105983054e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_049,axiom,
! [P,Q,R] : hAPP_n37219812l_bool(hAPP_f635381775l_bool(cOMBB_1370228356ol_nat(P),Q),R) = hAPP_f1767618879l_bool(P,hAPP_n1919155532a_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__,axiom,
! [P,Q,R] : hAPP_f1695230391l_bool(hAPP_f536631715l_bool(cOMBB_1575464575a_bool(P),Q),R) = hAPP_f2110825313l_bool(P,hAPP_f1767618879l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_050,axiom,
! [P,Q,R] : hAPP_f1695230391l_bool(hAPP_f396832789l_bool(hAPP_f754896967l_bool(cOMBC_996544418l_bool,P),Q),R) = hAPP_f2110825313l_bool(hAPP_f293818473l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_051,axiom,
! [P,Q,R] : hAPP_p1910214954l_bool(hAPP_f1577042203l_bool(cOMBB_1363536318_pname(P),Q),R) = hAPP_f1767618879l_bool(P,hAPP_p1743421830a_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_052,axiom,
! [P,Q,R] : hAPP_H426895267a_bool(hAPP_f1181346091a_bool(hAPP_f571476211a_bool(cOMBC_1570214144a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_H1743777351a_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_053,axiom,
! [P,Q,R] : hAPP_H1275418130_state(hAPP_f1573424489_state(hAPP_f1527065593_state(cOMBS_1436317352_state,P),Q),R) = hAPP_c27135337_state(hAPP_H1476318469_state(P,R),hAPP_H463278718_a_com(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_054,axiom,
! [P,Q,R] : hAPP_f1874848592_state(hAPP_f582141064_state(hAPP_f1784570101_state(cOMBS_988488459_state,P),Q),R) = hAPP_f497755132_state(hAPP_f1310841988_state(P,R),hAPP_f1246524253e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_055,axiom,
! [P,Q,R] : hAPP_f1820482984iple_a(hAPP_f159541635iple_a(hAPP_f2023640211iple_a(cOMBS_1949899292iple_a,P),Q),R) = hAPP_c142510605iple_a(hAPP_f1784500635iple_a(P,R),hAPP_f1968907248ol_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_n1753616192iple_a(hAPP_f1921807086iple_a(cOMBB_1443236341_a_nat(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_n1063102567e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__056,axiom,
! [P,Q,R] : hAPP_p805859462iple_a(hAPP_f854147694iple_a(cOMBB_2054374575_pname(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_p635540397e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Hoare____Mirabell,axiom,
! [P,Q,R] : hAPP_n37219812l_bool(hAPP_f924569416l_bool(hAPP_f1384990677l_bool(cOMBC_1645572109l_bool,P),Q),R) = hAPP_f396832789l_bool(hAPP_n2002774088l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_057,axiom,
! [P,Q,R] : hAPP_n131076574a_bool(hAPP_f1402630535a_bool(cOMBB_2115959324ol_nat(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_n261501868iple_a(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_058,axiom,
! [P,Q,R] : hAPP_f20753329a_bool(hAPP_f1706700729a_bool(hAPP_f957014749a_bool(cOMBC_288844080a_bool,P),Q),R) = hAPP_f20753329a_bool(hAPP_f1706700729a_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_059,axiom,
! [P,Q,R] : hAPP_f1310841988_state(hAPP_f1235235423_state(hAPP_f1151038867_state(cOMBS_1113512696_state,P),Q),R) = hAPP_c27135337_state(hAPP_f1439241847_state(P,R),hAPP_f1968907248ol_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_060,axiom,
! [P,Q,R] : hAPP_p624562724a_bool(hAPP_f682420871a_bool(cOMBB_1481150806_pname(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_p346744818iple_a(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___061,axiom,
! [P,Q,R] : hAPP_H216526335e_bool(hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__,axiom,
! [P,Q,R] : hAPP_n2011101340_state(hAPP_f432895259_state(cOMBB_1531938296te_nat(P),Q),R) = hAPP_f274181323_state(P,hAPP_n1252169848e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___062,axiom,
! [P,Q,R] : hAPP_p357103842_state(hAPP_f804744487_state(cOMBB_2084106034_pname(P),Q),R) = hAPP_f274181323_state(P,hAPP_p1637813682e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__063,axiom,
! [P,Q,R] : hAPP_H189037865iple_a(hAPP_f338450734iple_a(cOMBB_1799328076iple_a(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_H1893885264e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___064,axiom,
! [P,Q,R] : hAPP_n525995272e_bool(hAPP_f953597140e_bool(cOMBB_1524346879ol_nat(P),Q),R) = hAPP_H1902130436e_bool(P,hAPP_n1036200171_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___065,axiom,
! [P,Q,R] : hAPP_p105983054e_bool(hAPP_f2028971360e_bool(cOMBB_667059641_pname(P),Q),R) = hAPP_H1902130436e_bool(P,hAPP_p1751618853_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_066,axiom,
! [P,Q,R] : hAPP_H1743777351a_bool(hAPP_f181951559a_bool(cOMBB_1722563443iple_a(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_H905846293iple_a(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__067,axiom,
! [P,Q,R] : hAPP_f1784500635iple_a(hAPP_f1787234632iple_a(cOMBB_1013749676a_bool(P),Q),R) = hAPP_f1350218798iple_a(P,hAPP_f477771714e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_068,axiom,
! [P,Q,R] : hAPP_f1767618879l_bool(hAPP_f759941367l_bool(hAPP_f254338943l_bool(cOMBC_1324894996l_bool,P),Q),R) = hAPP_f396832789l_bool(hAPP_f1376242083l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___069,axiom,
! [P,Q,R] : hAPP_H1476318469_state(hAPP_f1874377965_state(cOMBB_1269509967iple_a(P),Q),R) = hAPP_f274181323_state(P,hAPP_H838560847e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It__a_J_00_070,axiom,
! [P,Q,R] : hAPP_f1706700729a_bool(hAPP_f2116512939a_bool(cOMBB_734913733a_bool(P),Q),R) = hAPP_H1743777351a_bool(P,hAPP_f1693662087iple_a(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_071,axiom,
! [P,Q,R] : hAPP_n2002774088l_bool(hAPP_f992030835l_bool(cOMBB_1467678496ol_nat(P),Q),R) = hAPP_f1376242083l_bool(P,hAPP_n1919155532a_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___072,axiom,
! [P,Q,R] : hAPP_f1439241847_state(hAPP_f868277077_state(cOMBB_989249001a_bool(P),Q),R) = hAPP_f274181323_state(P,hAPP_f1246524253e_bool(Q,R)) ).
%----Conjectures (2)
fof(conj_0,hypothesis,
! [N] :
( ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f20753329a_bool(hAPP_f1706700729a_bool(semila1114547555a_bool,g),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),p)),body)),q)),procs))))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)) )
=> ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),p)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body_1))),q)),procs)))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,N),X)) ) ) ).
fof(conj_1,conjecture,
( ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),g))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,n),X)) )
=> ! [X] :
( hBOOL(hAPP_f1695230391l_bool(hAPP_H622608077l_bool(member1797258804iple_a,X),hAPP_f2034373396a_bool(image_1738210978iple_a(hAPP_f961776218iple_a(hAPP_f327379420iple_a(cOMBS_343917116iple_a,hAPP_f316273229iple_a(hAPP_f1559918364iple_a(cOMBS_839225263iple_a,hAPP_f854147694iple_a(cOMBB_2054374575_pname(hoare_1916936827iple_a),p)),body)),q)),procs)))
=> hBOOL(hAPP_H1037229737a_bool(hAPP_n1919155532a_bool(hoare_2056833131alid_a,n),X)) ) ) ).
%------------------------------------------------------------------------------