TPTP Problem File: SWW474+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW474+2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 440, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : hoare_500_fofmg_l440 [Bla11]
% Status : Theorem
% Rating : 0.39 v8.2.0, 0.36 v8.1.0, 0.42 v7.5.0, 0.44 v7.4.0, 0.37 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.30 v7.0.0, 0.43 v6.4.0, 0.42 v6.2.0, 0.52 v6.1.0, 0.63 v6.0.0, 0.57 v5.5.0, 0.63 v5.4.0, 0.71 v5.3.0
% Syntax : Number of formulae : 868 ( 313 unt; 0 def)
% Number of atoms : 2187 ( 620 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1559 ( 240 ~; 51 |; 169 &)
% ( 116 <=>; 983 =>; 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 : 361 ( 361 usr; 113 con; 0-2 aty)
% Number of variables : 2223 (2175 !; 48 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:54:54
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (54)
fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname,axiom,
! [B_1_1] :
( is_bool(B_1_1)
=> is_fun_pname_bool(cOMBK_bool_pname(B_1_1)) ) ).
fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1] :
( is_bool(B_1_1)
=> is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1)) ) ).
fof(gsy_c_Com_OWT__bodies,hypothesis,
is_bool(wT_bodies) ).
fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,axiom,
is_fun1661590463l_bool(finite_finite_pname) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] : is_bool(finite1282449217_pname(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple,axiom,
! [B_1_1,B_2_1] : is_bool(finite774711482_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____ddpglwnxwg,axiom,
! [B_1_1,B_2_1] : is_bool(finite132673334e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] : is_bool(finite89670078_pname(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O,axiom,
! [B_1_1,B_2_1] : is_bool(finite506823037_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____ddpg,axiom,
! [B_1_1,B_2_1] : is_bool(finite959343283e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
is_pname(undefined_pname(pname)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ).
fof(gsy_c_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__ddpglwnxwg_Ostate__not__singleton,hypothesis,
is_bool(hoare_298929751gleton) ).
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_Option_Ooption_OSome_000tc__Com__Opname,axiom,
! [B_1_1] :
( is_pname(B_1_1)
=> is_option_pname(some_pname(B_1_1)) ) ).
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_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
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__Opname_000tc__Com__Opname,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_pname(hAPP_pname_pname(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( ( is_fun_pname_bool(B_1_1)
& is_pname(B_2_1) )
=> is_bool(hAPP_pname_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] :
( is_pname(B_2_1)
=> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__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__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_H1344248906_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_001,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_002,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H1632039476e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0_003,axiom,
! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_H737849090l_bool(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__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__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O,axiom,
! [B_1_1,B_2_1] : is_pname(hAPP_f1008690464_pname(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_004,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_005,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f1745235422e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O_006,axiom,
! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_f748867288l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
! [B_1_1,B_2_1] :
( is_fun1661590463l_bool(B_2_1)
=> is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_007,axiom,
! [B_1_1,B_2_1] :
( is_fun1661590463l_bool(B_2_1)
=> is_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_008,axiom,
! [B_1_1,B_2_1] :
( is_fun1661590463l_bool(B_2_1)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f239102607l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_It_009,axiom,
! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f280588268e_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____ddpglwnxwg__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1904669497l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_pn,hypothesis,
is_pname(pn) ).
%----Relevant facts (699)
fof(fact_0_empty,axiom,
! [G_1] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool)) ).
fof(fact_1_asm,axiom,
! [Ts,G_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),G_1))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) ).
fof(fact_2_weaken,axiom,
! [Ts,G_1,Ts_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ts_1))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) ) ).
fof(fact_3_thin,axiom,
! [G_1,G_2,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G_2),G_1))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) ) ).
fof(fact_4_cut,axiom,
! [G_1,G_2,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) ) ).
fof(fact_5_hoare__derivs_Oinsert,axiom,
! [Ts,G_1,T] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) ) ) ).
fof(fact_6_derivs__insertD,axiom,
! [G_1,T,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool)))
& hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) ) ).
fof(fact_7_MGT__BodyN,axiom,
! [Pn_1,G_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo1055319631e_bool))) ) ).
fof(fact_8_finite__Collect__subsets,axiom,
! [A_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,hAPP_f783502055l_bool(collec1613912337l_bool,hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,ord_le675606854l_bool),A_1)))) ) ).
fof(fact_9_finite__Collect__subsets,axiom,
! [A_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> hBOOL(hAPP_f1904669497l_bool(finite1586217244l_bool,hAPP_f1987093l_bool(collec1277803610l_bool,hAPP_f1269496639l_bool(hAPP_f1508257257l_bool(cOMBC_1084925030l_bool,ord_le1076702565l_bool),A_1)))) ) ).
fof(fact_10_finite__Collect__subsets,axiom,
! [A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,ord_le1720872323e_bool),A_1)))) ) ).
fof(fact_11_finite__Collect__subsets,axiom,
! [A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,ord_le313189616e_bool),A_1)))) ) ).
fof(fact_12_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f748867288l_bool(image_1259634916e_bool(H),Fa))) ) ).
fof(fact_13_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f854625363l_bool(image_277167759e_bool(H),Fa))) ) ).
fof(fact_14_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(H),Fa))) ) ).
fof(fact_15_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1874607724l_bool(image_505480954e_bool(H),Fa))) ) ).
fof(fact_16_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f780887186e_bool(image_936554724_state(H),Fa))) ) ).
fof(fact_17_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f772567431e_bool(image_774712299_state(H),Fa))) ) ).
fof(fact_18_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(H),Fa))) ) ).
fof(fact_19_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f280588268e_bool(image_636285904_pname(H),Fa))) ) ).
fof(fact_20_finite__imageI,axiom,
! [H,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(H),Fa))) ) ).
fof(fact_21_empty__subsetI,axiom,
! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1)) ).
fof(fact_22_empty__subsetI,axiom,
! [A_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A_1)) ).
fof(fact_23_finite_OinsertI,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1))) ) ).
fof(fact_24_finite_OinsertI,axiom,
! [A,A_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),A_1))) ) ).
fof(fact_25_finite_OinsertI,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1))) ) ).
fof(fact_26_finite_OinsertI,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))) ) ).
fof(fact_27_finite_OemptyI,axiom,
hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)) ).
fof(fact_28_finite_OemptyI,axiom,
hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,bot_bo1325454745l_bool)) ).
fof(fact_29_finite_OemptyI,axiom,
hBOOL(hAPP_f1760790145l_bool(finite784854244_state,bot_bo1055319631e_bool)) ).
fof(fact_30_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).
fof(fact_31_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_32_finite__Collect__conjI,axiom,
! [Q_1,P_1] :
( ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)))
| hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) )
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),P_1)),Q_1)))) ) ).
fof(fact_33_finite__Collect__conjI,axiom,
! [Q_1,P_1] :
( ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,P_1)))
| hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,Q_1))) )
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),P_1)),Q_1)))) ) ).
fof(fact_34_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_35_image__constant__conv,axiom,
! [C,A_1] :
( ( A_1 = bot_bo1055319631e_bool
=> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = bot_bo844097828e_bool )
& ( A_1 != bot_bo1055319631e_bool
=> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ).
fof(fact_36_image__constant__conv,axiom,
! [C,A_1] :
( is_fun_pname_bool(A_1)
=> ( ( A_1 = bot_bo844097828e_bool
=> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = bot_bo1055319631e_bool )
& ( A_1 != bot_bo844097828e_bool
=> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool) ) ) ) ).
fof(fact_37_image__constant,axiom,
! [C,X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hAPP_f1745235422e_bool(image_1925245338_pname(cOMBK_588224941_state(C)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ).
fof(fact_38_image__constant,axiom,
! [C,X_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hAPP_f631639356e_bool(image_275883510_state(cOMBK_90103121_pname(C)),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),bot_bo1055319631e_bool) ) ).
fof(fact_39_insert__dom,axiom,
! [F,X_1,Y_1] :
( hAPP_p799580910on_com(F,X_1) = some_com(Y_1)
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F) ) ).
fof(fact_40_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).
fof(fact_41_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f854625363l_bool(image_277167759e_bool(F),A_1)))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) ) ) ).
fof(fact_42_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_43_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).
fof(fact_44_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1)))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B)) ) ) ).
fof(fact_45_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_46_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f780887186e_bool(image_936554724_state(F),A_1)))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) ) ) ).
fof(fact_47_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f772567431e_bool(image_774712299_state(F),A_1)))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) ) ) ).
fof(fact_48_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_49_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f280588268e_bool(image_636285904_pname(F),A_1)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
fof(fact_50_finite__surj,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B)) ) ) ).
fof(fact_51_subset__singletonD,axiom,
! [A_1,X_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))
=> ( A_1 = bot_bo844097828e_bool
| A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ) ) ) ).
fof(fact_52_subset__singletonD,axiom,
! [A_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))
=> ( A_1 = bot_bo1055319631e_bool
| A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool) ) ) ).
fof(fact_53_MGF,axiom,
! [C] :
( hBOOL(hoare_298929751gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) ) ).
fof(fact_54_emptyE,axiom,
! [A] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),bot_bo844097828e_bool)) ).
fof(fact_55_emptyE,axiom,
! [A] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),bot_bo1055319631e_bool)) ).
fof(fact_56_insertCI,axiom,
! [B_1,A,B] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B))
=> A = B_1 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).
fof(fact_57_insertCI,axiom,
! [B_1,A,B] :
( ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B))
=> A = B_1 )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))) ) ).
fof(fact_58_insertE,axiom,
! [A,B_1,A_1] :
( ( is_pname(A)
& is_pname(B_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))
=> ( A != B_1
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) ) ) ) ).
fof(fact_59_insertE,axiom,
! [A,B_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),A_1)))
=> ( A != B_1
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) ) ) ).
fof(fact_60_equalityI,axiom,
! [A_1,B] :
( ( is_fun_pname_bool(A_1)
& is_fun_pname_bool(B) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
=> A_1 = B ) ) ) ).
fof(fact_61_equalityI,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1))
=> A_1 = B ) ) ).
fof(fact_62_subsetD,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_63_subsetD,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ) ).
fof(fact_64_image__eqI,axiom,
! [A_1,B_1,F,X_1] :
( B_1 = hAPP_H1344248906_pname(F,X_1)
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) ) ) ).
fof(fact_65_image__eqI,axiom,
! [A_1,B_1,F,X_1] :
( B_1 = hAPP_p1842370726_state(F,X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) ) ) ).
fof(fact_66_equals0D,axiom,
! [A,A_1] :
( A_1 = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) ) ).
fof(fact_67_equals0D,axiom,
! [A,A_1] :
( A_1 = bot_bo1055319631e_bool
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) ) ).
fof(fact_68_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_69_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_70_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f1970439265l_bool(collec111528142e_bool,P_1) = bot_bo1325454745l_bool
<=> ! [X_2] : ~ hBOOL(hAPP_f1760790145l_bool(P_1,X_2)) ) ).
fof(fact_71_Collect__empty__eq,axiom,
! [P_1] :
( hAPP_f921536533e_bool(collec727977250_state,P_1) = bot_bo1055319631e_bool
<=> ! [X_2] : ~ hBOOL(hAPP_H513860823e_bool(P_1,X_2)) ) ).
fof(fact_72_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool)) ).
fof(fact_73_empty__iff,axiom,
! [C] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),bot_bo1055319631e_bool)) ).
fof(fact_74_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_75_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_76_empty__Collect__eq,axiom,
! [P_1] :
( bot_bo1325454745l_bool = hAPP_f1970439265l_bool(collec111528142e_bool,P_1)
<=> ! [X_2] : ~ hBOOL(hAPP_f1760790145l_bool(P_1,X_2)) ) ).
fof(fact_77_empty__Collect__eq,axiom,
! [P_1] :
( bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,P_1)
<=> ! [X_2] : ~ hBOOL(hAPP_H513860823e_bool(P_1,X_2)) ) ).
fof(fact_78_ex__in__conv,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) )
<=> A_1 != bot_bo844097828e_bool ) ) ).
fof(fact_79_ex__in__conv,axiom,
! [A_1] :
( ? [X_2] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
<=> A_1 != bot_bo1055319631e_bool ) ).
fof(fact_80_all__not__in__conv,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( ! [X_2] :
( is_pname(X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) )
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_81_all__not__in__conv,axiom,
! [A_1] :
( ! [X_2] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
<=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_82_empty__def,axiom,
bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,cOMBK_bool_pname(fFalse)) ).
fof(fact_83_empty__def,axiom,
bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,cOMBK_1857069011e_bool(fFalse)) ).
fof(fact_84_empty__def,axiom,
bot_bo1325454745l_bool = hAPP_f1970439265l_bool(collec111528142e_bool,cOMBK_564432736e_bool(fFalse)) ).
fof(fact_85_empty__def,axiom,
bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)) ).
fof(fact_86_insert__absorb,axiom,
! [A,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = A_1 ) ) ).
fof(fact_87_insert__absorb,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = A_1 ) ).
fof(fact_88_insertI2,axiom,
! [B_1,A,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).
fof(fact_89_insertI2,axiom,
! [B_1,A,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))) ) ).
fof(fact_90_insert__ident,axiom,
! [B,X_1,A_1] :
( ( is_fun_pname_bool(B)
& is_fun_pname_bool(A_1) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)
<=> A_1 = B ) ) ) ) ).
fof(fact_91_insert__ident,axiom,
! [B,X_1,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))
=> ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B)
<=> A_1 = B ) ) ) ).
fof(fact_92_insert__code,axiom,
! [Y_1,A_1,X_1] :
( ( is_pname(Y_1)
& is_pname(X_1) )
=> ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1),X_1))
<=> ( Y_1 = X_1
| hBOOL(hAPP_pname_bool(A_1,X_1)) ) ) ) ).
fof(fact_93_insert__code,axiom,
! [Y_1,A_1,X_1] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A_1),X_1))
<=> ( Y_1 = X_1
| hBOOL(hAPP_H513860823e_bool(A_1,X_1)) ) ) ).
fof(fact_94_insert__iff,axiom,
! [A,B_1,A_1] :
( ( is_pname(A)
& is_pname(B_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))
<=> ( A = B_1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) ) ) ) ).
fof(fact_95_insert__iff,axiom,
! [A,B_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),A_1)))
<=> ( A = B_1
| hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) ) ) ).
fof(fact_96_insert__commute,axiom,
! [X_1,Y_1,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) ).
fof(fact_97_insert__commute,axiom,
! [X_1,Y_1,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) ).
fof(fact_98_insert__absorb2,axiom,
! [X_1,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1) ).
fof(fact_99_insert__absorb2,axiom,
! [X_1,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1) ).
fof(fact_100_insert__Collect,axiom,
! [A,P_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),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)))),P_1)) ).
fof(fact_101_insert__Collect,axiom,
! [A,P_1] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),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)))),P_1)) ).
fof(fact_102_insert__Collect,axiom,
! [A,P_1] : hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),hAPP_f1970439265l_bool(collec111528142e_bool,P_1)) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fimplies),hAPP_f1970439265l_bool(cOMBB_1957242197e_bool(fNot),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A)))),P_1)) ).
fof(fact_103_insert__Collect,axiom,
! [A,P_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,P_1)) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A)))),P_1)) ).
fof(fact_104_insert__compr,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),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))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).
fof(fact_105_insert__compr,axiom,
! [A,B] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_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_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).
fof(fact_106_insert__compr,axiom,
! [A,B] : hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B))) ).
fof(fact_107_insert__compr,axiom,
! [A,B] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B))) ).
fof(fact_108_insertI1,axiom,
! [A,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) ).
fof(fact_109_insertI1,axiom,
! [A,B] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))) ).
fof(fact_110_equalityE,axiom,
! [A_1,B] :
( A_1 = B
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) ) ) ).
fof(fact_111_equalityE,axiom,
! [A_1,B] :
( A_1 = B
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) ) ) ).
fof(fact_112_subset__trans,axiom,
! [C_1,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),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_1),C_1)) ) ) ).
fof(fact_113_subset__trans,axiom,
! [C_1,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),C_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1)) ) ) ).
fof(fact_114_set__mp,axiom,
! [X_1,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).
fof(fact_115_set__mp,axiom,
! [X_1,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) ) ) ).
fof(fact_116_set__rev__mp,axiom,
! [B,X_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).
fof(fact_117_set__rev__mp,axiom,
! [B,X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) ) ) ).
fof(fact_118_in__mono,axiom,
! [X_1,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).
fof(fact_119_in__mono,axiom,
! [X_1,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B)) ) ) ).
fof(fact_120_equalityD2,axiom,
! [A_1,B] :
( A_1 = B
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) ) ).
fof(fact_121_equalityD2,axiom,
! [A_1,B] :
( A_1 = B
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) ) ).
fof(fact_122_equalityD1,axiom,
! [A_1,B] :
( A_1 = B
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ).
fof(fact_123_equalityD1,axiom,
! [A_1,B] :
( A_1 = B
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) ) ).
fof(fact_124_set__eq__subset,axiom,
! [A_1,B] :
( ( is_fun_pname_bool(A_1)
& is_fun_pname_bool(B) )
=> ( A_1 = B
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) ) ) ) ).
fof(fact_125_set__eq__subset,axiom,
! [A_1,B] :
( A_1 = B
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1)) ) ) ).
fof(fact_126_subset__refl,axiom,
! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1)) ).
fof(fact_127_subset__refl,axiom,
! [A_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),A_1)) ).
fof(fact_128_rev__image__eqI,axiom,
! [B_1,F,X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ( B_1 = hAPP_H1344248906_pname(F,X_1)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) ) ) ).
fof(fact_129_rev__image__eqI,axiom,
! [B_1,F,X_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ( B_1 = hAPP_p1842370726_state(F,X_1)
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) ) ) ).
fof(fact_130_imageI,axiom,
! [F,X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1344248906_pname(F,X_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1))) ) ).
fof(fact_131_imageI,axiom,
! [F,X_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F,X_1)),hAPP_f631639356e_bool(image_275883510_state(F),A_1))) ) ).
fof(fact_132_image__iff,axiom,
! [Z,F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Z),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))
<=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
& Z = hAPP_p1842370726_state(F,X_2) ) ) ).
fof(fact_133_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_134_finite__Collect__disjI,axiom,
! [P_1,Q_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)))
& hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) ) ) ).
fof(fact_135_finite__Collect__disjI,axiom,
! [P_1,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,P_1)))
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,Q_1))) ) ) ).
fof(fact_136_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_137_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_138_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_139_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),Xa) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),X_2))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),Xa))) ).
fof(fact_140_insert__compr__raw,axiom,
! [X_2,Xa] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),Xa) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),X_2))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),Xa))) ).
fof(fact_141_singleton__inject,axiom,
! [A,B_1] :
( ( is_pname(A)
& is_pname(B_1) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)
=> A = B_1 ) ) ).
fof(fact_142_singleton__inject,axiom,
! [A,B_1] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),bot_bo1055319631e_bool)
=> A = B_1 ) ).
fof(fact_143_singletonE,axiom,
! [B_1,A] :
( ( is_pname(B_1)
& is_pname(A) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)))
=> B_1 = A ) ) ).
fof(fact_144_singletonE,axiom,
! [B_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))
=> B_1 = A ) ).
fof(fact_145_doubleton__eq__iff,axiom,
! [A,B_1,C,D] :
( ( is_pname(A)
& is_pname(B_1)
& is_pname(C)
& is_pname(D) )
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),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),bot_bo844097828e_bool))
<=> ( ( A = C
& B_1 = D )
| ( A = D
& B_1 = C ) ) ) ) ).
fof(fact_146_doubleton__eq__iff,axiom,
! [A,B_1,C,D] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,C),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D),bot_bo1055319631e_bool))
<=> ( ( A = C
& B_1 = D )
| ( A = D
& B_1 = C ) ) ) ).
fof(fact_147_singleton__iff,axiom,
! [B_1,A] :
( ( is_pname(B_1)
& is_pname(A) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)))
<=> B_1 = A ) ) ).
fof(fact_148_singleton__iff,axiom,
! [B_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))
<=> B_1 = A ) ).
fof(fact_149_insert__not__empty,axiom,
! [A,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) != bot_bo844097828e_bool ).
fof(fact_150_insert__not__empty,axiom,
! [A,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) != bot_bo1055319631e_bool ).
fof(fact_151_empty__not__insert,axiom,
! [A,A_1] : bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) ).
fof(fact_152_empty__not__insert,axiom,
! [A,A_1] : bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) ).
fof(fact_153_finite__insert,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ).
fof(fact_154_finite__insert,axiom,
! [A,A_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),A_1)))
<=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) ) ).
fof(fact_155_finite__insert,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ).
fof(fact_156_finite__insert,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)))
<=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) ) ).
fof(fact_157_subset__empty,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool))
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_158_subset__empty,axiom,
! [A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),bot_bo1055319631e_bool))
<=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_159_image__is__empty,axiom,
! [F,A_1] :
( hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) = bot_bo844097828e_bool
<=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_160_image__is__empty,axiom,
! [F,A_1] :
( is_fun_pname_bool(A_1)
=> ( hAPP_f631639356e_bool(image_275883510_state(F),A_1) = bot_bo1055319631e_bool
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_161_image__empty,axiom,
! [F] : hAPP_f1745235422e_bool(image_1925245338_pname(F),bot_bo1055319631e_bool) = bot_bo844097828e_bool ).
fof(fact_162_image__empty,axiom,
! [F] : hAPP_f631639356e_bool(image_275883510_state(F),bot_bo844097828e_bool) = bot_bo1055319631e_bool ).
fof(fact_163_empty__is__image,axiom,
! [F,A_1] :
( bot_bo844097828e_bool = hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)
<=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_164_empty__is__image,axiom,
! [F,A_1] :
( is_fun_pname_bool(A_1)
=> ( bot_bo1055319631e_bool = hAPP_f631639356e_bool(image_275883510_state(F),A_1)
<=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_165_finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ) ).
fof(fact_166_finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) ) ) ).
fof(fact_167_finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) ) ) ).
fof(fact_168_finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ) ).
fof(fact_169_rev__finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ) ).
fof(fact_170_rev__finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1)) ) ) ).
fof(fact_171_rev__finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) ) ) ).
fof(fact_172_rev__finite__subset,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ) ).
fof(fact_173_insert__mono,axiom,
! [A,C_1,D_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),D_1))) ) ).
fof(fact_174_insert__mono,axiom,
! [A,C_1,D_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),D_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),C_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),D_1))) ) ).
fof(fact_175_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
<=> hBOOL(hAPP_pname_bool(A_1,X_1)) ) ).
fof(fact_176_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
<=> hBOOL(hAPP_H513860823e_bool(A_1,X_1)) ) ).
fof(fact_177_Collect__def,axiom,
! [P_1] : hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ).
fof(fact_178_Collect__def,axiom,
! [P_1] :
( is_fun_pname_bool(P_1)
=> hAPP_f759274231e_bool(collect_pname,P_1) = P_1 ) ).
fof(fact_179_Collect__def,axiom,
! [P_1] :
( is_fun1661590463l_bool(P_1)
=> hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1 ) ).
fof(fact_180_Collect__def,axiom,
! [P_1] : hAPP_f1970439265l_bool(collec111528142e_bool,P_1) = P_1 ).
fof(fact_181_subset__insertI2,axiom,
! [B_1,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).
fof(fact_182_subset__insertI2,axiom,
! [B_1,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B_1),B))) ) ).
fof(fact_183_subset__insert,axiom,
! [B,X_1,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ) ).
fof(fact_184_subset__insert,axiom,
! [B,X_1,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B)))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) ) ) ).
fof(fact_185_insert__subset,axiom,
! [X_1,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),B))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ) ).
fof(fact_186_insert__subset,axiom,
! [X_1,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)),B))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) ) ) ).
fof(fact_187_subset__insertI,axiom,
! [B,A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) ).
fof(fact_188_subset__insertI,axiom,
! [B,A] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B))) ).
fof(fact_189_insert__image,axiom,
! [F,X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1344248906_pname(F,X_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)) = hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1) ) ).
fof(fact_190_insert__image,axiom,
! [F,X_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F,X_1)),hAPP_f631639356e_bool(image_275883510_state(F),A_1)) = hAPP_f631639356e_bool(image_275883510_state(F),A_1) ) ).
fof(fact_191_image__insert,axiom,
! [F,A,B] : hAPP_f1745235422e_bool(image_1925245338_pname(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1344248906_pname(F,A)),hAPP_f1745235422e_bool(image_1925245338_pname(F),B)) ).
fof(fact_192_image__insert,axiom,
! [F,A,B] : hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_p1842370726_state(F,A)),hAPP_f631639356e_bool(image_275883510_state(F),B)) ).
fof(fact_193_image__mono,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)),hAPP_f1745235422e_bool(image_1925245338_pname(F),B))) ) ).
fof(fact_194_image__mono,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B))) ) ).
fof(fact_195_subset__image__iff,axiom,
! [B,F,A_1] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))
<=> ? [AA] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,AA),A_1))
& B = hAPP_f1745235422e_bool(image_1925245338_pname(F),AA) ) ) ) ).
fof(fact_196_subset__image__iff,axiom,
! [B,F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))
<=> ? [AA] :
( is_fun_pname_bool(AA)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1))
& B = hAPP_f631639356e_bool(image_275883510_state(F),AA) ) ) ).
fof(fact_197_domI,axiom,
! [M_1,A,B_1] :
( hAPP_p799580910on_com(M_1,A) = some_com(B_1)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1))) ) ).
fof(fact_198_Collect__conv__if,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_pname_bool(P_1,A))
=> 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))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(P_1,A))
=> 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))),P_1)) = bot_bo844097828e_bool ) ) ).
fof(fact_199_Collect__conv__if,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_f1664156314l_bool(P_1,A))
=> 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))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A))
=> 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))),P_1)) = bot_bo1649642514l_bool ) ) ).
fof(fact_200_Collect__conv__if,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_f1760790145l_bool(P_1,A))
=> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),P_1)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(P_1,A))
=> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),P_1)) = bot_bo1325454745l_bool ) ) ).
fof(fact_201_Collect__conv__if,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_H513860823e_bool(P_1,A))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),P_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) )
& ( ~ hBOOL(hAPP_H513860823e_bool(P_1,A))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),P_1)) = bot_bo1055319631e_bool ) ) ).
fof(fact_202_Collect__conv__if2,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_pname_bool(P_1,A))
=> 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))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(P_1,A))
=> 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))),P_1)) = bot_bo844097828e_bool ) ) ).
fof(fact_203_Collect__conv__if2,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_f1664156314l_bool(P_1,A))
=> 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))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A))
=> 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))),P_1)) = bot_bo1649642514l_bool ) ) ).
fof(fact_204_Collect__conv__if2,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_f1760790145l_bool(P_1,A))
=> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(fequal1746921144e_bool,A))),P_1)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(P_1,A))
=> hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f854625363l_bool(fequal1746921144e_bool,A))),P_1)) = bot_bo1325454745l_bool ) ) ).
fof(fact_205_Collect__conv__if2,axiom,
! [P_1,A] :
( ( hBOOL(hAPP_H513860823e_bool(P_1,A))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A))),P_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) )
& ( ~ hBOOL(hAPP_H513860823e_bool(P_1,A))
=> hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_H1645666623e_bool(fequal1531560888_state,A))),P_1)) = bot_bo1055319631e_bool ) ) ).
fof(fact_206_singleton__conv,axiom,
! [A] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) ).
fof(fact_207_singleton__conv,axiom,
! [A] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) ).
fof(fact_208_singleton__conv,axiom,
! [A] : hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool) ).
fof(fact_209_singleton__conv,axiom,
! [A] : hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) ).
fof(fact_210_singleton__conv2,axiom,
! [A] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) ).
fof(fact_211_singleton__conv2,axiom,
! [A] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) ).
fof(fact_212_singleton__conv2,axiom,
! [A] : hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(fequal1746921144e_bool,A)) = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),bot_bo1325454745l_bool) ).
fof(fact_213_singleton__conv2,axiom,
! [A] : hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(fequal1531560888_state,A)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) ).
fof(fact_214_MGF__lemma1,axiom,
! [C,G_1] :
( hBOOL(hoare_298929751gleton)
=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo1055319631e_bool))) ) )
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) ) ).
fof(fact_215_WT__bodiesD,axiom,
! [Pn,B_4] :
( hBOOL(wT_bodies)
=> ( hAPP_p799580910on_com(body,Pn) = some_com(B_4)
=> hBOOL(hAPP_com_bool(wt,B_4)) ) ) ).
fof(fact_216_imageE,axiom,
! [B_1,F,A_1] :
( is_pname(B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))
=> ~ ! [X_2] :
( B_1 = hAPP_H1344248906_pname(F,X_2)
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) ) ) ) ).
fof(fact_217_imageE,axiom,
! [B_1,F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_1),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))
=> ~ ! [X_2] :
( is_pname(X_2)
=> ( B_1 = hAPP_p1842370726_state(F,X_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) ) ) ) ).
fof(fact_218_finite__subset__induct,axiom,
! [P_1,A_1,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
=> ( ! [A_3,F_1] :
( ( is_fun_pname_bool(A_3)
& is_fun1661590463l_bool(F_1) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),A_1))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),F_1))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),F_1))) ) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_219_finite__subset__induct,axiom,
! [P_1,A_1,Fa] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,Fa),A_1))
=> ( hBOOL(hAPP_f239102607l_bool(P_1,bot_bo1325454745l_bool))
=> ( ! [A_3,F_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_3),A_1))
=> ( ~ hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,A_3),F_1))
=> ( hBOOL(hAPP_f239102607l_bool(P_1,F_1))
=> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A_3),F_1))) ) ) ) )
=> hBOOL(hAPP_f239102607l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_220_finite__subset__induct,axiom,
! [P_1,A_1,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
=> ( ! [A_3,F_1] :
( ( is_pname(A_3)
& is_fun_pname_bool(F_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),F_1))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_221_finite__subset__induct,axiom,
! [P_1,A_1,Fa] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Fa),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(P_1,bot_bo1055319631e_bool))
=> ( ! [A_3,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(P_1,F_1))
=> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),F_1))) ) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_222_WTs__elim__cases_I7_J,axiom,
! [P] :
( hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P)))
=> ~ ! [Y_2] : hAPP_p799580910on_com(body,P) != some_com(Y_2) ) ).
fof(fact_223_subsetI,axiom,
! [B,A_1] :
( ! [X_2] :
( is_pname(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),B)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ).
fof(fact_224_subsetI,axiom,
! [B,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B)) ) ).
fof(fact_225_finite__subset__image,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f780887186e_bool(image_936554724_state(F),A_1)))
=> ? [C_3] :
( is_fun1661590463l_bool(C_3)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
& B = hAPP_f780887186e_bool(image_936554724_state(F),C_3) ) ) ) ).
fof(fact_226_finite__subset__image,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f772567431e_bool(image_774712299_state(F),A_1)))
=> ? [C_3] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,C_3),A_1))
& hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,C_3))
& B = hAPP_f772567431e_bool(image_774712299_state(F),C_3) ) ) ) ).
fof(fact_227_finite__subset__image,axiom,
! [F,A_1,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_1)))
=> ? [C_3] :
( is_fun1661590463l_bool(C_3)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
& B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3) ) ) ) ) ).
fof(fact_228_finite__subset__image,axiom,
! [F,A_1,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_f280588268e_bool(image_636285904_pname(F),A_1)))
=> ? [C_3] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,C_3),A_1))
& hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,C_3))
& B = hAPP_f280588268e_bool(image_636285904_pname(F),C_3) ) ) ) ) ).
fof(fact_229_finite__subset__image,axiom,
! [F,A_1,B] :
( is_fun1661590463l_bool(B)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1)))
=> ? [C_3] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1))
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3))
& B = hAPP_f748867288l_bool(image_1259634916e_bool(F),C_3) ) ) ) ) ).
fof(fact_230_finite__subset__image,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f854625363l_bool(image_277167759e_bool(F),A_1)))
=> ? [C_3] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1))
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3))
& B = hAPP_f854625363l_bool(image_277167759e_bool(F),C_3) ) ) ) ).
fof(fact_231_finite__subset__image,axiom,
! [F,A_1,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_f1745235422e_bool(image_1925245338_pname(F),A_1)))
=> ? [C_3] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_3),A_1))
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,C_3))
& B = hAPP_f1745235422e_bool(image_1925245338_pname(F),C_3) ) ) ) ) ).
fof(fact_232_finite__subset__image,axiom,
! [F,A_1,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_1)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f434788991l_bool(image_47868345e_bool(F),C_3) ) ) ) ) ).
fof(fact_233_finite__subset__image,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f1874607724l_bool(image_505480954e_bool(F),C_3) ) ) ) ).
fof(fact_234_finite__subset__image,axiom,
! [F,A_1,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_1)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f759274231e_bool(image_pname_pname(F),C_3) ) ) ) ) ).
fof(fact_235_finite__subset__image,axiom,
! [F,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f631639356e_bool(image_275883510_state(F),A_1)))
=> ? [C_3] :
( is_fun_pname_bool(C_3)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
& B = hAPP_f631639356e_bool(image_275883510_state(F),C_3) ) ) ) ).
fof(fact_236_finite__dom__body,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))) ).
fof(fact_237_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_1] :
( ( is_fun_pname_bool(X_2)
& is_fun1661590463l_bool(F_1) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1))) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ).
fof(fact_238_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(P_1,bot_bo1325454745l_bool))
=> ( ! [X_2,F_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1))
=> ( ~ hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),F_1))
=> ( hBOOL(hAPP_f239102607l_bool(P_1,F_1))
=> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),F_1))) ) ) )
=> hBOOL(hAPP_f239102607l_bool(P_1,Fa)) ) ) ) ).
fof(fact_239_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_1] :
( ( is_pname(X_2)
& is_fun_pname_bool(F_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ).
fof(fact_240_finite__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(P_1,bot_bo1055319631e_bool))
=> ( ! [X_2,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(P_1,F_1))
=> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_1))) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(P_1,Fa)) ) ) ) ).
fof(fact_241_finite_Osimps,axiom,
! [A] :
( is_fun1661590463l_bool(A)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
<=> ( A = bot_bo1649642514l_bool
| ? [A_4,A_3] :
( is_fun1661590463l_bool(A_4)
& is_fun_pname_bool(A_3)
& A = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),A_4)
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4)) ) ) ) ) ).
fof(fact_242_finite_Osimps,axiom,
! [A] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A))
<=> ( A = bot_bo1325454745l_bool
| ? [A_4,A_3] :
( A = hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A_3),A_4)
& hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_4)) ) ) ) ).
fof(fact_243_finite_Osimps,axiom,
! [A] :
( is_fun_pname_bool(A)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
<=> ( A = bot_bo844097828e_bool
| ? [A_4,A_3] :
( is_fun_pname_bool(A_4)
& is_pname(A_3)
& A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),A_4)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4)) ) ) ) ) ).
fof(fact_244_finite_Osimps,axiom,
! [A] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
<=> ( A = bot_bo1055319631e_bool
| ? [A_4,A_3] :
( A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_4)
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_4)) ) ) ) ).
fof(fact_245_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A_1)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_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_246_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1874607724l_bool(image_505480954e_bool(F),A_1)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f1745235422e_bool(hAPP_f1558052123e_bool(cOMBC_2140141647l_bool,hAPP_f2081555625l_bool(cOMBB_44445098_pname(fequal1746921144e_bool),F)),hAPP_p877885514e_bool(F,X_2)))))) ) ) ) ).
fof(fact_247_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(image_650584225_state(F),A_1)))
=> ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
& ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,hAPP_f1844318385e_bool(cOMBB_291471741_state(fequal1531560888_state),F)),hAPP_H563960305_state(F,X_2)))))) ) ) ) ).
fof(fact_248_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f780887186e_bool(image_936554724_state(F),A_1)))
=> ? [X_2] :
( is_fun_pname_bool(X_2)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_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),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_H737849090l_bool(hAPP_f261382953l_bool(cOMBC_2107548985e_bool,hAPP_f547518321e_bool(cOMBB_1170234304e_bool(fequal1531560888_state),F)),hAPP_f1308959284_state(F,X_2)))))) ) ) ) ).
fof(fact_249_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f772567431e_bool(image_774712299_state(F),A_1)))
=> ? [X_2] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1))
& ~ hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_H248360617l_bool(hAPP_f492098723l_bool(cOMBC_1305755390e_bool,hAPP_f481659057e_bool(cOMBB_1099197107e_bool(fequal1531560888_state),F)),hAPP_f2143211163_state(F,X_2)))))) ) ) ) ).
fof(fact_250_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A_1)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X_2)))))) ) ) ) ).
fof(fact_251_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)))
=> ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
& ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_p877885514e_bool(hAPP_f294904177e_bool(cOMBC_725526061e_bool,hAPP_f833390165e_bool(cOMBB_1456120487_state(fequal_pname),F)),hAPP_H1344248906_pname(F,X_2)))))) ) ) ) ).
fof(fact_252_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A_1)))
=> ? [X_2] :
( is_fun_pname_bool(X_2)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_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),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),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_253_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f280588268e_bool(image_636285904_pname(F),A_1)))
=> ? [X_2] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1))
& ~ hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_p1617973726l_bool(hAPP_f2070658331l_bool(cOMBC_367297061e_bool,hAPP_f1973135743e_bool(cOMBB_1671808265e_bool(fequal_pname),F)),hAPP_f1008690464_pname(F,X_2)))))) ) ) ) ).
fof(fact_254_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f748867288l_bool(image_1259634916e_bool(F),A_1)))
=> ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
& ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f631639356e_bool(hAPP_f1721106985e_bool(cOMBC_498627897l_bool,hAPP_f376825399l_bool(cOMBB_1722165949_state(fequal533582459e_bool),F)),hAPP_H1632039476e_bool(F,X_2)))))) ) ) ) ).
fof(fact_255_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f854625363l_bool(image_277167759e_bool(F),A_1)))
=> ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
& ~ hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,hAPP_f1862834069l_bool(cOMBB_1239130257_state(fequal1746921144e_bool),F)),hAPP_H1645666623e_bool(F,X_2)))))) ) ) ) ).
fof(fact_256_pigeonhole__infinite,axiom,
! [F,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f631639356e_bool(image_275883510_state(F),A_1)))
=> ? [X_2] :
( is_pname(X_2)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,hAPP_f998786331e_bool(cOMBB_799949246_pname(fequal1531560888_state),F)),hAPP_p1842370726_state(F,X_2)))))) ) ) ) ).
fof(fact_257_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_258_MGT__Body,axiom,
! [G_1,Procs] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs)))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),Procs))) ) ) ).
fof(fact_259_domD,axiom,
! [A,M_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1)))
=> ? [B_3] : hAPP_p799580910on_com(M_1,A) = some_com(B_3) ) ).
fof(fact_260_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_261_the__elem__eq,axiom,
! [X_1] : hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = X_1 ).
fof(fact_262_image__subsetI,axiom,
! [F,B,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1344248906_pname(F,X_2)),B)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1745235422e_bool(image_1925245338_pname(F),A_1)),B)) ) ).
fof(fact_263_image__subsetI,axiom,
! [F,B,A_1] :
( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_p1842370726_state(F,X_2)),B)) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),B)) ) ).
fof(fact_264_order__refl,axiom,
! [X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1)) ).
fof(fact_265_order__refl,axiom,
! [X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),X_1)) ).
fof(fact_266_nonempty__iff,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( A_1 != bot_bo844097828e_bool
<=> ? [X_2,B_2] :
( is_pname(X_2)
& is_fun_pname_bool(B_2)
& A_1 = 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_267_nonempty__iff,axiom,
! [A_1] :
( A_1 != bot_bo1055319631e_bool
<=> ? [X_2,B_2] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_2)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_2)) ) ) ).
fof(fact_268_the_Osimps,axiom,
! [X_4] : hAPP_option_com_com(the_com,some_com(X_4)) = X_4 ).
fof(fact_269_weak__Body,axiom,
! [G_1,P_1,Pn_1,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1055319631e_bool))) ) ).
fof(fact_270_UnCI,axiom,
! [A_1,C,B] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ) ).
fof(fact_271_UnCI,axiom,
! [A_1,C,B] :
( ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) ) ).
fof(fact_272_UnE,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_273_UnE,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ) ).
fof(fact_274_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_275_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_276_Collect__disj__eq,axiom,
! [P_1,Q_1] : hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),P_1)),Q_1)) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1)) ).
fof(fact_277_Collect__disj__eq,axiom,
! [P_1,Q_1] : hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),P_1)),Q_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1)) ).
fof(fact_278_triple_Oinject,axiom,
! [Fun1_2,Com_2,Fun2_2,Fun1_1,Com_1,Fun2_1] :
( hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_2),Com_2),Fun2_2) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1_1),Com_1),Fun2_1)
<=> ( Fun1_2 = Fun1_1
& Com_2 = Com_1
& Fun2_2 = Fun2_1 ) ) ).
fof(fact_279_UnI2,axiom,
! [A_1,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_1),B))) ) ).
fof(fact_280_UnI2,axiom,
! [A_1,C,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) ) ).
fof(fact_281_UnI1,axiom,
! [B,C,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ) ).
fof(fact_282_UnI1,axiom,
! [B,C,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) ) ).
fof(fact_283_ball__Un,axiom,
! [P_1,A_1,B] :
( ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))
=> hBOOL(hAPP_H513860823e_bool(P_1,X_2)) )
<=> ( ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_H513860823e_bool(P_1,X_2)) )
& ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B))
=> hBOOL(hAPP_H513860823e_bool(P_1,X_2)) ) ) ) ).
fof(fact_284_bex__Un,axiom,
! [P_1,A_1,B] :
( ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))
& hBOOL(hAPP_H513860823e_bool(P_1,X_2)) )
<=> ( ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
& hBOOL(hAPP_H513860823e_bool(P_1,X_2)) )
| ? [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B))
& hBOOL(hAPP_H513860823e_bool(P_1,X_2)) ) ) ) ).
fof(fact_285_Un__assoc,axiom,
! [A_1,B,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) ).
fof(fact_286_Un__iff,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_287_Un__iff,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
| hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ) ).
fof(fact_288_Un__left__commute,axiom,
! [A_1,B,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C_1)) ).
fof(fact_289_Un__left__absorb,axiom,
! [A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) ).
fof(fact_290_Un__commute,axiom,
! [A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1) ).
fof(fact_291_Un__def,axiom,
! [A_1,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),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_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).
fof(fact_292_Un__def,axiom,
! [A_1,B] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),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_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).
fof(fact_293_Un__def,axiom,
! [A_1,B] : hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fdisj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B))) ).
fof(fact_294_Un__def,axiom,
! [A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B))) ).
fof(fact_295_Un__absorb,axiom,
! [A_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),A_1) = A_1 ).
fof(fact_296_Un__empty,axiom,
! [A_1,B] :
( ( is_fun_pname_bool(A_1)
& is_fun_pname_bool(B) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = bot_bo844097828e_bool
<=> ( A_1 = bot_bo844097828e_bool
& B = bot_bo844097828e_bool ) ) ) ).
fof(fact_297_Un__empty,axiom,
! [A_1,B] :
( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = bot_bo1055319631e_bool
<=> ( A_1 = bot_bo1055319631e_bool
& B = bot_bo1055319631e_bool ) ) ).
fof(fact_298_Un__empty__right,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),bot_bo844097828e_bool) = A_1 ) ).
fof(fact_299_Un__empty__right,axiom,
! [A_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),bot_bo1055319631e_bool) = A_1 ).
fof(fact_300_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_301_Un__empty__left,axiom,
! [B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),B) = B ).
fof(fact_302_finite__UnI,axiom,
! [G_1,Fa] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1))) ) ) ).
fof(fact_303_finite__UnI,axiom,
! [G_1,Fa] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,Fa),G_1))) ) ) ).
fof(fact_304_finite__UnI,axiom,
! [G_1,Fa] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1))) ) ) ).
fof(fact_305_finite__UnI,axiom,
! [G_1,Fa] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Fa),G_1))) ) ) ).
fof(fact_306_finite__Un,axiom,
! [Fa,G_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1)))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) ) ) ).
fof(fact_307_finite__Un,axiom,
! [Fa,G_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,Fa),G_1)))
<=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
& hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) ) ) ).
fof(fact_308_finite__Un,axiom,
! [Fa,G_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1)))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) ) ) ).
fof(fact_309_finite__Un,axiom,
! [Fa,G_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Fa),G_1)))
<=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) ) ) ).
fof(fact_310_Un__insert__left,axiom,
! [A,B,C_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) ).
fof(fact_311_Un__insert__left,axiom,
! [A,B,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) ).
fof(fact_312_Un__insert__right,axiom,
! [A_1,A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) ).
fof(fact_313_Un__insert__right,axiom,
! [A_1,A,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) ).
fof(fact_314_Un__mono,axiom,
! [B,D_1,A_1,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D_1))) ) ) ).
fof(fact_315_Un__mono,axiom,
! [B,D_1,A_1,C_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),D_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),D_1))) ) ) ).
fof(fact_316_Un__least,axiom,
! [B,A_1,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),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_1),B)),C_1)) ) ) ).
fof(fact_317_Un__least,axiom,
! [B,A_1,C_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),C_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),C_1)) ) ) ).
fof(fact_318_Un__absorb2,axiom,
! [B,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = A_1 ) ) ).
fof(fact_319_Un__absorb2,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = A_1 ) ).
fof(fact_320_Un__absorb1,axiom,
! [A_1,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B ) ) ).
fof(fact_321_Un__absorb1,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = B ) ).
fof(fact_322_subset__Un__eq,axiom,
! [A_1,B] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
<=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B ) ) ).
fof(fact_323_subset__Un__eq,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
<=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B) = B ) ).
fof(fact_324_Un__upper2,axiom,
! [B,A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ).
fof(fact_325_Un__upper2,axiom,
! [B,A_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) ).
fof(fact_326_Un__upper1,axiom,
! [A_1,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ).
fof(fact_327_Un__upper1,axiom,
! [A_1,B] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))) ).
fof(fact_328_image__Un,axiom,
! [F,A_1,B] : hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B)) ).
fof(fact_329_insert__def,axiom,
! [A,B] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),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))),B) ).
fof(fact_330_insert__def,axiom,
! [A,B] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(collec727977250_state,hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,fequal1531560888_state),A))),B) ).
fof(fact_331_insert__def,axiom,
! [A,B] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),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))),B) ).
fof(fact_332_insert__def,axiom,
! [A,B] : hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,A),B) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,fequal1746921144e_bool),A))),B) ).
fof(fact_333_insert__is__Un,axiom,
! [A,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)),A_1) ).
fof(fact_334_insert__is__Un,axiom,
! [A,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) ).
fof(fact_335_hoare__derivs_OBody,axiom,
! [G_1,P_1,Q_1,Procs] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))) ) ).
fof(fact_336_xt1_I6_J,axiom,
! [Z,Y_1,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) ) ) ).
fof(fact_337_xt1_I6_J,axiom,
! [Z,Y_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),Y_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_1)) ) ) ).
fof(fact_338_xt1_I5_J,axiom,
! [Y_1,X_1] :
( ( is_fun_pname_bool(Y_1)
& is_fun_pname_bool(X_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
=> X_1 = Y_1 ) ) ) ).
fof(fact_339_xt1_I5_J,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> X_1 = Y_1 ) ) ).
fof(fact_340_order__trans,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).
fof(fact_341_order__trans,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),Z))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)) ) ) ).
fof(fact_342_order__antisym,axiom,
! [X_1,Y_1] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
=> X_1 = Y_1 ) ) ) ).
fof(fact_343_order__antisym,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> X_1 = Y_1 ) ) ).
fof(fact_344_xt1_I4_J,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A))
=> ( B_1 = C
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A)) ) ) ).
fof(fact_345_xt1_I4_J,axiom,
! [C,B_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A))
=> ( B_1 = C
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),A)) ) ) ).
fof(fact_346_ord__le__eq__trans,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B_1))
=> ( B_1 = C
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) ) ) ).
fof(fact_347_ord__le__eq__trans,axiom,
! [C,A,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B_1))
=> ( B_1 = C
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) ) ) ).
fof(fact_348_xt1_I3_J,axiom,
! [C,A,B_1] :
( A = 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)) ) ) ).
fof(fact_349_xt1_I3_J,axiom,
! [C,A,B_1] :
( A = B_1
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),A)) ) ) ).
fof(fact_350_ord__eq__le__trans,axiom,
! [C,A,B_1] :
( A = 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),C)) ) ) ).
fof(fact_351_ord__eq__le__trans,axiom,
! [C,A,B_1] :
( A = B_1
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C)) ) ) ).
fof(fact_352_order__antisym__conv,axiom,
! [Y_1,X_1] :
( ( is_fun_pname_bool(Y_1)
& is_fun_pname_bool(X_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
<=> X_1 = Y_1 ) ) ) ).
fof(fact_353_order__antisym__conv,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
<=> X_1 = Y_1 ) ) ).
fof(fact_354_order__eq__refl,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) ) ).
fof(fact_355_order__eq__refl,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) ) ).
fof(fact_356_order__eq__iff,axiom,
! [X_1,Y_1] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y_1) )
=> ( X_1 = Y_1
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) ) ) ) ).
fof(fact_357_order__eq__iff,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) ) ) ).
fof(fact_358_option_Oinject,axiom,
! [A,A_2] :
( some_com(A) = some_com(A_2)
<=> A = A_2 ) ).
fof(fact_359_constant,axiom,
! [G_1,P_1,C,Q_1,C_1] :
( ( hBOOL(C_1)
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),C_1)),C),Q_1)),bot_bo1055319631e_bool))) ) ).
fof(fact_360_Body1,axiom,
! [Pn_1,G_1,P_1,Q_1,Procs] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),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_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo1055319631e_bool))) ) ) ).
fof(fact_361_le__bot,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_362_le__bot,axiom,
! [A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool))
=> A = bot_bo1055319631e_bool ) ).
fof(fact_363_bot__unique,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_364_bot__unique,axiom,
! [A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool))
<=> A = bot_bo1055319631e_bool ) ).
fof(fact_365_bot__least,axiom,
! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A)) ).
fof(fact_366_bot__least,axiom,
! [A] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A)) ).
fof(fact_367_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_368_le__funE,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))) ) ).
fof(fact_369_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_370_le__funD,axiom,
! [X_1,F,G] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))) ) ).
fof(fact_371_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_372_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G))
<=> ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2))) ) ).
fof(fact_373_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_374_bot__apply,axiom,
! [X_1] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_375_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_376_bot__fun__def,axiom,
! [X_2] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_377_BodyN,axiom,
! [P_1,Pn_1,Q_1,G_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1055319631e_bool))) ) ).
fof(fact_378_finite__pointwise,axiom,
! [P_1,Q_1,G_1,P_2,C0_1,Q_2,U_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1))
=> ( ! [P_3] :
( is_pname(P_3)
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_2,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_2,P_3))),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_p1637813682e_bool(P_1,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_1,P_3))),bot_bo1055319631e_bool))) ) )
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_2)),C0_1)),Q_2)),U_1)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).
fof(fact_379_escape,axiom,
! [G_1,C,Q_1,P_1] :
( ! [Z_2,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,cOMBK_631994958_state(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),cOMBK_631994958_state(hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo1055319631e_bool))) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) ) ).
fof(fact_380_Body__sound__lemma,axiom,
! [G_1,P_1,Q_1,Procs] :
( hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_1),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,hAPP_f950918952_state(cOMBB_2123334001_pname(hoare_1575745797_state),P_1)),body_1)),Q_1)),Procs))) ) ).
fof(fact_381_conseq1,axiom,
! [P_1,G_1,P_2,C,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_2),C),Q_1)),bot_bo1055319631e_bool)))
=> ( ! [Z_2,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_2),S_3)) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_382_conseq2,axiom,
! [Q_1,G_1,P_1,C,Q_2] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_2)),bot_bo1055319631e_bool)))
=> ( ! [Z_2,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_2),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_3)) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_383_MGF__complete,axiom,
! [P_1,Q_1,C] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_384_sup1E,axiom,
! [A_1,B,X_1] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1))
=> ( ~ hBOOL(hAPP_H513860823e_bool(A_1,X_1))
=> hBOOL(hAPP_H513860823e_bool(B,X_1)) ) ) ).
fof(fact_385_sup1CI,axiom,
! [A_1,B,X_1] :
( ( ~ hBOOL(hAPP_H513860823e_bool(B,X_1))
=> hBOOL(hAPP_H513860823e_bool(A_1,X_1)) )
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)) ) ).
fof(fact_386_hoare__sound,axiom,
! [G_1,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
=> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_1),Ts)) ) ).
fof(fact_387_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_388_bot__empty__eq,axiom,
! [X_2] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),bot_bo1055319631e_bool)) ) ).
fof(fact_389_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_390_rev__predicate1D,axiom,
! [Q_1,P_1,X_1] :
( hBOOL(hAPP_H513860823e_bool(P_1,X_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1))
=> hBOOL(hAPP_H513860823e_bool(Q_1,X_1)) ) ) ).
fof(fact_391_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_392_predicate1D,axiom,
! [X_1,P_1,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1))
=> ( hBOOL(hAPP_H513860823e_bool(P_1,X_1))
=> hBOOL(hAPP_H513860823e_bool(Q_1,X_1)) ) ) ).
fof(fact_393_sup1I2,axiom,
! [A_1,B,X_1] :
( hBOOL(hAPP_H513860823e_bool(B,X_1))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)) ) ).
fof(fact_394_sup1I1,axiom,
! [B,A_1,X_1] :
( hBOOL(hAPP_H513860823e_bool(A_1,X_1))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B),X_1)) ) ).
fof(fact_395_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_396_pred__subset__eq,axiom,
! [R_1,S] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,R_1),S)) ) ).
fof(fact_397_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_398_sup__Un__eq,axiom,
! [R_1,S,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)),X_2))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,R_1),S))) ) ).
fof(fact_399_conseq12,axiom,
! [Q_1,P_1,G_1,P_2,C,Q_2] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_2),C),Q_2)),bot_bo1055319631e_bool)))
=> ( ! [Z_2,S_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3))
=> ! [S_4] :
( ! [Z_3] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_3))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_4)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_4)) ) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_400_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_401_le__funI,axiom,
! [F,G] :
( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2)))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) ) ).
fof(fact_402_Option_Oset_Osimps_I2_J,axiom,
! [X_1] : set_pname(some_pname(X_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ).
fof(fact_403_Option_Oset_Osimps_I2_J,axiom,
! [X_1] : set_Ho1831989999_state(some_H1133819688_state(X_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool) ).
fof(fact_404_Option_Oset_Osimps_I2_J,axiom,
! [X_1] : set_com(some_com(X_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) ).
fof(fact_405_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 = some_pname(X_1) ) ) ).
fof(fact_406_elem__set,axiom,
! [X_1,Xo] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),set_Ho1831989999_state(Xo)))
<=> Xo = some_H1133819688_state(X_1) ) ).
fof(fact_407_elem__set,axiom,
! [X_1,Xo] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo)))
<=> Xo = some_com(X_1) ) ).
fof(fact_408_ospec,axiom,
! [X_1,P_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A_1)))
=> hBOOL(hAPP_com_bool(P_1,X_2)) )
=> ( A_1 = some_com(X_1)
=> hBOOL(hAPP_com_bool(P_1,X_1)) ) ) ).
fof(fact_409_sup__fun__def,axiom,
! [F,G,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),G),X_2))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2))) ) ).
fof(fact_410_sup__apply,axiom,
! [F,G,X_1] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,F),G),X_1))
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1))) ) ).
fof(fact_411_single__stateE,axiom,
( hBOOL(hoare_298929751gleton)
=> ! [T_2] :
~ ! [S_3] : S_3 = T_2 ) ).
fof(fact_412_state__not__singleton__def,axiom,
( hBOOL(hoare_298929751gleton)
<=> ? [S_3,T_2] : S_3 != T_2 ) ).
fof(fact_413_sup__assoc,axiom,
! [X_1,Y_1,Z] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) ).
fof(fact_414_inf__sup__aci_I6_J,axiom,
! [X_1,Y_1,Z] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) ).
fof(fact_415_sup_Oassoc,axiom,
! [A,B_1,C] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),C) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C)) ).
fof(fact_416_sup__left__commute,axiom,
! [X_1,Y_1,Z] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)) ).
fof(fact_417_inf__sup__aci_I7_J,axiom,
! [X_1,Y_1,Z] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)) ).
fof(fact_418_sup_Oleft__commute,axiom,
! [B_1,A,C] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),C)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),C)) ).
fof(fact_419_sup__left__idem,axiom,
! [X_1,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) ).
fof(fact_420_inf__sup__aci_I8_J,axiom,
! [X_1,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) ).
fof(fact_421_sup_Oleft__idem,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) ).
fof(fact_422_sup__commute,axiom,
! [X_1,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1) ).
fof(fact_423_inf__sup__aci_I5_J,axiom,
! [X_1,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1) ).
fof(fact_424_sup_Ocommute,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B_1),A) ).
fof(fact_425_sup__idem,axiom,
! [X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),X_1) = X_1 ).
fof(fact_426_sup_Oidem,axiom,
! [A] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),A) = A ).
fof(fact_427_le__supE,axiom,
! [A,B_1,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) ) ) ).
fof(fact_428_le__supE,axiom,
! [A,B_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),X_1))
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1))
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1)) ) ) ).
fof(fact_429_sup__mono,axiom,
! [B_1,D,A,C] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D))) ) ) ).
fof(fact_430_sup__mono,axiom,
! [B_1,D,A,C] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),D))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C),D))) ) ) ).
fof(fact_431_sup__least,axiom,
! [Z,Y_1,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),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_1),Z)),X_1)) ) ) ).
fof(fact_432_sup__least,axiom,
! [Z,Y_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)),X_1)) ) ) ).
fof(fact_433_le__supI,axiom,
! [B_1,A,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),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),B_1)),X_1)) ) ) ).
fof(fact_434_le__supI,axiom,
! [B_1,A,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1)),X_1)) ) ) ).
fof(fact_435_sup__absorb1,axiom,
! [Y_1,X_1] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = X_1 ) ) ).
fof(fact_436_sup__absorb1,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = X_1 ) ).
fof(fact_437_sup__absorb2,axiom,
! [X_1,Y_1] :
( is_fun_pname_bool(Y_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1 ) ) ).
fof(fact_438_sup__absorb2,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = Y_1 ) ).
fof(fact_439_le__supI2,axiom,
! [A,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),B_1))) ) ).
fof(fact_440_le__supI2,axiom,
! [A,X_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) ) ).
fof(fact_441_le__supI1,axiom,
! [B_1,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) ) ).
fof(fact_442_le__supI1,axiom,
! [B_1,X_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A),B_1))) ) ).
fof(fact_443_le__sup__iff,axiom,
! [X_1,Y_1,Z] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),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_1),Z)) ) ) ).
fof(fact_444_le__sup__iff,axiom,
! [X_1,Y_1,Z] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),Z))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),Z)) ) ) ).
fof(fact_445_le__iff__sup,axiom,
! [X_1,Y_1] :
( is_fun_pname_bool(Y_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
<=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1 ) ) ).
fof(fact_446_le__iff__sup,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
<=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = Y_1 ) ).
fof(fact_447_sup__ge2,axiom,
! [Y_1,X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).
fof(fact_448_sup__ge2,axiom,
! [Y_1,X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1))) ).
fof(fact_449_inf__sup__ord_I4_J,axiom,
! [Y_1,X_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).
fof(fact_450_inf__sup__ord_I4_J,axiom,
! [Y_1,X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1))) ).
fof(fact_451_sup__ge1,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).
fof(fact_452_sup__ge1,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1))) ).
fof(fact_453_inf__sup__ord_I3_J,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).
fof(fact_454_inf__sup__ord_I3_J,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1))) ).
fof(fact_455_sup__eq__bot__iff,axiom,
! [X_1,Y_1] :
( ( is_fun_pname_bool(X_1)
& is_fun_pname_bool(Y_1) )
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = bot_bo844097828e_bool
<=> ( X_1 = bot_bo844097828e_bool
& Y_1 = bot_bo844097828e_bool ) ) ) ).
fof(fact_456_sup__eq__bot__iff,axiom,
! [X_1,Y_1] :
( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1) = bot_bo1055319631e_bool
<=> ( X_1 = bot_bo1055319631e_bool
& Y_1 = bot_bo1055319631e_bool ) ) ).
fof(fact_457_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_458_sup__bot__right,axiom,
! [X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),bot_bo1055319631e_bool) = X_1 ).
fof(fact_459_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_460_sup__bot__left,axiom,
! [X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,bot_bo1055319631e_bool),X_1) = X_1 ).
fof(fact_461_folding__one__idem_Ounion__idem,axiom,
! [B,A_1,F,Fa] :
( ( is_fun1661590463l_bool(B)
& is_fun1661590463l_bool(A_1) )
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( A_1 != 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_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ).
fof(fact_462_folding__one__idem_Ounion__idem,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite959343283e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( A_1 != bot_bo1325454745l_bool
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> ( B != bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)) ) ) ) ) ) ).
fof(fact_463_folding__one__idem_Ounion__idem,axiom,
! [B,A_1,F,Fa] :
( ( is_fun_pname_bool(B)
& is_fun_pname_bool(A_1) )
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != 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_1),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ).
fof(fact_464_folding__one__idem_Ounion__idem,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite506823037_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( B != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B)) ) ) ) ) ) ).
fof(fact_465_folding__one__idem_Osubset__idem,axiom,
! [B,A_1,F,Fa] :
( is_fun1661590463l_bool(B)
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( B != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1) ) ) ) ) ) ).
fof(fact_466_folding__one__idem_Osubset__idem,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite959343283e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( B != bot_bo1325454745l_bool
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,B),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,B)),hAPP_f772567431e_bool(Fa,A_1)) = hAPP_f772567431e_bool(Fa,A_1) ) ) ) ) ).
fof(fact_467_folding__one__idem_Osubset__idem,axiom,
! [B,A_1,F,Fa] :
( is_fun_pname_bool(B)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( B != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1) ) ) ) ) ) ).
fof(fact_468_folding__one__idem_Osubset__idem,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite506823037_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( B != bot_bo1055319631e_bool
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,B)),hAPP_f2143211163_state(Fa,A_1)) = hAPP_f2143211163_state(Fa,A_1) ) ) ) ) ).
fof(fact_469_hoare__derivs_OSkip,axiom,
! [G_1,P_1] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),skip),P_1)),bot_bo1055319631e_bool))) ).
fof(fact_470_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_1,F,Fa] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) ) ) ) ) ).
fof(fact_471_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite506823037_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)) ) ) ) ).
fof(fact_472_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_1,F,Fa] :
( is_fun1661590463l_bool(A_1)
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) ) ) ) ) ).
fof(fact_473_folding__one__idem_Oinsert__idem,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite959343283e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( A_1 != bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)) ) ) ) ).
fof(fact_474_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_1] :
( ( is_pname(X_2)
& is_fun_pname_bool(F_1) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( F_1 != bot_bo844097828e_bool
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
=> hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ) ).
fof(fact_475_finite__ne__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
=> ( Fa != bot_bo1055319631e_bool
=> ( ! [X_2] : hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))
=> ( ! [X_2,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( F_1 != bot_bo1055319631e_bool
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(P_1,F_1))
=> hBOOL(hAPP_f1760790145l_bool(P_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),F_1))) ) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_476_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_1] :
( ( is_fun_pname_bool(X_2)
& is_fun1661590463l_bool(F_1) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
=> ( F_1 != bot_bo1649642514l_bool
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
=> hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1))) ) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ) ).
fof(fact_477_finite__ne__induct,axiom,
! [P_1,Fa] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
=> ( Fa != bot_bo1325454745l_bool
=> ( ! [X_2] : hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),bot_bo1325454745l_bool)))
=> ( ! [X_2,F_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,F_1))
=> ( F_1 != bot_bo1325454745l_bool
=> ( ~ hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),F_1))
=> ( hBOOL(hAPP_f239102607l_bool(P_1,F_1))
=> hBOOL(hAPP_f239102607l_bool(P_1,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),F_1))) ) ) ) )
=> hBOOL(hAPP_f239102607l_bool(P_1,Fa)) ) ) ) ) ).
fof(fact_478_com_Osimps_I19_J,axiom,
! [Pname] : hAPP_pname_com(body_1,Pname) != skip ).
fof(fact_479_com_Osimps_I18_J,axiom,
! [Pname] : skip != hAPP_pname_com(body_1,Pname) ).
fof(fact_480_WT_OSkip,axiom,
hBOOL(hAPP_com_bool(wt,skip)) ).
fof(fact_481_folding__one__idem_Oin__idem,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite89670078_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1) ) ) ) ).
fof(fact_482_folding__one__idem_Oin__idem,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite506823037_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)) = hAPP_f2143211163_state(Fa,A_1) ) ) ) ).
fof(fact_483_folding__one__idem_Oin__idem,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite1268145088e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1) ) ) ) ).
fof(fact_484_folding__one__idem_Oin__idem,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite959343283e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)) = hAPP_f772567431e_bool(Fa,A_1) ) ) ) ).
fof(fact_485_folding__one__idem_Ohom__commute,axiom,
! [N,H,F,Fa] :
( is_fun1661590463l_bool(N)
=> ( hBOOL(finite1268145088e_bool(F,Fa))
=> ( ! [X_2,Y_2] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_2) )
=> hAPP_f759274231e_bool(H,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H,X_2)),hAPP_f759274231e_bool(H,Y_2)) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N))
=> ( N != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(H,hAPP_f674760225e_bool(Fa,N)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H),N)) ) ) ) ) ) ).
fof(fact_486_folding__one__idem_Ohom__commute,axiom,
! [N,H,F,Fa] :
( hBOOL(finite959343283e_bool(F,Fa))
=> ( ! [X_2,Y_2] : hAPP_f921536533e_bool(H,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_2),Y_2)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f921536533e_bool(H,X_2)),hAPP_f921536533e_bool(H,Y_2))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,N))
=> ( N != bot_bo1325454745l_bool
=> hAPP_f921536533e_bool(H,hAPP_f772567431e_bool(Fa,N)) = hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(image_505022149e_bool(H),N)) ) ) ) ) ).
fof(fact_487_folding__one__idem_Ohom__commute,axiom,
! [N,H,F,Fa] :
( is_fun_pname_bool(N)
=> ( hBOOL(finite89670078_pname(F,Fa))
=> ( ! [X_2,Y_2] :
( ( is_pname(X_2)
& is_pname(Y_2) )
=> hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H,X_2)),hAPP_pname_pname(H,Y_2)) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N))
=> ( N != bot_bo844097828e_bool
=> hAPP_pname_pname(H,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H),N)) ) ) ) ) ) ).
fof(fact_488_folding__one__idem_Ohom__commute,axiom,
! [N,H,F,Fa] :
( hBOOL(finite506823037_state(F,Fa))
=> ( ! [X_2,Y_2] : hAPP_H563960305_state(H,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_H563960305_state(H,X_2)),hAPP_H563960305_state(H,Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,N))
=> ( N != bot_bo1055319631e_bool
=> hAPP_H563960305_state(H,hAPP_f2143211163_state(Fa,N)) = hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(image_650584225_state(H),N)) ) ) ) ) ).
fof(fact_489_LoopF,axiom,
! [G_1,P_1,B_1,C] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B_1))),while(B_1,C)),P_1)),bot_bo1055319631e_bool))) ).
fof(fact_490_Comp,axiom,
! [D,R_1,G_1,P_1,C,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),C),Q_1)),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Q_1),D),R_1)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,P_1),semi(C,D)),R_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_491_the__elem__def,axiom,
! [X_3] : hAPP_f1297739591_pname(the_elem_pname,X_3) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_3)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))) ).
fof(fact_492_the__elem__def,axiom,
! [X_3] : hAPP_f2143211163_state(the_el23965208_state,X_3) = hAPP_f2143211163_state(the_Ho10452358_state,hAPP_f1456107715e_bool(cOMBB_1653402815_state(hAPP_f854625363l_bool(fequal1746921144e_bool,X_3)),hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,insert1835143293_state),bot_bo1055319631e_bool))) ).
fof(fact_493_WTs__elim__cases_I6_J,axiom,
! [B_1,C] :
( hBOOL(hAPP_com_bool(wt,while(B_1,C)))
=> hBOOL(hAPP_com_bool(wt,C)) ) ).
fof(fact_494_WTs__elim__cases_I4_J,axiom,
! [C1,C2] :
( hBOOL(hAPP_com_bool(wt,semi(C1,C2)))
=> ~ ( hBOOL(hAPP_com_bool(wt,C1))
=> ~ hBOOL(hAPP_com_bool(wt,C2)) ) ) ).
fof(fact_495_com_Osimps_I46_J,axiom,
! [Com1_3,Com2_3,Fun,Com_1] : semi(Com1_3,Com2_3) != while(Fun,Com_1) ).
fof(fact_496_com_Osimps_I47_J,axiom,
! [Fun,Com_1,Com1_3,Com2_3] : while(Fun,Com_1) != semi(Com1_3,Com2_3) ).
fof(fact_497_com_Osimps_I3_J,axiom,
! [Com1_3,Com2_3,Com1_2,Com2_2] :
( semi(Com1_3,Com2_3) = semi(Com1_2,Com2_2)
<=> ( Com1_3 = Com1_2
& Com2_3 = Com2_2 ) ) ).
fof(fact_498_com_Osimps_I5_J,axiom,
! [Fun_1,Com_2,Fun,Com_1] :
( while(Fun_1,Com_2) = while(Fun,Com_1)
<=> ( Fun_1 = Fun
& Com_2 = Com_1 ) ) ).
fof(fact_499_com_Osimps_I59_J,axiom,
! [Pname_1,Fun_1,Com_2] : hAPP_pname_com(body_1,Pname_1) != while(Fun_1,Com_2) ).
fof(fact_500_com_Osimps_I58_J,axiom,
! [Fun_1,Com_2,Pname_1] : while(Fun_1,Com_2) != hAPP_pname_com(body_1,Pname_1) ).
fof(fact_501_While,axiom,
! [B_1,C] :
( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_com_bool(wt,while(B_1,C))) ) ).
fof(fact_502_com_Osimps_I16_J,axiom,
! [Fun,Com_1] : skip != while(Fun,Com_1) ).
fof(fact_503_com_Osimps_I17_J,axiom,
! [Fun,Com_1] : while(Fun,Com_1) != skip ).
fof(fact_504_com_Osimps_I49_J,axiom,
! [Pname,Com1_1,Com2_1] : hAPP_pname_com(body_1,Pname) != semi(Com1_1,Com2_1) ).
fof(fact_505_com_Osimps_I48_J,axiom,
! [Com1_1,Com2_1,Pname] : semi(Com1_1,Com2_1) != hAPP_pname_com(body_1,Pname) ).
fof(fact_506_WT_OSemi,axiom,
! [C1,C0] :
( hBOOL(hAPP_com_bool(wt,C0))
=> ( hBOOL(hAPP_com_bool(wt,C1))
=> hBOOL(hAPP_com_bool(wt,semi(C0,C1))) ) ) ).
fof(fact_507_com_Osimps_I12_J,axiom,
! [Com1,Com2] : skip != semi(Com1,Com2) ).
fof(fact_508_com_Osimps_I13_J,axiom,
! [Com1,Com2] : semi(Com1,Com2) != skip ).
fof(fact_509_folding__one_Oinsert,axiom,
! [X_1,A_1,F,Fa] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ( A_1 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) ) ) ) ) ) ).
fof(fact_510_folding__one_Oinsert,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,A_1)) ) ) ) ) ).
fof(fact_511_folding__one_Oinsert,axiom,
! [X_1,A_1,F,Fa] :
( is_fun1661590463l_bool(A_1)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) ) ) ) ) ) ).
fof(fact_512_folding__one_Oinsert,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite132673334e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( ~ hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1))
=> ( A_1 != bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,A_1)) ) ) ) ) ).
fof(fact_513_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_514_folding__one_Osingleton,axiom,
! [X_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = X_1 ) ).
fof(fact_515_folding__one_Oclosed,axiom,
! [A_1,F,Fa] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> ( ! [X_2,Y_2] :
( ( is_pname(X_2)
& is_pname(Y_2) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A_1)),A_1)) ) ) ) ) ) ).
fof(fact_516_folding__one_Oclosed,axiom,
! [A_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> ( ! [X_2,Y_2] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),bot_bo1055319631e_bool))))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(Fa,A_1)),A_1)) ) ) ) ) ).
fof(fact_517_folding__one_Oclosed,axiom,
! [A_1,F,Fa] :
( is_fun1661590463l_bool(A_1)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> ( ! [X_2,Y_2] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_2) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_2),bot_bo1649642514l_bool)))) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A_1)),A_1)) ) ) ) ) ) ).
fof(fact_518_folding__one_Oclosed,axiom,
! [A_1,F,Fa] :
( hBOOL(finite132673334e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( A_1 != bot_bo1325454745l_bool
=> ( ! [X_2,Y_2] : hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_2),Y_2)),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_2),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,Y_2),bot_bo1325454745l_bool))))
=> hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,hAPP_f772567431e_bool(Fa,A_1)),A_1)) ) ) ) ) ).
fof(fact_519_triple_Oexhaust,axiom,
! [Y_1] :
~ ! [Fun1,Com,Fun2] : Y_1 != hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,Fun1),Com),Fun2) ).
fof(fact_520_image__cong,axiom,
! [F,G,M,N] :
( M = N
=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N))
=> hAPP_p1842370726_state(F,X_2) = hAPP_p1842370726_state(G,X_2) ) )
=> hAPP_f631639356e_bool(image_275883510_state(F),M) = hAPP_f631639356e_bool(image_275883510_state(G),N) ) ) ).
fof(fact_521_Collect__mono,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( hBOOL(hAPP_H513860823e_bool(P_1,X_2))
=> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1))) ) ).
fof(fact_522_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_523_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_524_Collect__mono,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(P_1,X_2))
=> hBOOL(hAPP_f1760790145l_bool(Q_1,X_2)) )
=> hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1))) ) ).
fof(fact_525_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_526_predicate1I,axiom,
! [Q_1,P_1] :
( ! [X_2] :
( hBOOL(hAPP_H513860823e_bool(P_1,X_2))
=> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,P_1),Q_1)) ) ).
fof(fact_527_mk__disjoint__insert,axiom,
! [A,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> ? [B_2] :
( is_fun_pname_bool(B_2)
& A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B_2)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B_2)) ) ) ) ).
fof(fact_528_mk__disjoint__insert,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> ? [B_2] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_2)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_2)) ) ) ).
fof(fact_529_Set_Oset__insert,axiom,
! [X_1,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ~ ! [B_2] :
( is_fun_pname_bool(B_2)
=> ( A_1 = 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_530_Set_Oset__insert,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ~ ! [B_2] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B_2)
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_2)) ) ) ).
fof(fact_531_equals0I,axiom,
! [A_1] :
( is_fun_pname_bool(A_1)
=> ( ! [Y_2] :
( is_pname(Y_2)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_2),A_1)) )
=> A_1 = bot_bo844097828e_bool ) ) ).
fof(fact_532_equals0I,axiom,
! [A_1] :
( ! [Y_2] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_2),A_1))
=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_533_MGT__alternD,axiom,
! [G_1,C] :
( hBOOL(hoare_298929751gleton)
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_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_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_534_MGT__alternI,axiom,
! [G_1,C] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_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_bo1055319631e_bool))) ) ).
fof(fact_535_MGT__def,axiom,
! [C] : hAPP_c1546227244_state(hoare_Mirabelle_MGT,C) = hAPP_f588507005_state(hAPP_c408625258_state(hAPP_f1949912908_state(hoare_1575745797_state,fequal_state),C),evalc(C)) ).
fof(fact_536_evalc_OBody,axiom,
! [Pn,S0,S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0),S1_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0),S1_1)) ) ).
fof(fact_537_evalc__elim__cases_I6_J,axiom,
! [P,S_2,S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_2),S1_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_2),S1_1)) ) ).
fof(fact_538_evalc__elim__cases_I1_J,axiom,
! [S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),T_1))
=> T_1 = S_2 ) ).
fof(fact_539_evalc_OWhileFalse,axiom,
! [C,B_1,S_1] :
( ~ hBOOL(hAPP_state_bool(B_1,S_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),S_1)) ) ).
fof(fact_540_evalc_OWhileTrue,axiom,
! [S2_1,C,S1_2,B_1,S0_1] :
( hBOOL(hAPP_state_bool(B_1,S0_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0_1),S1_2))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1_2),S2_1))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S0_1),S2_1)) ) ) ) ).
fof(fact_541_evalc_OSemi,axiom,
! [C1,S2,C0,S0,S1_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0),S1_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_1),S2))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0,C1)),S0),S2)) ) ) ).
fof(fact_542_evalc_OSkip,axiom,
! [S_2] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),S_2)) ).
fof(fact_543_com__det,axiom,
! [U,C_2,S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1))
=> ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),U))
=> U = T_1 ) ) ).
fof(fact_544_evalc__elim__cases_I4_J,axiom,
! [C1,C2,S_2,T_1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1,C2)),S_2),T_1))
=> ~ ! [S1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_2),S1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)) ) ) ).
fof(fact_545_evalc__WHILE__case,axiom,
! [B_1,C,S_1,T] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),T))
=> ( ( T = S_1
=> hBOOL(hAPP_state_bool(B_1,S_1)) )
=> ~ ( hBOOL(hAPP_state_bool(B_1,S_1))
=> ! [S1] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_1),S1))
=> ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1),T)) ) ) ) ) ).
fof(fact_546_xt1_I15_J,axiom,
! [C,A,F,B_1] :
( A = hAPP_f759274231e_bool(F,B_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1))
=> ( ! [X_2,Y_2] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2))) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A)) ) ) ) ).
fof(fact_547_xt1_I15_J,axiom,
! [C,A,F,B_1] :
( A = hAPP_f921536533e_bool(F,B_1)
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),B_1))
=> ( ! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_2)),hAPP_f921536533e_bool(F,X_2))) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,C)),A)) ) ) ) ).
fof(fact_548_xt1_I16_J,axiom,
! [F,C,B_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A))
=> ( hAPP_f759274231e_bool(F,B_1) = C
=> ( ! [X_2,Y_2] :
( ( is_fun_pname_bool(X_2)
& is_fun_pname_bool(Y_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2))) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A))) ) ) ) ).
fof(fact_549_xt1_I16_J,axiom,
! [F,C,B_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A))
=> ( hAPP_f921536533e_bool(F,B_1) = C
=> ( ! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_2)),hAPP_f921536533e_bool(F,X_2))) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),hAPP_f921536533e_bool(F,A))) ) ) ) ).
fof(fact_550_folding__one_Ounion__inter,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) != bot_bo1649642514l_bool
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ).
fof(fact_551_folding__one_Ounion__inter,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite132673334e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> ( hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) != bot_bo1325454745l_bool
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B))),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B))) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)) ) ) ) ) ).
fof(fact_552_folding__one_Ounion__inter,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) != bot_bo844097828e_bool
=> hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ).
fof(fact_553_folding__one_Ounion__inter,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) != bot_bo1055319631e_bool
=> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B))),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B)) ) ) ) ) ).
fof(fact_554_folding__one_Ounion__disjoint,axiom,
! [B,A_1,F,Fa] :
( ( is_fun1661590463l_bool(B)
& is_fun1661590463l_bool(A_1) )
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( A_1 != bot_bo1649642514l_bool
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
=> ( B != bot_bo1649642514l_bool
=> ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) = bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ) ).
fof(fact_555_folding__one_Ounion__disjoint,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite132673334e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( A_1 != bot_bo1325454745l_bool
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,B))
=> ( B != bot_bo1325454745l_bool
=> ( hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) = bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila2055205435l_bool,A_1),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,hAPP_f772567431e_bool(Fa,A_1)),hAPP_f772567431e_bool(Fa,B)) ) ) ) ) ) ) ).
fof(fact_556_folding__one_Ounion__disjoint,axiom,
! [B,A_1,F,Fa] :
( ( is_fun_pname_bool(B)
& is_fun_pname_bool(A_1) )
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( A_1 != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
=> ( B != bot_bo844097828e_bool
=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ) ).
fof(fact_557_folding__one_Ounion__disjoint,axiom,
! [B,A_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B))
=> ( B != bot_bo1055319631e_bool
=> ( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)) = hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(Fa,A_1)),hAPP_f2143211163_state(Fa,B)) ) ) ) ) ) ) ).
fof(fact_558_IntI,axiom,
! [B,C,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> ( 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_1),B))) ) ) ).
fof(fact_559_IntI,axiom,
! [B,C,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) ) ) ).
fof(fact_560_IntE,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_561_IntE,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ) ).
fof(fact_562_finite__Int,axiom,
! [G_1,Fa] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_1))) ) ).
fof(fact_563_finite__Int,axiom,
! [G_1,Fa] :
( ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,Fa))
| hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,G_1)) )
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,Fa),G_1))) ) ).
fof(fact_564_finite__Int,axiom,
! [G_1,Fa] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_1))) ) ).
fof(fact_565_finite__Int,axiom,
! [G_1,Fa] :
( ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,Fa))
| hBOOL(hAPP_f1760790145l_bool(finite784854244_state,G_1)) )
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Fa),G_1))) ) ).
fof(fact_566_disjoint__iff__not__equal,axiom,
! [A_1,B] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = bot_bo844097828e_bool
<=> ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ! [Xa] :
( is_pname(Xa)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B))
=> X_2 != Xa ) ) ) ) ) ).
fof(fact_567_disjoint__iff__not__equal,axiom,
! [A_1,B] :
( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = bot_bo1055319631e_bool
<=> ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ! [Xa] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Xa),B))
=> X_2 != Xa ) ) ) ).
fof(fact_568_Int__empty__right,axiom,
! [A_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),bot_bo844097828e_bool) = bot_bo844097828e_bool ).
fof(fact_569_Int__empty__right,axiom,
! [A_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),bot_bo1055319631e_bool) = bot_bo1055319631e_bool ).
fof(fact_570_Int__empty__left,axiom,
! [B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),B) = bot_bo844097828e_bool ).
fof(fact_571_Int__empty__left,axiom,
! [B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),B) = bot_bo1055319631e_bool ).
fof(fact_572_Int__def,axiom,
! [A_1,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),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_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).
fof(fact_573_Int__def,axiom,
! [A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),A_1))),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),B))) ).
fof(fact_574_Int__def,axiom,
! [A_1,B] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),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_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).
fof(fact_575_Int__def,axiom,
! [A_1,B] : hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),B) = hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),A_1))),hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,member402455436e_bool),B))) ).
fof(fact_576_Int__iff,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_577_Int__iff,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
& hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ) ).
fof(fact_578_IntD1,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) ) ).
fof(fact_579_IntD1,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1)) ) ).
fof(fact_580_IntD2,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ).
fof(fact_581_IntD2,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ).
fof(fact_582_Collect__conj__eq,axiom,
! [P_1,Q_1] : hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),P_1)),Q_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(collec727977250_state,P_1)),hAPP_f921536533e_bool(collec727977250_state,Q_1)) ).
fof(fact_583_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_584_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_585_Collect__conj__eq,axiom,
! [P_1,Q_1] : hAPP_f1970439265l_bool(collec111528142e_bool,hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,hAPP_f482022705l_bool(cOMBB_2020112947e_bool(fconj),P_1)),Q_1)) = hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,hAPP_f1970439265l_bool(collec111528142e_bool,P_1)),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1)) ).
fof(fact_586_Int__Collect,axiom,
! [X_1,A_1,P_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1))))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
& hBOOL(hAPP_pname_bool(P_1,X_1)) ) ) ).
fof(fact_587_Int__Collect,axiom,
! [X_1,A_1,P_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(collec727977250_state,P_1))))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
& hBOOL(hAPP_H513860823e_bool(P_1,X_1)) ) ) ).
fof(fact_588_Int__Collect,axiom,
! [X_1,A_1,P_1] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))))
<=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
& hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ) ).
fof(fact_589_Int__Collect,axiom,
! [X_1,A_1,P_1] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),hAPP_f1970439265l_bool(collec111528142e_bool,P_1))))
<=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1))
& hBOOL(hAPP_f1760790145l_bool(P_1,X_1)) ) ) ).
fof(fact_590_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_591_inf__Int__eq,axiom,
! [R_1,S,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),R_1)),hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,member1758697444_state),S)),X_2))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,R_1),S))) ) ).
fof(fact_592_Un__Int__crazy,axiom,
! [A_1,B,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A_1)) ).
fof(fact_593_Un__Int__distrib2,axiom,
! [B,C_1,A_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),A_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,C_1),A_1)) ).
fof(fact_594_Int__Un__distrib2,axiom,
! [B,C_1,A_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),A_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),A_1)) ).
fof(fact_595_Un__Int__distrib,axiom,
! [A_1,B,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,A_1),C_1)) ).
fof(fact_596_Int__Un__distrib,axiom,
! [A_1,B,C_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),C_1)) ).
fof(fact_597_Int__mono,axiom,
! [B,D_1,A_1,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D_1))) ) ) ).
fof(fact_598_Int__mono,axiom,
! [B,D_1,A_1,C_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),D_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C_1),D_1))) ) ) ).
fof(fact_599_Int__greatest,axiom,
! [B,C_1,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1))
=> ( 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_1),B))) ) ) ).
fof(fact_600_Int__greatest,axiom,
! [B,C_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B))) ) ) ).
fof(fact_601_Int__absorb1,axiom,
! [B,A_1] :
( is_fun_pname_bool(B)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = B ) ) ).
fof(fact_602_Int__absorb1,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = B ) ).
fof(fact_603_Int__absorb2,axiom,
! [A_1,B] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = A_1 ) ) ).
fof(fact_604_Int__absorb2,axiom,
! [A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) = A_1 ) ).
fof(fact_605_Int__lower2,axiom,
! [A_1,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),B)) ).
fof(fact_606_Int__lower2,axiom,
! [A_1,B] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),B)) ).
fof(fact_607_Int__lower1,axiom,
! [A_1,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),A_1)) ).
fof(fact_608_Int__lower1,axiom,
! [A_1,B] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),A_1)) ).
fof(fact_609_Int__insert__left__if1,axiom,
! [B,A,C_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) ) ).
fof(fact_610_Int__insert__left__if1,axiom,
! [B,A,C_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) ) ).
fof(fact_611_Int__insert__right__if1,axiom,
! [B,A,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) ) ).
fof(fact_612_Int__insert__right__if1,axiom,
! [B,A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)) ) ).
fof(fact_613_Int__insert__left__if0,axiom,
! [B,A,C_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ).
fof(fact_614_Int__insert__left__if0,axiom,
! [B,A,C_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1) ) ).
fof(fact_615_Int__insert__right__if0,axiom,
! [B,A,A_1] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) ) ).
fof(fact_616_Int__insert__right__if0,axiom,
! [B,A,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) ) ).
fof(fact_617_insert__inter__insert,axiom,
! [A,A_1,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) ).
fof(fact_618_insert__inter__insert,axiom,
! [A,A_1,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)) ).
fof(fact_619_Int__insert__left,axiom,
! [B,A,C_1] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ) ).
fof(fact_620_Int__insert__left,axiom,
! [B,A,C_1] :
( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),C_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),C_1) ) ) ).
fof(fact_621_Int__insert__right,axiom,
! [B,A,A_1] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) ) ) ).
fof(fact_622_Int__insert__right,axiom,
! [B,A,A_1] :
( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B) ) ) ).
fof(fact_623_inf__sup__ord_I1_J,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1)) ).
fof(fact_624_inf__sup__ord_I1_J,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),X_1)) ).
fof(fact_625_inf__le1,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1)) ).
fof(fact_626_inf__le1,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),X_1)) ).
fof(fact_627_inf__sup__ord_I2_J,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1)) ).
fof(fact_628_inf__sup__ord_I2_J,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),Y_1)) ).
fof(fact_629_inf__le2,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1)) ).
fof(fact_630_inf__le2,axiom,
! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),Y_1)) ).
fof(fact_631_le__iff__inf,axiom,
! [X_1,Y_1] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
<=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = X_1 ) ) ).
fof(fact_632_le__iff__inf,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
<=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = X_1 ) ).
fof(fact_633_le__inf__iff,axiom,
! [X_1,Y_1,Z] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).
fof(fact_634_le__inf__iff,axiom,
! [X_1,Y_1,Z] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z)) ) ) ).
fof(fact_635_le__infI1,axiom,
! [B_1,A,X_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)) ) ).
fof(fact_636_le__infI1,axiom,
! [B_1,A,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),X_1)) ) ).
fof(fact_637_le__infI2,axiom,
! [A,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),B_1)),X_1)) ) ).
fof(fact_638_le__infI2,axiom,
! [A,B_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),X_1)) ) ).
fof(fact_639_inf__absorb1,axiom,
! [X_1,Y_1] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = X_1 ) ) ).
fof(fact_640_inf__absorb1,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = X_1 ) ).
fof(fact_641_inf__absorb2,axiom,
! [Y_1,X_1] :
( is_fun_pname_bool(Y_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = Y_1 ) ) ).
fof(fact_642_inf__absorb2,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1) = Y_1 ) ).
fof(fact_643_le__infI,axiom,
! [B_1,X_1,A] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A))
=> ( 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),B_1))) ) ) ).
fof(fact_644_le__infI,axiom,
! [B_1,X_1,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1))) ) ) ).
fof(fact_645_inf__greatest,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
=> ( 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_1),Z))) ) ) ).
fof(fact_646_inf__greatest,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Z))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z))) ) ) ).
fof(fact_647_inf__mono,axiom,
! [B_1,D,A,C] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D))) ) ) ).
fof(fact_648_inf__mono,axiom,
! [B_1,D,A,C] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),C))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),D))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,C),D))) ) ) ).
fof(fact_649_le__infE,axiom,
! [X_1,A,B_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) ) ) ).
fof(fact_650_le__infE,axiom,
! [X_1,A,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A),B_1)))
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),A))
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),B_1)) ) ) ).
fof(fact_651_inf__sup__absorb,axiom,
! [X_1,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)) = X_1 ).
fof(fact_652_sup__inf__absorb,axiom,
! [X_1,Y_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)) = X_1 ).
fof(fact_653_inf__sup__distrib1,axiom,
! [X_1,Y_1,Z] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z)) ).
fof(fact_654_sup__inf__distrib1,axiom,
! [X_1,Y_1,Z] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)) ).
fof(fact_655_inf__sup__distrib2,axiom,
! [Y_1,Z,X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)),X_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),X_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Z),X_1)) ).
fof(fact_656_sup__inf__distrib2,axiom,
! [Y_1,Z,X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)),X_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),X_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Z),X_1)) ).
fof(fact_657_inf__bot__right,axiom,
! [X_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),bot_bo844097828e_bool) = bot_bo844097828e_bool ).
fof(fact_658_inf__bot__right,axiom,
! [X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),bot_bo1055319631e_bool) = bot_bo1055319631e_bool ).
fof(fact_659_inf__bot__left,axiom,
! [X_1] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),X_1) = bot_bo844097828e_bool ).
fof(fact_660_inf__bot__left,axiom,
! [X_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,bot_bo1055319631e_bool),X_1) = bot_bo1055319631e_bool ).
fof(fact_661_distrib__sup__le,axiom,
! [X_1,Y_1,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_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)))) ).
fof(fact_662_distrib__sup__le,axiom,
! [X_1,Y_1,Z] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)))) ).
fof(fact_663_distrib__inf__le,axiom,
! [X_1,Y_1,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_1)),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_1),Z)))) ).
fof(fact_664_distrib__inf__le,axiom,
! [X_1,Y_1,Z] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)))) ).
fof(fact_665_image__Int__subset,axiom,
! [F,A_1,B] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f631639356e_bool(image_275883510_state(F),A_1)),hAPP_f631639356e_bool(image_275883510_state(F),B)))) ).
fof(fact_666_Un__Int__assoc__eq,axiom,
! [A_1,B,C_1] :
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1)) ) ).
fof(fact_667_Un__Int__assoc__eq,axiom,
! [A_1,B,C_1] :
( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),B)),C_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,B),C_1))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C_1),A_1)) ) ).
fof(fact_668_if__image__distrib,axiom,
! [P_1,F,G,S] : hAPP_f631639356e_bool(image_275883510_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,hAPP_f1405979047_state(cOMBB_707293872_pname(if_Hoa533980679_state),P_1)),F)),G)),S) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f631639356e_bool(image_275883510_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f631639356e_bool(image_275883510_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_669_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_670_Int__Collect__mono,axiom,
! [Q_1,P_1,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
=> ( ! [X_2] :
( is_pname(X_2)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
=> ( 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_1),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_671_Int__Collect__mono,axiom,
! [Q_1,P_1,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B))
=> ( ! [X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ( hBOOL(hAPP_H513860823e_bool(P_1,X_2))
=> hBOOL(hAPP_H513860823e_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,A_1),hAPP_f921536533e_bool(collec727977250_state,P_1))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,B),hAPP_f921536533e_bool(collec727977250_state,Q_1)))) ) ) ).
fof(fact_672_Int__Collect__mono,axiom,
! [Q_1,P_1,A_1,B] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B))
=> ( ! [X_2] :
( is_fun_pname_bool(X_2)
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1))
=> ( 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_1),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_673_Int__Collect__mono,axiom,
! [Q_1,P_1,A_1,B] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,A_1),B))
=> ( ! [X_2] :
( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_2),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(P_1,X_2))
=> hBOOL(hAPP_f1760790145l_bool(Q_1,X_2)) ) )
=> hBOOL(hAPP_f239102607l_bool(hAPP_f1269496639l_bool(ord_le1076702565l_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,A_1),hAPP_f1970439265l_bool(collec111528142e_bool,P_1))),hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(semila1410775201l_bool,B),hAPP_f1970439265l_bool(collec111528142e_bool,Q_1)))) ) ) ).
fof(fact_674_distrib__imp1,axiom,
! [X_1,Y_1,Z] :
( ! [X_2,Y_2,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_2),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_2),Z_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_1),Z)) ) ).
fof(fact_675_distrib__imp2,axiom,
! [X_1,Y_1,Z] :
( ! [X_2,Y_2,Z_1] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,Y_2),Z_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Y_2)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,X_2),Z_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,Y_1),Z)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila2145357127e_bool,X_1),Z)) ) ).
fof(fact_676_folding__one_Oremove,axiom,
! [X_1,A_1,F,Fa] :
( is_pname(X_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,A_1) = X_1 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,A_1) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ) ).
fof(fact_677_folding__one_Oremove,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> ( ( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,A_1) = X_1 )
& ( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))) ) ) ) ) ) ).
fof(fact_678_folding__one_Oremove,axiom,
! [X_1,A_1,F,Fa] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
=> ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,A_1) = X_1 )
& ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool
=> hAPP_f674760225e_bool(Fa,A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ) ).
fof(fact_679_folding__one_Oremove,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite132673334e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( hBOOL(hAPP_f239102607l_bool(hAPP_f105100493l_bool(member402455436e_bool,X_1),A_1))
=> ( ( hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) = bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,A_1) = X_1 )
& ( hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) != bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)))) ) ) ) ) ) ).
fof(fact_680_folding__one_Oinsert__remove,axiom,
! [X_1,A_1,F,Fa] :
( is_pname(X_1)
=> ( hBOOL(finite1282449217_pname(F,Fa))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = X_1 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),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_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ).
fof(fact_681_folding__one_Oinsert__remove,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite774711482_state(F,Fa))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = X_1 )
& ( hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),hAPP_f2143211163_state(Fa,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))) ) ) ) ) ).
fof(fact_682_folding__one_Oinsert__remove,axiom,
! [X_1,A_1,F,Fa] :
( is_fun_pname_bool(X_1)
=> ( hBOOL(finite1626890877e_bool(F,Fa))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),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_1)) = X_1 )
& ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),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_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ).
fof(fact_683_folding__one_Oinsert__remove,axiom,
! [X_1,A_1,F,Fa] :
( hBOOL(finite132673334e_bool(F,Fa))
=> ( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> ( ( hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) = bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = X_1 )
& ( hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)) != bot_bo1325454745l_bool
=> hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),A_1)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(F,X_1),hAPP_f772567431e_bool(Fa,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),hAPP_f1970439265l_bool(hAPP_f601642911l_bool(insert1991711667e_bool,X_1),bot_bo1325454745l_bool)))) ) ) ) ) ).
fof(fact_684_DiffI,axiom,
! [B,C,A_1] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> ( ~ 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_1),B))) ) ) ).
fof(fact_685_DiffI,axiom,
! [B,C,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B))) ) ) ).
fof(fact_686_DiffE,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).
fof(fact_687_DiffE,axiom,
! [C,A_1,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B)))
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,C),B)) ) ) ).
fof(fact_688_finite__Diff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),B))) ) ).
fof(fact_689_finite__Diff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,A_1))
=> hBOOL(hAPP_f239102607l_bool(finite899049100e_bool,hAPP_f1970439265l_bool(hAPP_f1587382801l_bool(minus_164259166l_bool,A_1),B))) ) ).
fof(fact_690_finite__Diff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))) ) ).
fof(fact_691_finite__Diff,axiom,
! [B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),B))) ) ).
fof(fact_692_insert__Diff,axiom,
! [A,A_1] :
( is_fun_pname_bool(A_1)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = A_1 ) ) ).
fof(fact_693_insert__Diff,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = A_1 ) ).
fof(fact_694_Diff__insert__absorb,axiom,
! [X_1,A_1] :
( is_fun_pname_bool(A_1)
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A_1 ) ) ).
fof(fact_695_Diff__insert__absorb,axiom,
! [X_1,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)) = A_1 ) ).
fof(fact_696_insert__Diff__single,axiom,
! [A,A_1] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) ).
fof(fact_697_insert__Diff__single,axiom,
! [A,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) ).
fof(fact_698_Diff__insert2,axiom,
! [A_1,A,B] : hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B)) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,hAPP_f921536533e_bool(hAPP_f1583986009e_bool(minus_2076558538e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),B) ).
%----Helper facts (107)
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__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__Opname_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_pname_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_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_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__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1664156314l_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(cOMBK_631994958_state(P),Q) = P ).
fof(help_If_1_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate,axiom,
! [X,Y] : hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fTrue),X),Y) = X ).
fof(help_If_2_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate,axiom,
! [X,Y] : hAPP_H563960305_state(hAPP_H521649881_state(hAPP_b798484845_state(if_Hoa533980679_state,fFalse),X),Y) = Y ).
fof(help_If_3_1_If_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_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_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,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_010,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,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__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H513860823e_bool(cOMBK_1079618832_state(P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_,axiom,
! [P,Q] :
( is_pname(P)
=> hAPP_H1344248906_pname(cOMBK_588224941_state(P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q] : hAPP_p1842370726_state(cOMBK_90103121_pname(P),Q) = P ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_bool,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(fequal1746921144e_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_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____ddpglwnxwg__O,axiom,
! [P,Q,R] : hAPP_p1842370726_state(hAPP_f1758910594_state(cOMBB_422605457_pname(P),Q),R) = hAPP_c1546227244_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_H513860823e_bool(hAPP_f921536533e_bool(cOMBB_416661851_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f760664097e_bool(cOMBS_1248383340l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_H1632039476e_bool(hAPP_f167506745e_bool(cOMBC_290948233e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_p877885514e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_p877885514e_bool(hAPP_f294904177e_bool(cOMBC_725526061e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H1632039476e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,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_012,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_013,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____ddp,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1760790145l_bool(cOMBK_564432736e_bool(P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
! [P,Q,R] : hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(cOMBB_1957242197e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1760790145l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_014,axiom,
! [P,Q,R] : hAPP_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I,axiom,
! [P,Q,R] : hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(hAPP_f1850463605l_bool(cOMBS_2138645332l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1508101115l_bool(P,R),hAPP_f1760790145l_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____dd,axiom,
! [P,Q,R] : hAPP_pname_bool(hAPP_f1745235422e_bool(hAPP_f1558052123e_bool(cOMBC_2140141647l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_p1617973726l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___015,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f631639356e_bool(hAPP_f1721106985e_bool(cOMBC_498627897l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H737849090l_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_H737849090l_bool(hAPP_f261382953l_bool(cOMBC_2107548985e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_f631639356e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I,axiom,
! [P,Q,R] : hAPP_f1760790145l_bool(hAPP_p1617973726l_bool(hAPP_f2070658331l_bool(cOMBC_367297061e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f1745235422e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_016,axiom,
! [P,Q,R] : hAPP_H1632039476e_bool(hAPP_f833390165e_bool(cOMBB_1456120487_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H1344248906_pname(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_017,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_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_018,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__019,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____ddpglwnxwg__Otriple_Itc__Com___020,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_H1645666623e_bool(hAPP_f262880489e_bool(cOMBC_1424981238e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg_,axiom,
! [P,Q,R] : hAPP_p1842370726_state(hAPP_f1661207211_state(hAPP_f137248406_state(cOMBS_843273363_state,P),Q),R) = hAPP_H563960305_state(hAPP_p80247908_state(P,R),hAPP_p1842370726_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_021,axiom,
! [P,Q,R] : hAPP_f1508101115l_bool(hAPP_f482022705l_bool(cOMBB_2020112947e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1760790145l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_022,axiom,
! [P,Q,R] : hAPP_f1745235422e_bool(hAPP_f1973135743e_bool(cOMBB_1671808265e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1008690464_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_p1842370726_state(hAPP_f1296386871_state(hAPP_f358330902_state(cOMBS_1615712031_state,P),Q),R) = hAPP_f588507005_state(hAPP_p1712839024_state(P,R),hAPP_p1637813682e_bool(Q,R)) ).
fof(help_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__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__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f1456107715e_bool(cOMBB_1653402815_state(P),Q),R) = hAPP_f1760790145l_bool(P,hAPP_H1645666623e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___023,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_f1262649863e_bool(cOMBC_764456866l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_024,axiom,
! [P,Q,R] : hAPP_f1760790145l_bool(hAPP_H248360617l_bool(hAPP_f492098723l_bool(cOMBC_1305755390e_bool,P),Q),R) = hAPP_H513860823e_bool(hAPP_f921536533e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_p877885514e_bool(hAPP_f998786331e_bool(cOMBB_799949246_pname(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_p1842370726_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025,axiom,
! [P,Q,R] : hAPP_H737849090l_bool(hAPP_f376825399l_bool(cOMBB_1722165949_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H1632039476e_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_p1712839024_state(hAPP_f2136041130_state(hAPP_f1777033564_state(cOMBS_1401555724_state,P),Q),R) = hAPP_c408625258_state(hAPP_p2032835427_state(P,R),hAPP_pname_com(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_026,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____ddpglwnxwg__Otriple_I_027,axiom,
! [P,Q,R] : hAPP_f1760790145l_bool(hAPP_f854625363l_bool(hAPP_f2119687429l_bool(cOMBC_1018307482l_bool,P),Q),R) = hAPP_f1760790145l_bool(hAPP_f854625363l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___028,axiom,
! [P,Q,R] : hAPP_f631639356e_bool(hAPP_f547518321e_bool(cOMBB_1170234304e_bool(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_f1308959284_state(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___029,axiom,
! [P,Q,R] : hAPP_H1645666623e_bool(hAPP_f1844318385e_bool(cOMBB_291471741_state(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_H563960305_state(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____ddpglwnxwg__030,axiom,
! [P,Q,R] : hAPP_p80247908_state(hAPP_f2101567797_state(hAPP_f939130838_state(cOMBS_381334199_state,P),Q),R) = hAPP_H521649881_state(hAPP_p964374716_state(P,R),hAPP_p1842370726_state(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_031,axiom,
! [P,Q,R] : hAPP_f1760790145l_bool(hAPP_f1970439265l_bool(hAPP_f517001763l_bool(cOMBC_1166591542l_bool,P),Q),R) = hAPP_f239102607l_bool(hAPP_f105100493l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_032,axiom,
! [P,Q,R] : hAPP_p1617973726l_bool(hAPP_f2081555625l_bool(cOMBB_44445098_pname(P),Q),R) = hAPP_f854625363l_bool(P,hAPP_p877885514e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___033,axiom,
! [P,Q,R] : hAPP_f921536533e_bool(hAPP_f481659057e_bool(cOMBB_1099197107e_bool(P),Q),R) = hAPP_H1645666623e_bool(P,hAPP_f2143211163_state(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___034,axiom,
! [P,Q,R] : hAPP_H1645666623e_bool(hAPP_f762269719e_bool(hAPP_f964290431e_bool(cOMBC_488258100e_bool,P),Q),R) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____ddp,axiom,
! [P,Q,R] : hAPP_p964374716_state(hAPP_f1405979047_state(cOMBB_707293872_pname(P),Q),R) = hAPP_b798484845_state(P,hAPP_pname_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__,axiom,
! [P,Q,R] : hAPP_f239102607l_bool(hAPP_f1269496639l_bool(hAPP_f1508257257l_bool(cOMBC_1084925030l_bool,P),Q),R) = hAPP_f239102607l_bool(hAPP_f1269496639l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___035,axiom,
! [P,Q,R] : hAPP_p2032835427_state(hAPP_f950918952_state(cOMBB_2123334001_pname(P),Q),R) = hAPP_f1949912908_state(P,hAPP_p1637813682e_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_I_036,axiom,
! [P,Q,R] : hAPP_H248360617l_bool(hAPP_f1862834069l_bool(cOMBB_1239130257_state(P),Q),R) = hAPP_f854625363l_bool(P,hAPP_H1645666623e_bool(Q,R)) ).
%----Conjectures (8)
fof(conj_0,hypothesis,
hBOOL(hoare_298929751gleton) ).
fof(conj_1,hypothesis,
hBOOL(wT_bodies) ).
fof(conj_2,hypothesis,
hBOOL(hAPP_f1760790145l_bool(finite784854244_state,fa)) ).
fof(conj_3,hypothesis,
~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),fa)) ).
fof(conj_4,hypothesis,
hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,fa),hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_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) = some_com(y) ).
fof(conj_6,hypothesis,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),fa)) ).
fof(conj_7,conjecture,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool))) ).
%------------------------------------------------------------------------------