TPTP Problem File: SWW474+3.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW474+3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 440, 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_l440 [Bla11]
% Status : Theorem
% Rating : 0.47 v7.5.0, 0.53 v7.4.0, 0.50 v7.3.0, 0.45 v7.2.0, 0.41 v7.1.0, 0.39 v7.0.0, 0.47 v6.4.0, 0.50 v6.3.0, 0.42 v6.2.0, 0.52 v6.1.0, 0.67 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.75 v5.3.0
% Syntax : Number of formulae : 1441 ( 524 unt; 0 def)
% Number of atoms : 3532 (1044 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 2466 ( 375 ~; 64 |; 247 &)
% ( 250 <=>;1530 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% Number of functors : 573 ( 573 usr; 174 con; 0-4 aty)
% Number of variables : 3670 (3592 !; 78 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 18:09:16
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (82)
fof(gsy_c_Com_OWT__bodies,hypothesis,
is_bool(wT_bodies) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mt,axiom,
! [B_1_1] : is_bool(finite1653727294m_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Opname_000tc__fun_Itc__Com__Opnam,axiom,
! [B_1_1] : is_bool(finite2017903282e_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1] : is_bool(finite318301748l_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otri,axiom,
! [B_1_1] : is_bool(finite2036162504e_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1] : is_bool(finite367769966e_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvf,axiom,
! [B_1_1] : is_bool(finite1765632844e_bool(B_1_1)) ).
fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,axiom,
is_fun1661590463l_bool(finite_finite_pname) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Ocom,axiom,
! [B_1_1,B_2_1] : is_bool(finite860057415ne_com(B_1_1,B_2_1)) ).
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(finite683959609_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] : is_bool(finite1626890877e_bool(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(finite2009063477e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Ocom,axiom,
! [B_1_1,B_2_1] : is_bool(finite666746948em_com(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(finite416071164_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
! [B_1_1,B_2_1] : is_bool(finite1268145088e_bool(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(finite688249778e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [B_1_1] : is_fun1661590463l_bool(inj_on_pname_pname(B_1_1)) ).
fof(gsy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [B_1_1] : is_fun1661590463l_bool(inj_on621632009_state(B_1_1)) ).
fof(gsy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J,axiom,
! [B_1_1] : is_fun1661590463l_bool(inj_on737724108_pname(B_1_1)) ).
fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
is_pname(undefined_pname(pname)) ).
fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))) ).
fof(gsy_c_Hoare__Mirabelle__uwgpyvfjxg_Ostate__not__singleton,hypothesis,
is_bool(hoare_1795711768gleton) ).
fof(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,hypothesis,
! [B_1_1] : is_fun_pname_bool(dom_pname_com(B_1_1)) ).
fof(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [B_1_1] : is_fun_pname_bool(dom_pname_pname(B_1_1)) ).
fof(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otrip,axiom,
! [B_1_1] : is_fun_pname_bool(dom_pn480909800_state(B_1_1)) ).
fof(gsy_c_Option_Ois__none_000tc__Com__Ocom,axiom,
! [B_1_1] : is_bool(is_none_com(B_1_1)) ).
fof(gsy_c_Option_Ois__none_000tc__Com__Opname,axiom,
! [B_1_1] :
( is_option_pname(B_1_1)
=> is_bool(is_none_pname(B_1_1)) ) ).
fof(gsy_c_Option_Ois__none_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [B_1_1] : is_bool(is_non1379144176_state(B_1_1)) ).
fof(gsy_c_Option_Ooption_ONone_000tc__Com__Opname,axiom,
is_option_pname(none_pname) ).
fof(gsy_c_Option_Oset_000tc__Com__Opname,axiom,
! [B_1_1] :
( is_option_pname(B_1_1)
=> is_fun_pname_bool(set_pname(B_1_1)) ) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(bot_bo844097828e_bool) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__,axiom,
is_fun1661590463l_bool(bot_bo1649642514l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(top_to2127735616e_bool) ).
fof(gsy_c_Set_Ovimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__Ot,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(vimage1011814463_state(B_1_1,B_2_1)) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Com__Ocom_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_com_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Com__Ocom_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_com_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Com__Ocom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_c1967741679e_bool(B_1_1,B_2_1)) ).
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__Option__Ooption_Itc__Com__Opname_J,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_option_pname(hAPP_p1252095976_pname(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__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__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__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__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun1661590463l_bool(hAPP_b357632156l_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_pname(hAPP_H1193503499_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_001,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_002,axiom,
! [B_1_1,B_2_1] : is_option_pname(hAPP_H1671063474_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate_J_0_003,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_004,axiom,
! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_H358531139l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_option_com_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__fun_Itc__Com__Opname_M,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_o1092643708e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Option__Ooption_Itc__Com__Opname_J_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] :
( is_option_pname(B_2_1)
=> is_pname(hAPP_o593586696_pname(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f990396704l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f1438183293e_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__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f327114704l_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_bool(hAPP_f387058535l_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_pname(hAPP_f88366945_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O_005,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_f1378282496l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O_006,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f1083669085e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__O_007,axiom,
! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_f1709493145l_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_008,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_009,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_f1410040974l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_It_010,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f306376939e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f389811538l_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_f1178960312l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_pn,hypothesis,
is_pname(pn) ).
%----Relevant facts (1199)
fof(fact_0_empty,axiom,
! [G_2] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),bot_bo784226126e_bool)) ).
fof(fact_1_asm,axiom,
! [Ts,G_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),G_2))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) ) ).
fof(fact_2_weaken,axiom,
! [Ts,G_2,Ts_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Ts),Ts_1))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) ) ) ).
fof(fact_3_thin,axiom,
! [G_2,G_3,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_3),Ts))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,G_3),G_2))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) ) ) ).
fof(fact_4_cut,axiom,
! [G_2,G_3,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_3),Ts))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),G_3))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) ) ) ).
fof(fact_5_hoare__derivs_Oinsert,axiom,
! [Ts,G_2,T] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),Ts))) ) ) ).
fof(fact_6_derivs__insertD,axiom,
! [G_2,T,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),Ts)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,T),bot_bo784226126e_bool)))
& hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts)) ) ) ).
fof(fact_7_MGT__BodyN,axiom,
! [Pn_1,G_2] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_2)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo784226126e_bool))) ) ).
fof(fact_8_finite__Collect__subsets,axiom,
! [A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,hAPP_f783502055l_bool(collec1613912337l_bool,hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,ord_le675606854l_bool),A)))) ) ).
fof(fact_9_finite__Collect__subsets,axiom,
! [A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hBOOL(hAPP_f1178960312l_bool(finite1203709595l_bool,hAPP_f347786453l_bool(collec895295961l_bool,hAPP_f1516997247l_bool(hAPP_f1901243753l_bool(cOMBC_991209188l_bool,ord_le694194916l_bool),A)))) ) ).
fof(fact_10_finite__Collect__subsets,axiom,
! [A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,ord_le1449778818e_bool),A)))) ) ).
fof(fact_11_finite__Collect__subsets,axiom,
! [A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,ord_le313189616e_bool),A)))) ) ).
fof(fact_12_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f1709493145l_bool(image_1403607267e_bool(H_1),Fa))) ) ).
fof(fact_13_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f849457489l_bool(image_995511119e_bool(H_1),Fa))) ) ).
fof(fact_14_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(H_1),Fa))) ) ).
fof(fact_15_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f1492100075l_bool(image_234387449e_bool(H_1),Fa))) ) ).
fof(fact_16_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f509793681e_bool(image_845802851_state(H_1),Fa))) ) ).
fof(fact_17_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f1216288071e_bool(image_1497401961_state(H_1),Fa))) ) ).
fof(fact_18_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(H_1),Fa))) ) ).
fof(fact_19_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f306376939e_bool(image_1863446033_pname(H_1),Fa))) ) ).
fof(fact_20_finite__imageI,axiom,
! [H_1,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(H_1),Fa))) ) ).
fof(fact_21_empty__subsetI,axiom,
! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A)) ).
fof(fact_22_empty__subsetI,axiom,
! [A] : hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,bot_bot_fun_com_bool),A)) ).
fof(fact_23_empty__subsetI,axiom,
! [A] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A)) ).
fof(fact_24_finite_OinsertI,axiom,
! [A_4,A] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A))) ) ).
fof(fact_25_finite_OinsertI,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A))) ) ).
fof(fact_26_finite_OinsertI,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A))) ) ).
fof(fact_27_finite_OinsertI,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A))) ) ).
fof(fact_28_finite_OinsertI,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A))) ) ).
fof(fact_29_finite_OemptyI,axiom,
hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)) ).
fof(fact_30_finite_OemptyI,axiom,
hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,bot_bo942947096l_bool)) ).
fof(fact_31_finite_OemptyI,axiom,
hBOOL(hAPP_f990396704l_bool(finite_finite_com,bot_bot_fun_com_bool)) ).
fof(fact_32_finite_OemptyI,axiom,
hBOOL(hAPP_f1378282496l_bool(finite694102371_state,bot_bo784226126e_bool)) ).
fof(fact_33_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).
fof(fact_34_finite__Collect__conjI,axiom,
! [Q_1,P_1] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)))) ) ).
fof(fact_35_finite__Collect__conjI,axiom,
! [Q_1,P_1] :
( ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)))
| hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))) )
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),P_1)),Q_1)))) ) ).
fof(fact_36_finite__Collect__conjI,axiom,
! [Q_1,P_1] :
( ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,P_1)))
| hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,Q_1))) )
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),P_1)),Q_1)))) ) ).
fof(fact_37_finite__Collect__conjI,axiom,
! [Q_1,P_1] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_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),P_1)),Q_1)))) ) ).
fof(fact_38_image__constant__conv,axiom,
! [C,A] :
( ( A = bot_bo784226126e_bool
=> hAPP_f1083669085e_bool(image_1774499931_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,C)),A) = bot_bo844097828e_bool )
& ( A != bot_bo784226126e_bool
=> hAPP_f1083669085e_bool(image_1774499931_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ).
fof(fact_39_image__constant__conv,axiom,
! [C,A] :
( ( A = bot_bo784226126e_bool
=> hAPP_f1815646051m_bool(image_741143905te_com(hAPP_c57939194te_com(cOMBK_131063602_state,C)),A) = bot_bot_fun_com_bool )
& ( A != bot_bo784226126e_bool
=> hAPP_f1815646051m_bool(image_741143905te_com(hAPP_c57939194te_com(cOMBK_131063602_state,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool) ) ) ).
fof(fact_40_image__constant__conv,axiom,
! [C,A] :
( ( A = bot_bot_fun_com_bool
=> hAPP_f457085749e_bool(image_2605051_state(hAPP_H275587026_state(cOMBK_869602456te_com,C)),A) = bot_bo784226126e_bool )
& ( A != bot_bot_fun_com_bool
=> hAPP_f457085749e_bool(image_2605051_state(hAPP_H275587026_state(cOMBK_869602456te_com,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool) ) ) ).
fof(fact_41_image__constant__conv,axiom,
! [C,A] :
( is_fun_pname_bool(A)
=> ( ( A = bot_bo844097828e_bool
=> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C)),A) = bot_bo784226126e_bool )
& ( A != bot_bo844097828e_bool
=> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool) ) ) ) ).
fof(fact_42_image__constant,axiom,
! [C,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_f1083669085e_bool(image_1774499931_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ).
fof(fact_43_image__constant,axiom,
! [C,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_f1815646051m_bool(image_741143905te_com(hAPP_c57939194te_com(cOMBK_131063602_state,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool) ) ).
fof(fact_44_image__constant,axiom,
! [C,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ).
fof(fact_45_image__constant,axiom,
! [C,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f1206115581m_bool(image_pname_com(hAPP_c1494068046me_com(cOMBK_com_pname,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool) ) ).
fof(fact_46_image__constant,axiom,
! [C,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hAPP_f457085749e_bool(image_2605051_state(hAPP_H275587026_state(cOMBK_869602456te_com,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool) ) ).
fof(fact_47_image__constant,axiom,
! [C,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f360545851e_bool(image_185131637_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,C)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),bot_bo784226126e_bool) ) ).
fof(fact_48_insert__dom,axiom,
! [F,X_1,Y_2] :
( hAPP_com_option_com(F,X_1) = hAPP_com_option_com(some_com,Y_2)
=> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),dom_com_com(F)) = dom_com_com(F) ) ).
fof(fact_49_insert__dom,axiom,
! [F,X_1,Y_2] :
( hAPP_H1671063474_pname(F,X_1) = hAPP_p1252095976_pname(some_pname,Y_2)
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),dom_Ho2070278094_pname(F)) = dom_Ho2070278094_pname(F) ) ).
fof(fact_50_insert__dom,axiom,
! [F,X_1,Y_2] :
( hAPP_H1633077406_state(F,X_1) = hAPP_H1633077406_state(some_H1043067815_state,Y_2)
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),dom_Ho1607160812_state(F)) = dom_Ho1607160812_state(F) ) ).
fof(fact_51_insert__dom,axiom,
! [F,X_1,Y_2] :
( hAPP_p799580910on_com(F,X_1) = hAPP_com_option_com(some_com,Y_2)
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F) ) ).
fof(fact_52_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f1709493145l_bool(image_1403607267e_bool(F),A)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).
fof(fact_53_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f849457489l_bool(image_995511119e_bool(F),A)))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) ) ) ).
fof(fact_54_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_55_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).
fof(fact_56_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f1492100075l_bool(image_234387449e_bool(F),A)))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B)) ) ) ).
fof(fact_57_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_58_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f509793681e_bool(image_845802851_state(F),A)))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) ) ) ).
fof(fact_59_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f1216288071e_bool(image_1497401961_state(F),A)))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) ) ) ).
fof(fact_60_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_61_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f306376939e_bool(image_1863446033_pname(F),A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_62_finite__surj,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A)))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B)) ) ) ).
fof(fact_63_subset__singletonD,axiom,
! [A,X_1] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))
=> ( A = bot_bo844097828e_bool
| A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ) ) ) ).
fof(fact_64_subset__singletonD,axiom,
! [A,X_1] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))
=> ( A = bot_bot_fun_com_bool
| A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) ) ) ).
fof(fact_65_subset__singletonD,axiom,
! [A,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))
=> ( A = bot_bo784226126e_bool
| A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool) ) ) ).
fof(fact_66_MGF,axiom,
! [C] :
( hBOOL(hoare_1795711768gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))) ) ) ) ).
fof(fact_67_emptyE,axiom,
! [A_4] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),bot_bot_fun_com_bool)) ).
fof(fact_68_emptyE,axiom,
! [A_4] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),bot_bo784226126e_bool)) ).
fof(fact_69_emptyE,axiom,
! [A_4] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),bot_bo844097828e_bool)) ).
fof(fact_70_insertCI,axiom,
! [B_1,A_4,B] :
( ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B))
=> A_4 = B_1 )
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))) ) ).
fof(fact_71_insertCI,axiom,
! [B_1,A_4,B] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B))
=> A_4 = B_1 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).
fof(fact_72_insertCI,axiom,
! [B_1,A_4,B] :
( ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),B))
=> A_4 = B_1 )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B))) ) ).
fof(fact_73_insertE,axiom,
! [A_4,B_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),A)))
=> ( A_4 != B_1
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) ) ) ).
fof(fact_74_insertE,axiom,
! [A_4,B_1,A] :
( ( is_pname(A_4)
& is_pname(B_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A)))
=> ( A_4 != B_1
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) ) ) ) ).
fof(fact_75_insertE,axiom,
! [A_4,B_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A)))
=> ( A_4 != B_1
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) ) ) ).
fof(fact_76_equalityI,axiom,
! [A,B] :
( ( is_fun_pname_bool(A)
& is_fun_pname_bool(B) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
=> A = B ) ) ) ).
fof(fact_77_equalityI,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A))
=> A = B ) ) ).
fof(fact_78_subsetD,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_79_subsetD,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_80_subsetD,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_81_image__eqI,axiom,
! [A,B_1,F,X_1] :
( B_1 = hAPP_H46530577te_com(F,X_1)
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1815646051m_bool(image_741143905te_com(F),A))) ) ) ).
fof(fact_82_image__eqI,axiom,
! [A,B_1,F,X_1] :
( B_1 = hAPP_pname_com(F,X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A))) ) ) ).
fof(fact_83_image__eqI,axiom,
! [A,B_1,F,X_1] :
( B_1 = hAPP_c1455475371_state(F,X_1)
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f457085749e_bool(image_2605051_state(F),A))) ) ) ).
fof(fact_84_image__eqI,axiom,
! [A,B_1,F,X_1] :
( B_1 = hAPP_com_pname(F,X_1)
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A))) ) ) ).
fof(fact_85_image__eqI,axiom,
! [A,B_1,F,X_1] :
( B_1 = hAPP_p1751618853_state(F,X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A))) ) ) ).
fof(fact_86_equals0D,axiom,
! [A_4,A] :
( A = bot_bot_fun_com_bool
=> ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) ) ).
fof(fact_87_equals0D,axiom,
! [A_4,A] :
( A = bot_bo784226126e_bool
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) ) ).
fof(fact_88_equals0D,axiom,
! [A_4,A] :
( A = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) ) ).
fof(fact_89_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f759274231e_bool(collect_pname,P_1) = bot_bo844097828e_bool
<=> ! [X_2] :
( is_pname(X_2)
=> ~ hBOOL(hAPP_pname_bool(P_1,X_2)) ) ) ).
fof(fact_90_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = bot_bo1649642514l_bool
<=> ! [X_2] :
( is_fun_pname_bool(X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) ) ) ).
fof(fact_91_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f734420447l_bool(collec1987918285e_bool,P_1) = bot_bo942947096l_bool
<=> ! [X_2] : ~ hBOOL(hAPP_f1378282496l_bool(P_1,X_2)) ) ).
fof(fact_92_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f1682609283m_bool(collect_com,P_1) = bot_bot_fun_com_bool
<=> ! [X_2] : ~ hBOOL(hAPP_com_bool(P_1,X_2)) ) ).
fof(fact_93_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f806699093e_bool(collec637225377_state,P_1) = bot_bo784226126e_bool
<=> ! [X_2] : ~ hBOOL(hAPP_H242767318e_bool(P_1,X_2)) ) ).
fof(fact_94_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),bot_bot_fun_com_bool)) ).
fof(fact_95_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),bot_bo784226126e_bool)) ).
fof(fact_96_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool)) ).
fof(fact_97_empty__Collect__eq,axiom,
! [P_1] :
( bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,P_1)
<=> ! [X_2] :
( is_pname(X_2)
=> ~ hBOOL(hAPP_pname_bool(P_1,X_2)) ) ) ).
fof(fact_98_empty__Collect__eq,axiom,
! [P_1] :
( bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,P_1)
<=> ! [X_2] :
( is_fun_pname_bool(X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) ) ) ).
fof(fact_99_empty__Collect__eq,axiom,
! [P_1] :
( bot_bo942947096l_bool = hAPP_f734420447l_bool(collec1987918285e_bool,P_1)
<=> ! [X_2] : ~ hBOOL(hAPP_f1378282496l_bool(P_1,X_2)) ) ).
fof(fact_100_empty__Collect__eq,axiom,
! [P_1] :
( bot_bot_fun_com_bool = hAPP_f1682609283m_bool(collect_com,P_1)
<=> ! [X_2] : ~ hBOOL(hAPP_com_bool(P_1,X_2)) ) ).
fof(fact_101_empty__Collect__eq,axiom,
! [P_1] :
( bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,P_1)
<=> ! [X_2] : ~ hBOOL(hAPP_H242767318e_bool(P_1,X_2)) ) ).
fof(fact_102_ex__in__conv,axiom,
! [A] :
( ? [X_2] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
<=> A != bot_bot_fun_com_bool ) ).
fof(fact_103_ex__in__conv,axiom,
! [A] :
( ? [X_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
<=> A != bot_bo784226126e_bool ) ).
fof(fact_104_ex__in__conv,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) )
<=> A != bot_bo844097828e_bool ) ) ).
fof(fact_105_all__not__in__conv,axiom,
! [A] :
( ! [X_2] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
<=> A = bot_bot_fun_com_bool ) ).
fof(fact_106_all__not__in__conv,axiom,
! [A] :
( ! [X_2] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
<=> A = bot_bo784226126e_bool ) ).
fof(fact_107_all__not__in__conv,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( ! [X_2] :
( is_pname(X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) )
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_108_empty__def,axiom,
bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,hAPP_b76515610e_bool(cOMBK_bool_pname,fFalse)) ).
fof(fact_109_empty__def,axiom,
bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_b357632156l_bool(cOMBK_1857069011e_bool,fFalse)) ).
fof(fact_110_empty__def,axiom,
bot_bo942947096l_bool = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_b167205134l_bool(cOMBK_293339231e_bool,fFalse)) ).
fof(fact_111_empty__def,axiom,
bot_bot_fun_com_bool = hAPP_f1682609283m_bool(collect_com,hAPP_b1153789088m_bool(cOMBK_bool_com,fFalse)) ).
fof(fact_112_empty__def,axiom,
bot_bo784226126e_bool = hAPP_f806699093e_bool(collec637225377_state,hAPP_b974863576e_bool(cOMBK_988866959_state,fFalse)) ).
fof(fact_113_insert__absorb,axiom,
! [A_4,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) = A ) ).
fof(fact_114_insert__absorb,axiom,
! [A_4,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) = A ) ) ).
fof(fact_115_insert__absorb,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) = A ) ).
fof(fact_116_insertI2,axiom,
! [B_1,A_4,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))) ) ).
fof(fact_117_insertI2,axiom,
! [B_1,A_4,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).
fof(fact_118_insertI2,axiom,
! [B_1,A_4,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B))) ) ).
fof(fact_119_insert__ident,axiom,
! [B,X_1,A] :
( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
=> ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B)
<=> A = B ) ) ) ).
fof(fact_120_insert__ident,axiom,
! [B,X_1,A] :
( ( is_fun_pname_bool(B)
& is_fun_pname_bool(A) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)
<=> A = B ) ) ) ) ).
fof(fact_121_insert__ident,axiom,
! [B,X_1,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))
=> ( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B)
<=> A = B ) ) ) ).
fof(fact_122_insert__code,axiom,
! [Y_2,A,X_1] :
( ( is_pname(Y_2)
& is_pname(X_1) )
=> ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),A),X_1))
<=> ( Y_2 = X_1
| hBOOL(hAPP_pname_bool(A,X_1)) ) ) ) ).
fof(fact_123_insert__code,axiom,
! [Y_2,A,X_1] :
( hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),A),X_1))
<=> ( Y_2 = X_1
| hBOOL(hAPP_com_bool(A,X_1)) ) ) ).
fof(fact_124_insert__code,axiom,
! [Y_2,A,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),A),X_1))
<=> ( Y_2 = X_1
| hBOOL(hAPP_H242767318e_bool(A,X_1)) ) ) ).
fof(fact_125_insert__iff,axiom,
! [A_4,B_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),A)))
<=> ( A_4 = B_1
| hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) ) ) ).
fof(fact_126_insert__iff,axiom,
! [A_4,B_1,A] :
( ( is_pname(A_4)
& is_pname(B_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A)))
<=> ( A_4 = B_1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) ) ) ) ).
fof(fact_127_insert__iff,axiom,
! [A_4,B_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),A)))
<=> ( A_4 = B_1
| hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A)) ) ) ).
fof(fact_128_insert__commute,axiom,
! [X_1,Y_2,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) ).
fof(fact_129_insert__commute,axiom,
! [X_1,Y_2,A] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),A)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) ).
fof(fact_130_insert__commute,axiom,
! [X_1,Y_2,A] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),A)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) ).
fof(fact_131_insert__absorb2,axiom,
! [X_1,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) ).
fof(fact_132_insert__absorb2,axiom,
! [X_1,A] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A) ).
fof(fact_133_insert__absorb2,axiom,
! [X_1,A] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A) ).
fof(fact_134_insert__Collect,axiom,
! [A_4,P_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(collect_pname,P_1)) = 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_4)))),P_1)) ).
fof(fact_135_insert__Collect,axiom,
! [A_4,P_1] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(collect_com,P_1)) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fimplies),hAPP_f1682609283m_bool(cOMBB_bool_bool_com(fNot),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4)))),P_1)) ).
fof(fact_136_insert__Collect,axiom,
! [A_4,P_1] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fimplies),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4)))),P_1)) ).
fof(fact_137_insert__Collect,axiom,
! [A_4,P_1] : hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),hAPP_f734420447l_bool(collec1987918285e_bool,P_1)) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fimplies),hAPP_f734420447l_bool(cOMBB_1686148692e_bool(fNot),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4)))),P_1)) ).
fof(fact_138_insert__Collect,axiom,
! [A_4,P_1] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(collec637225377_state,P_1)) = 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_4)))),P_1)) ).
fof(fact_139_insert__compr,axiom,
! [A_4,B] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))) ).
fof(fact_140_insert__compr,axiom,
! [A_4,B] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).
fof(fact_141_insert__compr,axiom,
! [A_4,B] : hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B))) ).
fof(fact_142_insert__compr,axiom,
! [A_4,B] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B) = 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_4))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).
fof(fact_143_insert__compr,axiom,
! [A_4,B] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B) = 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_4))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B))) ).
fof(fact_144_insertI1,axiom,
! [A_4,B] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B))) ).
fof(fact_145_insertI1,axiom,
! [A_4,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B))) ).
fof(fact_146_insertI1,axiom,
! [A_4,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B))) ).
fof(fact_147_equalityE,axiom,
! [A,B] :
( A = B
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ) ).
fof(fact_148_equalityE,axiom,
! [A,B] :
( A = B
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) ) ) ).
fof(fact_149_subset__trans,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1)) ) ) ).
fof(fact_150_subset__trans,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),C_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1)) ) ) ).
fof(fact_151_set__mp,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) ) ) ).
fof(fact_152_set__mp,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) ) ) ).
fof(fact_153_set__mp,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).
fof(fact_154_set__rev__mp,axiom,
! [B,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) ) ) ).
fof(fact_155_set__rev__mp,axiom,
! [B,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) ) ) ).
fof(fact_156_set__rev__mp,axiom,
! [B,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).
fof(fact_157_in__mono,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) ) ) ).
fof(fact_158_in__mono,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B)) ) ) ).
fof(fact_159_in__mono,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).
fof(fact_160_equalityD2,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ).
fof(fact_161_equalityD2,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) ) ).
fof(fact_162_equalityD1,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ).
fof(fact_163_equalityD1,axiom,
! [A,B] :
( A = B
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) ) ).
fof(fact_164_set__eq__subset,axiom,
! [A,B] :
( ( is_fun_pname_bool(A)
& is_fun_pname_bool(B) )
=> ( A = B
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ) ) ).
fof(fact_165_set__eq__subset,axiom,
! [A,B] :
( A = B
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A)) ) ) ).
fof(fact_166_subset__refl,axiom,
! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)) ).
fof(fact_167_subset__refl,axiom,
! [A] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),A)) ).
fof(fact_168_rev__image__eqI,axiom,
! [B_1,F,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ( B_1 = hAPP_H46530577te_com(F,X_1)
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1815646051m_bool(image_741143905te_com(F),A))) ) ) ).
fof(fact_169_rev__image__eqI,axiom,
! [B_1,F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( B_1 = hAPP_pname_com(F,X_1)
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A))) ) ) ).
fof(fact_170_rev__image__eqI,axiom,
! [B_1,F,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( B_1 = hAPP_c1455475371_state(F,X_1)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f457085749e_bool(image_2605051_state(F),A))) ) ) ).
fof(fact_171_rev__image__eqI,axiom,
! [B_1,F,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( B_1 = hAPP_com_pname(F,X_1)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A))) ) ) ).
fof(fact_172_rev__image__eqI,axiom,
! [B_1,F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( B_1 = hAPP_p1751618853_state(F,X_1)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A))) ) ) ).
fof(fact_173_imageI,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_H46530577te_com(F,X_1)),hAPP_f1815646051m_bool(image_741143905te_com(F),A))) ) ).
fof(fact_174_imageI,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_pname_com(F,X_1)),hAPP_f1206115581m_bool(image_pname_com(F),A))) ) ).
fof(fact_175_imageI,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_c1455475371_state(F,X_1)),hAPP_f457085749e_bool(image_2605051_state(F),A))) ) ).
fof(fact_176_imageI,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_com_pname(F,X_1)),hAPP_f1438183293e_bool(image_com_pname(F),A))) ) ).
fof(fact_177_imageI,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_1)),hAPP_f360545851e_bool(image_185131637_state(F),A))) ) ).
fof(fact_178_image__iff,axiom,
! [Z,F,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Z),hAPP_f360545851e_bool(image_185131637_state(F),A)))
<=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& Z = hAPP_p1751618853_state(F,X_2) ) ) ).
fof(fact_179_finite__Collect__disjI,axiom,
! [P_1,Q_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) ) ) ).
fof(fact_180_finite__Collect__disjI,axiom,
! [P_1,Q_1] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)))
& hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))) ) ) ).
fof(fact_181_finite__Collect__disjI,axiom,
! [P_1,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,P_1)))
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,Q_1))) ) ) ).
fof(fact_182_finite__Collect__disjI,axiom,
! [P_1,Q_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(fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) ) ) ).
fof(fact_183_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),Xa) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),X_2))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),Xa))) ).
fof(fact_184_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),Xa) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),X_2))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),Xa))) ).
fof(fact_185_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),Xa) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),X_2))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),Xa))) ).
fof(fact_186_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),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_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa))) ).
fof(fact_187_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),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_2))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),Xa))) ).
fof(fact_188_singleton__inject,axiom,
! [A_4,B_1] :
( ( is_pname(A_4)
& is_pname(B_1) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)
=> A_4 = B_1 ) ) ).
fof(fact_189_singleton__inject,axiom,
! [A_4,B_1] :
( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)
=> A_4 = B_1 ) ).
fof(fact_190_singleton__inject,axiom,
! [A_4,B_1] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)
=> A_4 = B_1 ) ).
fof(fact_191_singletonE,axiom,
! [B_1,A_4] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)))
=> B_1 = A_4 ) ).
fof(fact_192_singletonE,axiom,
! [B_1,A_4] :
( ( is_pname(B_1)
& is_pname(A_4) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)))
=> B_1 = A_4 ) ) ).
fof(fact_193_singletonE,axiom,
! [B_1,A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)))
=> B_1 = A_4 ) ).
fof(fact_194_doubleton__eq__iff,axiom,
! [A_4,B_1,C,D_1] :
( ( is_pname(A_4)
& is_pname(B_1)
& is_pname(C)
& is_pname(D_1) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D_1),bot_bo844097828e_bool))
<=> ( ( A_4 = C
& B_1 = D_1 )
| ( A_4 = D_1
& B_1 = C ) ) ) ) ).
fof(fact_195_doubleton__eq__iff,axiom,
! [A_4,B_1,C,D_1] :
( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,D_1),bot_bot_fun_com_bool))
<=> ( ( A_4 = C
& B_1 = D_1 )
| ( A_4 = D_1
& B_1 = C ) ) ) ).
fof(fact_196_doubleton__eq__iff,axiom,
! [A_4,B_1,C,D_1] :
( hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,C),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,D_1),bot_bo784226126e_bool))
<=> ( ( A_4 = C
& B_1 = D_1 )
| ( A_4 = D_1
& B_1 = C ) ) ) ).
fof(fact_197_singleton__iff,axiom,
! [B_1,A_4] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)))
<=> B_1 = A_4 ) ).
fof(fact_198_singleton__iff,axiom,
! [B_1,A_4] :
( ( is_pname(B_1)
& is_pname(A_4) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)))
<=> B_1 = A_4 ) ) ).
fof(fact_199_singleton__iff,axiom,
! [B_1,A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)))
<=> B_1 = A_4 ) ).
fof(fact_200_insert__not__empty,axiom,
! [A_4,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) != bot_bo844097828e_bool ).
fof(fact_201_insert__not__empty,axiom,
! [A_4,A] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) != bot_bot_fun_com_bool ).
fof(fact_202_insert__not__empty,axiom,
! [A_4,A] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) != bot_bo784226126e_bool ).
fof(fact_203_empty__not__insert,axiom,
! [A_4,A] : bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) ).
fof(fact_204_empty__not__insert,axiom,
! [A_4,A] : bot_bot_fun_com_bool != hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) ).
fof(fact_205_empty__not__insert,axiom,
! [A_4,A] : bot_bo784226126e_bool != hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) ).
fof(fact_206_finite__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)))
<=> hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) ) ).
fof(fact_207_finite__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ).
fof(fact_208_finite__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)))
<=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) ) ).
fof(fact_209_finite__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ).
fof(fact_210_finite__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) ) ).
fof(fact_211_subset__empty,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool))
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_212_subset__empty,axiom,
! [A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),bot_bot_fun_com_bool))
<=> A = bot_bot_fun_com_bool ) ).
fof(fact_213_subset__empty,axiom,
! [A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),bot_bo784226126e_bool))
<=> A = bot_bo784226126e_bool ) ).
fof(fact_214_image__is__empty,axiom,
! [F,A] :
( hAPP_f457085749e_bool(image_2605051_state(F),A) = bot_bo784226126e_bool
<=> A = bot_bot_fun_com_bool ) ).
fof(fact_215_image__is__empty,axiom,
! [F,A] :
( hAPP_f1083669085e_bool(image_1774499931_pname(F),A) = bot_bo844097828e_bool
<=> A = bot_bo784226126e_bool ) ).
fof(fact_216_image__is__empty,axiom,
! [F,A] :
( hAPP_f1815646051m_bool(image_741143905te_com(F),A) = bot_bot_fun_com_bool
<=> A = bot_bo784226126e_bool ) ).
fof(fact_217_image__is__empty,axiom,
! [F,A] :
( is_fun_pname_bool(A)
=> ( hAPP_f360545851e_bool(image_185131637_state(F),A) = bot_bo784226126e_bool
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_218_image__empty,axiom,
! [F] : hAPP_f1083669085e_bool(image_1774499931_pname(F),bot_bo784226126e_bool) = bot_bo844097828e_bool ).
fof(fact_219_image__empty,axiom,
! [F] : hAPP_f1815646051m_bool(image_741143905te_com(F),bot_bo784226126e_bool) = bot_bot_fun_com_bool ).
fof(fact_220_image__empty,axiom,
! [F] : hAPP_f457085749e_bool(image_2605051_state(F),bot_bot_fun_com_bool) = bot_bo784226126e_bool ).
fof(fact_221_image__empty,axiom,
! [F] : hAPP_f360545851e_bool(image_185131637_state(F),bot_bo844097828e_bool) = bot_bo784226126e_bool ).
fof(fact_222_empty__is__image,axiom,
! [F,A] :
( bot_bo784226126e_bool = hAPP_f457085749e_bool(image_2605051_state(F),A)
<=> A = bot_bot_fun_com_bool ) ).
fof(fact_223_empty__is__image,axiom,
! [F,A] :
( bot_bo844097828e_bool = hAPP_f1083669085e_bool(image_1774499931_pname(F),A)
<=> A = bot_bo784226126e_bool ) ).
fof(fact_224_empty__is__image,axiom,
! [F,A] :
( bot_bot_fun_com_bool = hAPP_f1815646051m_bool(image_741143905te_com(F),A)
<=> A = bot_bo784226126e_bool ) ).
fof(fact_225_empty__is__image,axiom,
! [F,A] :
( is_fun_pname_bool(A)
=> ( bot_bo784226126e_bool = hAPP_f360545851e_bool(image_185131637_state(F),A)
<=> A = bot_bo844097828e_bool ) ) ).
fof(fact_226_finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).
fof(fact_227_finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),B))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) ) ) ).
fof(fact_228_finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) ) ) ).
fof(fact_229_finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).
fof(fact_230_rev__finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).
fof(fact_231_rev__finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),B))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) ) ) ).
fof(fact_232_rev__finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) ) ) ).
fof(fact_233_rev__finite__subset,axiom,
! [A,B] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).
fof(fact_234_insert__mono,axiom,
! [A_4,C_1,D] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),D))) ) ).
fof(fact_235_insert__mono,axiom,
! [A_4,C_1,D] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,C_1),D))
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),C_1)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),D))) ) ).
fof(fact_236_insert__mono,axiom,
! [A_4,C_1,D] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),D))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),C_1)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),D))) ) ).
fof(fact_237_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
<=> hBOOL(hAPP_com_bool(A,X_1)) ) ).
fof(fact_238_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
<=> hBOOL(hAPP_H242767318e_bool(A,X_1)) ) ).
fof(fact_239_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
<=> hBOOL(hAPP_pname_bool(A,X_1)) ) ).
fof(fact_240_Collect__def,axiom,
! [P_1] : hAPP_f806699093e_bool(collec637225377_state,P_1) = P_1 ).
fof(fact_241_Collect__def,axiom,
! [P_1] :
( is_fun_pname_bool(P_1)
=> hAPP_f759274231e_bool(collect_pname,P_1) = P_1 ) ).
fof(fact_242_Collect__def,axiom,
! [P_1] :
( is_fun1661590463l_bool(P_1)
=> hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1 ) ).
fof(fact_243_Collect__def,axiom,
! [P_1] : hAPP_f734420447l_bool(collec1987918285e_bool,P_1) = P_1 ).
fof(fact_244_subset__insertI2,axiom,
! [B_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).
fof(fact_245_subset__insertI2,axiom,
! [B_1,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))) ) ).
fof(fact_246_subset__insertI2,axiom,
! [B_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),B))) ) ).
fof(fact_247_subset__insert,axiom,
! [B,X_1,A] :
( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B)))
<=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ) ).
fof(fact_248_subset__insert,axiom,
! [B,X_1,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).
fof(fact_249_subset__insert,axiom,
! [B,X_1,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B)))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) ) ) ).
fof(fact_250_insert__subset,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B))
<=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
& hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ) ).
fof(fact_251_insert__subset,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).
fof(fact_252_insert__subset,axiom,
! [X_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) ) ) ).
fof(fact_253_subset__insertI,axiom,
! [B,A_4] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B))) ).
fof(fact_254_subset__insertI,axiom,
! [B,A_4] : hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,B),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B))) ).
fof(fact_255_subset__insertI,axiom,
! [B,A_4] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B))) ).
fof(fact_256_insert__image,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1193503499_pname(F,X_1)),hAPP_f1083669085e_bool(image_1774499931_pname(F),A)) = hAPP_f1083669085e_bool(image_1774499931_pname(F),A) ) ).
fof(fact_257_insert__image,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_H46530577te_com(F,X_1)),hAPP_f1815646051m_bool(image_741143905te_com(F),A)) = hAPP_f1815646051m_bool(image_741143905te_com(F),A) ) ).
fof(fact_258_insert__image,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F,X_1)),hAPP_f759274231e_bool(image_pname_pname(F),A)) = hAPP_f759274231e_bool(image_pname_pname(F),A) ) ).
fof(fact_259_insert__image,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_pname_com(F,X_1)),hAPP_f1206115581m_bool(image_pname_com(F),A)) = hAPP_f1206115581m_bool(image_pname_com(F),A) ) ).
fof(fact_260_insert__image,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(F,X_1)),hAPP_f457085749e_bool(image_2605051_state(F),A)) = hAPP_f457085749e_bool(image_2605051_state(F),A) ) ).
fof(fact_261_insert__image,axiom,
! [F,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,X_1)),hAPP_f360545851e_bool(image_185131637_state(F),A)) = hAPP_f360545851e_bool(image_185131637_state(F),A) ) ).
fof(fact_262_image__insert,axiom,
! [F,A_4,B] : hAPP_f1083669085e_bool(image_1774499931_pname(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1193503499_pname(F,A_4)),hAPP_f1083669085e_bool(image_1774499931_pname(F),B)) ).
fof(fact_263_image__insert,axiom,
! [F,A_4,B] : hAPP_f1815646051m_bool(image_741143905te_com(F),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_H46530577te_com(F,A_4)),hAPP_f1815646051m_bool(image_741143905te_com(F),B)) ).
fof(fact_264_image__insert,axiom,
! [F,A_4,B] : hAPP_f457085749e_bool(image_2605051_state(F),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(F,A_4)),hAPP_f457085749e_bool(image_2605051_state(F),B)) ).
fof(fact_265_image__insert,axiom,
! [F,A_4,B] : hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_p1751618853_state(F,A_4)),hAPP_f360545851e_bool(image_185131637_state(F),B)) ).
fof(fact_266_image__mono,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)),hAPP_f1083669085e_bool(image_1774499931_pname(F),B))) ) ).
fof(fact_267_image__mono,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B))) ) ).
fof(fact_268_subset__image__iff,axiom,
! [B,F,A] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A)))
<=> ? [AA] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,AA),A))
& B = hAPP_f1083669085e_bool(image_1774499931_pname(F),AA) ) ) ) ).
fof(fact_269_subset__image__iff,axiom,
! [B,F,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A)))
<=> ? [AA] :
( is_fun_pname_bool(AA)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
& B = hAPP_f360545851e_bool(image_185131637_state(F),AA) ) ) ).
fof(fact_270_domI,axiom,
! [M,A_4,B_1] :
( hAPP_com_option_com(M,A_4) = hAPP_com_option_com(some_com,B_1)
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),dom_com_com(M))) ) ).
fof(fact_271_domI,axiom,
! [M,A_4,B_1] :
( hAPP_H1671063474_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_1)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho2070278094_pname(M))) ) ).
fof(fact_272_domI,axiom,
! [M,A_4,B_1] :
( hAPP_H1633077406_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_1)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho1607160812_state(M))) ) ).
fof(fact_273_domI,axiom,
! [M,A_4,B_1] :
( hAPP_p1252095976_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_1)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_pname(M))) ) ).
fof(fact_274_domI,axiom,
! [M,A_4,B_1] :
( hAPP_p485182952_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_1)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pn480909800_state(M))) ) ).
fof(fact_275_domI,axiom,
! [M,A_4,B_1] :
( hAPP_p799580910on_com(M,A_4) = hAPP_com_option_com(some_com,B_1)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M))) ) ).
fof(fact_276_Collect__conv__if,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_pname_bool(P_1,A_4))
=> 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_4))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(P_1,A_4))
=> 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_4))),P_1)) = bot_bo844097828e_bool ) ) ).
fof(fact_277_Collect__conv__if,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_com_bool(P_1,A_4))
=> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),P_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) )
& ( ~ hBOOL(hAPP_com_bool(P_1,A_4))
=> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),P_1)) = bot_bot_fun_com_bool ) ) ).
fof(fact_278_Collect__conv__if,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
=> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
=> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),P_1)) = bot_bo1649642514l_bool ) ) ).
fof(fact_279_Collect__conv__if,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_f1378282496l_bool(P_1,A_4))
=> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),P_1)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(P_1,A_4))
=> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),P_1)) = bot_bo942947096l_bool ) ) ).
fof(fact_280_Collect__conv__if,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_H242767318e_bool(P_1,A_4))
=> 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_4))),P_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool) )
& ( ~ hBOOL(hAPP_H242767318e_bool(P_1,A_4))
=> 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_4))),P_1)) = bot_bo784226126e_bool ) ) ).
fof(fact_281_Collect__conv__if2,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_pname_bool(P_1,A_4))
=> 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_4))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(P_1,A_4))
=> 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_4))),P_1)) = bot_bo844097828e_bool ) ) ).
fof(fact_282_Collect__conv__if2,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_com_bool(P_1,A_4))
=> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(fequal_com,A_4))),P_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) )
& ( ~ hBOOL(hAPP_com_bool(P_1,A_4))
=> hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(fequal_com,A_4))),P_1)) = bot_bot_fun_com_bool ) ) ).
fof(fact_283_Collect__conv__if2,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
=> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A_4))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
=> hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A_4))),P_1)) = bot_bo1649642514l_bool ) ) ).
fof(fact_284_Collect__conv__if2,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_f1378282496l_bool(P_1,A_4))
=> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(fequal1475827639e_bool,A_4))),P_1)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(P_1,A_4))
=> hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f849457489l_bool(fequal1475827639e_bool,A_4))),P_1)) = bot_bo942947096l_bool ) ) ).
fof(fact_285_Collect__conv__if2,axiom,
! [P_1,A_4] :
( ( hBOOL(hAPP_H242767318e_bool(P_1,A_4))
=> 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_4))),P_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool) )
& ( ~ hBOOL(hAPP_H242767318e_bool(P_1,A_4))
=> 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_4))),P_1)) = bot_bo784226126e_bool ) ) ).
fof(fact_286_singleton__conv,axiom,
! [A_4] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) ).
fof(fact_287_singleton__conv,axiom,
! [A_4] : hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) ).
fof(fact_288_singleton__conv,axiom,
! [A_4] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) ).
fof(fact_289_singleton__conv,axiom,
! [A_4] : hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool) ).
fof(fact_290_singleton__conv,axiom,
! [A_4] : hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,fequal1440809015_state),A_4)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool) ).
fof(fact_291_singleton__conv2,axiom,
! [A_4] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_4)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) ).
fof(fact_292_singleton__conv2,axiom,
! [A_4] : hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(fequal_com,A_4)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) ).
fof(fact_293_singleton__conv2,axiom,
! [A_4] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A_4)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) ).
fof(fact_294_singleton__conv2,axiom,
! [A_4] : hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(fequal1475827639e_bool,A_4)) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),bot_bo942947096l_bool) ).
fof(fact_295_singleton__conv2,axiom,
! [A_4] : hAPP_f806699093e_bool(collec637225377_state,hAPP_H216526335e_bool(fequal1440809015_state,A_4)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool) ).
fof(fact_296_MGF__lemma1,axiom,
! [C,G_2] :
( hBOOL(hoare_1795711768gleton)
=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo784226126e_bool))) ) )
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))) ) ) ) ).
fof(fact_297_WT__bodiesD,axiom,
! [Pn,B_4] :
( hBOOL(wT_bodies)
=> ( hAPP_p799580910on_com(body,Pn) = hAPP_com_option_com(some_com,B_4)
=> hBOOL(hAPP_com_bool(wt,B_4)) ) ) ).
fof(fact_298_imageE,axiom,
! [B_1,F,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f457085749e_bool(image_2605051_state(F),A)))
=> ~ ! [X_2] :
( B_1 = hAPP_c1455475371_state(F,X_2)
=> ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) ) ) ).
fof(fact_299_imageE,axiom,
! [B_1,F,A] :
( is_pname(B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A)))
=> ~ ! [X_2] :
( B_1 = hAPP_com_pname(F,X_2)
=> ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) ) ) ) ).
fof(fact_300_imageE,axiom,
! [B_1,F,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1815646051m_bool(image_741143905te_com(F),A)))
=> ~ ! [X_2] :
( B_1 = hAPP_H46530577te_com(F,X_2)
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A)) ) ) ).
fof(fact_301_imageE,axiom,
! [B_1,F,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A)))
=> ~ ! [X_2] :
( is_pname(X_2)
=> ( B_1 = hAPP_pname_com(F,X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ) ) ).
fof(fact_302_imageE,axiom,
! [B_1,F,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,B_1),hAPP_f360545851e_bool(image_185131637_state(F),A)))
=> ~ ! [X_2] :
( is_pname(X_2)
=> ( B_1 = hAPP_p1751618853_state(F,X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ) ) ).
fof(fact_303_finite__subset__induct,axiom,
! [P_1,A,Fa] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,Fa),A))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool))
=> ( ! [A_2,F_2] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),A))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),F_2))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,F_2))
=> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f990396704l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_304_finite__subset__induct,axiom,
! [P_1,A,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
=> ( ! [A_2,F_2] :
( ( is_fun_pname_bool(A_2)
& is_fun1661590463l_bool(F_2) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_2))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),F_2))) ) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_305_finite__subset__induct,axiom,
! [P_1,A,Fa] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,Fa),A))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,bot_bo942947096l_bool))
=> ( ! [A_2,F_2] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,F_2))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_2),A))
=> ( ~ hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_2),F_2))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,F_2))
=> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1410040974l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_306_finite__subset__induct,axiom,
! [P_1,A,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
=> ( ! [A_2,F_2] :
( ( is_pname(A_2)
& is_fun_pname_bool(F_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_2))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),F_2))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_307_finite__subset__induct,axiom,
! [P_1,A,Fa] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Fa),A))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,bot_bo784226126e_bool))
=> ( ! [A_2,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,F_2))
=> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_308_WTs__elim__cases_I7_J,axiom,
! [P] :
( hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P)))
=> ~ ! [Y_3] : hAPP_p799580910on_com(body,P) != hAPP_com_option_com(some_com,Y_3) ) ).
fof(fact_309_subsetI,axiom,
! [B,A] :
( ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),B)) )
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ).
fof(fact_310_subsetI,axiom,
! [B,A] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) ) ).
fof(fact_311_subsetI,axiom,
! [B,A] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ).
fof(fact_312_finite__subset__image,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f509793681e_bool(image_845802851_state(F),A)))
=> ? [C_3] :
( is_fun1661590463l_bool(C_3)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
& B = hAPP_f509793681e_bool(image_845802851_state(F),C_3) ) ) ) ).
fof(fact_313_finite__subset__image,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f1216288071e_bool(image_1497401961_state(F),A)))
=> ? [C_3] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,C_3),A))
& hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,C_3))
& B = hAPP_f1216288071e_bool(image_1497401961_state(F),C_3) ) ) ) ).
fof(fact_314_finite__subset__image,axiom,
! [F,A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A)))
=> ? [C_3] :
( is_fun1661590463l_bool(C_3)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
& B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3) ) ) ) ) ).
fof(fact_315_finite__subset__image,axiom,
! [F,A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f306376939e_bool(image_1863446033_pname(F),A)))
=> ? [C_3] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,C_3),A))
& hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,C_3))
& B = hAPP_f306376939e_bool(image_1863446033_pname(F),C_3) ) ) ) ) ).
fof(fact_316_finite__subset__image,axiom,
! [F,A,B] :
( is_fun1661590463l_bool(B)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f1709493145l_bool(image_1403607267e_bool(F),A)))
=> ? [C_3] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_3),A))
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,C_3))
& B = hAPP_f1709493145l_bool(image_1403607267e_bool(F),C_3) ) ) ) ) ).
fof(fact_317_finite__subset__image,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f849457489l_bool(image_995511119e_bool(F),A)))
=> ? [C_3] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_3),A))
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,C_3))
& B = hAPP_f849457489l_bool(image_995511119e_bool(F),C_3) ) ) ) ).
fof(fact_318_finite__subset__image,axiom,
! [F,A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A)))
=> ? [C_3] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_3),A))
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,C_3))
& B = hAPP_f1083669085e_bool(image_1774499931_pname(F),C_3) ) ) ) ) ).
fof(fact_319_finite__subset__image,axiom,
! [F,A,B] :
( is_fun1661590463l_bool(B)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f434788991l_bool(image_47868345e_bool(F),C_3) ) ) ) ) ).
fof(fact_320_finite__subset__image,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),hAPP_f1492100075l_bool(image_234387449e_bool(F),A)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f1492100075l_bool(image_234387449e_bool(F),C_3) ) ) ) ).
fof(fact_321_finite__subset__image,axiom,
! [F,A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f759274231e_bool(image_pname_pname(F),C_3) ) ) ) ) ).
fof(fact_322_finite__subset__image,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f360545851e_bool(image_185131637_state(F),C_3) ) ) ) ).
fof(fact_323_finite__dom__body,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))) ).
fof(fact_324_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),F_2))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,F_2))
=> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f990396704l_bool(P_1,Fa)) ) ) ) ).
fof(fact_325_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
=> ( ! [X_2,F_2] :
( ( is_fun_pname_bool(X_2)
& is_fun1661590463l_bool(F_2) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_2))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_2))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ).
fof(fact_326_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,bot_bo942947096l_bool))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,F_2))
=> ( ~ hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),F_2))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,F_2))
=> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f1410040974l_bool(P_1,Fa)) ) ) ) ).
fof(fact_327_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
=> ( ! [X_2,F_2] :
( ( is_pname(X_2)
& 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_2),F_2))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_2))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ).
fof(fact_328_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,bot_bo784226126e_bool))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,F_2))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,F_2))
=> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(P_1,Fa)) ) ) ) ).
fof(fact_329_finite_Osimps,axiom,
! [A_4] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_4))
<=> ( A_4 = bot_bot_fun_com_bool
| ? [A_7,A_2] :
( A_4 = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),A_7)
& hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_7)) ) ) ) ).
fof(fact_330_finite_Osimps,axiom,
! [A_4] :
( is_fun1661590463l_bool(A_4)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4))
<=> ( A_4 = bot_bo1649642514l_bool
| ? [A_7,A_2] :
( is_fun1661590463l_bool(A_7)
& is_fun_pname_bool(A_2)
& A_4 = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A_7)
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_7)) ) ) ) ) ).
fof(fact_331_finite_Osimps,axiom,
! [A_4] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_4))
<=> ( A_4 = bot_bo942947096l_bool
| ? [A_7,A_2] :
( A_4 = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_2),A_7)
& hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_7)) ) ) ) ).
fof(fact_332_finite_Osimps,axiom,
! [A_4] :
( is_fun_pname_bool(A_4)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4))
<=> ( A_4 = bot_bo844097828e_bool
| ? [A_7,A_2] :
( is_fun_pname_bool(A_7)
& is_pname(A_2)
& A_4 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_7)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_7)) ) ) ) ) ).
fof(fact_333_finite_Osimps,axiom,
! [A_4] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_4))
<=> ( A_4 = bot_bo784226126e_bool
| ? [A_7,A_2] :
( A_4 = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),A_7)
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_7)) ) ) ) ).
fof(fact_334_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f457085749e_bool(image_2605051_state(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
& ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_H313059897m_bool(hAPP_f235185669m_bool(cOMBC_114640782e_bool,hAPP_f475997903e_bool(cOMBB_1327031172ol_com(fequal1440809015_state),F)),hAPP_c1455475371_state(F,X_2)))))) ) ) ) ).
fof(fact_335_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(image_661047967_state(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
& ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_H216526335e_bool(hAPP_f1902016361e_bool(cOMBC_1967329268e_bool,hAPP_f596278895e_bool(cOMBB_1563888316_state(fequal1440809015_state),F)),hAPP_H574424047_state(F,X_2)))))) ) ) ) ).
fof(fact_336_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f509793681e_bool(image_845802851_state(F),A)))
=> ? [X_2] :
( is_fun_pname_bool(X_2)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_H358531139l_bool(hAPP_f1186253673l_bool(cOMBC_1836455480e_bool,hAPP_f2113567599e_bool(cOMBB_1724041344e_bool(fequal1440809015_state),F)),hAPP_f1218207411_state(F,X_2)))))) ) ) ) ).
fof(fact_337_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f1216288071e_bool(image_1497401961_state(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A))
& ~ hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_H2039996199l_bool(hAPP_f1463049441l_bool(cOMBC_754402940e_bool,hAPP_f610934515e_bool(cOMBB_1840094962e_bool(fequal1440809015_state),F)),hAPP_f718417177_state(F,X_2)))))) ) ) ) ).
fof(fact_338_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1438183293e_bool(image_com_pname(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
& ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_p1639923567m_bool(hAPP_f734198589m_bool(cOMBC_com_pname_bool,hAPP_f835719487e_bool(cOMBB_1083901850ol_com(fequal_pname),F)),hAPP_com_pname(F,X_2)))))) ) ) ) ).
fof(fact_339_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
& ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_p606792009e_bool(hAPP_f1720171569e_bool(cOMBC_1952686190e_bool,hAPP_f777604691e_bool(cOMBB_1365368614_state(fequal_pname),F)),hAPP_H1193503499_pname(F,X_2)))))) ) ) ) ).
fof(fact_340_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X_2)))))) ) ) ) ).
fof(fact_341_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A)))
=> ? [X_2] :
( is_fun_pname_bool(X_2)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,hAPP_f1385420507e_bool(cOMBB_598082538e_bool(fequal_pname),F)),hAPP_f1297739591_pname(F,X_2)))))) ) ) ) ).
fof(fact_342_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f306376939e_bool(image_1863446033_pname(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A))
& ~ hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_p1235466077l_bool(hAPP_f780571929l_bool(cOMBC_1558112230e_bool,hAPP_f700046015e_bool(cOMBB_1400714760e_bool(fequal_pname),F)),hAPP_f88366945_pname(F,X_2)))))) ) ) ) ).
fof(fact_343_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f1709493145l_bool(image_1403607267e_bool(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
& ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f360545851e_bool(hAPP_f591683433e_bool(cOMBC_1984545208l_bool,hAPP_f381060343l_bool(cOMBB_1631414076_state(fequal533582459e_bool),F)),hAPP_H1776011827e_bool(F,X_2)))))) ) ) ) ).
fof(fact_344_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f849457489l_bool(image_995511119e_bool(F),A)))
=> ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
& ~ hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,hAPP_f1191357267l_bool(cOMBB_639263758_state(fequal1475827639e_bool),F)),hAPP_H216526335e_bool(F,X_2)))))) ) ) ) ).
fof(fact_345_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,hAPP_f567934427l_bool(cOMBB_408569982_pname(fequal533582459e_bool),F)),hAPP_p61793385e_bool(F,X_2)))))) ) ) ) ).
fof(fact_346_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f1492100075l_bool(image_234387449e_bool(F),A)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f1083669085e_bool(hAPP_f568104217e_bool(cOMBC_1757633998l_bool,hAPP_f1143533991l_bool(cOMBB_949755692_pname(fequal1475827639e_bool),F)),hAPP_p606792009e_bool(F,X_2)))))) ) ) ) ).
fof(fact_347_pigeonhole__infinite,axiom,
! [F,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(F),A)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_H1776011827e_bool(hAPP_f343137017e_bool(cOMBC_19854728e_bool,hAPP_f472107739e_bool(cOMBB_181781758_pname(fequal1440809015_state),F)),hAPP_p1751618853_state(F,X_2)))))) ) ) ) ).
fof(fact_348_com_Osimps_I6_J,axiom,
! [Pname_2,Pname_1] :
( ( is_pname(Pname_2)
& is_pname(Pname_1) )
=> ( hAPP_pname_com(body_1,Pname_2) = hAPP_pname_com(body_1,Pname_1)
<=> Pname_2 = Pname_1 ) ) ).
fof(fact_349_MGT__Body,axiom,
! [G_2,Procs] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs)))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),Procs))) ) ) ).
fof(fact_350_domD,axiom,
! [A_4,M] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),dom_com_com(M)))
=> ? [B_3] : hAPP_com_option_com(M,A_4) = hAPP_com_option_com(some_com,B_3) ) ).
fof(fact_351_domD,axiom,
! [A_4,M] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho2070278094_pname(M)))
=> ? [B_3] :
( is_pname(B_3)
& hAPP_H1671063474_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_3) ) ) ).
fof(fact_352_domD,axiom,
! [A_4,M] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),dom_Ho1607160812_state(M)))
=> ? [B_3] : hAPP_H1633077406_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_3) ) ).
fof(fact_353_domD,axiom,
! [A_4,M] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_pname(M)))
=> ? [B_3] :
( is_pname(B_3)
& hAPP_p1252095976_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_3) ) ) ).
fof(fact_354_domD,axiom,
! [A_4,M] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pn480909800_state(M)))
=> ? [B_3] : hAPP_p485182952_state(M,A_4) = hAPP_H1633077406_state(some_H1043067815_state,B_3) ) ).
fof(fact_355_domD,axiom,
! [A_4,M] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M)))
=> ? [B_3] : hAPP_p799580910on_com(M,A_4) = hAPP_com_option_com(some_com,B_3) ) ).
fof(fact_356_the__elem__eq,axiom,
! [X_1] :
( is_pname(X_1)
=> hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1 ) ).
fof(fact_357_the__elem__eq,axiom,
! [X_1] : hAPP_f1276420679ol_com(the_elem_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = X_1 ).
fof(fact_358_the__elem__eq,axiom,
! [X_1] : hAPP_f718417177_state(the_el2080696983_state,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1 ).
fof(fact_359_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_H46530577te_com(F,X_2)),B)) )
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1815646051m_bool(image_741143905te_com(F),A)),B)) ) ).
fof(fact_360_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1193503499_pname(F,X_2)),B)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)),B)) ) ).
fof(fact_361_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_pname_com(F,X_2)),B)) ) )
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1206115581m_bool(image_pname_com(F),A)),B)) ) ).
fof(fact_362_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_2)),B)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(image_pname_pname(F),A)),B)) ) ).
fof(fact_363_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_c1455475371_state(F,X_2)),B)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f457085749e_bool(image_2605051_state(F),A)),B)) ) ).
fof(fact_364_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_com_pname(F,X_2)),B)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1438183293e_bool(image_com_pname(F),A)),B)) ) ).
fof(fact_365_image__subsetI,axiom,
! [F,B,A] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_2)),B)) ) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),B)) ) ).
fof(fact_366_order__refl,axiom,
! [X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1)) ).
fof(fact_367_order__refl,axiom,
! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),X_1)) ).
fof(fact_368_order__refl,axiom,
! [X_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),X_1)) ).
fof(fact_369_nonempty__iff,axiom,
! [A] :
( A != bot_bot_fun_com_bool
<=> ? [X_2,B_2] :
( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),B_2)
& ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),B_2)) ) ) ).
fof(fact_370_nonempty__iff,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( A != bot_bo844097828e_bool
<=> ? [X_2,B_2] :
( is_pname(X_2)
& is_fun_pname_bool(B_2)
& A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2)) ) ) ) ).
fof(fact_371_nonempty__iff,axiom,
! [A] :
( A != bot_bo784226126e_bool
<=> ? [X_2,B_2] :
( A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),B_2)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B_2)) ) ) ).
fof(fact_372_the_Osimps,axiom,
! [X_5] :
( is_pname(X_5)
=> hAPP_o593586696_pname(the_pname_1,hAPP_p1252095976_pname(some_pname,X_5)) = X_5 ) ).
fof(fact_373_the_Osimps,axiom,
! [X_5] : hAPP_o1912464824_state(the_Ho32424093_state,hAPP_H1633077406_state(some_H1043067815_state,X_5)) = X_5 ).
fof(fact_374_the_Osimps,axiom,
! [X_5] : hAPP_option_com_com(the_com,hAPP_com_option_com(some_com,X_5)) = X_5 ).
fof(fact_375_weak__Body,axiom,
! [G_2,P_1,Pn_1,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo784226126e_bool))) ) ).
fof(fact_376_BodyN,axiom,
! [P_1,Pn_1,Q_1,G_2] :
( 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,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_2)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo784226126e_bool))) ) ).
fof(fact_377_state__not__singleton__def,axiom,
( hBOOL(hoare_1795711768gleton)
<=> ? [S_1,T_2] : S_1 != T_2 ) ).
fof(fact_378_UnCI,axiom,
! [A,C,B] :
( ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) )
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) ) ).
fof(fact_379_UnCI,axiom,
! [A,C,B] :
( ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) ) ).
fof(fact_380_UnCI,axiom,
! [A,C,B] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ) ).
fof(fact_381_UnE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_382_UnE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_383_UnE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_384_triple_Oinject,axiom,
! [Fun1_2,Com_1,Fun2_2,Fun1_1,Com_2,Fun2_1] :
( hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_2),Com_1),Fun2_2) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1_1),Com_2),Fun2_1)
<=> ( Fun1_2 = Fun1_1
& Com_1 = Com_2
& Fun2_2 = Fun2_1 ) ) ).
fof(fact_385_UnI2,axiom,
! [A,C,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) ) ).
fof(fact_386_UnI2,axiom,
! [A,C,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) ) ).
fof(fact_387_UnI2,axiom,
! [A,C,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ) ).
fof(fact_388_UnI1,axiom,
! [B,C,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) ) ).
fof(fact_389_UnI1,axiom,
! [B,C,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) ) ).
fof(fact_390_UnI1,axiom,
! [B,C,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ) ).
fof(fact_391_ball__Un,axiom,
! [P_1,A,B] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
=> hBOOL(hAPP_pname_bool(P_1,X_2)) ) )
<=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_pname_bool(P_1,X_2)) ) )
& ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
=> hBOOL(hAPP_pname_bool(P_1,X_2)) ) ) ) ) ).
fof(fact_392_ball__Un,axiom,
! [P_1,A,B] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)))
=> hBOOL(hAPP_H242767318e_bool(P_1,X_2)) )
<=> ( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
=> hBOOL(hAPP_H242767318e_bool(P_1,X_2)) )
& ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B))
=> hBOOL(hAPP_H242767318e_bool(P_1,X_2)) ) ) ) ).
fof(fact_393_bex__Un,axiom,
! [P_1,A,B] :
( ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
& hBOOL(hAPP_pname_bool(P_1,X_2)) )
<=> ( ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
& hBOOL(hAPP_pname_bool(P_1,X_2)) )
| ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
& hBOOL(hAPP_pname_bool(P_1,X_2)) ) ) ) ).
fof(fact_394_bex__Un,axiom,
! [P_1,A,B] :
( ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)))
& hBOOL(hAPP_H242767318e_bool(P_1,X_2)) )
<=> ( ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
& hBOOL(hAPP_H242767318e_bool(P_1,X_2)) )
| ? [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),B))
& hBOOL(hAPP_H242767318e_bool(P_1,X_2)) ) ) ) ).
fof(fact_395_Un__assoc,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) ).
fof(fact_396_Un__assoc,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) ).
fof(fact_397_Un__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)))
<=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
| hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_398_Un__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
| hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_399_Un__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_400_Un__left__commute,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1)) ).
fof(fact_401_Un__left__commute,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),C_1)) ).
fof(fact_402_Un__left__absorb,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) ).
fof(fact_403_Un__left__absorb,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) ).
fof(fact_404_Un__commute,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A) ).
fof(fact_405_Un__commute,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),A) ).
fof(fact_406_Un__def,axiom,
! [A,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))) ).
fof(fact_407_Un__def,axiom,
! [A,B] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).
fof(fact_408_Un__def,axiom,
! [A,B] : hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B))) ).
fof(fact_409_Un__def,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = 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))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B))) ).
fof(fact_410_Un__def,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).
fof(fact_411_Un__absorb,axiom,
! [A] :
( is_fun_pname_bool(A)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),A) = A ) ).
fof(fact_412_Un__absorb,axiom,
! [A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),A) = A ).
fof(fact_413_Collect__disj__eq,axiom,
! [P_1,Q_1] : hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1)) ).
fof(fact_414_Collect__disj__eq,axiom,
! [P_1,Q_1] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1)) ).
fof(fact_415_Collect__disj__eq,axiom,
! [P_1,Q_1] : hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fdisj),P_1)),Q_1)) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1)) ).
fof(fact_416_Collect__disj__eq,axiom,
! [P_1,Q_1] : hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fdisj),P_1)),Q_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(collec637225377_state,P_1)),hAPP_f806699093e_bool(collec637225377_state,Q_1)) ).
fof(fact_417_Un__empty,axiom,
! [A,B] :
( ( is_fun_pname_bool(A)
& is_fun_pname_bool(B) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = bot_bo844097828e_bool
<=> ( A = bot_bo844097828e_bool
& B = bot_bo844097828e_bool ) ) ) ).
fof(fact_418_Un__empty,axiom,
! [A,B] :
( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = bot_bot_fun_com_bool
<=> ( A = bot_bot_fun_com_bool
& B = bot_bot_fun_com_bool ) ) ).
fof(fact_419_Un__empty,axiom,
! [A,B] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = bot_bo784226126e_bool
<=> ( A = bot_bo784226126e_bool
& B = bot_bo784226126e_bool ) ) ).
fof(fact_420_Un__empty__right,axiom,
! [A] :
( is_fun_pname_bool(A)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),bot_bo844097828e_bool) = A ) ).
fof(fact_421_Un__empty__right,axiom,
! [A] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),bot_bot_fun_com_bool) = A ).
fof(fact_422_Un__empty__right,axiom,
! [A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),bot_bo784226126e_bool) = A ).
fof(fact_423_Un__empty__left,axiom,
! [B] :
( is_fun_pname_bool(B)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B) = B ) ).
fof(fact_424_Un__empty__left,axiom,
! [B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,bot_bot_fun_com_bool),B) = B ).
fof(fact_425_Un__empty__left,axiom,
! [B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),B) = B ).
fof(fact_426_finite__UnI,axiom,
! [G_2,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_2))) ) ) ).
fof(fact_427_finite__UnI,axiom,
! [G_2,Fa] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,G_2))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,Fa),G_2))) ) ) ).
fof(fact_428_finite__UnI,axiom,
! [G_2,Fa] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,G_2))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Fa),G_2))) ) ) ).
fof(fact_429_finite__UnI,axiom,
! [G_2,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_2))) ) ) ).
fof(fact_430_finite__Un,axiom,
! [Fa,G_2] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_2)))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)) ) ) ).
fof(fact_431_finite__Un,axiom,
! [Fa,G_2] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,Fa),G_2)))
<=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
& hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,G_2)) ) ) ).
fof(fact_432_finite__Un,axiom,
! [Fa,G_2] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Fa),G_2)))
<=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
& hBOOL(hAPP_f1378282496l_bool(finite694102371_state,G_2)) ) ) ).
fof(fact_433_finite__Un,axiom,
! [Fa,G_2] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_2)))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)) ) ) ).
fof(fact_434_Un__insert__left,axiom,
! [A_4,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) ).
fof(fact_435_Un__insert__left,axiom,
! [A_4,B,C_1] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,B),C_1)) ).
fof(fact_436_Un__insert__left,axiom,
! [A_4,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) ).
fof(fact_437_Un__insert__right,axiom,
! [A,A_4,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) ).
fof(fact_438_Un__insert__right,axiom,
! [A,A_4,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) ).
fof(fact_439_Un__insert__right,axiom,
! [A,A_4,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) ).
fof(fact_440_Un__mono,axiom,
! [B,D,A,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D))) ) ) ).
fof(fact_441_Un__mono,axiom,
! [B,D,A,C_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),D))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C_1),D))) ) ) ).
fof(fact_442_Un__least,axiom,
! [B,A,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1)) ) ) ).
fof(fact_443_Un__least,axiom,
! [B,A,C_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),C_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),C_1)) ) ) ).
fof(fact_444_Un__absorb2,axiom,
! [B,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = A ) ) ).
fof(fact_445_Un__absorb2,axiom,
! [B,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = A ) ).
fof(fact_446_Un__absorb1,axiom,
! [A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = B ) ) ).
fof(fact_447_Un__absorb1,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = B ) ).
fof(fact_448_subset__Un__eq,axiom,
! [A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
<=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = B ) ) ).
fof(fact_449_subset__Un__eq,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
<=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = B ) ).
fof(fact_450_Un__upper2,axiom,
! [B,A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ).
fof(fact_451_Un__upper2,axiom,
! [B,A] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) ).
fof(fact_452_Un__upper1,axiom,
! [A,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ).
fof(fact_453_Un__upper1,axiom,
! [A,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))) ).
fof(fact_454_image__Un,axiom,
! [F,A,B] : hAPP_f1083669085e_bool(image_1774499931_pname(F),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F),A)),hAPP_f1083669085e_bool(image_1774499931_pname(F),B)) ).
fof(fact_455_image__Un,axiom,
! [F,A,B] : hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B)) ).
fof(fact_456_insert__def,axiom,
! [A_4,B] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B) = 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_4))),B) ).
fof(fact_457_insert__def,axiom,
! [A_4,B] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),B) ).
fof(fact_458_insert__def,axiom,
! [A_4,B] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4))),B) ).
fof(fact_459_insert__def,axiom,
! [A_4,B] : hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),B) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,fequal1475827639e_bool),A_4))),B) ).
fof(fact_460_insert__def,axiom,
! [A_4,B] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B) = 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_4))),B) ).
fof(fact_461_insert__is__Un,axiom,
! [A_4,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)),A) ).
fof(fact_462_insert__is__Un,axiom,
! [A_4,A] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)),A) ).
fof(fact_463_insert__is__Un,axiom,
! [A_4,A] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)),A) ).
fof(fact_464_hoare__derivs_OBody,axiom,
! [G_2,P_1,Q_1,Procs] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),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)),body_1)),Q_1)),Procs))),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)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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)),body_1)),Q_1)),Procs))) ) ).
fof(fact_465_xt1_I6_J,axiom,
! [Z,Y_2,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) ) ) ).
fof(fact_466_xt1_I6_J,axiom,
! [Z,Y_2,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_1)) ) ) ).
fof(fact_467_xt1_I6_J,axiom,
! [Z,Y_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z),Y_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z),X_1)) ) ) ).
fof(fact_468_xt1_I5_J,axiom,
! [Y_2,X_1] :
( ( is_fun_pname_bool(Y_2)
& is_fun_pname_bool(X_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
=> X_1 = Y_2 ) ) ) ).
fof(fact_469_xt1_I5_J,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
=> ( hBOOL(X_1)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_470_xt1_I5_J,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
=> X_1 = Y_2 ) ) ).
fof(fact_471_order__trans,axiom,
! [Z,X_1,Y_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).
fof(fact_472_order__trans,axiom,
! [Z,X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)) ) ) ).
fof(fact_473_order__trans,axiom,
! [Z,X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),Z))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z)) ) ) ).
fof(fact_474_order__antisym,axiom,
! [X_1,Y_2] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> X_1 = Y_2 ) ) ) ).
fof(fact_475_order__antisym,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(X_1)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_476_order__antisym,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> X_1 = Y_2 ) ) ).
fof(fact_477_xt1_I4_J,axiom,
! [C,B_1,A_4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_4))
=> ( B_1 = C
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A_4)) ) ) ).
fof(fact_478_xt1_I4_J,axiom,
! [C,B_1,A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_4))
=> ( ( hBOOL(B_1)
<=> hBOOL(C) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),A_4)) ) ) ).
fof(fact_479_xt1_I4_J,axiom,
! [C,B_1,A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),A_4))
=> ( B_1 = C
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),A_4)) ) ) ).
fof(fact_480_ord__le__eq__trans,axiom,
! [C,A_4,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),B_1))
=> ( B_1 = C
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C)) ) ) ).
fof(fact_481_ord__le__eq__trans,axiom,
! [C,A_4,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),B_1))
=> ( ( hBOOL(B_1)
<=> hBOOL(C) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C)) ) ) ).
fof(fact_482_ord__le__eq__trans,axiom,
! [C,A_4,B_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),B_1))
=> ( B_1 = C
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C)) ) ) ).
fof(fact_483_xt1_I3_J,axiom,
! [C,A_4,B_1] :
( A_4 = B_1
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A_4)) ) ) ).
fof(fact_484_xt1_I3_J,axiom,
! [C,B_1,A_4] :
( ( hBOOL(A_4)
<=> hBOOL(B_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),B_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),A_4)) ) ) ).
fof(fact_485_xt1_I3_J,axiom,
! [C,A_4,B_1] :
( A_4 = B_1
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),B_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),A_4)) ) ) ).
fof(fact_486_ord__eq__le__trans,axiom,
! [C,A_4,B_1] :
( A_4 = B_1
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C)) ) ) ).
fof(fact_487_ord__eq__le__trans,axiom,
! [C,B_1,A_4] :
( ( hBOOL(A_4)
<=> hBOOL(B_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C)) ) ) ).
fof(fact_488_ord__eq__le__trans,axiom,
! [C,A_4,B_1] :
( A_4 = B_1
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),C))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C)) ) ) ).
fof(fact_489_order__antisym__conv,axiom,
! [Y_2,X_1] :
( ( is_fun_pname_bool(Y_2)
& is_fun_pname_bool(X_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
<=> X_1 = Y_2 ) ) ) ).
fof(fact_490_order__antisym__conv,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
<=> ( hBOOL(X_1)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_491_order__antisym__conv,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
<=> X_1 = Y_2 ) ) ).
fof(fact_492_order__eq__refl,axiom,
! [X_1,Y_2] :
( X_1 = Y_2
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) ) ).
fof(fact_493_order__eq__refl,axiom,
! [Y_2,X_1] :
( ( hBOOL(X_1)
<=> hBOOL(Y_2) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) ) ).
fof(fact_494_order__eq__refl,axiom,
! [X_1,Y_2] :
( X_1 = Y_2
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2)) ) ).
fof(fact_495_order__eq__iff,axiom,
! [X_1,Y_2] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y_2) )
=> ( X_1 = Y_2
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) ) ) ) ).
fof(fact_496_order__eq__iff,axiom,
! [Y_2,X_1] :
( ( hBOOL(X_1)
<=> hBOOL(Y_2) )
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
& hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) ) ) ).
fof(fact_497_order__eq__iff,axiom,
! [X_1,Y_2] :
( X_1 = Y_2
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1)) ) ) ).
fof(fact_498_option_Oinject,axiom,
! [A_4,A_8] :
( ( is_pname(A_4)
& is_pname(A_8) )
=> ( hAPP_p1252095976_pname(some_pname,A_4) = hAPP_p1252095976_pname(some_pname,A_8)
<=> A_4 = A_8 ) ) ).
fof(fact_499_option_Oinject,axiom,
! [A_4,A_8] :
( hAPP_H1633077406_state(some_H1043067815_state,A_4) = hAPP_H1633077406_state(some_H1043067815_state,A_8)
<=> A_4 = A_8 ) ).
fof(fact_500_option_Oinject,axiom,
! [A_4,A_8] :
( hAPP_com_option_com(some_com,A_4) = hAPP_com_option_com(some_com,A_8)
<=> A_4 = A_8 ) ).
fof(fact_501_constant,axiom,
! [G_2,P_1,C,Q_1,C_1] :
( ( hBOOL(C_1)
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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)),P_1))),C_1)),C),Q_1)),bot_bo784226126e_bool))) ) ).
fof(fact_502_Body1,axiom,
! [Pn_1,G_2,P_1,Q_1,Procs] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),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)),body_1)),Q_1)),Procs))),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)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procs))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo784226126e_bool))) ) ) ).
fof(fact_503_le__bot,axiom,
! [A_4] :
( is_fun_pname_bool(A_4)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),bot_bo844097828e_bool))
=> A_4 = bot_bo844097828e_bool ) ) ).
fof(fact_504_le__bot,axiom,
! [A_4] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A_4),bot_bot_fun_com_bool))
=> A_4 = bot_bot_fun_com_bool ) ).
fof(fact_505_le__bot,axiom,
! [A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),bot_bot_bool))
=> ( hBOOL(A_4)
<=> hBOOL(bot_bot_bool) ) ) ).
fof(fact_506_le__bot,axiom,
! [A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),bot_bo784226126e_bool))
=> A_4 = bot_bo784226126e_bool ) ).
fof(fact_507_bot__unique,axiom,
! [A_4] :
( is_fun_pname_bool(A_4)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),bot_bo844097828e_bool))
<=> A_4 = bot_bo844097828e_bool ) ) ).
fof(fact_508_bot__unique,axiom,
! [A_4] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A_4),bot_bot_fun_com_bool))
<=> A_4 = bot_bot_fun_com_bool ) ).
fof(fact_509_bot__unique,axiom,
! [A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),bot_bot_bool))
<=> ( hBOOL(A_4)
<=> hBOOL(bot_bot_bool) ) ) ).
fof(fact_510_bot__unique,axiom,
! [A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),bot_bo784226126e_bool))
<=> A_4 = bot_bo784226126e_bool ) ).
fof(fact_511_bot__least,axiom,
! [A_4] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_4)) ).
fof(fact_512_bot__least,axiom,
! [A_4] : hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,bot_bot_fun_com_bool),A_4)) ).
fof(fact_513_bot__least,axiom,
! [A_4] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_4)) ).
fof(fact_514_bot__least,axiom,
! [A_4] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,bot_bo784226126e_bool),A_4)) ).
fof(fact_515_le__funE,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))) ) ).
fof(fact_516_le__funE,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))) ) ).
fof(fact_517_le__funD,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))) ) ).
fof(fact_518_le__funD,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))) ) ).
fof(fact_519_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G))
<=> ! [X_2] :
( is_pname(X_2)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))) ) ) ).
fof(fact_520_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G))
<=> ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2))) ) ).
fof(fact_521_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_522_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_523_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_524_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_525_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_526_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_527_finite__pointwise,axiom,
! [P_1,Q_1,G_2,P_3,C0_1,Q_3,U_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1))
=> ( ! [P_4] :
( is_fun_pname_bool(P_4)
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f887530048e_bool(P_3,P_4)),hAPP_f792846925ol_com(C0_1,P_4)),hAPP_f887530048e_bool(Q_3,P_4))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f887530048e_bool(P_1,P_4)),hAPP_f792846925ol_com(C0_1,P_4)),hAPP_f887530048e_bool(Q_1,P_4))),bot_bo784226126e_bool))) ) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f509793681e_bool(image_845802851_state(hAPP_f819036232_state(hAPP_f815143704_state(cOMBS_858986606_state,hAPP_f240260249_state(hAPP_f578932784_state(cOMBS_384351451_state,hAPP_f1633046421_state(cOMBB_1794358604e_bool(hoare_1191504582_state),P_3)),C0_1)),Q_3)),U_1)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f509793681e_bool(image_845802851_state(hAPP_f819036232_state(hAPP_f815143704_state(cOMBS_858986606_state,hAPP_f240260249_state(hAPP_f578932784_state(cOMBS_384351451_state,hAPP_f1633046421_state(cOMBB_1794358604e_bool(hoare_1191504582_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).
fof(fact_528_finite__pointwise,axiom,
! [P_1,Q_1,G_2,P_3,C0_1,Q_3,U_1] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,U_1))
=> ( ! [P_4] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1487042470e_bool(P_3,P_4)),hAPP_f1547517799ol_com(C0_1,P_4)),hAPP_f1487042470e_bool(Q_3,P_4))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1487042470e_bool(P_1,P_4)),hAPP_f1547517799ol_com(C0_1,P_4)),hAPP_f1487042470e_bool(Q_1,P_4))),bot_bo784226126e_bool))) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f1216288071e_bool(image_1497401961_state(hAPP_f578501918_state(hAPP_f886846002_state(cOMBS_57685138_state,hAPP_f824259881_state(hAPP_f37848848_state(cOMBS_1164062463_state,hAPP_f250550847_state(cOMBB_2049797414e_bool(hoare_1191504582_state),P_3)),C0_1)),Q_3)),U_1)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f1216288071e_bool(image_1497401961_state(hAPP_f578501918_state(hAPP_f886846002_state(cOMBS_57685138_state,hAPP_f824259881_state(hAPP_f37848848_state(cOMBS_1164062463_state,hAPP_f250550847_state(cOMBB_2049797414e_bool(hoare_1191504582_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).
fof(fact_529_finite__pointwise,axiom,
! [P_1,Q_1,G_2,P_3,C0_1,Q_3,U_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1))
=> ( ! [P_4] :
( is_pname(P_4)
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_p1637813682e_bool(P_3,P_4)),hAPP_pname_com(C0_1,P_4)),hAPP_p1637813682e_bool(Q_3,P_4))),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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_4)),hAPP_pname_com(C0_1,P_4)),hAPP_p1637813682e_bool(Q_1,P_4))),bot_bo784226126e_bool))) ) )
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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_3)),C0_1)),Q_3)),U_1)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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_1)),Q_1)),U_1))) ) ) ) ).
fof(fact_530_escape,axiom,
! [G_2,C,Q_1,P_1] :
( ! [Z_2,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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_1))),C),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo784226126e_bool))) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) ) ).
fof(fact_531_Body__sound__lemma,axiom,
! [G_2,P_1,Q_1,Procs] :
( hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,G_2),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)),body_1)),Q_1)),Procs))),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)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(G_2),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)),body_1)),Q_1)),Procs))) ) ).
fof(fact_532_conseq1,axiom,
! [P_1,G_2,P_3,C,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_3),C),Q_1)),bot_bo784226126e_bool)))
=> ( ! [Z_2,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_3,Z_2),S_1)) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) ) ) ).
fof(fact_533_conseq2,axiom,
! [Q_1,G_2,P_1,C,Q_3] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_3)),bot_bo784226126e_bool)))
=> ( ! [Z_2,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_2),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_1)) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) ) ) ).
fof(fact_534_MGF__complete,axiom,
! [P_1,Q_1,C] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(bot_bo784226126e_bool),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) ) ) ).
fof(fact_535_sup1E,axiom,
! [A,B,X_1] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1))
=> ( ~ hBOOL(hAPP_pname_bool(A,X_1))
=> hBOOL(hAPP_pname_bool(B,X_1)) ) ) ).
fof(fact_536_sup1E,axiom,
! [A,B,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1))
=> ( ~ hBOOL(hAPP_H242767318e_bool(A,X_1))
=> hBOOL(hAPP_H242767318e_bool(B,X_1)) ) ) ).
fof(fact_537_sup1CI,axiom,
! [A,B,X_1] :
( ( ~ hBOOL(hAPP_pname_bool(B,X_1))
=> hBOOL(hAPP_pname_bool(A,X_1)) )
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) ) ).
fof(fact_538_sup1CI,axiom,
! [A,B,X_1] :
( ( ~ hBOOL(hAPP_H242767318e_bool(B,X_1))
=> hBOOL(hAPP_H242767318e_bool(A,X_1)) )
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)) ) ).
fof(fact_539_conseq12,axiom,
! [Q_1,P_1,G_2,P_3,C,Q_3] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_3),C),Q_3)),bot_bo784226126e_bool)))
=> ( ! [Z_2,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
=> ! [S_2] :
( ! [Z_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_3,Z_3),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_3),S_2)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_2)) ) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) ) ) ).
fof(fact_540_hoare__sound,axiom,
! [G_2,Ts] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),Ts))
=> hBOOL(hAPP_f1378282496l_bool(hoare_919241616_state(G_2),Ts)) ) ).
fof(fact_541_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_2))
<=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),bot_bot_fun_com_bool)) ) ).
fof(fact_542_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_H242767318e_bool(bot_bo784226126e_bool,X_2))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),bot_bo784226126e_bool)) ) ).
fof(fact_543_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),bot_bo844097828e_bool)) ) ).
fof(fact_544_rev__predicate1D,axiom,
! [Q_1,P_1,X_1] :
( hBOOL(hAPP_pname_bool(P_1,X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1))
=> hBOOL(hAPP_pname_bool(Q_1,X_1)) ) ) ).
fof(fact_545_rev__predicate1D,axiom,
! [Q_1,P_1,X_1] :
( hBOOL(hAPP_H242767318e_bool(P_1,X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,P_1),Q_1))
=> hBOOL(hAPP_H242767318e_bool(Q_1,X_1)) ) ) ).
fof(fact_546_predicate1D,axiom,
! [X_1,P_1,Q_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1))
=> ( hBOOL(hAPP_pname_bool(P_1,X_1))
=> hBOOL(hAPP_pname_bool(Q_1,X_1)) ) ) ).
fof(fact_547_predicate1D,axiom,
! [X_1,P_1,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,P_1),Q_1))
=> ( hBOOL(hAPP_H242767318e_bool(P_1,X_1))
=> hBOOL(hAPP_H242767318e_bool(Q_1,X_1)) ) ) ).
fof(fact_548_sup1I2,axiom,
! [A,B,X_1] :
( hBOOL(hAPP_pname_bool(B,X_1))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) ) ).
fof(fact_549_sup1I2,axiom,
! [A,B,X_1] :
( hBOOL(hAPP_H242767318e_bool(B,X_1))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)) ) ).
fof(fact_550_sup1I1,axiom,
! [B,A,X_1] :
( hBOOL(hAPP_pname_bool(A,X_1))
=> hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) ) ).
fof(fact_551_sup1I1,axiom,
! [B,A,X_1] :
( hBOOL(hAPP_H242767318e_bool(A,X_1))
=> hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B),X_1)) ) ).
fof(fact_552_pred__subset__eq,axiom,
! [R_1,S] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)))
<=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,R_1),S)) ) ).
fof(fact_553_pred__subset__eq,axiom,
! [R_1,S] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_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)))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,R_1),S)) ) ).
fof(fact_554_pred__subset__eq,axiom,
! [R_1,S] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,R_1),S)) ) ).
fof(fact_555_sup__Un__eq,axiom,
! [R_1,S,X_2] :
( hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)),X_2))
<=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,R_1),S))) ) ).
fof(fact_556_sup__Un__eq,axiom,
! [R_1,S,X_2] :
( 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)),X_2))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,R_1),S))) ) ).
fof(fact_557_sup__Un__eq,axiom,
! [R_1,S,X_2] :
( 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)),X_2))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S))) ) ).
fof(fact_558_le__funI,axiom,
! [F,G] :
( ! [X_2] :
( is_pname(X_2)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) ) ).
fof(fact_559_le__funI,axiom,
! [F,G] :
( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H242767318e_bool(F,X_2)),hAPP_H242767318e_bool(G,X_2)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,F),G)) ) ).
fof(fact_560_Option_Oset_Osimps_I2_J,axiom,
! [X_1] : set_pname(hAPP_p1252095976_pname(some_pname,X_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ).
fof(fact_561_Option_Oset_Osimps_I2_J,axiom,
! [X_1] : set_com(hAPP_com_option_com(some_com,X_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) ).
fof(fact_562_Option_Oset_Osimps_I2_J,axiom,
! [X_1] : set_Ho1741238126_state(hAPP_H1633077406_state(some_H1043067815_state,X_1)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool) ).
fof(fact_563_sup__apply,axiom,
! [F,G,X_1] :
( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))) ) ).
fof(fact_564_sup__apply,axiom,
! [F,G,X_1] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,F),G),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H242767318e_bool(F,X_1)),hAPP_H242767318e_bool(G,X_1))) ) ).
fof(fact_565_sup__fun__def,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_566_sup__fun__def,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_567_single__stateE,axiom,
( hBOOL(hoare_1795711768gleton)
=> ! [T_2] :
~ ! [S_1] : S_1 = T_2 ) ).
fof(fact_568_sup__eq__bot__iff,axiom,
! [X_1,Y_2] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y_2) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = bot_bo844097828e_bool
<=> ( X_1 = bot_bo844097828e_bool
& Y_2 = bot_bo844097828e_bool ) ) ) ).
fof(fact_569_sup__eq__bot__iff,axiom,
! [X_1,Y_2] :
( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,X_1),Y_2) = bot_bot_fun_com_bool
<=> ( X_1 = bot_bot_fun_com_bool
& Y_2 = bot_bot_fun_com_bool ) ) ).
fof(fact_570_sup__eq__bot__iff,axiom,
! [X_1,Y_2] :
( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
<=> hBOOL(bot_bot_bool) )
<=> ( ( hBOOL(X_1)
<=> hBOOL(bot_bot_bool) )
& ( hBOOL(Y_2)
<=> hBOOL(bot_bot_bool) ) ) ) ).
fof(fact_571_sup__eq__bot__iff,axiom,
! [X_1,Y_2] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = bot_bo784226126e_bool
<=> ( X_1 = bot_bo784226126e_bool
& Y_2 = bot_bo784226126e_bool ) ) ).
fof(fact_572_elem__set,axiom,
! [X_1,Xo] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo)))
<=> Xo = hAPP_com_option_com(some_com,X_1) ) ).
fof(fact_573_elem__set,axiom,
! [X_1,Xo] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),set_Ho1741238126_state(Xo)))
<=> Xo = hAPP_H1633077406_state(some_H1043067815_state,X_1) ) ).
fof(fact_574_elem__set,axiom,
! [X_1,Xo] :
( is_option_pname(Xo)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),set_pname(Xo)))
<=> Xo = hAPP_p1252095976_pname(some_pname,X_1) ) ) ).
fof(fact_575_sup_Oidem,axiom,
! [A_4] :
( is_fun_pname_bool(A_4)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),A_4) = A_4 ) ).
fof(fact_576_sup_Oidem,axiom,
! [A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),A_4))
<=> hBOOL(A_4) ) ).
fof(fact_577_sup_Oidem,axiom,
! [A_4] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),A_4) = A_4 ).
fof(fact_578_sup__idem,axiom,
! [X_1] :
( is_fun_pname_bool(X_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),X_1) = X_1 ) ).
fof(fact_579_sup__idem,axiom,
! [X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),X_1))
<=> hBOOL(X_1) ) ).
fof(fact_580_sup__idem,axiom,
! [X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),X_1) = X_1 ).
fof(fact_581_sup_Ocommute,axiom,
! [A_4,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A_4) ).
fof(fact_582_sup_Ocommute,axiom,
! [A_4,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),A_4)) ) ).
fof(fact_583_sup_Ocommute,axiom,
! [A_4,B_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),A_4) ).
fof(fact_584_inf__sup__aci_I5_J,axiom,
! [X_1,Y_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1) ).
fof(fact_585_inf__sup__aci_I5_J,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)) ) ).
fof(fact_586_inf__sup__aci_I5_J,axiom,
! [X_1,Y_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),X_1) ).
fof(fact_587_sup__commute,axiom,
! [X_1,Y_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1) ).
fof(fact_588_sup__commute,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)) ) ).
fof(fact_589_sup__commute,axiom,
! [X_1,Y_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),X_1) ).
fof(fact_590_sup_Oleft__idem,axiom,
! [A_4,B_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1) ).
fof(fact_591_sup_Oleft__idem,axiom,
! [A_4,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)) ) ).
fof(fact_592_sup_Oleft__idem,axiom,
! [A_4,B_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1) ).
fof(fact_593_inf__sup__aci_I8_J,axiom,
! [X_1,Y_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) ).
fof(fact_594_inf__sup__aci_I8_J,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) ) ).
fof(fact_595_inf__sup__aci_I8_J,axiom,
! [X_1,Y_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) ).
fof(fact_596_sup__left__idem,axiom,
! [X_1,Y_2] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) ).
fof(fact_597_sup__left__idem,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) ) ).
fof(fact_598_sup__left__idem,axiom,
! [X_1,Y_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) ).
fof(fact_599_sup_Oleft__commute,axiom,
! [B_1,A_4,C] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),C)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C)) ).
fof(fact_600_sup_Oleft__commute,axiom,
! [B_1,A_4,C] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),C)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))) ) ).
fof(fact_601_sup_Oleft__commute,axiom,
! [B_1,A_4,C] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),C)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C)) ).
fof(fact_602_inf__sup__aci_I7_J,axiom,
! [X_1,Y_2,Z] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ).
fof(fact_603_inf__sup__aci_I7_J,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ).
fof(fact_604_inf__sup__aci_I7_J,axiom,
! [X_1,Y_2,Z] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z)) ).
fof(fact_605_sup__left__commute,axiom,
! [X_1,Y_2,Z] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ).
fof(fact_606_sup__left__commute,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ).
fof(fact_607_sup__left__commute,axiom,
! [X_1,Y_2,Z] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z)) ).
fof(fact_608_sup_Oassoc,axiom,
! [A_4,B_1,C] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),C) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C)) ).
fof(fact_609_sup_Oassoc,axiom,
! [A_4,B_1,C] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),C))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))) ) ).
fof(fact_610_sup_Oassoc,axiom,
! [A_4,B_1,C] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),C) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C)) ).
fof(fact_611_inf__sup__aci_I6_J,axiom,
! [X_1,Y_2,Z] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) ).
fof(fact_612_inf__sup__aci_I6_J,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) ) ).
fof(fact_613_inf__sup__aci_I6_J,axiom,
! [X_1,Y_2,Z] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),Z) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) ).
fof(fact_614_sup__assoc,axiom,
! [X_1,Y_2,Z] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) ).
fof(fact_615_sup__assoc,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) ) ).
fof(fact_616_sup__assoc,axiom,
! [X_1,Y_2,Z] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),Z) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) ).
fof(fact_617_inf__sup__ord_I3_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2))) ).
fof(fact_618_inf__sup__ord_I3_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).
fof(fact_619_inf__sup__ord_I3_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2))) ).
fof(fact_620_sup__ge1,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2))) ).
fof(fact_621_sup__ge1,axiom,
! [X_1,Y_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).
fof(fact_622_sup__ge1,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2))) ).
fof(fact_623_inf__sup__ord_I4_J,axiom,
! [Y_2,X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2))) ).
fof(fact_624_inf__sup__ord_I4_J,axiom,
! [Y_2,X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).
fof(fact_625_inf__sup__ord_I4_J,axiom,
! [Y_2,X_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2))) ).
fof(fact_626_sup__ge2,axiom,
! [Y_2,X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2))) ).
fof(fact_627_sup__ge2,axiom,
! [Y_2,X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).
fof(fact_628_sup__ge2,axiom,
! [Y_2,X_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2))) ).
fof(fact_629_le__iff__sup,axiom,
! [X_1,Y_2] :
( is_fun_pname_bool(Y_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
<=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = Y_2 ) ) ).
fof(fact_630_le__iff__sup,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
<=> hBOOL(Y_2) ) ) ).
fof(fact_631_le__iff__sup,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
<=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = Y_2 ) ).
fof(fact_632_le__sup__iff,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z)) ) ) ).
fof(fact_633_le__sup__iff,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z))
& hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z)) ) ) ).
fof(fact_634_le__sup__iff,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),Z))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),Z)) ) ) ).
fof(fact_635_le__supI1,axiom,
! [B_1,X_1,A_4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1))) ) ).
fof(fact_636_le__supI1,axiom,
! [B_1,X_1,A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))) ) ).
fof(fact_637_le__supI1,axiom,
! [B_1,X_1,A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),A_4))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1))) ) ).
fof(fact_638_le__supI2,axiom,
! [A_4,X_1,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1))) ) ).
fof(fact_639_le__supI2,axiom,
! [A_4,X_1,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))) ) ).
fof(fact_640_le__supI2,axiom,
! [A_4,X_1,B_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),B_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1))) ) ).
fof(fact_641_sup__absorb2,axiom,
! [X_1,Y_2] :
( is_fun_pname_bool(Y_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = Y_2 ) ) ).
fof(fact_642_sup__absorb2,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
<=> hBOOL(Y_2) ) ) ).
fof(fact_643_sup__absorb2,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = Y_2 ) ).
fof(fact_644_sup__absorb1,axiom,
! [Y_2,X_1] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = X_1 ) ) ).
fof(fact_645_sup__absorb1,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
<=> hBOOL(X_1) ) ) ).
fof(fact_646_sup__absorb1,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2) = X_1 ) ).
fof(fact_647_le__supI,axiom,
! [B_1,A_4,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),X_1)) ) ) ).
fof(fact_648_le__supI,axiom,
! [B_1,A_4,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),X_1)) ) ) ).
fof(fact_649_le__supI,axiom,
! [B_1,A_4,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),X_1)) ) ) ).
fof(fact_650_sup__least,axiom,
! [Z,Y_2,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)),X_1)) ) ) ).
fof(fact_651_sup__least,axiom,
! [Z,Y_2,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)),X_1)) ) ) ).
fof(fact_652_sup__least,axiom,
! [Z,Y_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Z),X_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)),X_1)) ) ) ).
fof(fact_653_sup__mono,axiom,
! [B_1,D_1,A_4,C] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D_1))) ) ) ).
fof(fact_654_sup__mono,axiom,
! [B_1,D_1,A_4,C] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),D_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,C),D_1))) ) ) ).
fof(fact_655_sup__mono,axiom,
! [B_1,D_1,A_4,C] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),D_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C),D_1))) ) ) ).
fof(fact_656_le__supE,axiom,
! [A_4,B_1,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),X_1))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) ) ) ).
fof(fact_657_le__supE,axiom,
! [A_4,B_1,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),X_1))
=> ~ ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1))
=> ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1)) ) ) ).
fof(fact_658_le__supE,axiom,
! [A_4,B_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),X_1))
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),X_1))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_1)) ) ) ).
fof(fact_659_sup__bot__left,axiom,
! [X_1] :
( is_fun_pname_bool(X_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_1) = X_1 ) ).
fof(fact_660_sup__bot__left,axiom,
! [X_1] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,bot_bot_fun_com_bool),X_1) = X_1 ).
fof(fact_661_sup__bot__left,axiom,
! [X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_1))
<=> hBOOL(X_1) ) ).
fof(fact_662_sup__bot__left,axiom,
! [X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,bot_bo784226126e_bool),X_1) = X_1 ).
fof(fact_663_sup__bot__right,axiom,
! [X_1] :
( is_fun_pname_bool(X_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),bot_bo844097828e_bool) = X_1 ) ).
fof(fact_664_sup__bot__right,axiom,
! [X_1] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,X_1),bot_bot_fun_com_bool) = X_1 ).
fof(fact_665_sup__bot__right,axiom,
! [X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),bot_bot_bool))
<=> hBOOL(X_1) ) ).
fof(fact_666_sup__bot__right,axiom,
! [X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),bot_bo784226126e_bool) = X_1 ).
fof(fact_667_ospec,axiom,
! [X_1,P_1,A] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),set_pname(A)))
=> hBOOL(hAPP_pname_bool(P_1,X_2)) ) )
=> ( A = hAPP_p1252095976_pname(some_pname,X_1)
=> hBOOL(hAPP_pname_bool(P_1,X_1)) ) ) ).
fof(fact_668_ospec,axiom,
! [X_1,P_1,A] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),set_Ho1741238126_state(A)))
=> hBOOL(hAPP_H242767318e_bool(P_1,X_2)) )
=> ( A = hAPP_H1633077406_state(some_H1043067815_state,X_1)
=> hBOOL(hAPP_H242767318e_bool(P_1,X_1)) ) ) ).
fof(fact_669_ospec,axiom,
! [X_1,P_1,A] :
( ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A)))
=> hBOOL(hAPP_com_bool(P_1,X_2)) )
=> ( A = hAPP_com_option_com(some_com,X_1)
=> hBOOL(hAPP_com_bool(P_1,X_1)) ) ) ).
fof(fact_670_folding__one__idem_Ounion__idem,axiom,
! [B,A,F,Fa] :
( ( is_fun1661590463l_bool(B)
& is_fun1661590463l_bool(A) )
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( B != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ).
fof(fact_671_folding__one__idem_Ounion__idem,axiom,
! [B,A,F,Fa] :
( hBOOL(finite688249778e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( A != bot_bo942947096l_bool
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( B != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,A)),hAPP_f1216288071e_bool(Fa,B)) ) ) ) ) ) ).
fof(fact_672_folding__one__idem_Ounion__idem,axiom,
! [B,A,F,Fa] :
( hBOOL(finite666746948em_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( A != bot_bot_fun_com_bool
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,B))
=> ( B != bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)) ) ) ) ) ) ).
fof(fact_673_folding__one__idem_Ounion__idem,axiom,
! [B,A,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( A != bot_bo784226126e_bool
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( B != bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,A)),hAPP_f718417177_state(Fa,B)) ) ) ) ) ) ).
fof(fact_674_folding__one__idem_Ounion__idem,axiom,
! [B,A,F,Fa] :
( ( is_fun_pname_bool(B)
& is_fun_pname_bool(A) )
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( B != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ).
fof(fact_675_folding__one__idem_Osubset__idem,axiom,
! [B,A,F,Fa] :
( is_fun1661590463l_bool(B)
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( B != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A)) = hAPP_f674760225e_bool(Fa,A) ) ) ) ) ) ).
fof(fact_676_folding__one__idem_Osubset__idem,axiom,
! [B,A,F,Fa] :
( hBOOL(finite688249778e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( B != bot_bo942947096l_bool
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,B),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,B)),hAPP_f1216288071e_bool(Fa,A)) = hAPP_f1216288071e_bool(Fa,A) ) ) ) ) ).
fof(fact_677_folding__one__idem_Osubset__idem,axiom,
! [B,A,F,Fa] :
( hBOOL(finite666746948em_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( B != bot_bot_fun_com_bool
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,B),A))
=> hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,B)),hAPP_f1276420679ol_com(Fa,A)) = hAPP_f1276420679ol_com(Fa,A) ) ) ) ) ).
fof(fact_678_folding__one__idem_Osubset__idem,axiom,
! [B,A,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( B != bot_bo784226126e_bool
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A))
=> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,B)),hAPP_f718417177_state(Fa,A)) = hAPP_f718417177_state(Fa,A) ) ) ) ) ).
fof(fact_679_folding__one__idem_Osubset__idem,axiom,
! [B,A,F,Fa] :
( is_fun_pname_bool(B)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( B != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A)) = hAPP_f1297739591_pname(Fa,A) ) ) ) ) ) ).
fof(fact_680_hoare__derivs_OSkip,axiom,
! [G_2,P_1] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),skip),P_1)),bot_bo784226126e_bool))) ).
fof(fact_681_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite666746948em_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( A != bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) ) ) ) ).
fof(fact_682_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A,F,Fa] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) ) ) ) ) ).
fof(fact_683_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite688249778e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( A != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,A)) ) ) ) ).
fof(fact_684_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A,F,Fa] :
( is_fun_pname_bool(A)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) ) ) ) ) ).
fof(fact_685_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( A != bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,A)) ) ) ) ).
fof(fact_686_finite__ne__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa))
=> ( Fa != bot_bot_fun_com_bool
=> ( ! [X_2] : hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),bot_bot_fun_com_bool)))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2))
=> ( F_2 != bot_bot_fun_com_bool
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),F_2))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,F_2))
=> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f990396704l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_687_finite__ne__induct,axiom,
! [P_1,Fa] :
( is_fun1661590463l_bool(Fa)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> ( Fa != bot_bo1649642514l_bool
=> ( ! [X_2] :
( is_fun_pname_bool(X_2)
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),bot_bo1649642514l_bool))) )
=> ( ! [X_2,F_2] :
( ( is_fun_pname_bool(X_2)
& is_fun1661590463l_bool(F_2) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
=> ( F_2 != bot_bo1649642514l_bool
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_2))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_2))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_2))) ) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ) ).
fof(fact_688_finite__ne__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
=> ( Fa != bot_bo942947096l_bool
=> ( ! [X_2] : hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),bot_bo942947096l_bool)))
=> ( ! [X_2,F_2] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,F_2))
=> ( F_2 != bot_bo942947096l_bool
=> ( ~ hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),F_2))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,F_2))
=> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1410040974l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_689_finite__ne__induct,axiom,
! [P_1,Fa] :
( is_fun_pname_bool(Fa)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> ( Fa != bot_bo844097828e_bool
=> ( ! [X_2] :
( is_pname(X_2)
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))) )
=> ( ! [X_2,F_2] :
( ( is_pname(X_2)
& 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_2),F_2))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_2))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ) ).
fof(fact_690_finite__ne__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
=> ( Fa != bot_bo784226126e_bool
=> ( ! [X_2] : hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),bot_bo784226126e_bool)))
=> ( ! [X_2,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_2),F_2))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,F_2))
=> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_691_LoopF,axiom,
! [G_2,P_1,B_1,C] : hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),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)),P_1))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B_1))),hAPP_com_com(while(B_1),C)),P_1)),bot_bo784226126e_bool))) ).
fof(fact_692_Comp,axiom,
! [D_1,R_1,G_2,P_1,C,Q_1] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool)))
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Q_1),D_1),R_1)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),hAPP_com_com(hAPP_com_fun_com_com(semi,C),D_1)),R_1)),bot_bo784226126e_bool))) ) ) ).
fof(fact_693_WTs__elim__cases_I6_J,axiom,
! [B_1,C] :
( hBOOL(hAPP_com_bool(wt,hAPP_com_com(while(B_1),C)))
=> hBOOL(hAPP_com_bool(wt,C)) ) ).
fof(fact_694_WTs__elim__cases_I4_J,axiom,
! [C1,C2] :
( hBOOL(hAPP_com_bool(wt,hAPP_com_com(hAPP_com_fun_com_com(semi,C1),C2)))
=> ~ ( hBOOL(hAPP_com_bool(wt,C1))
=> ~ hBOOL(hAPP_com_bool(wt,C2)) ) ) ).
fof(fact_695_folding__one__idem_Oidem,axiom,
! [X_1,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),X_1) = X_1 ) ).
fof(fact_696_folding__one__idem_Oidem,axiom,
! [X_1,F,Fa] :
( is_pname(X_1)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),X_1) = X_1 ) ) ).
fof(fact_697_com_Osimps_I12_J,axiom,
! [Com1_3,Com2_3] : skip != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_3),Com2_3) ).
fof(fact_698_com_Osimps_I16_J,axiom,
! [Fun_1,Com_2] : skip != hAPP_com_com(while(Fun_1),Com_2) ).
fof(fact_699_com_Osimps_I13_J,axiom,
! [Com1_3,Com2_3] : hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_3),Com2_3) != skip ).
fof(fact_700_com_Osimps_I17_J,axiom,
! [Fun_1,Com_2] : hAPP_com_com(while(Fun_1),Com_2) != skip ).
fof(fact_701_com_Osimps_I46_J,axiom,
! [Com1_2,Com2_2,Fun_1,Com_2] : hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) != hAPP_com_com(while(Fun_1),Com_2) ).
fof(fact_702_com_Osimps_I47_J,axiom,
! [Fun_1,Com_2,Com1_2,Com2_2] : hAPP_com_com(while(Fun_1),Com_2) != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) ).
fof(fact_703_com_Osimps_I3_J,axiom,
! [Com1_2,Com2_2,Com1_1,Com2_1] :
( hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) = hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_1),Com2_1)
<=> ( Com1_2 = Com1_1
& Com2_2 = Com2_1 ) ) ).
fof(fact_704_com_Osimps_I5_J,axiom,
! [Fun,Com_1,Fun_1,Com_2] :
( hAPP_com_com(while(Fun),Com_1) = hAPP_com_com(while(Fun_1),Com_2)
<=> ( Fun = Fun_1
& Com_1 = Com_2 ) ) ).
fof(fact_705_com_Osimps_I59_J,axiom,
! [Pname_1,Fun,Com_1] : hAPP_pname_com(body_1,Pname_1) != hAPP_com_com(while(Fun),Com_1) ).
fof(fact_706_com_Osimps_I58_J,axiom,
! [Fun,Com_1,Pname_1] : hAPP_com_com(while(Fun),Com_1) != hAPP_pname_com(body_1,Pname_1) ).
fof(fact_707_While,axiom,
! [B_1,C] :
( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_com_bool(wt,hAPP_com_com(while(B_1),C))) ) ).
fof(fact_708_com_Osimps_I49_J,axiom,
! [Pname,Com1,Com2] : hAPP_pname_com(body_1,Pname) != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1),Com2) ).
fof(fact_709_com_Osimps_I48_J,axiom,
! [Com1,Com2,Pname] : hAPP_com_com(hAPP_com_fun_com_com(semi,Com1),Com2) != hAPP_pname_com(body_1,Pname) ).
fof(fact_710_WT_OSemi,axiom,
! [C1,C0] :
( hBOOL(hAPP_com_bool(wt,C0))
=> ( hBOOL(hAPP_com_bool(wt,C1))
=> hBOOL(hAPP_com_bool(wt,hAPP_com_com(hAPP_com_fun_com_com(semi,C0),C1))) ) ) ).
fof(fact_711_com_Osimps_I18_J,axiom,
! [Pname] : skip != hAPP_pname_com(body_1,Pname) ).
fof(fact_712_com_Osimps_I19_J,axiom,
! [Pname] : hAPP_pname_com(body_1,Pname) != skip ).
fof(fact_713_WT_OSkip,axiom,
hBOOL(hAPP_com_bool(wt,skip)) ).
fof(fact_714_folding__one__idem_Oin__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite666746948em_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) = hAPP_f1276420679ol_com(Fa,A) ) ) ) ).
fof(fact_715_folding__one__idem_Oin__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) = hAPP_f1297739591_pname(Fa,A) ) ) ) ).
fof(fact_716_folding__one__idem_Oin__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,A)) = hAPP_f718417177_state(Fa,A) ) ) ) ).
fof(fact_717_folding__one__idem_Oin__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) = hAPP_f674760225e_bool(Fa,A) ) ) ) ).
fof(fact_718_folding__one__idem_Oin__idem,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite688249778e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,A)) = hAPP_f1216288071e_bool(Fa,A) ) ) ) ).
fof(fact_719_folding__one__idem_Ohom__commute,axiom,
! [N,H_1,F,Fa] :
( is_fun1661590463l_bool(N)
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( ! [X_2,Y_3] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_3) )
=> hAPP_f759274231e_bool(H_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_3)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H_1,X_2)),hAPP_f759274231e_bool(H_1,Y_3)) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N))
=> ( N != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(H_1,hAPP_f674760225e_bool(Fa,N)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H_1),N)) ) ) ) ) ) ).
fof(fact_720_folding__one__idem_Ohom__commute,axiom,
! [N,H_1,F,Fa] :
( hBOOL(finite688249778e_bool(F,Fa))
=> ( ! [X_2,Y_3] : hAPP_f806699093e_bool(H_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_2),Y_3)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f806699093e_bool(H_1,X_2)),hAPP_f806699093e_bool(H_1,Y_3))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,N))
=> ( N != bot_bo942947096l_bool
=> hAPP_f806699093e_bool(H_1,hAPP_f1216288071e_bool(Fa,N)) = hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(image_390184709e_bool(H_1),N)) ) ) ) ) ).
fof(fact_721_folding__one__idem_Ohom__commute,axiom,
! [N,H_1,F,Fa] :
( is_fun_pname_bool(N)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( ! [X_2,Y_3] :
( ( is_pname(X_2)
& is_pname(Y_3) )
=> hAPP_pname_pname(H_1,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_3)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H_1,X_2)),hAPP_pname_pname(H_1,Y_3)) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N))
=> ( N != bot_bo844097828e_bool
=> hAPP_pname_pname(H_1,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H_1),N)) ) ) ) ) ) ).
fof(fact_722_folding__one__idem_Ohom__commute,axiom,
! [N,H_1,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> ( ! [X_2,Y_3] : hAPP_H574424047_state(H_1,hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_3)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_H574424047_state(H_1,X_2)),hAPP_H574424047_state(H_1,Y_3))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,N))
=> ( N != bot_bo784226126e_bool
=> hAPP_H574424047_state(H_1,hAPP_f718417177_state(Fa,N)) = hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(image_661047967_state(H_1),N)) ) ) ) ) ).
fof(fact_723_folding__one__idem_Ohom__commute,axiom,
! [N,H_1,F,Fa] :
( hBOOL(finite666746948em_com(F,Fa))
=> ( ! [X_2,Y_3] : hAPP_com_com(H_1,hAPP_com_com(hAPP_com_fun_com_com(F,X_2),Y_3)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_com_com(H_1,X_2)),hAPP_com_com(H_1,Y_3))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,N))
=> ( N != bot_bot_fun_com_bool
=> hAPP_com_com(H_1,hAPP_f1276420679ol_com(Fa,N)) = hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(image_com_com(H_1),N)) ) ) ) ) ).
fof(fact_724_the__elem__def,axiom,
! [X_4] : hAPP_f1276420679ol_com(the_elem_com,X_4) = hAPP_f1276420679ol_com(the_com_1,hAPP_f1998868198m_bool(cOMBB_298914627ol_com(hAPP_f273696895l_bool(fequal_fun_com_bool,X_4)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool))) ).
fof(fact_725_the__elem__def,axiom,
! [X_4] : hAPP_f1297739591_pname(the_elem_pname,X_4) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_4)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))) ).
fof(fact_726_the__elem__def,axiom,
! [X_4] : hAPP_f718417177_state(the_el2080696983_state,X_4) = hAPP_f718417177_state(the_Ho2067184133_state,hAPP_f1900156034e_bool(cOMBB_1282391997_state(hAPP_f849457489l_bool(fequal1475827639e_bool,X_4)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool))) ).
fof(fact_727_folding__one_Oinsert,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( A != bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) ) ) ) ) ).
fof(fact_728_folding__one_Oinsert,axiom,
! [X_1,A,F,Fa] :
( is_fun_pname_bool(A)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( A != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) ) ) ) ) ) ).
fof(fact_729_folding__one_Oinsert,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ( A != bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,A)) ) ) ) ) ).
fof(fact_730_folding__one_Oinsert,axiom,
! [X_1,A,F,Fa] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
=> ( A != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) ) ) ) ) ) ).
fof(fact_731_folding__one_Oinsert,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( ~ hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A))
=> ( A != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,A)) ) ) ) ) ).
fof(fact_732_triple_Oexhaust,axiom,
! [Y_2] :
~ ! [Fun1,Com,Fun2] : Y_2 != hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,Fun1),Com),Fun2) ).
fof(fact_733_folding__one_Osingleton,axiom,
! [X_1,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = X_1 ) ).
fof(fact_734_folding__one_Osingleton,axiom,
! [X_1,F,Fa] :
( is_pname(X_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1 ) ) ).
fof(fact_735_folding__one_Osingleton,axiom,
! [X_1,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = X_1 ) ).
fof(fact_736_folding__one_Oclosed,axiom,
! [A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( A != bot_bot_fun_com_bool
=> ( ! [X_2,Y_3] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_com_com(hAPP_com_fun_com_com(F,X_2),Y_3)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_3),bot_bot_fun_com_bool))))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_f1276420679ol_com(Fa,A)),A)) ) ) ) ) ).
fof(fact_737_folding__one_Oclosed,axiom,
! [A,F,Fa] :
( is_fun_pname_bool(A)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> ( ! [X_2,Y_3] :
( ( is_pname(X_2)
& is_pname(Y_3) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_3),bot_bo844097828e_bool)))) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A)),A)) ) ) ) ) ) ).
fof(fact_738_folding__one_Oclosed,axiom,
! [A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( A != bot_bo784226126e_bool
=> ( ! [X_2,Y_3] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_H574424047_state(hAPP_H280516760_state(F,X_2),Y_3)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_3),bot_bo784226126e_bool))))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_f718417177_state(Fa,A)),A)) ) ) ) ) ).
fof(fact_739_folding__one_Oclosed,axiom,
! [A,F,Fa] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( ! [X_2,Y_3] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_3) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_3)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_3),bot_bo1649642514l_bool)))) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A)),A)) ) ) ) ) ) ).
fof(fact_740_folding__one_Oclosed,axiom,
! [A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( A != bot_bo942947096l_bool
=> ( ! [X_2,Y_3] : hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_2),Y_3)),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_2),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,Y_3),bot_bo942947096l_bool))))
=> hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,hAPP_f1216288071e_bool(Fa,A)),A)) ) ) ) ) ).
fof(fact_741_image__cong,axiom,
! [F,G,M_1,N] :
( M_1 = N
=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N))
=> hAPP_p1751618853_state(F,X_2) = hAPP_p1751618853_state(G,X_2) ) )
=> hAPP_f360545851e_bool(image_185131637_state(F),M_1) = hAPP_f360545851e_bool(image_185131637_state(G),N) ) ) ).
fof(fact_742_Collect__mono,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( hBOOL(hAPP_H242767318e_bool(P_1,X_2))
=> hBOOL(hAPP_H242767318e_bool(Q_1,X_2)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(collec637225377_state,P_1)),hAPP_f806699093e_bool(collec637225377_state,Q_1))) ) ).
fof(fact_743_Collect__mono,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_pname_bool(P_1,X_2))
=> hBOOL(hAPP_pname_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))) ) ).
fof(fact_744_Collect__mono,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( is_fun_pname_bool(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,X_2))
=> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) ) ).
fof(fact_745_Collect__mono,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(P_1,X_2))
=> hBOOL(hAPP_f1378282496l_bool(Q_1,X_2)) )
=> hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1))) ) ).
fof(fact_746_predicate1I,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_pname_bool(P_1,X_2))
=> hBOOL(hAPP_pname_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) ) ).
fof(fact_747_predicate1I,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( hBOOL(hAPP_H242767318e_bool(P_1,X_2))
=> hBOOL(hAPP_H242767318e_bool(Q_1,X_2)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,P_1),Q_1)) ) ).
fof(fact_748_mk__disjoint__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> ? [B_2] :
( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B_2)
& ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B_2)) ) ) ).
fof(fact_749_mk__disjoint__insert,axiom,
! [A_4,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> ? [B_2] :
( is_fun_pname_bool(B_2)
& A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B_2)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B_2)) ) ) ) ).
fof(fact_750_mk__disjoint__insert,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> ? [B_2] :
( A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B_2)
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),B_2)) ) ) ).
fof(fact_751_Set_Oset__insert,axiom,
! [X_1,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ~ ! [B_2] :
( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B_2)
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B_2)) ) ) ).
fof(fact_752_Set_Oset__insert,axiom,
! [X_1,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ~ ! [B_2] :
( is_fun_pname_bool(B_2)
=> ( A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B_2)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_2)) ) ) ) ) ).
fof(fact_753_Set_Oset__insert,axiom,
! [X_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ~ ! [B_2] :
( A = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B_2)
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B_2)) ) ) ).
fof(fact_754_equals0I,axiom,
! [A] :
( ! [Y_3] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,Y_3),A))
=> A = bot_bot_fun_com_bool ) ).
fof(fact_755_equals0I,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( ! [Y_3] :
( is_pname(Y_3)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_3),A)) )
=> A = bot_bo844097828e_bool ) ) ).
fof(fact_756_equals0I,axiom,
! [A] :
( ! [Y_3] : ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_3),A))
=> A = bot_bo784226126e_bool ) ).
fof(fact_757_MGT__alternD,axiom,
! [G_2,C] :
( hBOOL(hoare_1795711768gleton)
=> ( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool))) ) ) ).
fof(fact_758_xt1_I15_J,axiom,
! [C,F,B_1,A_4] :
( ( hBOOL(A_4)
<=> hBOOL(hAPP_bool_bool(F,B_1)) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),B_1))
=> ( ! [X_2,Y_3] :
( ( is_bool(X_2)
& is_bool(Y_3) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_3),X_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_3)),hAPP_bool_bool(F,X_2))) ) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,C)),A_4)) ) ) ) ).
fof(fact_759_xt1_I15_J,axiom,
! [C,A_4,F,B_1] :
( A_4 = hAPP_f759274231e_bool(F,B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1))
=> ( ! [X_2,Y_3] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_3) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_3),X_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_3)),hAPP_f759274231e_bool(F,X_2))) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A_4)) ) ) ) ).
fof(fact_760_xt1_I15_J,axiom,
! [C,A_4,F,B_1] :
( A_4 = hAPP_f806699093e_bool(F,B_1)
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),B_1))
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_3),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_3)),hAPP_f806699093e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,C)),A_4)) ) ) ) ).
fof(fact_761_MGT__alternI,axiom,
! [G_2,C] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,C)),bot_bo784226126e_bool)))
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo784226126e_bool))) ) ).
fof(fact_762_MGT__def,axiom,
! [C] : hAPP_c1455475371_state(hoare_Mirabelle_MGT,C) = hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,fequal_state),C),evalc(C)) ).
fof(fact_763_evalc__elim__cases_I6_J,axiom,
! [P,S_4,S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_4),S1_2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_4),S1_2)) ) ).
fof(fact_764_evalc_OBody,axiom,
! [Pn,S0_1,S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0_1),S1_2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0_1),S1_2)) ) ).
fof(fact_765_evalc__elim__cases_I1_J,axiom,
! [S_4,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_4),T_1))
=> T_1 = S_4 ) ).
fof(fact_766_evalc_OSkip,axiom,
! [S_4] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_4),S_4)) ).
fof(fact_767_evalc_OSemi,axiom,
! [C1,S2_1,C0,S0_1,S1_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0_1),S1_2))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_2),S2_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(hAPP_com_fun_com_com(semi,C0),C1)),S0_1),S2_1)) ) ) ).
fof(fact_768_evalc_OWhileTrue,axiom,
! [S2,C,S1_1,B_1,S0] :
( hBOOL(hAPP_state_bool(B_1,S0))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0),S1_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S1_1),S2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S0),S2)) ) ) ) ).
fof(fact_769_evalc_OWhileFalse,axiom,
! [C,B_1,S_3] :
( ~ hBOOL(hAPP_state_bool(B_1,S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S_3),S_3)) ) ).
fof(fact_770_com__det,axiom,
! [U,C_2,S_4,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_4),T_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_4),U))
=> U = T_1 ) ) ).
fof(fact_771_evalc__elim__cases_I4_J,axiom,
! [C1,C2,S_4,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(hAPP_com_fun_com_com(semi,C1),C2)),S_4),T_1))
=> ~ ! [S1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_4),S1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)) ) ) ).
fof(fact_772_evalc__WHILE__case,axiom,
! [B_1,C,S_3,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S_3),T))
=> ( ( T = S_3
=> hBOOL(hAPP_state_bool(B_1,S_3)) )
=> ~ ( hBOOL(hAPP_state_bool(B_1,S_3))
=> ! [S1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_3),S1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S1),T)) ) ) ) ) ).
fof(fact_773_xt1_I16_J,axiom,
! [C,F,B_1,A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_4))
=> ( ( hBOOL(hAPP_bool_bool(F,B_1))
<=> hBOOL(C) )
=> ( ! [X_2,Y_3] :
( ( is_bool(X_2)
& is_bool(Y_3) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_3),X_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_3)),hAPP_bool_bool(F,X_2))) ) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),hAPP_bool_bool(F,A_4))) ) ) ) ).
fof(fact_774_xt1_I16_J,axiom,
! [F,C,B_1,A_4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_4))
=> ( hAPP_f759274231e_bool(F,B_1) = C
=> ( ! [X_2,Y_3] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_3) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_3),X_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_3)),hAPP_f759274231e_bool(F,X_2))) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A_4))) ) ) ) ).
fof(fact_775_xt1_I16_J,axiom,
! [F,C,B_1,A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),A_4))
=> ( hAPP_f806699093e_bool(F,B_1) = C
=> ( ! [X_2,Y_3] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_3),X_2))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(F,Y_3)),hAPP_f806699093e_bool(F,X_2))) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C),hAPP_f806699093e_bool(F,A_4))) ) ) ) ).
fof(fact_776_folding__one_Ounion__inter,axiom,
! [B,A,F,Fa] :
( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ).
fof(fact_777_folding__one_Ounion__inter,axiom,
! [B,A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) != bot_bo942947096l_bool
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B))),hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B))) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,A)),hAPP_f1216288071e_bool(Fa,B)) ) ) ) ) ).
fof(fact_778_folding__one_Ounion__inter,axiom,
! [B,A,F,Fa] :
( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) != bot_bo844097828e_bool
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ).
fof(fact_779_folding__one_Ounion__inter,axiom,
! [B,A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) != bot_bo784226126e_bool
=> hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B))),hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,A)),hAPP_f718417177_state(Fa,B)) ) ) ) ) ).
fof(fact_780_folding__one_Ounion__inter,axiom,
! [B,A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,B))
=> ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) != bot_bot_fun_com_bool
=> hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)) ) ) ) ) ).
fof(fact_781_folding__one_Ounion__disjoint,axiom,
! [B,A,F,Fa] :
( ( is_fun1661590463l_bool(B)
& is_fun1661590463l_bool(A) )
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( B != bot_bo1649642514l_bool
=> ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ) ).
fof(fact_782_folding__one_Ounion__disjoint,axiom,
! [B,A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( A != bot_bo942947096l_bool
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( B != bot_bo942947096l_bool
=> ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) = bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,hAPP_f1216288071e_bool(Fa,A)),hAPP_f1216288071e_bool(Fa,B)) ) ) ) ) ) ) ).
fof(fact_783_folding__one_Ounion__disjoint,axiom,
! [B,A,F,Fa] :
( ( is_fun_pname_bool(B)
& is_fun_pname_bool(A) )
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( A != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( B != bot_bo844097828e_bool
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ) ).
fof(fact_784_folding__one_Ounion__disjoint,axiom,
! [B,A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( A != bot_bo784226126e_bool
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( B != bot_bo784226126e_bool
=> ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)) = hAPP_H574424047_state(hAPP_H280516760_state(F,hAPP_f718417177_state(Fa,A)),hAPP_f718417177_state(Fa,B)) ) ) ) ) ) ) ).
fof(fact_785_folding__one_Ounion__disjoint,axiom,
! [B,A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( A != bot_bot_fun_com_bool
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,B))
=> ( B != bot_bot_fun_com_bool
=> ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)) ) ) ) ) ) ) ).
fof(fact_786_folding__one_Oinsert__remove,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = X_1 )
& ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) != bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))) ) ) ) ) ).
fof(fact_787_folding__one_Oinsert__remove,axiom,
! [X_1,A,F,Fa] :
( is_pname(X_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = X_1 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ).
fof(fact_788_folding__one_Oinsert__remove,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = X_1 )
& ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) ) ) ) ) ).
fof(fact_789_folding__one_Oinsert__remove,axiom,
! [X_1,A,F,Fa] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = X_1 )
& ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ).
fof(fact_790_folding__one_Oinsert__remove,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) = bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = X_1 )
& ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)))) ) ) ) ) ).
fof(fact_791_folding__one_Oremove,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,A) = X_1 )
& ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) != bot_bot_fun_com_bool
=> hAPP_f1276420679ol_com(Fa,A) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))) ) ) ) ) ) ).
fof(fact_792_folding__one_Oremove,axiom,
! [X_1,A,F,Fa] :
( is_pname(X_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,A) = X_1 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,A) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ) ).
fof(fact_793_folding__one_Oremove,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> ( ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,A) = X_1 )
& ( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) != bot_bo784226126e_bool
=> hAPP_f718417177_state(Fa,A) = hAPP_H574424047_state(hAPP_H280516760_state(F,X_1),hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)))) ) ) ) ) ) ).
fof(fact_794_folding__one_Oremove,axiom,
! [X_1,A,F,Fa] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
=> ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,A) = X_1 )
& ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ) ).
fof(fact_795_folding__one_Oremove,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A))
=> ( ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) = bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,A) = X_1 )
& ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)) != bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(Fa,A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(F,X_1),hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),bot_bo942947096l_bool)))) ) ) ) ) ) ).
fof(fact_796_is__none__code_I2_J,axiom,
! [X_3] : ~ hBOOL(is_none_pname(hAPP_p1252095976_pname(some_pname,X_3))) ).
fof(fact_797_is__none__code_I2_J,axiom,
! [X_3] : ~ hBOOL(is_non1379144176_state(hAPP_H1633077406_state(some_H1043067815_state,X_3))) ).
fof(fact_798_is__none__code_I2_J,axiom,
! [X_3] : ~ hBOOL(is_none_com(hAPP_com_option_com(some_com,X_3))) ).
fof(fact_799_conseq,axiom,
! [Q_1,G_2,C,P_1] :
( ! [Z_2,S_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
=> ? [P_2,Q_2] :
( hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_2),C),Q_2)),bot_bo784226126e_bool)))
& ! [S_2] :
( ! [Z_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_2)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_2)) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(G_2),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_f497755132_state(hAPP_c27135337_state(hAPP_f274181323_state(hoare_1191504582_state,P_1),C),Q_1)),bot_bo784226126e_bool))) ) ).
fof(fact_800_IntE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
=> ~ ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_801_IntE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_802_IntE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_803_IntI,axiom,
! [B,C,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) ) ) ).
fof(fact_804_IntI,axiom,
! [B,C,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) ) ) ).
fof(fact_805_IntI,axiom,
! [B,C,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) ) ) ).
fof(fact_806_DiffE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
=> ~ ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_807_DiffE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_808_DiffE,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)))
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_809_DiffI,axiom,
! [B,C,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) ) ) ).
fof(fact_810_DiffI,axiom,
! [B,C,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ) ).
fof(fact_811_DiffI,axiom,
! [B,C,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) ) ) ).
fof(fact_812_finite__Int,axiom,
! [G_2,Fa] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_2))) ) ).
fof(fact_813_finite__Int,axiom,
! [G_2,Fa] :
( ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,Fa))
| hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,G_2)) )
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,Fa),G_2))) ) ).
fof(fact_814_finite__Int,axiom,
! [G_2,Fa] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_2))) ) ).
fof(fact_815_finite__Int,axiom,
! [G_2,Fa] :
( ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,Fa))
| hBOOL(hAPP_f1378282496l_bool(finite694102371_state,G_2)) )
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Fa),G_2))) ) ).
fof(fact_816_finite__Diff,axiom,
! [B,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))) ) ).
fof(fact_817_finite__Diff,axiom,
! [B,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B))) ) ).
fof(fact_818_finite__Diff,axiom,
! [B,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ).
fof(fact_819_finite__Diff,axiom,
! [B,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) ) ).
fof(fact_820_inf__Int__eq,axiom,
! [R_1,S,X_2] :
( hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)),X_2))
<=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,R_1),S))) ) ).
fof(fact_821_inf__Int__eq,axiom,
! [R_1,S,X_2] :
( 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)),X_2))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S))) ) ).
fof(fact_822_inf__Int__eq,axiom,
! [R_1,S,X_2] :
( hBOOL(hAPP_H242767318e_bool(hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_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)),X_2))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,R_1),S))) ) ).
fof(fact_823_Diff__disjoint,axiom,
! [A,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,B),A)) = bot_bot_fun_com_bool ).
fof(fact_824_Diff__disjoint,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = bot_bo844097828e_bool ).
fof(fact_825_Diff__disjoint,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)) = bot_bo784226126e_bool ).
fof(fact_826_Diff__triv,axiom,
! [A,B] :
( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) = A ) ).
fof(fact_827_Diff__triv,axiom,
! [A,B] :
( is_fun_pname_bool(A)
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = A ) ) ).
fof(fact_828_Diff__triv,axiom,
! [A,B] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = bot_bo784226126e_bool
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B) = A ) ).
fof(fact_829_DiffD2,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
=> ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ).
fof(fact_830_DiffD2,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ).
fof(fact_831_DiffD2,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ).
fof(fact_832_IntD2,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ).
fof(fact_833_IntD2,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ).
fof(fact_834_IntD2,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ).
fof(fact_835_IntD1,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) ) ).
fof(fact_836_IntD1,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) ) ).
fof(fact_837_IntD1,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) ) ).
fof(fact_838_DiffD1,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) ) ).
fof(fact_839_DiffD1,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) ) ).
fof(fact_840_DiffD1,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A)) ) ).
fof(fact_841_Int__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
<=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
& hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_842_Int__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_843_Int__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
& hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_844_Diff__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
<=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
& ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).
fof(fact_845_Diff__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_846_Diff__iff,axiom,
! [C,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),A))
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,C),B)) ) ) ).
fof(fact_847_Int__def,axiom,
! [A,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))) ).
fof(fact_848_Int__def,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).
fof(fact_849_Int__def,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B))) ).
fof(fact_850_Int__def,axiom,
! [A,B] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).
fof(fact_851_Int__def,axiom,
! [A,B] : hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B))) ).
fof(fact_852_set__diff__eq,axiom,
! [A,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(cOMBB_bool_bool_com(fNot),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B)))) ).
fof(fact_853_set__diff__eq,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A))),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) ).
fof(fact_854_set__diff__eq,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B) = hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),A))),hAPP_f806699093e_bool(cOMBB_325909978_state(fNot),hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),B)))) ).
fof(fact_855_set__diff__eq,axiom,
! [A,B] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) ).
fof(fact_856_set__diff__eq,axiom,
! [A,B] : hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B) = hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),A))),hAPP_f734420447l_bool(cOMBB_1686148692e_bool(fNot),hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,member131361931e_bool),B)))) ).
fof(fact_857_Int__Collect,axiom,
! [X_1,A,P_1] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(collect_com,P_1))))
<=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
& hBOOL(hAPP_com_bool(P_1,X_1)) ) ) ).
fof(fact_858_Int__Collect,axiom,
! [X_1,A,P_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(collect_pname,P_1))))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
& hBOOL(hAPP_pname_bool(P_1,X_1)) ) ) ).
fof(fact_859_Int__Collect,axiom,
! [X_1,A,P_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(collec637225377_state,P_1))))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
& hBOOL(hAPP_H242767318e_bool(P_1,X_1)) ) ) ).
fof(fact_860_Int__Collect,axiom,
! [X_1,A,P_1] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))))
<=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
& hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ) ).
fof(fact_861_Int__Collect,axiom,
! [X_1,A,P_1] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),hAPP_f734420447l_bool(collec1987918285e_bool,P_1))))
<=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A))
& hBOOL(hAPP_f1378282496l_bool(P_1,X_1)) ) ) ).
fof(fact_862_Collect__conj__eq,axiom,
! [P_1,Q_1] : hAPP_f806699093e_bool(collec637225377_state,hAPP_f806699093e_bool(hAPP_f1702629984e_bool(cOMBS_865875691l_bool,hAPP_f832587837l_bool(cOMBB_1291456124_state(fconj),P_1)),Q_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(collec637225377_state,P_1)),hAPP_f806699093e_bool(collec637225377_state,Q_1)) ).
fof(fact_863_Collect__conj__eq,axiom,
! [P_1,Q_1] : hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1)) ).
fof(fact_864_Collect__conj__eq,axiom,
! [P_1,Q_1] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1)) ).
fof(fact_865_Collect__conj__eq,axiom,
! [P_1,Q_1] : hAPP_f734420447l_bool(collec1987918285e_bool,hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,hAPP_f118042163l_bool(cOMBB_1749019442e_bool(fconj),P_1)),Q_1)) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,hAPP_f734420447l_bool(collec1987918285e_bool,P_1)),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1)) ).
fof(fact_866_Diff__Int,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)) ).
fof(fact_867_Diff__Int,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),C_1)) ).
fof(fact_868_Diff__Un,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)) ).
fof(fact_869_Diff__Un,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),C_1)) ).
fof(fact_870_Un__Diff__Int,axiom,
! [A,B] :
( is_fun_pname_bool(A)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) = A ) ).
fof(fact_871_Un__Diff__Int,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)) = A ).
fof(fact_872_inf__sup__ord_I1_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),X_1)) ).
fof(fact_873_inf__sup__ord_I1_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),X_1)) ).
fof(fact_874_inf__sup__ord_I1_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),X_1)) ).
fof(fact_875_inf__le1,axiom,
! [X_1,Y_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),X_1)) ).
fof(fact_876_inf__le1,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),X_1)) ).
fof(fact_877_inf__le1,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),X_1)) ).
fof(fact_878_inf__sup__ord_I2_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),Y_2)) ).
fof(fact_879_inf__sup__ord_I2_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),Y_2)) ).
fof(fact_880_inf__sup__ord_I2_J,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),Y_2)) ).
fof(fact_881_inf__le2,axiom,
! [X_1,Y_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),Y_2)) ).
fof(fact_882_inf__le2,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),Y_2)) ).
fof(fact_883_inf__le2,axiom,
! [X_1,Y_2] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),Y_2)) ).
fof(fact_884_le__iff__inf,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))
<=> hBOOL(X_1) ) ) ).
fof(fact_885_le__iff__inf,axiom,
! [X_1,Y_2] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
<=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = X_1 ) ) ).
fof(fact_886_le__iff__inf,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
<=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2) = X_1 ) ).
fof(fact_887_le__inf__iff,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
& hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)) ) ) ).
fof(fact_888_le__inf__iff,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).
fof(fact_889_le__inf__iff,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)))
<=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z)) ) ) ).
fof(fact_890_le__infI1,axiom,
! [B_1,A_4,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),X_1)) ) ).
fof(fact_891_le__infI1,axiom,
! [B_1,A_4,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),X_1)) ) ).
fof(fact_892_le__infI1,axiom,
! [B_1,A_4,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),X_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)),X_1)) ) ).
fof(fact_893_le__infI2,axiom,
! [A_4,B_1,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),X_1)) ) ).
fof(fact_894_le__infI2,axiom,
! [A_4,B_1,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),X_1)) ) ).
fof(fact_895_le__infI2,axiom,
! [A_4,B_1,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)),X_1)) ) ).
fof(fact_896_inf__absorb1,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))
<=> hBOOL(X_1) ) ) ).
fof(fact_897_inf__absorb1,axiom,
! [X_1,Y_2] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = X_1 ) ) ).
fof(fact_898_inf__absorb1,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2) = X_1 ) ).
fof(fact_899_inf__absorb2,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))
<=> hBOOL(Y_2) ) ) ).
fof(fact_900_inf__absorb2,axiom,
! [Y_2,X_1] :
( is_fun_pname_bool(Y_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = Y_2 ) ) ).
fof(fact_901_inf__absorb2,axiom,
! [Y_2,X_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,Y_2),X_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2) = Y_2 ) ).
fof(fact_902_le__infI,axiom,
! [B_1,X_1,A_4] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1))) ) ) ).
fof(fact_903_le__infI,axiom,
! [B_1,X_1,A_4] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1))) ) ) ).
fof(fact_904_le__infI,axiom,
! [B_1,X_1,A_4] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),A_4))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),B_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1))) ) ) ).
fof(fact_905_inf__greatest,axiom,
! [Z,X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))) ) ) ).
fof(fact_906_inf__greatest,axiom,
! [Z,X_1,Y_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z))) ) ) ).
fof(fact_907_inf__greatest,axiom,
! [Z,X_1,Y_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Y_2))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),Z))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z))) ) ) ).
fof(fact_908_inf__mono,axiom,
! [B_1,D_1,A_4,C] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),D_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,C),D_1))) ) ) ).
fof(fact_909_inf__mono,axiom,
! [B_1,D_1,A_4,C] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D_1))) ) ) ).
fof(fact_910_inf__mono,axiom,
! [B_1,D_1,A_4,C] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_4),C))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),D_1))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C),D_1))) ) ) ).
fof(fact_911_le__infE,axiom,
! [X_1,A_4,B_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)))
=> ~ ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4))
=> ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1)) ) ) ).
fof(fact_912_le__infE,axiom,
! [X_1,A_4,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) ) ) ).
fof(fact_913_le__infE,axiom,
! [X_1,A_4,B_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1)))
=> ~ ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),A_4))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_1),B_1)) ) ) ).
fof(fact_914_inf__bot__right,axiom,
! [X_1] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,X_1),bot_bot_fun_com_bool) = bot_bot_fun_com_bool ).
fof(fact_915_inf__bot__right,axiom,
! [X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),bot_bot_bool))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_916_inf__bot__right,axiom,
! [X_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),bot_bo844097828e_bool) = bot_bo844097828e_bool ).
fof(fact_917_inf__bot__right,axiom,
! [X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),bot_bo784226126e_bool) = bot_bo784226126e_bool ).
fof(fact_918_inf__bot__left,axiom,
! [X_1] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,bot_bot_fun_com_bool),X_1) = bot_bot_fun_com_bool ).
fof(fact_919_inf__bot__left,axiom,
! [X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,bot_bot_bool),X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_920_inf__bot__left,axiom,
! [X_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),X_1) = bot_bo844097828e_bool ).
fof(fact_921_inf__bot__left,axiom,
! [X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,bot_bo784226126e_bool),X_1) = bot_bo784226126e_bool ).
fof(fact_922_inf__sup__absorb,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))
<=> hBOOL(X_1) ) ).
fof(fact_923_inf__sup__absorb,axiom,
! [X_1,Y_2] :
( is_fun_pname_bool(X_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = X_1 ) ).
fof(fact_924_inf__sup__absorb,axiom,
! [X_1,Y_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)) = X_1 ).
fof(fact_925_sup__inf__absorb,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)))
<=> hBOOL(X_1) ) ).
fof(fact_926_sup__inf__absorb,axiom,
! [X_1,Y_2] :
( is_fun_pname_bool(X_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)) = X_1 ) ).
fof(fact_927_sup__inf__absorb,axiom,
! [X_1,Y_2] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)) = X_1 ).
fof(fact_928_inf__sup__distrib1,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))) ) ).
fof(fact_929_inf__sup__distrib1,axiom,
! [X_1,Y_2,Z] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z)) ).
fof(fact_930_inf__sup__distrib1,axiom,
! [X_1,Y_2,Z] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Z)) ).
fof(fact_931_sup__inf__distrib1,axiom,
! [X_1,Y_2,Z] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ).
fof(fact_932_sup__inf__distrib1,axiom,
! [X_1,Y_2,Z] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ).
fof(fact_933_sup__inf__distrib1,axiom,
! [X_1,Y_2,Z] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z)) ).
fof(fact_934_inf__sup__distrib2,axiom,
! [Y_2,Z,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),X_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Z),X_1))) ) ).
fof(fact_935_inf__sup__distrib2,axiom,
! [Y_2,Z,X_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)),X_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),X_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Z),X_1)) ).
fof(fact_936_inf__sup__distrib2,axiom,
! [Y_2,Z,X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)),X_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),X_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Z),X_1)) ).
fof(fact_937_sup__inf__distrib2,axiom,
! [Y_2,Z,X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Z),X_1))) ) ).
fof(fact_938_sup__inf__distrib2,axiom,
! [Y_2,Z,X_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)),X_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Z),X_1)) ).
fof(fact_939_sup__inf__distrib2,axiom,
! [Y_2,Z,X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)),X_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),X_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Z),X_1)) ).
fof(fact_940_Diff__cancel,axiom,
! [A] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),A) = bot_bot_fun_com_bool ).
fof(fact_941_Diff__cancel,axiom,
! [A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),A) = bot_bo844097828e_bool ).
fof(fact_942_Diff__cancel,axiom,
! [A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),A) = bot_bo784226126e_bool ).
fof(fact_943_Diff__empty,axiom,
! [A] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),bot_bot_fun_com_bool) = A ).
fof(fact_944_Diff__empty,axiom,
! [A] :
( is_fun_pname_bool(A)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),bot_bo844097828e_bool) = A ) ).
fof(fact_945_Diff__empty,axiom,
! [A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),bot_bo784226126e_bool) = A ).
fof(fact_946_empty__Diff,axiom,
! [A] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,bot_bot_fun_com_bool),A) = bot_bot_fun_com_bool ).
fof(fact_947_empty__Diff,axiom,
! [A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,bot_bo844097828e_bool),A) = bot_bo844097828e_bool ).
fof(fact_948_empty__Diff,axiom,
! [A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,bot_bo784226126e_bool),A) = bot_bo784226126e_bool ).
fof(fact_949_finite__Diff2,axiom,
! [A,B] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).
fof(fact_950_finite__Diff2,axiom,
! [A,B] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B)))
<=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A)) ) ) ).
fof(fact_951_finite__Diff2,axiom,
! [A,B] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).
fof(fact_952_finite__Diff2,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,B))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A)) ) ) ).
fof(fact_953_insert__Diff1,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) ) ).
fof(fact_954_insert__Diff1,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) ) ).
fof(fact_955_insert__Diff1,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B) ) ).
fof(fact_956_insert__Diff__if,axiom,
! [A,X_1,B] :
( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) )
& ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)) ) ) ).
fof(fact_957_insert__Diff__if,axiom,
! [A,X_1,B] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) ) ) ).
fof(fact_958_insert__Diff__if,axiom,
! [A,X_1,B] :
( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),B))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),B) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)) ) ) ).
fof(fact_959_disjoint__iff__not__equal,axiom,
! [A,B] :
( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool
<=> ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
=> ! [Xa] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,Xa),B))
=> X_2 != Xa ) ) ) ).
fof(fact_960_disjoint__iff__not__equal,axiom,
! [A,B] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool
<=> ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ! [Xa] :
( is_pname(Xa)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B))
=> X_2 != Xa ) ) ) ) ) ).
fof(fact_961_disjoint__iff__not__equal,axiom,
! [A,B] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = bot_bo784226126e_bool
<=> ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
=> ! [Xa] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Xa),B))
=> X_2 != Xa ) ) ) ).
fof(fact_962_Int__empty__right,axiom,
! [A] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),bot_bot_fun_com_bool) = bot_bot_fun_com_bool ).
fof(fact_963_Int__empty__right,axiom,
! [A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),bot_bo844097828e_bool) = bot_bo844097828e_bool ).
fof(fact_964_Int__empty__right,axiom,
! [A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),bot_bo784226126e_bool) = bot_bo784226126e_bool ).
fof(fact_965_Int__empty__left,axiom,
! [B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,bot_bot_fun_com_bool),B) = bot_bot_fun_com_bool ).
fof(fact_966_Int__empty__left,axiom,
! [B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),B) = bot_bo844097828e_bool ).
fof(fact_967_Int__empty__left,axiom,
! [B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,bot_bo784226126e_bool),B) = bot_bo784226126e_bool ).
fof(fact_968_double__diff,axiom,
! [C_1,A,B] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,C_1),A)) = A ) ) ) ).
fof(fact_969_double__diff,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),C_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_1),A)) = A ) ) ).
fof(fact_970_Diff__mono,axiom,
! [D,B,A,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,D),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,C_1),D))) ) ) ).
fof(fact_971_Diff__mono,axiom,
! [D,B,A,C_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,D),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,C_1),D))) ) ) ).
fof(fact_972_Diff__subset,axiom,
! [A,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),A)) ).
fof(fact_973_Diff__subset,axiom,
! [A,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),A)) ).
fof(fact_974_Un__Diff,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),C_1)) ).
fof(fact_975_Un__Diff,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),C_1)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),C_1)) ).
fof(fact_976_Un__Diff__cancel2,axiom,
! [B,A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A) ).
fof(fact_977_Un__Diff__cancel2,axiom,
! [B,A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),A) ).
fof(fact_978_Un__Diff__cancel,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) ).
fof(fact_979_Un__Diff__cancel,axiom,
! [A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) ).
fof(fact_980_Int__insert__left__if1,axiom,
! [B,A_4,C_1] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1)) ) ).
fof(fact_981_Int__insert__left__if1,axiom,
! [B,A_4,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) ) ).
fof(fact_982_Int__insert__left__if1,axiom,
! [B,A_4,C_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)) ) ).
fof(fact_983_Int__insert__right__if1,axiom,
! [B,A_4,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)) ) ).
fof(fact_984_Int__insert__right__if1,axiom,
! [B,A_4,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) ) ).
fof(fact_985_Int__insert__right__if1,axiom,
! [B,A_4,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)) ) ).
fof(fact_986_Int__insert__left__if0,axiom,
! [B,A_4,C_1] :
( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1) ) ).
fof(fact_987_Int__insert__left__if0,axiom,
! [B,A_4,C_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ).
fof(fact_988_Int__insert__left__if0,axiom,
! [B,A_4,C_1] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1) ) ).
fof(fact_989_Int__insert__right__if0,axiom,
! [B,A_4,A] :
( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) ) ).
fof(fact_990_Int__insert__right__if0,axiom,
! [B,A_4,A] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) ) ).
fof(fact_991_Int__insert__right__if0,axiom,
! [B,A_4,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) ) ).
fof(fact_992_insert__inter__insert,axiom,
! [A_4,A,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)) ).
fof(fact_993_insert__inter__insert,axiom,
! [A_4,A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) ).
fof(fact_994_insert__inter__insert,axiom,
! [A_4,A,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)) ).
fof(fact_995_Int__insert__left,axiom,
! [B,A_4,C_1] :
( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1)) )
& ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1) ) ) ).
fof(fact_996_Int__insert__left,axiom,
! [B,A_4,C_1] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ) ).
fof(fact_997_Int__insert__left,axiom,
! [B,A_4,C_1] :
( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),C_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1) ) ) ).
fof(fact_998_Int__insert__right,axiom,
! [B,A_4,A] :
( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)) )
& ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) ) ) ).
fof(fact_999_Int__insert__right,axiom,
! [B,A_4,A] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) ) ) ).
fof(fact_1000_Int__insert__right,axiom,
! [B,A_4,A] :
( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) ) ) ).
fof(fact_1001_Int__mono,axiom,
! [B,D,A,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D))) ) ) ).
fof(fact_1002_Int__mono,axiom,
! [B,D,A,C_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),C_1))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),D))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C_1),D))) ) ) ).
fof(fact_1003_Int__greatest,axiom,
! [B,C_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) ) ) ).
fof(fact_1004_Int__greatest,axiom,
! [B,C_1,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),B))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B))) ) ) ).
fof(fact_1005_Int__absorb1,axiom,
! [B,A] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = B ) ) ).
fof(fact_1006_Int__absorb1,axiom,
! [B,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = B ) ).
fof(fact_1007_Int__absorb2,axiom,
! [A,B] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = A ) ) ).
fof(fact_1008_Int__absorb2,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B) = A ) ).
fof(fact_1009_Int__lower2,axiom,
! [A,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),B)) ).
fof(fact_1010_Int__lower2,axiom,
! [A,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),B)) ).
fof(fact_1011_Int__lower1,axiom,
! [A,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),A)) ).
fof(fact_1012_Int__lower1,axiom,
! [A,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),A)) ).
fof(fact_1013_Un__Int__crazy,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A)) ).
fof(fact_1014_Un__Int__crazy,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C_1),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C_1),A)) ).
fof(fact_1015_Un__Int__distrib2,axiom,
! [B,C_1,A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A)) ).
fof(fact_1016_Un__Int__distrib2,axiom,
! [B,C_1,A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,C_1),A)) ).
fof(fact_1017_Int__Un__distrib2,axiom,
! [B,C_1,A] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A)) ).
fof(fact_1018_Int__Un__distrib2,axiom,
! [B,C_1,A] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,C_1),A)) ).
fof(fact_1019_Un__Int__distrib,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1)) ).
fof(fact_1020_Un__Int__distrib,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),C_1)) ).
fof(fact_1021_Int__Un__distrib,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),C_1)) ).
fof(fact_1022_Int__Un__distrib,axiom,
! [A,B,C_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),C_1)) ).
fof(fact_1023_distrib__inf__le,axiom,
! [X_1,Y_2,Z] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))) ).
fof(fact_1024_distrib__inf__le,axiom,
! [X_1,Y_2,Z] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)))) ).
fof(fact_1025_distrib__inf__le,axiom,
! [X_1,Y_2,Z] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Z))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)))) ).
fof(fact_1026_distrib__sup__le,axiom,
! [X_1,Y_2,Z] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z)))) ).
fof(fact_1027_distrib__sup__le,axiom,
! [X_1,Y_2,Z] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)))) ).
fof(fact_1028_distrib__sup__le,axiom,
! [X_1,Y_2,Z] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z)))) ).
fof(fact_1029_insert__Diff,axiom,
! [A_4,A] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
=> hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) = A ) ).
fof(fact_1030_insert__Diff,axiom,
! [A_4,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) = A ) ) ).
fof(fact_1031_insert__Diff,axiom,
! [A_4,A] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_4),A))
=> hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) = A ) ).
fof(fact_1032_Diff__insert__absorb,axiom,
! [X_1,A] :
( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = A ) ).
fof(fact_1033_Diff__insert__absorb,axiom,
! [X_1,A] :
( is_fun_pname_bool(A)
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A ) ) ).
fof(fact_1034_Diff__insert__absorb,axiom,
! [X_1,A] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool)) = A ) ).
fof(fact_1035_insert__Diff__single,axiom,
! [A_4,A] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) ).
fof(fact_1036_insert__Diff__single,axiom,
! [A_4,A] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) ).
fof(fact_1037_insert__Diff__single,axiom,
! [A_4,A] : hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A) ).
fof(fact_1038_Diff__insert2,axiom,
! [A,A_4,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))),B) ).
fof(fact_1039_Diff__insert2,axiom,
! [A,A_4,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))),B) ).
fof(fact_1040_Diff__insert2,axiom,
! [A,A_4,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool))),B) ).
fof(fact_1041_Diff__insert,axiom,
! [A,A_4,B] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)) ).
fof(fact_1042_Diff__insert,axiom,
! [A,A_4,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)) ).
fof(fact_1043_Diff__insert,axiom,
! [A,A_4,B] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),bot_bo784226126e_bool)) ).
fof(fact_1044_finite__Diff__insert,axiom,
! [A,A_4,B] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B))))
<=> hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) ) ).
fof(fact_1045_finite__Diff__insert,axiom,
! [A,A_4,B] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B))))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ).
fof(fact_1046_finite__Diff__insert,axiom,
! [A,A_4,B] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),B))))
<=> hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B))) ) ).
fof(fact_1047_finite__Diff__insert,axiom,
! [A,A_4,B] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B))))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))) ) ).
fof(fact_1048_finite__Diff__insert,axiom,
! [A,A_4,B] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),B))))
<=> hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A),B))) ) ).
fof(fact_1049_image__diff__subset,axiom,
! [F,A,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B))),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))) ).
fof(fact_1050_Diff__partition,axiom,
! [A,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = B ) ) ).
fof(fact_1051_Diff__partition,axiom,
! [A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A)) = B ) ).
fof(fact_1052_Diff__subset__conv,axiom,
! [A,B,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),C_1))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))) ) ).
fof(fact_1053_Diff__subset__conv,axiom,
! [A,B,C_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),B)),C_1))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))) ) ).
fof(fact_1054_image__Int__subset,axiom,
! [F,A,B] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B)))) ).
fof(fact_1055_Un__Int__assoc__eq,axiom,
! [A,B,C_1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A)) ) ).
fof(fact_1056_Un__Int__assoc__eq,axiom,
! [A,B,C_1] :
( hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),B)),C_1) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B),C_1))
<=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,C_1),A)) ) ).
fof(fact_1057_if__image__distrib,axiom,
! [P_1,F,G,S] : hAPP_f360545851e_bool(image_185131637_state(hAPP_f1343550633_state(hAPP_f799842582_state(cOMBS_853737105_state,hAPP_f1655792756_state(hAPP_f2119427284_state(cOMBS_140201078_state,hAPP_f1836930278_state(cOMBB_143651633_pname(if_Hoa443228806_state),P_1)),F)),G)),S) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f360545851e_bool(image_185131637_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1))))) ).
fof(fact_1058_dom__if,axiom,
! [P_1,F,G] : dom_pname_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,hAPP_f755519727on_com(cOMBB_1394247784_pname(if_option_com),P_1)),F)),G)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(G)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1)))) ).
fof(fact_1059_diff__single__insert,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))),B))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B))) ) ) ).
fof(fact_1060_diff__single__insert,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) ) ) ).
fof(fact_1061_diff__single__insert,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B))) ) ) ).
fof(fact_1062_subset__insert__iff,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B)))
<=> ( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))),B)) )
& ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ) ) ).
fof(fact_1063_subset__insert__iff,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
<=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ) ).
fof(fact_1064_subset__insert__iff,axiom,
! [A,X_1,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),B)))
<=> ( ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),bot_bo784226126e_bool))),B)) )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B)) ) ) ) ).
fof(fact_1065_finite__empty__induct,axiom,
! [P_1,A] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,A))
=> ( ! [A_2,A_7] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_7))
=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),A_7))
=> ( hBOOL(hAPP_f990396704l_bool(P_1,A_7))
=> hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A_7),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),bot_bot_fun_com_bool)))) ) ) )
=> hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool)) ) ) ) ).
fof(fact_1066_finite__empty__induct,axiom,
! [P_1,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,A))
=> ( ! [A_2,A_7] :
( ( is_pname(A_2)
& is_fun_pname_bool(A_7) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_7))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,A_7))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_7),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) ) ) ) ).
fof(fact_1067_finite__empty__induct,axiom,
! [P_1,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,A))
=> ( ! [A_2,A_7] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A_7))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,A_2),A_7))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,A_7))
=> hBOOL(hAPP_f1378282496l_bool(P_1,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A_7),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_2),bot_bo784226126e_bool)))) ) ) )
=> hBOOL(hAPP_f1378282496l_bool(P_1,bot_bo784226126e_bool)) ) ) ) ).
fof(fact_1068_finite__empty__induct,axiom,
! [P_1,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,A))
=> ( ! [A_2,A_7] :
( ( is_fun_pname_bool(A_2)
& is_fun1661590463l_bool(A_7) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_7))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_7))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,A_7))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_7),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),bot_bo1649642514l_bool)))) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) ) ) ) ).
fof(fact_1069_finite__empty__induct,axiom,
! [P_1,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,A))
=> ( ! [A_2,A_7] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A_7))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_2),A_7))
=> ( hBOOL(hAPP_f1410040974l_bool(P_1,A_7))
=> hBOOL(hAPP_f1410040974l_bool(P_1,hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,A_7),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_2),bot_bo942947096l_bool)))) ) ) )
=> hBOOL(hAPP_f1410040974l_bool(P_1,bot_bo942947096l_bool)) ) ) ) ).
fof(fact_1070_dom__override__on,axiom,
! [F,G,A] : dom_pname_com(overri1496249029on_com(F,G,A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),dom_pname_com(G)))))),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),dom_pname_com(G))))) ).
fof(fact_1071_Int__Collect__mono,axiom,
! [Q_1,P_1,A,B] :
( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
=> ( ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
=> ( hBOOL(hAPP_com_bool(P_1,X_2))
=> hBOOL(hAPP_com_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(collect_com,P_1))),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),hAPP_f1682609283m_bool(collect_com,Q_1)))) ) ) ).
fof(fact_1072_Int__Collect__mono,axiom,
! [Q_1,P_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( hBOOL(hAPP_pname_bool(P_1,X_2))
=> hBOOL(hAPP_pname_bool(Q_1,X_2)) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),hAPP_f759274231e_bool(collect_pname,Q_1)))) ) ) ).
fof(fact_1073_Int__Collect__mono,axiom,
! [Q_1,P_1,A,B] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),B))
=> ( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A))
=> ( hBOOL(hAPP_H242767318e_bool(P_1,X_2))
=> hBOOL(hAPP_H242767318e_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A),hAPP_f806699093e_bool(collec637225377_state,P_1))),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B),hAPP_f806699093e_bool(collec637225377_state,Q_1)))) ) ) ).
fof(fact_1074_Int__Collect__mono,axiom,
! [Q_1,P_1,A,B] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
=> ( ! [X_2] :
( is_fun_pname_bool(X_2)
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,X_2))
=> hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,B),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1)))) ) ) ).
fof(fact_1075_Int__Collect__mono,axiom,
! [Q_1,P_1,A,B] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),B))
=> ( ! [X_2] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A))
=> ( hBOOL(hAPP_f1378282496l_bool(P_1,X_2))
=> hBOOL(hAPP_f1378282496l_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),hAPP_f734420447l_bool(collec1987918285e_bool,P_1))),hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,B),hAPP_f734420447l_bool(collec1987918285e_bool,Q_1)))) ) ) ).
fof(fact_1076_distrib__imp2,axiom,
! [X_1,Y_2,Z] :
( ! [X_2,Y_3,Z_1] :
( ( is_bool(X_2)
& is_bool(Y_3)
& is_bool(Z_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_3),Z_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_3)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))) ) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))) ) ) ).
fof(fact_1077_distrib__imp2,axiom,
! [X_1,Y_2,Z] :
( ! [X_2,Y_3,Z_1] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_3)
& is_fun_pname_bool(Z_1) )
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_3),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1)) )
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z)) ) ).
fof(fact_1078_distrib__imp2,axiom,
! [X_1,Y_2,Z] :
( ! [X_2,Y_3,Z_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_3),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Y_3)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_2),Z_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_1),Z)) ) ).
fof(fact_1079_distrib__imp1,axiom,
! [X_1,Y_2,Z] :
( ! [X_2,Y_3,Z_1] :
( ( is_bool(X_2)
& is_bool(Y_3)
& is_bool(Z_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_3),Z_1)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),Y_3)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),Z_1))) ) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ) ).
fof(fact_1080_distrib__imp1,axiom,
! [X_1,Y_2,Z] :
( ! [X_2,Y_3,Z_1] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_3)
& is_fun_pname_bool(Z_1) )
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_3),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1)) )
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ) ).
fof(fact_1081_distrib__imp1,axiom,
! [X_1,Y_2,Z] :
( ! [X_2,Y_3,Z_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,Y_3),Z_1)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_2),Y_3)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,X_2),Z_1))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,Y_2),Z)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Y_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),Z)) ) ).
fof(fact_1082_flat__lub__def,axiom,
! [A,B_1] :
( ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)))
=> hAPP_f1276420679ol_com(partial_flat_lub_com(B_1),A) = B_1 )
& ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)))
=> hAPP_f1276420679ol_com(partial_flat_lub_com(B_1),A) = hAPP_f1276420679ol_com(the_com_1,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)))) ) ) ).
fof(fact_1083_flat__lub__def,axiom,
! [A,B_1] :
( is_pname(B_1)
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)))
=> hAPP_f1297739591_pname(partia752020666_pname(B_1),A) = B_1 )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)))
=> hAPP_f1297739591_pname(partia752020666_pname(B_1),A) = hAPP_f1297739591_pname(the_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)))) ) ) ) ).
fof(fact_1084_flat__lub__def,axiom,
! [A,B_1] :
( ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)))
=> hAPP_f718417177_state(partia325231104_state(B_1),A) = B_1 )
& ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)))
=> hAPP_f718417177_state(partia325231104_state(B_1),A) = hAPP_f718417177_state(the_Ho2067184133_state,hAPP_f806699093e_bool(hAPP_f1184122441e_bool(cOMBC_538205282l_bool,member1667945571_state),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,B_1),bot_bo784226126e_bool)))) ) ) ).
fof(fact_1085_comp__fun__idem__remove,axiom,
hBOOL(finite1653727294m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,minus_59609839m_bool)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool)))) ).
fof(fact_1086_comp__fun__idem__remove,axiom,
hBOOL(finite2017903282e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,minus_1015773161e_bool)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) ).
fof(fact_1087_comp__fun__idem__remove,axiom,
hBOOL(finite2036162504e_bool(hAPP_f241329646e_bool(cOMBB_604855927_state(hAPP_f2061951445e_bool(cOMBC_528733435e_bool,minus_1805465033e_bool)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool)))) ).
fof(fact_1088_fun__upd__image,axiom,
! [F,Y_2,X_1,A] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f360545851e_bool(image_185131637_state(fun_up1055265789_state(F,X_1,Y_2)),A) = hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,Y_2),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f360545851e_bool(image_185131637_state(fun_up1055265789_state(F,X_1,Y_2)),A) = hAPP_f360545851e_bool(image_185131637_state(F),A) ) ) ).
fof(fact_1089_comp__fun__idem__insert,axiom,
hBOOL(finite1653727294m_bool(insert_com)) ).
fof(fact_1090_comp__fun__idem__insert,axiom,
hBOOL(finite2017903282e_bool(insert_pname)) ).
fof(fact_1091_comp__fun__idem__insert,axiom,
hBOOL(finite2036162504e_bool(insert1744391420_state)) ).
fof(fact_1092_comp__fun__idem__sup,axiom,
hBOOL(finite318301748l_bool(semila1168014441p_bool)) ).
fof(fact_1093_comp__fun__idem__sup,axiom,
hBOOL(finite367769966e_bool(semila278973382e_bool)) ).
fof(fact_1094_comp__fun__idem__sup,axiom,
hBOOL(finite1765632844e_bool(semila176469292e_bool)) ).
fof(fact_1095_inj__on__Un,axiom,
! [F,A,B] :
( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
<=> ( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A))
& hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),B))
& hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A))) = bot_bo784226126e_bool ) ) ).
fof(fact_1096_dom__eq__singleton__conv,axiom,
! [F,X_1] :
( dom_pname_com(F) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)
<=> ? [V] : F = fun_up879233478on_com(hAPP_o129566686on_com(cOMBK_413306633_pname,none_com),X_1,hAPP_com_option_com(some_com,V)) ) ).
fof(fact_1097_minus__fold__remove,axiom,
! [B,A] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,B),A) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(finite1275301314m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,minus_59609839m_bool)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool))),B),A) ) ).
fof(fact_1098_minus__fold__remove,axiom,
! [B,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(finite315386934e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,minus_1015773161e_bool)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))),B),A) ) ).
fof(fact_1099_minus__fold__remove,axiom,
! [B,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),A) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(finite1230907212e_bool(hAPP_f241329646e_bool(cOMBB_604855927_state(hAPP_f2061951445e_bool(cOMBC_528733435e_bool,minus_1805465033e_bool)),hAPP_f874203478e_bool(hAPP_f1802364479e_bool(cOMBC_1229155955e_bool,insert1744391420_state),bot_bo784226126e_bool))),B),A) ) ).
fof(fact_1100_minus__fold__remove,axiom,
! [B,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,B),A) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(finite1627341516l_bool(hAPP_f1149191722l_bool(cOMBB_631815671e_bool(hAPP_f1477350485l_bool(cOMBC_694979519l_bool,minus_1290075917l_bool)),hAPP_f417341722l_bool(hAPP_f836143551l_bool(cOMBC_772615479l_bool,insert1325755072e_bool),bot_bo1649642514l_bool))),B),A) ) ).
fof(fact_1101_minus__fold__remove,axiom,
! [B,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hAPP_f734420447l_bool(hAPP_f1847120l_bool(minus_1929235165l_bool,B),A) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(finite1943735070l_bool(hAPP_f1316144452l_bool(cOMBB_494346593e_bool(hAPP_f1573805579l_bool(cOMBC_1377256501l_bool,minus_1929235165l_bool)),hAPP_f2059879088l_bool(hAPP_f476955937l_bool(cOMBC_1639502213l_bool,insert1720618162e_bool),bot_bo942947096l_bool))),B),A) ) ).
fof(fact_1102_image__eq__fold__image,axiom,
! [F,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hAPP_f360545851e_bool(image_185131637_state(F),A) = 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) ) ).
fof(fact_1103_inj__Some,axiom,
! [A] : hBOOL(hAPP_f1664156314l_bool(inj_on737724108_pname(some_pname),A)) ).
fof(fact_1104_inj__Some,axiom,
! [A] : hBOOL(hAPP_f1378282496l_bool(inj_on264996226_state(some_H1043067815_state),A)) ).
fof(fact_1105_inj__Some,axiom,
! [A] : hBOOL(hAPP_f990396704l_bool(inj_on11367768on_com(some_com),A)) ).
fof(fact_1106_option_Osimps_I2_J,axiom,
! [A_6] : none_com != hAPP_com_option_com(some_com,A_6) ).
fof(fact_1107_option_Osimps_I2_J,axiom,
! [A_6] : none_pname != hAPP_p1252095976_pname(some_pname,A_6) ).
fof(fact_1108_option_Osimps_I2_J,axiom,
! [A_6] : none_H175086635_state != hAPP_H1633077406_state(some_H1043067815_state,A_6) ).
fof(fact_1109_option_Osimps_I3_J,axiom,
! [A_5] : hAPP_com_option_com(some_com,A_5) != none_com ).
fof(fact_1110_option_Osimps_I3_J,axiom,
! [A_5] : hAPP_p1252095976_pname(some_pname,A_5) != none_pname ).
fof(fact_1111_option_Osimps_I3_J,axiom,
! [A_5] : hAPP_H1633077406_state(some_H1043067815_state,A_5) != none_H175086635_state ).
fof(fact_1112_not__Some__eq,axiom,
! [X_1] :
( ! [Y_3] : X_1 != hAPP_com_option_com(some_com,Y_3)
<=> X_1 = none_com ) ).
fof(fact_1113_not__Some__eq,axiom,
! [X_1] :
( is_option_pname(X_1)
=> ( ! [Y_3] :
( is_pname(Y_3)
=> X_1 != hAPP_p1252095976_pname(some_pname,Y_3) )
<=> X_1 = none_pname ) ) ).
fof(fact_1114_not__Some__eq,axiom,
! [X_1] :
( ! [Y_3] : X_1 != hAPP_H1633077406_state(some_H1043067815_state,Y_3)
<=> X_1 = none_H175086635_state ) ).
fof(fact_1115_not__None__eq,axiom,
! [X_1] :
( X_1 != none_com
<=> ? [Y_3] : X_1 = hAPP_com_option_com(some_com,Y_3) ) ).
fof(fact_1116_not__None__eq,axiom,
! [X_1] :
( is_option_pname(X_1)
=> ( X_1 != none_pname
<=> ? [Y_3] :
( is_pname(Y_3)
& X_1 = hAPP_p1252095976_pname(some_pname,Y_3) ) ) ) ).
fof(fact_1117_not__None__eq,axiom,
! [X_1] :
( X_1 != none_H175086635_state
<=> ? [Y_3] : X_1 = hAPP_H1633077406_state(some_H1043067815_state,Y_3) ) ).
fof(fact_1118_dom__def,axiom,
! [M] : dom_pname_com(M) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),M)),none_com))) ).
fof(fact_1119_domIff,axiom,
! [A_4,M] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M)))
<=> hAPP_p799580910on_com(M,A_4) != none_com ) ).
fof(fact_1120_finite__imageD,axiom,
! [F,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,hAPP_f360545851e_bool(image_185131637_state(F),A)))
=> ( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).
fof(fact_1121_inj__on__Un__image__eq__iff,axiom,
! [F,A,B] :
( ( is_fun_pname_bool(A)
& is_fun_pname_bool(B) )
=> ( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
=> ( hAPP_f360545851e_bool(image_185131637_state(F),A) = hAPP_f360545851e_bool(image_185131637_state(F),B)
<=> A = B ) ) ) ).
fof(fact_1122_is__none__def,axiom,
! [X_1] :
( hBOOL(is_none_com(X_1))
<=> X_1 = none_com ) ).
fof(fact_1123_is__none__code_I1_J,axiom,
hBOOL(is_none_com(none_com)) ).
fof(fact_1124_inj__on__fun__updI,axiom,
! [X_1,Y_2,F,A] :
( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,Y_2),hAPP_f360545851e_bool(image_185131637_state(F),A)))
=> hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(fun_up1055265789_state(F,X_1,Y_2)),A)) ) ) ).
fof(fact_1125_sup__le__fold__sup,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_4),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),A))) ) ) ).
fof(fact_1126_sup__le__fold__sup,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_4),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),B_1)),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),B_1),A))) ) ) ).
fof(fact_1127_sup__le__fold__sup,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_4),A))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),A))) ) ) ).
fof(fact_1128_fold__inf__le__inf,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_4),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1))) ) ) ).
fof(fact_1129_fold__inf__le__inf,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,A_4),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),B_1),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),B_1))) ) ) ).
fof(fact_1130_fold__inf__le__inf,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_4),A))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila310582991f_bool),B_1),A)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1))) ) ) ).
fof(fact_1131_fold__sup__insert,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),A)) ) ).
fof(fact_1132_fold__sup__insert,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),B_1),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A_4),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),B_1),A)) ) ).
fof(fact_1133_fold__sup__insert,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,A_4),A)))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),A))) ) ) ).
fof(fact_1134_fold__inf__insert,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),A)) ) ).
fof(fact_1135_fold__inf__insert,axiom,
! [B_1,A_4,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),B_1),hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,A_4),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),B_1),A)) ) ).
fof(fact_1136_dom__eq__empty__conv,axiom,
! [F] :
( dom_pname_com(F) = bot_bo844097828e_bool
<=> ! [X_2] :
( is_pname(X_2)
=> hAPP_p799580910on_com(F,X_2) = none_com ) ) ).
fof(fact_1137_dom__empty,axiom,
dom_pname_com(hAPP_o129566686on_com(cOMBK_413306633_pname,none_com)) = bot_bo844097828e_bool ).
fof(fact_1138_Option_Oset_Osimps_I1_J,axiom,
set_com(none_com) = bot_bot_fun_com_bool ).
fof(fact_1139_Option_Oset_Osimps_I1_J,axiom,
set_pname(none_pname) = bot_bo844097828e_bool ).
fof(fact_1140_Option_Oset_Osimps_I1_J,axiom,
set_Ho1741238126_state(none_H175086635_state) = bot_bo784226126e_bool ).
fof(fact_1141_set__empty__eq,axiom,
! [Xo] :
( set_com(Xo) = bot_bot_fun_com_bool
<=> Xo = none_com ) ).
fof(fact_1142_set__empty__eq,axiom,
! [Xo] :
( is_option_pname(Xo)
=> ( set_pname(Xo) = bot_bo844097828e_bool
<=> Xo = none_pname ) ) ).
fof(fact_1143_set__empty__eq,axiom,
! [Xo] :
( set_Ho1741238126_state(Xo) = bot_bo784226126e_bool
<=> Xo = none_H175086635_state ) ).
fof(fact_1144_endo__inj__surj,axiom,
! [F,A] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(image_2063528359e_bool(F),A)),A))
=> ( hBOOL(hAPP_f1935102916l_bool(inj_on1490514707e_bool(F),A))
=> hAPP_f559147733l_bool(image_2063528359e_bool(F),A) = A ) ) ) ) ).
fof(fact_1145_endo__inj__surj,axiom,
! [F,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,hAPP_f734420447l_bool(image_390184709e_bool(F),A)),A))
=> ( hBOOL(hAPP_f1410040974l_bool(inj_on2143431281e_bool(F),A))
=> hAPP_f734420447l_bool(image_390184709e_bool(F),A) = A ) ) ) ).
fof(fact_1146_endo__inj__surj,axiom,
! [F,A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(image_pname_pname(F),A)),A))
=> ( hBOOL(hAPP_f1664156314l_bool(inj_on_pname_pname(F),A))
=> hAPP_f759274231e_bool(image_pname_pname(F),A) = A ) ) ) ) ).
fof(fact_1147_endo__inj__surj,axiom,
! [F,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(image_661047967_state(F),A)),A))
=> ( hBOOL(hAPP_f1378282496l_bool(inj_on535898123_state(F),A))
=> hAPP_f806699093e_bool(image_661047967_state(F),A) = A ) ) ) ).
fof(fact_1148_finite__surj__inj,axiom,
! [F,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),hAPP_f559147733l_bool(image_2063528359e_bool(F),A)))
=> hBOOL(hAPP_f1935102916l_bool(inj_on1490514707e_bool(F),A)) ) ) ).
fof(fact_1149_finite__surj__inj,axiom,
! [F,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(ord_le694194916l_bool,A),hAPP_f734420447l_bool(image_390184709e_bool(F),A)))
=> hBOOL(hAPP_f1410040974l_bool(inj_on2143431281e_bool(F),A)) ) ) ).
fof(fact_1150_finite__surj__inj,axiom,
! [F,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(image_pname_pname(F),A)))
=> hBOOL(hAPP_f1664156314l_bool(inj_on_pname_pname(F),A)) ) ) ).
fof(fact_1151_finite__surj__inj,axiom,
! [F,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A),hAPP_f806699093e_bool(image_661047967_state(F),A)))
=> hBOOL(hAPP_f1378282496l_bool(inj_on535898123_state(F),A)) ) ) ).
fof(fact_1152_inj__on__image__Int,axiom,
! [B,A,F,C_1] :
( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
=> hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B)) ) ) ) ).
fof(fact_1153_inj__on__image__set__diff,axiom,
! [B,A,F,C_1] :
( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
=> hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,hAPP_f360545851e_bool(image_185131637_state(F),A)),hAPP_f360545851e_bool(image_185131637_state(F),B)) ) ) ) ).
fof(fact_1154_union__fold__insert,axiom,
! [B,A] :
( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(finite1275301314m_bool(insert_com),B),A) ) ).
fof(fact_1155_union__fold__insert,axiom,
! [B,A] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(finite315386934e_bool(insert_pname),B),A) ) ).
fof(fact_1156_union__fold__insert,axiom,
! [B,A] :
( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,A),B) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(finite1230907212e_bool(insert1744391420_state),B),A) ) ).
fof(fact_1157_union__fold__insert,axiom,
! [B,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(finite1627341516l_bool(insert1325755072e_bool),B),A) ) ).
fof(fact_1158_union__fold__insert,axiom,
! [B,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(finite1943735070l_bool(insert1720618162e_bool),B),A) ) ).
fof(fact_1159_dom__minus,axiom,
! [A,F,X_1] :
( hAPP_p799580910on_com(F,X_1) = none_com
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),A) ) ).
fof(fact_1160_Sup__fin_Oidem,axiom,
! [X_1] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),X_1))
<=> hBOOL(X_1) ) ).
fof(fact_1161_Sup__fin_Oidem,axiom,
! [X_1] :
( is_fun_pname_bool(X_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),X_1) = X_1 ) ).
fof(fact_1162_Sup__fin_Oidem,axiom,
! [X_1] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,X_1),X_1) = X_1 ).
fof(fact_1163_folding__one_Oeq__fold_H,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite860057415ne_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_f1276420679ol_com(hAPP_c1546426672ol_com(finite_fold_com_com(F),X_1),A) ) ) ) ).
fof(fact_1164_folding__one_Oeq__fold_H,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f1297739591_pname(hAPP_p1630511146_pname(finite1657623752_pname(F),X_1),A) ) ) ) ).
fof(fact_1165_folding__one_Oeq__fold_H,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite683959609_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> ( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),A))
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,X_1),A)) = hAPP_f718417177_state(hAPP_H1440241088_state(finite212984546_state(F),X_1),A) ) ) ) ).
fof(fact_1166_folding__one_Oeq__fold_H,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(F),X_1),A) ) ) ) ).
fof(fact_1167_folding__one_Oeq__fold_H,axiom,
! [X_1,A,F,Fa] :
( hBOOL(finite2009063477e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( ~ hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_1),A))
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,X_1),A)) = hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(F),X_1),A) ) ) ) ).
fof(fact_1168_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_4,A,F,Fa] :
( hBOOL(finite666746948em_com(F,Fa))
=> ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
=> hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)) = hAPP_f1276420679ol_com(hAPP_c1546426672ol_com(finite_fold_com_com(F),A_4),A) ) ) ).
fof(fact_1169_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_4,A,F,Fa] :
( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)) = hAPP_f1297739591_pname(hAPP_p1630511146_pname(finite1657623752_pname(F),A_4),A) ) ) ).
fof(fact_1170_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_4,A,F,Fa] :
( hBOOL(finite416071164_state(F,Fa))
=> ( hBOOL(hAPP_f1378282496l_bool(finite694102371_state,A))
=> hAPP_f718417177_state(Fa,hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,A_4),A)) = hAPP_f718417177_state(hAPP_H1440241088_state(finite212984546_state(F),A_4),A) ) ) ).
fof(fact_1171_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_4,A,F,Fa] :
( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(F),A_4),A) ) ) ).
fof(fact_1172_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A_4,A,F,Fa] :
( hBOOL(finite688249778e_bool(F,Fa))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> hAPP_f1216288071e_bool(Fa,hAPP_f734420447l_bool(hAPP_f1472090462l_bool(insert1720618162e_bool,A_4),A)) = hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(F),A_4),A) ) ) ).
fof(fact_1173_WT_OBody,axiom,
! [Pn] :
( hAPP_p799580910on_com(body,Pn) != none_com
=> hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,Pn))) ) ).
fof(fact_1174_inj__on__insert,axiom,
! [F,A_4,A] :
( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)))
<=> ( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F),A))
& ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,A_4)),hAPP_f360545851e_bool(image_185131637_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))))) ) ) ).
fof(fact_1175_dom__fun__upd,axiom,
! [F,X_1,Y_2] :
( ( Y_2 = none_com
=> dom_pname_com(fun_up879233478on_com(F,X_1,Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) )
& ( Y_2 != none_com
=> dom_pname_com(fun_up879233478on_com(F,X_1,Y_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) ) ) ).
fof(fact_1176_inf__le__fold__inf,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( ! [X_2] :
( is_fun_pname_bool(X_2)
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_2)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),C)),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),C),A))) ) ) ).
fof(fact_1177_inf__le__fold__inf,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( ! [X_2] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,B_1),X_2)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,B_1),C)),hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila1874263622e_bool),C),A))) ) ) ).
fof(fact_1178_inf__le__fold__inf,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_2)) ) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,B_1),C)),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila310582991f_bool),C),A))) ) ) ).
fof(fact_1179_fold__sup__le__sup,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( ! [X_2] :
( is_fun_pname_bool(X_2)
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),B_1)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),C),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C))) ) ) ).
fof(fact_1180_fold__sup__le__sup,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( ! [X_2] :
( hBOOL(hAPP_f1410040974l_bool(hAPP_f631019661l_bool(member131361931e_bool,X_2),A))
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,X_2),B_1)) )
=> hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f1216288071e_bool(hAPP_f1712138014e_bool(finite391880392e_bool(semila176469292e_bool),C),A)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila176469292e_bool,B_1),C))) ) ) ).
fof(fact_1181_fold__sup__le__sup,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
=> ( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),B_1)) ) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),C),A)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))) ) ) ).
fof(fact_1182_inj__on__iff__surj,axiom,
! [A_3,A] :
( A != bot_bo784226126e_bool
=> ( ? [F_1] :
( hBOOL(hAPP_f1378282496l_bool(inj_on63516655_pname(F_1),A))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1083669085e_bool(image_1774499931_pname(F_1),A)),A_3)) )
<=> ? [G_1] : hAPP_f360545851e_bool(image_185131637_state(G_1),A_3) = A ) ) ).
fof(fact_1183_inj__on__iff__surj,axiom,
! [A_3,A] :
( is_fun_pname_bool(A)
=> ( A != bot_bo844097828e_bool
=> ( ? [F_1] :
( hBOOL(hAPP_f1664156314l_bool(inj_on621632009_state(F_1),A))
& hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F_1),A)),A_3)) )
<=> ? [G_1] : hAPP_f1083669085e_bool(image_1774499931_pname(G_1),A_3) = A ) ) ) ).
fof(fact_1184_option_Oexhaust,axiom,
! [Y_1] :
( Y_1 != none_com
=> ~ ! [A_2] : Y_1 != hAPP_com_option_com(some_com,A_2) ) ).
fof(fact_1185_option_Oexhaust,axiom,
! [Y_1] :
( is_option_pname(Y_1)
=> ( Y_1 != none_pname
=> ~ ! [A_2] :
( is_pname(A_2)
=> Y_1 != hAPP_p1252095976_pname(some_pname,A_2) ) ) ) ).
fof(fact_1186_option_Oexhaust,axiom,
! [Y_1] :
( Y_1 != none_H175086635_state
=> ~ ! [A_2] : Y_1 != hAPP_H1633077406_state(some_H1043067815_state,A_2) ) ).
fof(fact_1187_Cantor__Bernstein__aux,axiom,
! [G,B,F,A] :
? [A_1] :
( is_fun_pname_bool(A_1)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A))
& ! [X_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f1083669085e_bool(image_1774499931_pname(G),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A_1))))) )
& ? [H] :
( ! [X_2] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hAPP_p1751618853_state(H,X_2) = hAPP_p1751618853_state(F,X_2) )
& ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),A_1)))
=> ( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(H,X_2)),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,B),hAPP_f360545851e_bool(image_185131637_state(F),A_1))))
& X_2 = hAPP_H1193503499_pname(G,hAPP_p1751618853_state(H,X_2)) ) ) ) ) ) ).
fof(fact_1188_Cantor__Bernstein__aux,axiom,
! [G,B,F,A] :
? [A_1] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,A_1),A))
& ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1))
=> ~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f360545851e_bool(image_185131637_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A_1))))) )
& ? [H] :
( ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),A_1))
=> hAPP_H1193503499_pname(H,X_2) = hAPP_H1193503499_pname(F,X_2) )
& ! [X_2] :
( hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_2),hAPP_f806699093e_bool(hAPP_f1794460506e_bool(minus_1805465033e_bool,A),A_1)))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1193503499_pname(H,X_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f1083669085e_bool(image_1774499931_pname(F),A_1))))
& X_2 = hAPP_p1751618853_state(G,hAPP_H1193503499_pname(H,X_2)) ) ) ) ) ).
fof(fact_1189_image__vimage__subset,axiom,
! [F,A] : hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,hAPP_f360545851e_bool(image_185131637_state(F),vimage1011814463_state(F,A))),A)) ).
fof(fact_1190_dom__restrict,axiom,
! [M,A] : dom_pname_com(restri1382200118me_com(M,A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(M)),A) ).
fof(fact_1191_Inf__fin_Ounion__disjoint,axiom,
! [B,A] :
( ( is_fun1661590463l_bool(B)
& is_fun1661590463l_bool(A) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( A != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( B != bot_bo1649642514l_bool
=> ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,A)),hAPP_f674760225e_bool(big_la28065288e_bool,B)) ) ) ) ) ) ) ).
fof(fact_1192_Inf__fin_Ounion__disjoint,axiom,
! [B,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( A != bot_bo942947096l_bool
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( B != bot_bo942947096l_bool
=> ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) = bot_bo942947096l_bool
=> hAPP_f1216288071e_bool(big_la236972906e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B)) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f1216288071e_bool(big_la236972906e_bool,A)),hAPP_f1216288071e_bool(big_la236972906e_bool,B)) ) ) ) ) ) ).
fof(fact_1193_Inf__fin_Ounion__inter,axiom,
! [B,A] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B))),hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,A)),hAPP_f674760225e_bool(big_la28065288e_bool,B)) ) ) ) ).
fof(fact_1194_Inf__fin_Ounion__inter,axiom,
! [B,A] :
( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,A))
=> ( hBOOL(hAPP_f1410040974l_bool(finite627955595e_bool,B))
=> ( hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B) != bot_bo942947096l_bool
=> hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f1216288071e_bool(big_la236972906e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1672697786l_bool,A),B))),hAPP_f1216288071e_bool(big_la236972906e_bool,hAPP_f734420447l_bool(hAPP_f1847120l_bool(semila1028267552l_bool,A),B))) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(semila1874263622e_bool,hAPP_f1216288071e_bool(big_la236972906e_bool,A)),hAPP_f1216288071e_bool(big_la236972906e_bool,B)) ) ) ) ).
fof(fact_1195_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),top_top_fun_com_bool)) ).
fof(fact_1196_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),top_to2127735616e_bool)) ).
fof(fact_1197_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,X_1),top_to215444530e_bool)) ).
fof(fact_1198_rangeI,axiom,
! [F,X_1] : hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_p1751618853_state(F,X_1)),hAPP_f360545851e_bool(image_185131637_state(F),top_to2127735616e_bool))) ).
%----Helper facts (152)
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_fAll_1_1_fAll_000tc__Com__Ostate_U,axiom,
! [X,P] :
( ~ hBOOL(hAPP_f327114704l_bool(fAll_state,P))
| hBOOL(hAPP_state_bool(P,X)) ) ).
fof(help_fequal_1_1_fequal_000tc__Com__Ocom_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_com_bool(hAPP_c1396316405m_bool(fequal_com,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Com__Ocom_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_com_bool(hAPP_c1396316405m_bool(fequal_com,X),Y)) ) ).
fof(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
! [X,Y] :
( ( is_pname(X)
& is_pname(Y) )
=> ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) ) ).
fof(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ocom_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_com_bool(hAPP_b1153789088m_bool(cOMBK_bool_com,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Com__Ocom_000tc__Com__Opname_U,axiom,
! [P,Q] : hAPP_pname_com(hAPP_c1494068046me_com(cOMBK_com_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_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
! [X,Y] : hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fTrue),X),Y) = X ).
fof(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
! [X,Y] : hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fFalse),X),Y) = Y ).
fof(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
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__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_option_com_bool(hAPP_o1684370239m_bool(fequal_option_com,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_option_com_bool(hAPP_o1684370239m_bool(fequal_option_com,X),Y)) ) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(fequal_fun_com_bool,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(fequal_fun_com_bool,X),Y)) ) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X,Y] :
( ( is_fun_pname_bool(X)
& is_fun_pname_bool(Y) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Com__Ocom_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,P),Q),R) = hAPP_com_bool(hAPP_c1396316405m_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ocom_U,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_f1682609283m_bool(cOMBB_bool_bool_com(P),Q),R) = hAPP_bool_bool(P,hAPP_com_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Ocom_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_c1580157610l_bool(P,R),hAPP_com_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_p1639923567m_bool(hAPP_f734198589m_bool(cOMBC_com_pname_bool,P),Q),R) = hAPP_pname_bool(hAPP_c1967741679e_bool(P,R),Q) ).
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_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Opname_,axiom,
! [P,Q] : hAPP_p799580910on_com(hAPP_o129566686on_com(cOMBK_413306633_pname,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1664156314l_bool(hAPP_b357632156l_bool(cOMBK_1857069011e_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
! [P,Q] : hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(cOMBK_631994958_state,P),Q) = P ).
fof(help_If_1_1_If_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate,axiom,
! [X,Y] : hAPP_H574424047_state(hAPP_H280516760_state(hAPP_b993469484_state(if_Hoa443228806_state,fTrue),X),Y) = X ).
fof(help_If_2_1_If_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate,axiom,
! [X,Y] : hAPP_H574424047_state(hAPP_H280516760_state(hAPP_b993469484_state(if_Hoa443228806_state,fFalse),X),Y) = Y ).
fof(help_If_3_1_If_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__Ostate,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_H242767318e_bool(hAPP_H216526335e_bool(fequal1440809015_state,X),Y)) ) ).
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_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,P),Q),R) = hAPP_option_com_bool(hAPP_p558118546m_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_f1998868198m_bool(cOMBB_298914627ol_com(P),Q),R) = hAPP_f990396704l_bool(P,hAPP_c1396316405m_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,P),Q),R) = hAPP_f990396704l_bool(hAPP_c667411853l_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_c1580157610l_bool(hAPP_f954469007l_bool(cOMBB_886968260ol_com(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_com_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [P,Q,R] : hAPP_c1967741679e_bool(hAPP_f835719487e_bool(cOMBB_1083901850ol_com(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_com_pname(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBB_307249310e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,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_012,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_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_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_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
! [P,Q,R] : hAPP_state_bool(hAPP_f1012183542e_bool(cOMBB_1911358915_state(P),Q),R) = hAPP_f327114704l_bool(P,hAPP_s1806633685e_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_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_013,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_COMBK_1_1_COMBK_000tc__Com__Ocom_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [P,Q] : hAPP_H46530577te_com(hAPP_c57939194te_com(cOMBK_131063602_state,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q] : hAPP_c1455475371_state(hAPP_H275587026_state(cOMBK_869602456te_com,P),Q) = P ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____uwgpyvfjxg__,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__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_,axiom,
! [P,Q] :
( is_pname(P)
=> hAPP_H1193503499_pname(hAPP_p1227118702_pname(cOMBK_497473068_state,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___014,axiom,
! [P,Q] : hAPP_p1751618853_state(hAPP_H1938877132_state(cOMBK_2086841362_pname,P),Q) = P ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(fequal1475827639e_bool,X),Y)) ) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_,axiom,
! [P,Q,R] : hAPP_p799580910on_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,P),Q),R) = hAPP_o356497025on_com(hAPP_p1086945780on_com(P,R),hAPP_p799580910on_com(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [P,Q,R] : hAPP_com_bool(hAPP_H313059897m_bool(hAPP_f235185669m_bool(cOMBC_114640782e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_c1311333443e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____uwgpyvfjxg__O,axiom,
! [P,Q,R] : hAPP_p1751618853_state(hAPP_f1377420673_state(cOMBB_271860050_pname(P),Q),R) = hAPP_c1455475371_state(P,hAPP_pname_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,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__Ocom_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool__015,axiom,
! [P,Q,R] : hAPP_c1396316405m_bool(hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,P),Q),R) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_,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__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_p606792009e_bool(hAPP_f1720171569e_bool(cOMBC_1952686190e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H1776011827e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016,axiom,
! [P,Q,R] : hAPP_f1476298914l_bool(hAPP_f143162813l_bool(cOMBB_2095475776e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017,axiom,
! [P,Q,R] : hAPP_f759274231e_bool(hAPP_f1385420507e_bool(cOMBB_598082538e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_018,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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____uwg,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1378282496l_bool(hAPP_b167205134l_bool(cOMBK_293339231e_bool,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__fun_Itc__Opt,axiom,
! [P,Q,R] : hAPP_p558118546m_bool(hAPP_f919496731m_bool(cOMBB_418828222_pname(P),Q),R) = hAPP_o1684370239m_bool(P,hAPP_p799580910on_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
! [P,Q,R] : hAPP_f1378282496l_bool(hAPP_f734420447l_bool(cOMBB_1686148692e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1378282496l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_019,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_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,axiom,
! [P,Q,R] : hAPP_f1378282496l_bool(hAPP_f734420447l_bool(hAPP_f524831474l_bool(cOMBS_1162100051l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f2067558332l_bool(P,R),hAPP_f1378282496l_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_f1083669085e_bool(hAPP_f568104217e_bool(cOMBC_1757633998l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_p1235466077l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___020,axiom,
! [P,Q,R] : hAPP_H242767318e_bool(hAPP_f360545851e_bool(hAPP_f591683433e_bool(cOMBC_1984545208l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H358531139l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [P,Q,R] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,P),Q),R) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_,axiom,
! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_H358531139l_bool(hAPP_f1186253673l_bool(cOMBC_1836455480e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_f360545851e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,axiom,
! [P,Q,R] : hAPP_f1378282496l_bool(hAPP_p1235466077l_bool(hAPP_f780571929l_bool(cOMBC_1558112230e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f1083669085e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_021,axiom,
! [P,Q,R] : hAPP_H1776011827e_bool(hAPP_f777604691e_bool(cOMBB_1365368614_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H1193503499_pname(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_022,axiom,
! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [P,Q,R] : hAPP_p338031245l_bool(hAPP_f567934427l_bool(cOMBB_408569982_pname(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [P,Q,R] : hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023,axiom,
! [P,Q,R] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_024,axiom,
! [P,Q,R] : hAPP_s336103912e_bool(hAPP_f249262236e_bool(cOMBB_1476898461_state(P),Q),R) = hAPP_f1863945078e_bool(P,hAPP_s1806633685e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__,axiom,
! [P,Q,R] : hAPP_s1806633685e_bool(hAPP_f1935169308e_bool(cOMBB_1036740637_state(P),Q),R) = hAPP_f1012183542e_bool(P,hAPP_s336103912e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J__025,axiom,
! [P,Q,R] : hAPP_p1086945780on_com(hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,P),Q),R) = hAPP_o334540577on_com(hAPP_p1164893188on_com(P,R),hAPP_p799580910on_com(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___026,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_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg_,axiom,
! [P,Q,R] : hAPP_p1751618853_state(hAPP_f1343550633_state(hAPP_f799842582_state(cOMBS_853737105_state,P),Q),R) = hAPP_H574424047_state(hAPP_p1947457250_state(P,R),hAPP_p1751618853_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_027,axiom,
! [P,Q,R] : hAPP_f2067558332l_bool(hAPP_f118042163l_bool(cOMBB_1749019442e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1378282496l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [P,Q,R] : hAPP_c566651504m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(P),Q),R) = hAPP_f1120618594m_bool(P,hAPP_c1396316405m_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_028,axiom,
! [P,Q,R] : hAPP_f1083669085e_bool(hAPP_f700046015e_bool(cOMBB_1400714760e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f88366945_pname(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_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
! [P,Q,R] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H,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_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_029,axiom,
! [P,Q,R] : hAPP_p905327722e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(P),Q),R) = hAPP_f1388330588e_bool(P,hAPP_p61793385e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Option__Ooption_Itc__Com_,axiom,
! [P,Q,R] : hAPP_p1164893188on_com(hAPP_f755519727on_com(cOMBB_1394247784_pname(P),Q),R) = hAPP_b1679505845on_com(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_c1311333443e_bool(hAPP_f475997903e_bool(cOMBB_1327031172ol_com(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_c1455475371_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I,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___030,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_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_031,axiom,
! [P,Q,R] : hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(hAPP_f1463049441l_bool(cOMBC_754402940e_bool,P),Q),R) = hAPP_H242767318e_bool(hAPP_f806699093e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___032,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__Opname_Mtc__HOL__Obool_J_000tc__fun_It_033,axiom,
! [P,Q,R] : hAPP_H358531139l_bool(hAPP_f381060343l_bool(cOMBB_1631414076_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H1776011827e_bool(Q,R)) ).
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_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [P,Q,R] : hAPP_f1218207411_state(hAPP_f819036232_state(hAPP_f815143704_state(cOMBS_858986606_state,P),Q),R) = hAPP_f497755132_state(hAPP_f1867816801_state(P,R),hAPP_f887530048e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_034,axiom,
! [P,Q,R] : hAPP_f434788991l_bool(hAPP_f417341722l_bool(hAPP_f836143551l_bool(cOMBC_772615479l_bool,P),Q),R) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_035,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_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_036,axiom,
! [P,Q,R] : hAPP_f1378282496l_bool(hAPP_f849457489l_bool(hAPP_f1348212993l_bool(cOMBC_1350613978l_bool,P),Q),R) = hAPP_f1378282496l_bool(hAPP_f849457489l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___037,axiom,
! [P,Q,R] : hAPP_f360545851e_bool(hAPP_f2113567599e_bool(cOMBB_1724041344e_bool(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_f1218207411_state(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____uw_038,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_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
! [P,Q,R] : hAPP_f1867816801_state(hAPP_f240260249_state(hAPP_f578932784_state(cOMBS_384351451_state,P),Q),R) = hAPP_c27135337_state(hAPP_f2099268820_state(P,R),hAPP_f792846925ol_com(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__039,axiom,
! [P,Q,R] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(hAPP_f1477350485l_bool(cOMBC_694979519l_bool,P),Q),R) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___040,axiom,
! [P,Q,R] : hAPP_H216526335e_bool(hAPP_f596278895e_bool(cOMBB_1563888316_state(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_H574424047_state(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____uwgpyvfjxg__041,axiom,
! [P,Q,R] : hAPP_p1947457250_state(hAPP_f1655792756_state(hAPP_f2119427284_state(cOMBS_140201078_state,P),Q),R) = hAPP_H280516760_state(hAPP_p1159359355_state(P,R),hAPP_p1751618853_state(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_042,axiom,
! [P,Q,R] : hAPP_f1378282496l_bool(hAPP_f734420447l_bool(hAPP_f1236719585l_bool(cOMBC_1484018740l_bool,P),Q),R) = hAPP_f1410040974l_bool(hAPP_f631019661l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_043,axiom,
! [P,Q,R] : hAPP_p1235466077l_bool(hAPP_f1143533991l_bool(cOMBB_949755692_pname(P),Q),R) = hAPP_f849457489l_bool(P,hAPP_p606792009e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_044,axiom,
! [P,Q,R] : hAPP_f718417177_state(hAPP_f578501918_state(hAPP_f886846002_state(cOMBS_57685138_state,P),Q),R) = hAPP_f497755132_state(hAPP_f1554347387_state(P,R),hAPP_f1487042470e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___045,axiom,
! [P,Q,R] : hAPP_f806699093e_bool(hAPP_f610934515e_bool(cOMBB_1840094962e_bool(P),Q),R) = hAPP_H216526335e_bool(P,hAPP_f718417177_state(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___046,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__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____uwg,axiom,
! [P,Q,R] : hAPP_p1159359355_state(hAPP_f1836930278_state(cOMBB_143651633_pname(P),Q),R) = hAPP_b993469484_state(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__,axiom,
! [P,Q,R] : hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(hAPP_f1901243753l_bool(cOMBC_991209188l_bool,P),Q),R) = hAPP_f1410040974l_bool(hAPP_f1516997247l_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_047,axiom,
! [P,Q,R] : hAPP_f1554347387_state(hAPP_f824259881_state(hAPP_f37848848_state(cOMBS_1164062463_state,P),Q),R) = hAPP_c27135337_state(hAPP_f403544558_state(P,R),hAPP_f1547517799ol_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___048,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_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
! [P,Q,R] : hAPP_f1320879424l_bool(hAPP_f1149191722l_bool(cOMBB_631815671e_bool(P),Q),R) = hAPP_f230953622l_bool(P,hAPP_f434788991l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_049,axiom,
! [P,Q,R] : hAPP_H2039996199l_bool(hAPP_f1191357267l_bool(cOMBB_639263758_state(P),Q),R) = hAPP_f849457489l_bool(P,hAPP_H216526335e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_050,axiom,
! [P,Q,R] : hAPP_f806699093e_bool(hAPP_f1794460506e_bool(hAPP_f2061951445e_bool(cOMBC_528733435e_bool,P),Q),R) = hAPP_f806699093e_bool(hAPP_f1794460506e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_Itc__Com___051,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__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___052,axiom,
! [P,Q,R] : hAPP_f2099268820_state(hAPP_f1633046421_state(cOMBB_1794358604e_bool(P),Q),R) = hAPP_f274181323_state(P,hAPP_f887530048e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_053,axiom,
! [P,Q,R] : hAPP_f849457489l_bool(hAPP_f2059879088l_bool(hAPP_f476955937l_bool(cOMBC_1639502213l_bool,P),Q),R) = hAPP_f734420447l_bool(hAPP_f1472090462l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___054,axiom,
! [P,Q,R] : hAPP_f403544558_state(hAPP_f250550847_state(cOMBB_2049797414e_bool(P),Q),R) = hAPP_f274181323_state(P,hAPP_f1487042470e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__Otriple_I_055,axiom,
! [P,Q,R] : hAPP_H1902130436e_bool(hAPP_f241329646e_bool(cOMBB_604855927_state(P),Q),R) = hAPP_f1794460506e_bool(P,hAPP_H216526335e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg___056,axiom,
! [P,Q,R] : hAPP_f734420447l_bool(hAPP_f1847120l_bool(hAPP_f1573805579l_bool(cOMBC_1377256501l_bool,P),Q),R) = hAPP_f734420447l_bool(hAPP_f1847120l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____uwgpyvfjxg__,axiom,
! [P,Q,R] : hAPP_f1472090462l_bool(hAPP_f1316144452l_bool(cOMBB_494346593e_bool(P),Q),R) = hAPP_f1847120l_bool(P,hAPP_f849457489l_bool(Q,R)) ).
%----Conjectures (8)
fof(conj_0,hypothesis,
hBOOL(hoare_1795711768gleton) ).
fof(conj_1,hypothesis,
hBOOL(wT_bodies) ).
fof(conj_2,hypothesis,
hBOOL(hAPP_f1378282496l_bool(finite694102371_state,fa)) ).
fof(conj_3,hypothesis,
~ hBOOL(hAPP_f1378282496l_bool(hAPP_H2039996199l_bool(member1667945571_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,y)),fa)) ).
fof(conj_4,hypothesis,
hBOOL(hAPP_f1378282496l_bool(hAPP_f849457489l_bool(ord_le1449778818e_bool,fa),hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),dom_pname_com(body)))) ).
fof(conj_5,hypothesis,
hAPP_p799580910on_com(body,pn) = hAPP_com_option_com(some_com,y) ).
fof(conj_6,hypothesis,
hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),fa)) ).
fof(conj_7,conjecture,
hBOOL(hAPP_f1378282496l_bool(hoare_512830354_state(hAPP_f360545851e_bool(image_185131637_state(hAPP_f1377420673_state(cOMBB_271860050_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f806699093e_bool(hAPP_H1902130436e_bool(insert1744391420_state,hAPP_c1455475371_state(hoare_Mirabelle_MGT,y)),bot_bo784226126e_bool))) ).
%------------------------------------------------------------------------------