TPTP Problem File: SWW472+2.p
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%------------------------------------------------------------------------------
% File : SWW472+2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 327, 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_l327 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 354 ( 71 unt; 0 def)
% Number of atoms : 1009 ( 192 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 771 ( 116 ~; 28 |; 47 &)
% ( 84 <=>; 496 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 81 ( 81 usr; 26 con; 0-3 aty)
% Number of variables : 991 ( 973 !; 18 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:34:35
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (15)
fof(gsy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____ddpglwnxwg__,axiom,
! [B_1_1,B_2_1] : is_bool(big_se1303371297_state(B_1_1,B_2_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____ddpglwnxwg__O,axiom,
! [B_1_1] : is_bool(finite1710211309_state(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__Otri,axiom,
! [B_1_1] : is_bool(finite372259688_state(B_1_1)) ).
fof(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__Otri_001,axiom,
! [B_1_1] : is_bool(finite1317819144e_bool(B_1_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__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_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
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_bool(hAPP_H513860823e_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1)) ).
%----Relevant facts (315)
fof(fact_0_empty,axiom,
! [G_2] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),bot_bo1055319631e_bool)) ).
fof(fact_1_triple_Oinject,axiom,
! [Fun1_2,Com_2,Fun2_2,Fun1_1,Com_1,Fun2_1] :
( hoare_1575745797_state(Fun1_2,Com_2,Fun2_2) = hoare_1575745797_state(Fun1_1,Com_1,Fun2_1)
<=> ( Fun1_2 = Fun1_1
& Com_2 = Com_1
& Fun2_2 = Fun2_1 ) ) ).
fof(fact_2_hoare__sound,axiom,
! [G_2,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_2),Ts)) ) ).
fof(fact_3_cut,axiom,
! [G_2,G_1,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),G_1))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) ) ) ).
fof(fact_4_hoare__derivs_Oinsert,axiom,
! [Ts,G_2,T] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) ) ) ).
fof(fact_5_derivs__insertD,axiom,
! [G_2,T,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool)))
& hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) ) ) ).
fof(fact_6_conseq2,axiom,
! [Qa,G_2,Pa,Ca,Q_2] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_2)),bot_bo1055319631e_bool)))
=> ( ! [Z_1,S] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_1),S))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_1),S)) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_7_conseq1,axiom,
! [Pa,G_2,P_2,Ca,Qa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_2,Ca,Qa)),bot_bo1055319631e_bool)))
=> ( ! [Z_1,S] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_1),S))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_1),S)) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_8_insertE,axiom,
! [A,B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A_1)))
=> ( A != B
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) ) ) ).
fof(fact_9_insertCI,axiom,
! [B,A,B_1] :
( ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_1))
=> A = B )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))) ) ).
fof(fact_10_conseq12,axiom,
! [Qa,Pa,G_2,P_2,Ca,Q_2] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_2,Ca,Q_2)),bot_bo1055319631e_bool)))
=> ( ! [Z_1,S] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_1),S))
=> ! [S_1] :
( ! [Z_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_1),S_1)) ) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_11_emptyE,axiom,
! [A] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),bot_bo1055319631e_bool)) ).
fof(fact_12_empty__not__insert,axiom,
! [A,A_1] : bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) ).
fof(fact_13_insert__not__empty,axiom,
! [A,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) != bot_bo1055319631e_bool ).
fof(fact_14_singleton__iff,axiom,
! [B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))
<=> B = A ) ).
fof(fact_15_doubleton__eq__iff,axiom,
! [A,B,Ca,D_1] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D_1),bot_bo1055319631e_bool))
<=> ( ( A = Ca
& B = D_1 )
| ( A = D_1
& B = Ca ) ) ) ).
fof(fact_16_equals0D,axiom,
! [A,A_1] :
( A_1 = bot_bo1055319631e_bool
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) ) ).
fof(fact_17_Collect__empty__eq,axiom,
! [Pa] :
( hAPP_f921536533e_bool(collec727977250_state,Pa) = bot_bo1055319631e_bool
<=> ! [X_1] : ~ hBOOL(hAPP_H513860823e_bool(Pa,X_1)) ) ).
fof(fact_18_empty__iff,axiom,
! [Ca] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),bot_bo1055319631e_bool)) ).
fof(fact_19_empty__Collect__eq,axiom,
! [Pa] :
( bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,Pa)
<=> ! [X_1] : ~ hBOOL(hAPP_H513860823e_bool(Pa,X_1)) ) ).
fof(fact_20_ex__in__conv,axiom,
! [A_1] :
( ? [X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
<=> A_1 != bot_bo1055319631e_bool ) ).
fof(fact_21_all__not__in__conv,axiom,
! [A_1] :
( ! [X_1] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
<=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_22_empty__def,axiom,
bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,hAPP_b1245957081e_bool(cOMBK_1079618832_state,fFalse)) ).
fof(fact_23_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_24_insertI2,axiom,
! [B,A,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))) ) ).
fof(fact_25_insert__ident,axiom,
! [B_1,X_2,A_1] :
( ~ 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_1))
=> ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1)
<=> A_1 = B_1 ) ) ) ).
fof(fact_26_insert__code,axiom,
! [Y_2,A_1,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),A_1),X_2))
<=> ( Y_2 = X_2
| hBOOL(hAPP_H513860823e_bool(A_1,X_2)) ) ) ).
fof(fact_27_insert__iff,axiom,
! [A,B,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A_1)))
<=> ( A = B
| hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) ) ) ).
fof(fact_28_insert__commute,axiom,
! [X_2,Y_2,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) ).
fof(fact_29_insert__absorb2,axiom,
! [X_2,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1) ).
fof(fact_30_insert__Collect,axiom,
! [A,Pa] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,Pa)) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(cOMBS_1248383340l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(cOMBC_1424981238e_bool(fequal1531560888_state),A)))),Pa)) ).
fof(fact_31_insert__compr,axiom,
! [A,B_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(cOMBS_1248383340l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(cOMBC_1424981238e_bool(fequal1531560888_state),A))),hAPP_f921536533e_bool(cOMBC_764456866l_bool(member1758697444_state),B_1))) ).
fof(fact_32_insertI1,axiom,
! [A,B_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1))) ).
fof(fact_33_singleton__inject,axiom,
! [A,B] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool)
=> A = B ) ).
fof(fact_34_singletonE,axiom,
! [B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))
=> B = A ) ).
fof(fact_35_the__elem__eq,axiom,
! [X_2] : hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2 ).
fof(fact_36_bot__apply,axiom,
! [X_2] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_37_bot__fun__def,axiom,
! [X_1] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_38_hoare__derivs_OSkip,axiom,
! [G_2,Pa] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,skip,Pa)),bot_bo1055319631e_bool))) ).
fof(fact_39_Comp,axiom,
! [D_1,R_1,G_2,Pa,Ca,Qa] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool)))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Qa,D_1,R_1)),bot_bo1055319631e_bool)))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,semi(Ca,D_1),R_1)),bot_bo1055319631e_bool))) ) ) ).
fof(fact_40_triple_Oexhaust,axiom,
! [Y_2] :
~ ! [Fun1,Com,Fun2] : Y_2 != hoare_1575745797_state(Fun1,Com,Fun2) ).
fof(fact_41_Set_Oset__insert,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ~ ! [B_3] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_3)
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_3)) ) ) ).
fof(fact_42_mk__disjoint__insert,axiom,
! [A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> ? [B_3] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_3)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_3)) ) ) ).
fof(fact_43_equals0I,axiom,
! [A_1] :
( ! [Y_1] : ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_1),A_1))
=> A_1 = bot_bo1055319631e_bool ) ).
fof(fact_44_conseq,axiom,
! [Qa,G_2,Ca,Pa] :
( ! [Z_1,S] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_1),S))
=> ? [P_1,Q_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_1,Ca,Q_1)),bot_bo1055319631e_bool)))
& ! [S_1] :
( ! [Z_2] :
( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_1),S_1)) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool))) ) ).
fof(fact_45_nonempty__iff,axiom,
! [A_1] :
( A_1 != bot_bo1055319631e_bool
<=> ? [X_1,B_3] :
( A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B_3)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_3)) ) ) ).
fof(fact_46_com_Osimps_I13_J,axiom,
! [Com1_2,Com2_2] : semi(Com1_2,Com2_2) != skip ).
fof(fact_47_com_Osimps_I12_J,axiom,
! [Com1_2,Com2_2] : skip != semi(Com1_2,Com2_2) ).
fof(fact_48_com_Osimps_I3_J,axiom,
! [Com1_1,Com2_1,Com1,Com2] :
( semi(Com1_1,Com2_1) = semi(Com1,Com2)
<=> ( Com1_1 = Com1
& Com2_1 = Com2 ) ) ).
fof(fact_49_fold1Set__sing,axiom,
! [F,A,B] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),B))
<=> A = B ) ).
fof(fact_50_folding__one_Osingleton,axiom,
! [X_2,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2 ) ).
fof(fact_51_bot__empty__eq,axiom,
! [X_1] :
( hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),bot_bo1055319631e_bool)) ) ).
fof(fact_52_fold1__singleton,axiom,
! [F,A] : hAPP_f2143211163_state(finite1346402327_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) = A ).
fof(fact_53_fold1__singleton__def,axiom,
! [A,G,F] :
( G = finite1346402327_state(F)
=> hAPP_f2143211163_state(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) = A ) ).
fof(fact_54_empty__fold1SetE,axiom,
! [F,X_2] : ~ hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),bot_bo1055319631e_bool),X_2)) ).
fof(fact_55_fold1Set__nonempty,axiom,
! [F,A_1,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),A_1),X_2))
=> A_1 != bot_bo1055319631e_bool ) ).
fof(fact_56_fold1Set_Ointros,axiom,
! [F,A,A_1,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),A),A_1),X_2))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)),X_2)) ) ) ).
fof(fact_57_folding__one_Oinsert,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,A_1)) ) ) ) ) ).
fof(fact_58_folding__one_Oeq__fold,axiom,
! [A_1,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f2143211163_state(F_1,A_1) = hAPP_f2143211163_state(finite1346402327_state(F),A_1) ) ) ).
fof(fact_59_folding__one_Oclosed,axiom,
! [A_1,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> ( ! [X_1,Y_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),bot_bo1055319631e_bool))))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(F_1,A_1)),A_1)) ) ) ) ) ).
fof(fact_60_insert__fold1SetE,axiom,
! [F,A,X_3,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),X_3)),X_2))
=> ~ ! [A_3,A_2] :
( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),X_3) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_2)
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),A_3),A_2),X_2))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_2)) ) ) ) ).
fof(fact_61_subset__singletonD,axiom,
! [A_1,X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))
=> ( A_1 = bot_bo1055319631e_bool
| A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool) ) ) ).
fof(fact_62_order__refl,axiom,
! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)) ).
fof(fact_63_order__refl,axiom,
! [X_2] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),X_2)) ).
fof(fact_64_subsetD,axiom,
! [Ca,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)) ) ) ).
fof(fact_65_equalityI,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1))
=> A_1 = B_1 ) ) ).
fof(fact_66_finite_OemptyI,axiom,
hBOOL(hAPP_f1760790145l_bool(finite784854244_state,bot_bo1055319631e_bool)) ).
fof(fact_67_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_68_empty__subsetI,axiom,
! [A_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A_1)) ).
fof(fact_69_rev__predicate1D,axiom,
! [Qa,Pa,X_2] :
( hBOOL(hAPP_H513860823e_bool(Pa,X_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Pa),Qa))
=> hBOOL(hAPP_H513860823e_bool(Qa,X_2)) ) ) ).
fof(fact_70_predicate1D,axiom,
! [X_2,Pa,Qa] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Pa),Qa))
=> ( hBOOL(hAPP_H513860823e_bool(Pa,X_2))
=> hBOOL(hAPP_H513860823e_bool(Qa,X_2)) ) ) ).
fof(fact_71_mem__def,axiom,
! [X_2,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
<=> hBOOL(hAPP_H513860823e_bool(A_1,X_2)) ) ).
fof(fact_72_Collect__def,axiom,
! [Pa] : hAPP_f921536533e_bool(collec727977250_state,Pa) = Pa ).
fof(fact_73_subset__refl,axiom,
! [A_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),A_1)) ).
fof(fact_74_set__eq__subset,axiom,
! [A_1,B_1] :
( A_1 = B_1
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)) ) ) ).
fof(fact_75_equalityD1,axiom,
! [A_1,B_1] :
( A_1 = B_1
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ).
fof(fact_76_equalityD2,axiom,
! [A_1,B_1] :
( A_1 = B_1
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)) ) ).
fof(fact_77_in__mono,axiom,
! [X_2,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( 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_1)) ) ) ).
fof(fact_78_set__rev__mp,axiom,
! [B_1,X_2,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) ) ) ).
fof(fact_79_set__mp,axiom,
! [X_2,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( 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_1)) ) ) ).
fof(fact_80_subset__trans,axiom,
! [C,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),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_1),C)) ) ) ).
fof(fact_81_equalityE,axiom,
! [A_1,B_1] :
( A_1 = B_1
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)) ) ) ).
fof(fact_82_le__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G))
<=> ! [X_1] : 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_83_order__eq__iff,axiom,
! [Y_2,X_2] :
( ( hBOOL(X_2)
<=> hBOOL(Y_2) )
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
& hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).
fof(fact_84_order__eq__iff,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) ) ) ).
fof(fact_85_rev__finite__subset,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) ) ) ).
fof(fact_86_order__eq__refl,axiom,
! [Y_2,X_2] :
( ( hBOOL(X_2)
<=> hBOOL(Y_2) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).
fof(fact_87_order__eq__refl,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) ) ).
fof(fact_88_le__funD,axiom,
! [X_2,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_2)),hAPP_H513860823e_bool(G,X_2))) ) ).
fof(fact_89_order__antisym__conv,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
<=> ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_90_order__antisym__conv,axiom,
! [Y_2,X_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,X_2),Y_2))
<=> X_2 = Y_2 ) ) ).
fof(fact_91_finite__subset,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) ) ) ).
fof(fact_92_ord__eq__le__trans,axiom,
! [Ca,B,A] :
( ( hBOOL(A)
<=> hBOOL(B) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),Ca))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),Ca)) ) ) ).
fof(fact_93_ord__eq__le__trans,axiom,
! [Ca,A,B] :
( A = B
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),Ca))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),Ca)) ) ) ).
fof(fact_94_xt1_I3_J,axiom,
! [Ca,B,A] :
( ( hBOOL(A)
<=> hBOOL(B) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),A)) ) ) ).
fof(fact_95_xt1_I3_J,axiom,
! [Ca,A,B] :
( A = B
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),A)) ) ) ).
fof(fact_96_ord__le__eq__trans,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B))
=> ( ( hBOOL(B)
<=> hBOOL(Ca) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),Ca)) ) ) ).
fof(fact_97_ord__le__eq__trans,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))
=> ( B = Ca
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),Ca)) ) ) ).
fof(fact_98_xt1_I4_J,axiom,
! [Ca,B,A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A))
=> ( ( hBOOL(B)
<=> hBOOL(Ca) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),A)) ) ) ).
fof(fact_99_xt1_I4_J,axiom,
! [Ca,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A))
=> ( B = Ca
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),A)) ) ) ).
fof(fact_100_order__antisym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_101_order__antisym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2))
=> X_2 = Y_2 ) ) ).
fof(fact_102_order__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z)) ) ) ).
fof(fact_103_order__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),Z))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Z)) ) ) ).
fof(fact_104_xt1_I5_J,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_105_xt1_I5_J,axiom,
! [Y_2,X_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,X_2),Y_2))
=> X_2 = Y_2 ) ) ).
fof(fact_106_xt1_I6_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_2)) ) ) ).
fof(fact_107_xt1_I6_J,axiom,
! [Z,Y_2,X_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,Z),Y_2))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_2)) ) ) ).
fof(fact_108_le__funE,axiom,
! [X_2,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_2)),hAPP_H513860823e_bool(G,X_2))) ) ).
fof(fact_109_bot__least,axiom,
! [A] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A)) ).
fof(fact_110_bot__least,axiom,
! [A] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A)) ).
fof(fact_111_bot__unique,axiom,
! [A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool))
<=> A = bot_bo1055319631e_bool ) ).
fof(fact_112_bot__unique,axiom,
! [A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),bot_bot_bool))
<=> ( hBOOL(A)
<=> hBOOL(bot_bot_bool) ) ) ).
fof(fact_113_le__bot,axiom,
! [A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool))
=> A = bot_bo1055319631e_bool ) ).
fof(fact_114_le__bot,axiom,
! [A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),bot_bot_bool))
=> ( hBOOL(A)
<=> hBOOL(bot_bot_bool) ) ) ).
fof(fact_115_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_116_subset__insertI,axiom,
! [B_1,A] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1))) ).
fof(fact_117_insert__subset,axiom,
! [X_2,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
& hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ) ).
fof(fact_118_subset__insert,axiom,
! [B_1,X_2,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1)))
<=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ) ).
fof(fact_119_subset__insertI2,axiom,
! [B,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))) ) ).
fof(fact_120_insert__mono,axiom,
! [A,C,D] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),D))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),C)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),D))) ) ).
fof(fact_121_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_122_asm,axiom,
! [Ts,G_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) ) ).
fof(fact_123_weaken,axiom,
! [Ts,G_2,Ts_1] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ts_1))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) ) ) ).
fof(fact_124_thin,axiom,
! [G_2,G_1,Ts] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) ) ) ).
fof(fact_125_fold__graph_OemptyI,axiom,
! [F,Z] : hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),bot_bo1055319631e_bool),Z)) ).
fof(fact_126_empty__fold__graphE,axiom,
! [F,Z,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),bot_bo1055319631e_bool),X_2))
=> X_2 = Z ) ).
fof(fact_127_fold__graph_OinsertI,axiom,
! [F,Z,Y_2,X_2,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2))) ) ) ).
fof(fact_128_finite__subset__induct,axiom,
! [Pa,A_1,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F_1),A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool))
=> ( ! [A_3,F_2] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2))
=> ( 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_2))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,F_2))
=> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),F_2))) ) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_129_finite__nonempty__imp__fold1Set,axiom,
! [F,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> ? [X1] : hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),A_1),X1)) ) ) ).
fof(fact_130_subsetI,axiom,
! [B_1,A_1] :
( ! [X_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_1)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ).
fof(fact_131_finite_Osimps,axiom,
! [A] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A))
<=> ( A = bot_bo1055319631e_bool
| ? [A_2,A_3] :
( A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_2)
& hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_2)) ) ) ) ).
fof(fact_132_finite__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool))
=> ( ! [X_1,F_2] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),F_2))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,F_2))
=> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),F_2))) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(Pa,F_1)) ) ) ) ).
fof(fact_133_finite__imp__fold__graph,axiom,
! [F,Z,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ? [X1] : hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),X1)) ) ).
fof(fact_134_le__funI,axiom,
! [F,G] :
( ! [X_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1)))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) ) ).
fof(fact_135_fold1Set_Osimps,axiom,
! [F,A1,A2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),A1),A2))
<=> ? [A_3,A_2,X_1] :
( A1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_2)
& A2 = X_1
& hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),A_3),A_2),X_1))
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_2)) ) ) ).
fof(fact_136_fold__graph_Osimps,axiom,
! [F,Z,A1,A2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A1),A2))
<=> ( ( A1 = bot_bo1055319631e_bool
& A2 = Z )
| ? [X_1,A_2,Y_1] :
( A1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_2)
& A2 = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),Y_1)
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_2))
& hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_2),Y_1)) ) ) ) ).
fof(fact_137_folding__one__idem_Osubset__idem,axiom,
! [B_1,A_1,F,F_1] :
( hBOOL(finite506823037_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( B_1 != bot_bo1055319631e_bool
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(F_1,B_1)),hAPP_f2143211163_state(F_1,A_1)) = hAPP_f2143211163_state(F_1,A_1) ) ) ) ) ).
fof(fact_138_folding__one__idem_Oinsert__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite506823037_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,A_1)) ) ) ) ).
fof(fact_139_finite__ne__induct,axiom,
! [Pa,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( F_1 != bot_bo1055319631e_bool
=> ( ! [X_1] : hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))
=> ( ! [X_1,F_2] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2))
=> ( F_2 != bot_bo1055319631e_bool
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),F_2))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,F_2))
=> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),F_2))) ) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(Pa,F_1)) ) ) ) ) ).
fof(fact_140_Collect__mono,axiom,
! [Qa,Pa] :
( ! [X_1] :
( hBOOL(hAPP_H513860823e_bool(Pa,X_1))
=> hBOOL(hAPP_H513860823e_bool(Qa,X_1)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(collec727977250_state,Pa)),hAPP_f921536533e_bool(collec727977250_state,Qa))) ) ).
fof(fact_141_folding__one__idem_Oidem,axiom,
! [X_2,F,F_1] :
( hBOOL(finite506823037_state(F,F_1))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),X_2) = X_2 ) ).
fof(fact_142_folding__one__idem_Oin__idem,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite506823037_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,A_1)) = hAPP_f2143211163_state(F_1,A_1) ) ) ) ).
fof(fact_143_predicate1I,axiom,
! [Qa,Pa] :
( ! [X_1] :
( hBOOL(hAPP_H513860823e_bool(Pa,X_1))
=> hBOOL(hAPP_H513860823e_bool(Qa,X_1)) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Pa),Qa)) ) ).
fof(fact_144_xt3,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_f1760790145l_bool(F,B)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Y_1)),hAPP_f1760790145l_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_f1760790145l_bool(F,A))) ) ) ) ).
fof(fact_145_xt3,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_b1245957081e_bool(F,B)))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_b1245957081e_bool(F,A))) ) ) ) ).
fof(fact_146_xt1_I16_J,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A))
=> ( ( hBOOL(hAPP_bool_bool(F,B))
<=> hBOOL(Ca) )
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_1)),hAPP_bool_bool(F,X_1))) ) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_bool_bool(F,A))) ) ) ) ).
fof(fact_147_xt1_I16_J,axiom,
! [F,Ca,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A))
=> ( hAPP_f921536533e_bool(F,B) = Ca
=> ( ! [X_1,Y_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,hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_f921536533e_bool(F,A))) ) ) ) ).
fof(fact_148_ord__le__eq__subst,axiom,
! [Ca,F,A,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))
=> ( ( hBOOL(hAPP_f1760790145l_bool(F,B))
<=> hBOOL(Ca) )
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,A)),Ca)) ) ) ) ).
fof(fact_149_ord__le__eq__subst,axiom,
! [F,Ca,A,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B))
=> ( hAPP_b1245957081e_bool(F,B) = Ca
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,A)),Ca)) ) ) ) ).
fof(fact_150_order__subst2,axiom,
! [F,Ca,A,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,B)),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,A)),Ca)) ) ) ) ).
fof(fact_151_order__subst2,axiom,
! [F,Ca,A,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,B)),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,A)),Ca)) ) ) ) ).
fof(fact_152_ord__eq__le__subst,axiom,
! [Ca,F,B,A] :
( ( hBOOL(A)
<=> hBOOL(hAPP_f1760790145l_bool(F,B)) )
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),hAPP_f1760790145l_bool(F,Ca))) ) ) ) ).
fof(fact_153_ord__eq__le__subst,axiom,
! [Ca,A,F,B] :
( A = hAPP_b1245957081e_bool(F,B)
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_b1245957081e_bool(F,Ca))) ) ) ) ).
fof(fact_154_xt2,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,B)),A))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Ca)),A)) ) ) ) ).
fof(fact_155_xt2,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,B)),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Y_1)),hAPP_f1760790145l_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Ca)),A)) ) ) ) ).
fof(fact_156_xt1_I15_J,axiom,
! [Ca,F,B,A] :
( ( hBOOL(A)
<=> hBOOL(hAPP_bool_bool(F,B)) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_1)),hAPP_bool_bool(F,X_1))) ) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Ca)),A)) ) ) ) ).
fof(fact_157_xt1_I15_J,axiom,
! [Ca,A,F,B] :
( A = hAPP_f921536533e_bool(F,B)
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B))
=> ( ! [X_1,Y_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,hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Ca)),A)) ) ) ) ).
fof(fact_158_order__subst1,axiom,
! [Ca,A,F,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_b1245957081e_bool(F,B)))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),Ca))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_b1245957081e_bool(F,Ca))) ) ) ) ).
fof(fact_159_order__subst1,axiom,
! [Ca,A,F,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),hAPP_f1760790145l_bool(F,B)))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),Ca))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),hAPP_f1760790145l_bool(F,Ca))) ) ) ) ).
fof(fact_160_semilattice__big_OF__eq,axiom,
! [A_1,F,F_1] :
( hBOOL(big_se1303371297_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f2143211163_state(F_1,A_1) = hAPP_f2143211163_state(finite1346402327_state(F),A_1) ) ) ).
fof(fact_161_folding__one_Oremove,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ( ( hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F_1,A_1) = X_2 )
& ( hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F_1,A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) ) ) ) ) ) ).
fof(fact_162_folding__one_Oinsert__remove,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ( hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = X_2 )
& ( hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) ) ) ) ) ).
fof(fact_163_DiffI,axiom,
! [B_1,Ca,A_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) ) ) ).
fof(fact_164_DiffE,axiom,
! [Ca,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)))
=> ~ ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)) ) ) ).
fof(fact_165_finite__Diff,axiom,
! [B_1,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) ) ).
fof(fact_166_set__diff__eq,axiom,
! [A_1,B_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(cOMBS_1248383340l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(cOMBC_764456866l_bool(member1758697444_state),A_1))),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_f921536533e_bool(cOMBC_764456866l_bool(member1758697444_state),B_1)))) ).
fof(fact_167_Diff__iff,axiom,
! [Ca,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1))
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)) ) ) ).
fof(fact_168_Diff__idemp,axiom,
! [A_1,B_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),B_1) = hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1) ).
fof(fact_169_DiffD1,axiom,
! [Ca,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)) ) ).
fof(fact_170_DiffD2,axiom,
! [Ca,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)))
=> ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)) ) ).
fof(fact_171_empty__Diff,axiom,
! [A_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(bot_bo1055319631e_bool),A_1) = bot_bo1055319631e_bool ).
fof(fact_172_Diff__empty,axiom,
! [A_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),bot_bo1055319631e_bool) = A_1 ).
fof(fact_173_Diff__cancel,axiom,
! [A_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),A_1) = bot_bo1055319631e_bool ).
fof(fact_174_finite__Diff2,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)))
<=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) ) ) ).
fof(fact_175_insert__Diff__if,axiom,
! [A_1,X_2,B_1] :
( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
=> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1) = hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
=> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)) ) ) ).
fof(fact_176_insert__Diff1,axiom,
! [A_1,X_2,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
=> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1) = hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1) ) ).
fof(fact_177_Diff__subset,axiom,
! [A_1,B_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),A_1)) ).
fof(fact_178_Diff__mono,axiom,
! [D,B_1,A_1,C] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,D),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),hAPP_f921536533e_bool(minus_2076558538e_bool(C),D))) ) ) ).
fof(fact_179_double__diff,axiom,
! [C,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C))
=> hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),hAPP_f921536533e_bool(minus_2076558538e_bool(C),A_1)) = A_1 ) ) ).
fof(fact_180_Diff__insert,axiom,
! [A_1,A,B_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)) = hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) ).
fof(fact_181_Diff__insert2,axiom,
! [A_1,A,B_1] : hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)) = hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),B_1) ).
fof(fact_182_insert__Diff__single,axiom,
! [A,A_1] : hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_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_183_Diff__insert__absorb,axiom,
! [X_2,A_1] :
( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = A_1 ) ).
fof(fact_184_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(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = A_1 ) ).
fof(fact_185_finite__Diff__insert,axiom,
! [A_1,A,B_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1))))
<=> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) ) ).
fof(fact_186_subset__insert__iff,axiom,
! [A_1,X_2,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1)))
<=> ( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))),B_1)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ) ) ).
fof(fact_187_diff__single__insert,axiom,
! [A_1,X_2,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1))) ) ) ).
fof(fact_188_finite__empty__induct,axiom,
! [Pa,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,A_1))
=> ( ! [A_3,A_2] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_2))
=> ( hBOOL(hAPP_f1760790145l_bool(Pa,A_2))
=> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(minus_2076558538e_bool(A_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),bot_bo1055319631e_bool)))) ) ) )
=> hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)) ) ) ) ).
fof(fact_189_minus__apply,axiom,
! [A_1,B_1,X_2] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1),X_2))
<=> hBOOL(hAPP_bool_bool(minus_minus_bool(hAPP_H513860823e_bool(A_1,X_2)),hAPP_H513860823e_bool(B_1,X_2))) ) ).
fof(fact_190_fun__diff__def,axiom,
! [A_1,B_1,X_1] :
( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1),X_1))
<=> hBOOL(hAPP_bool_bool(minus_minus_bool(hAPP_H513860823e_bool(A_1,X_1)),hAPP_H513860823e_bool(B_1,X_1))) ) ).
fof(fact_191_comp__fun__commute_Ofold__graph__insertE__aux,axiom,
! [A,Z,A_1,Y_2,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> ? [Y_3] :
( Y_2 = hAPP_H563960305_state(hAPP_H521649881_state(F,A),Y_3)
& hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),Y_3)) ) ) ) ) ).
fof(fact_192_comp__fun__commute_Ofun__left__comm,axiom,
! [X_2,Y_2,Z,F] :
( hBOOL(finite1710211309_state(F))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_H563960305_state(hAPP_H521649881_state(F,Y_2),Z)) = hAPP_H563960305_state(hAPP_H521649881_state(F,Y_2),hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)) ) ).
fof(fact_193_comp__fun__commute_Ofold__graph__determ,axiom,
! [Y_2,Z,A_1,X_2,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),X_2))
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2))
=> Y_2 = X_2 ) ) ) ).
fof(fact_194_comp__fun__commute_Ofold__graph__insertE,axiom,
! [Z,X_2,A_1,V,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),V))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> ~ ! [Y_1] :
( V = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_1)
=> ~ hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_1)) ) ) ) ) ).
fof(fact_195_min__leastR,axiom,
! [X_2,Least] :
( ! [X_1] :
( is_bool(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_min_bool,X_2),Least))
<=> hBOOL(Least) ) ) ).
fof(fact_196_min__leastR,axiom,
! [X_2,Least] :
( ! [X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_mi777828298e_bool,X_2),Least) = Least ) ).
fof(fact_197_min__leastL,axiom,
! [X_2,Least] :
( ! [X_1] :
( is_bool(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_min_bool,Least),X_2))
<=> hBOOL(Least) ) ) ).
fof(fact_198_min__leastL,axiom,
! [X_2,Least] :
( ! [X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_mi777828298e_bool,Least),X_2) = Least ) ).
fof(fact_199_min__ord__min,axiom,
ord_min_bool = min_bool(ord_less_eq_bool) ).
fof(fact_200_min__ord__min,axiom,
ord_mi777828298e_bool = min_fu513160078e_bool(ord_le1720872323e_bool) ).
fof(fact_201_comp__fun__commute_Ofold__insert__remove,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) ) ) ).
fof(fact_202_comp__fun__commute_Ofold__rec,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) ) ) ) ).
fof(fact_203_fold__empty,axiom,
! [F,Z] : hAPP_f2143211163_state(finite202520804_state(F,Z),bot_bo1055319631e_bool) = Z ).
fof(fact_204_comp__fun__commute_Ofold__fun__comm,axiom,
! [X_2,Z,A_1,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)),A_1) ) ) ).
fof(fact_205_comp__fun__commute_Ofold__equality,axiom,
! [Z,A_1,Y_2,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),A_1) = Y_2 ) ) ).
fof(fact_206_comp__fun__commute_Ofold__insert2,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)),A_1) ) ) ) ).
fof(fact_207_comp__fun__commute_Ofold__insert,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1)) ) ) ) ).
fof(fact_208_folding__one_Oeq__fold_H,axiom,
! [X_2,A_1,F,F_1] :
( hBOOL(finite774711482_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,X_2),A_1) ) ) ) ).
fof(fact_209_folding__one__idem_Oeq__fold__idem_H,axiom,
! [A,A_1,F,F_1] :
( hBOOL(finite506823037_state(F,F_1))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,A),A_1) ) ) ).
fof(fact_210_comp__fun__commute_Ofold__graph__fold,axiom,
! [Z,A_1,F] :
( hBOOL(finite1710211309_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1))) ) ) ).
fof(fact_211_comp__fun__idem_Ofold__insert__idem,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite372259688_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1)) ) ) ).
fof(fact_212_comp__fun__idem_Ofold__insert__idem,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite1317819144e_bool(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f921536533e_bool(finite512563852e_bool(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),hAPP_f921536533e_bool(finite512563852e_bool(F,Z),A_1)) ) ) ).
fof(fact_213_comp__fun__idem_Ofold__insert__idem2,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite372259688_state(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)),A_1) ) ) ).
fof(fact_214_comp__fun__idem_Ofold__insert__idem2,axiom,
! [Z,X_2,A_1,F] :
( hBOOL(finite1317819144e_bool(F))
=> ( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> hAPP_f921536533e_bool(finite512563852e_bool(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f921536533e_bool(finite512563852e_bool(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),Z)),A_1) ) ) ).
fof(fact_215_comp__fun__idem_Ofun__left__idem,axiom,
! [X_2,Z,F] :
( hBOOL(finite1317819144e_bool(F))
=> hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),Z)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),Z) ) ).
fof(fact_216_comp__fun__idem__insert,axiom,
hBOOL(finite1317819144e_bool(insert1835143293_state)) ).
fof(fact_217_setsum__diff1__nat,axiom,
! [F,A,A_1] :
( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = hAPP_nat_nat(minus_minus_nat(big_co272093296te_nat(F,A_1)),hAPP_H716259088te_nat(F,A)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = big_co272093296te_nat(F,A_1) ) ) ).
fof(fact_218_setsum__diff__nat,axiom,
! [F,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1))
=> big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)) = hAPP_nat_nat(minus_minus_nat(big_co272093296te_nat(F,A_1)),big_co272093296te_nat(F,B_1)) ) ) ).
fof(fact_219_setsum_Ocong,axiom,
! [G,H,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ! [X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hAPP_H716259088te_nat(G,X_1) = hAPP_H716259088te_nat(H,X_1) )
=> big_co272093296te_nat(G,A_1) = big_co272093296te_nat(H,A_1) ) ) ).
fof(fact_220_max__leastR,axiom,
! [X_2,Least] :
( ! [X_1] :
( is_bool(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_max_bool,X_2),Least))
<=> hBOOL(X_2) ) ) ).
fof(fact_221_max__leastR,axiom,
! [X_2,Least] :
( ! [X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_ma295552312e_bool,X_2),Least) = X_2 ) ).
fof(fact_222_max__leastL,axiom,
! [X_2,Least] :
( ! [X_1] :
( is_bool(X_1)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_max_bool,Least),X_2))
<=> hBOOL(X_2) ) ) ).
fof(fact_223_max__leastL,axiom,
! [X_2,Least] :
( ! [X_1] : hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))
=> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_ma295552312e_bool,Least),X_2) = X_2 ) ).
fof(fact_224_max__ord__max,axiom,
ord_max_bool = max_bool(ord_less_eq_bool) ).
fof(fact_225_max__ord__max,axiom,
ord_ma295552312e_bool = max_fu30884092e_bool(ord_le1720872323e_bool) ).
fof(fact_226_setsum_Oremove,axiom,
! [G,X_2,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> big_co272093296te_nat(G,A_1) = plus_plus_nat(hAPP_H716259088te_nat(G,X_2),big_co272093296te_nat(G,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) ) ) ).
fof(fact_227_setsum__diff1_H,axiom,
! [F,A,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))
=> big_co272093296te_nat(F,A_1) = plus_plus_nat(hAPP_H716259088te_nat(F,A),big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)))) ) ) ).
fof(fact_228_setsum_Oinsert,axiom,
! [G,X_2,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> big_co272093296te_nat(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = plus_plus_nat(hAPP_H716259088te_nat(G,X_2),big_co272093296te_nat(G,A_1)) ) ) ).
fof(fact_229_setsum__insert,axiom,
! [F,A,F_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1))
=> ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),F_1))
=> big_co272093296te_nat(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),F_1)) = plus_plus_nat(hAPP_H716259088te_nat(F,A),big_co272093296te_nat(F,F_1)) ) ) ).
fof(fact_230_setsum_Oinsert__remove,axiom,
! [G,X_2,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> big_co272093296te_nat(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = plus_plus_nat(hAPP_H716259088te_nat(G,X_2),big_co272093296te_nat(G,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))) ) ).
fof(fact_231_setsum__cong2,axiom,
! [F,G,A_1] :
( ! [X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hAPP_H716259088te_nat(F,X_1) = hAPP_H716259088te_nat(G,X_1) )
=> big_co272093296te_nat(F,A_1) = big_co272093296te_nat(G,A_1) ) ).
fof(fact_232_setsum__cong,axiom,
! [F,G,A_1,B_1] :
( A_1 = B_1
=> ( ! [X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_1))
=> hAPP_H716259088te_nat(F,X_1) = hAPP_H716259088te_nat(G,X_1) )
=> big_co272093296te_nat(F,A_1) = big_co272093296te_nat(G,B_1) ) ) ).
fof(fact_233_setsum_OF__cong,axiom,
! [H,G,A_1,B_1] :
( A_1 = B_1
=> ( ! [X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_1))
=> hAPP_H716259088te_nat(H,X_1) = hAPP_H716259088te_nat(G,X_1) )
=> big_co272093296te_nat(H,A_1) = big_co272093296te_nat(G,B_1) ) ) ).
fof(fact_234_not__less__bot,axiom,
! [A] : ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),bot_bo1055319631e_bool)) ).
fof(fact_235_not__less__bot,axiom,
! [A] : ~ hBOOL(hAPP_bool_bool(ord_less_bool(A),bot_bot_bool)) ).
fof(fact_236_bot__less,axiom,
! [A] :
( A != bot_bo1055319631e_bool
<=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(bot_bo1055319631e_bool),A)) ) ).
fof(fact_237_bot__less,axiom,
! [A] :
( ~ ( hBOOL(A)
<=> hBOOL(bot_bot_bool) )
<=> hBOOL(hAPP_bool_bool(ord_less_bool(bot_bot_bool),A)) ) ).
fof(fact_238_not__psubset__empty,axiom,
! [A_1] : ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),bot_bo1055319631e_bool)) ).
fof(fact_239_psubset__eq,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
& A_1 != B_1 ) ) ).
fof(fact_240_subset__iff__psubset__eq,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
<=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
| A_1 = B_1 ) ) ).
fof(fact_241_psubset__imp__subset,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ).
fof(fact_242_psubset__subset__trans,axiom,
! [C,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),C)) ) ) ).
fof(fact_243_subset__psubset__trans,axiom,
! [C,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B_1),C))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),C)) ) ) ).
fof(fact_244_order__less__asym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)) ) ).
fof(fact_245_order__less__asym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ~ hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)) ) ).
fof(fact_246_xt1_I10_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),Y_2))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),X_2)) ) ) ).
fof(fact_247_xt1_I10_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Z),Y_2))
=> hBOOL(hAPP_bool_bool(ord_less_bool(Z),X_2)) ) ) ).
fof(fact_248_order__less__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),Z))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Z)) ) ) ).
fof(fact_249_order__less__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),Z))
=> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Z)) ) ) ).
fof(fact_250_xt1_I2_J,axiom,
! [Ca,B,A] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A))
=> ( B = Ca
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),A)) ) ) ).
fof(fact_251_xt1_I2_J,axiom,
! [Ca,B,A] :
( hBOOL(hAPP_bool_bool(ord_less_bool(B),A))
=> ( ( hBOOL(B)
<=> hBOOL(Ca) )
=> hBOOL(hAPP_bool_bool(ord_less_bool(Ca),A)) ) ) ).
fof(fact_252_ord__less__eq__trans,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B))
=> ( B = Ca
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),Ca)) ) ) ).
fof(fact_253_ord__less__eq__trans,axiom,
! [Ca,A,B] :
( hBOOL(hAPP_bool_bool(ord_less_bool(A),B))
=> ( ( hBOOL(B)
<=> hBOOL(Ca) )
=> hBOOL(hAPP_bool_bool(ord_less_bool(A),Ca)) ) ) ).
fof(fact_254_xt1_I1_J,axiom,
! [Ca,A,B] :
( A = B
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),B))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),A)) ) ) ).
fof(fact_255_xt1_I1_J,axiom,
! [Ca,B,A] :
( ( hBOOL(A)
<=> hBOOL(B) )
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Ca),B))
=> hBOOL(hAPP_bool_bool(ord_less_bool(Ca),A)) ) ) ).
fof(fact_256_ord__eq__less__trans,axiom,
! [Ca,A,B] :
( A = B
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),Ca))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),Ca)) ) ) ).
fof(fact_257_ord__eq__less__trans,axiom,
! [Ca,B,A] :
( ( hBOOL(A)
<=> hBOOL(B) )
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(B),Ca))
=> hBOOL(hAPP_bool_bool(ord_less_bool(A),Ca)) ) ) ).
fof(fact_258_xt1_I9_J,axiom,
! [B,A] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A))
=> ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B)) ) ).
fof(fact_259_xt1_I9_J,axiom,
! [B,A] :
( hBOOL(hAPP_bool_bool(ord_less_bool(B),A))
=> ~ hBOOL(hAPP_bool_bool(ord_less_bool(A),B)) ) ).
fof(fact_260_order__less__asym_H,axiom,
! [A,B] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B))
=> ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)) ) ).
fof(fact_261_order__less__asym_H,axiom,
! [A,B] :
( hBOOL(hAPP_bool_bool(ord_less_bool(A),B))
=> ~ hBOOL(hAPP_bool_bool(ord_less_bool(B),A)) ) ).
fof(fact_262_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_263_order__less__imp__triv,axiom,
! [Pa,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_264_order__less__imp__not__eq2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> Y_2 != X_2 ) ).
fof(fact_265_order__less__imp__not__eq2,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ( hBOOL(Y_2)
<=> ~ hBOOL(X_2) ) ) ).
fof(fact_266_order__less__imp__not__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_267_order__less__imp__not__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ( hBOOL(X_2)
<=> ~ hBOOL(Y_2) ) ) ).
fof(fact_268_order__less__imp__not__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)) ) ).
fof(fact_269_order__less__imp__not__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ~ hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)) ) ).
fof(fact_270_order__less__not__sym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)) ) ).
fof(fact_271_order__less__not__sym,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ~ hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)) ) ).
fof(fact_272_less__imp__neq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> X_2 != Y_2 ) ).
fof(fact_273_less__imp__neq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ~ ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ).
fof(fact_274_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),X_2)) ).
fof(fact_275_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_bool_bool(ord_less_bool(X_2),X_2)) ).
fof(fact_276_order__less__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
& ~ ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_277_order__less__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
& X_2 != Y_2 ) ) ).
fof(fact_278_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
& ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).
fof(fact_279_less__le__not__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) ) ) ).
fof(fact_280_order__le__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
| ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_281_order__le__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
<=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
| X_2 = Y_2 ) ) ).
fof(fact_282_order__neq__le__trans,axiom,
! [B,A] :
( ~ ( hBOOL(A)
<=> hBOOL(B) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B))
=> hBOOL(hAPP_bool_bool(ord_less_bool(A),B)) ) ) ).
fof(fact_283_order__neq__le__trans,axiom,
! [A,B] :
( A != B
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B)) ) ) ).
fof(fact_284_xt1_I12_J,axiom,
! [B,A] :
( ~ ( hBOOL(A)
<=> hBOOL(B) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A))
=> hBOOL(hAPP_bool_bool(ord_less_bool(B),A)) ) ) ).
fof(fact_285_xt1_I12_J,axiom,
! [A,B] :
( A != B
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)) ) ) ).
fof(fact_286_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).
fof(fact_287_order__less__imp__le,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) ) ).
fof(fact_288_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
| ( hBOOL(X_2)
<=> hBOOL(Y_2) ) ) ) ).
fof(fact_289_order__le__imp__less__or__eq,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
| X_2 = Y_2 ) ) ).
fof(fact_290_order__le__neq__trans,axiom,
! [A,B] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B))
=> ( ~ ( hBOOL(A)
<=> hBOOL(B) )
=> hBOOL(hAPP_bool_bool(ord_less_bool(A),B)) ) ) ).
fof(fact_291_order__le__neq__trans,axiom,
! [A,B] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B))
=> ( A != B
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B)) ) ) ).
fof(fact_292_xt1_I11_J,axiom,
! [B,A] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A))
=> ( ~ ( hBOOL(A)
<=> hBOOL(B) )
=> hBOOL(hAPP_bool_bool(ord_less_bool(B),A)) ) ) ).
fof(fact_293_xt1_I11_J,axiom,
! [B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A))
=> ( A != B
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)) ) ) ).
fof(fact_294_order__less__le__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z))
=> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Z)) ) ) ).
fof(fact_295_order__less__le__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),Z))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Z)) ) ) ).
fof(fact_296_xt1_I7_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2))
=> hBOOL(hAPP_bool_bool(ord_less_bool(Z),X_2)) ) ) ).
fof(fact_297_xt1_I7_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),Y_2))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),X_2)) ) ) ).
fof(fact_298_order__le__less__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),Z))
=> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Z)) ) ) ).
fof(fact_299_order__le__less__trans,axiom,
! [Z,X_2,Y_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),Z))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Z)) ) ) ).
fof(fact_300_xt1_I8_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Z),Y_2))
=> hBOOL(hAPP_bool_bool(ord_less_bool(Z),X_2)) ) ) ).
fof(fact_301_xt1_I8_J,axiom,
! [Z,Y_2,X_2] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),Y_2))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),X_2)) ) ) ).
fof(fact_302_less__fun__def,axiom,
! [F,G] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(F),G))
<=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G))
& ~ hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G),F)) ) ) ).
fof(fact_303_psubset__insert__iff,axiom,
! [A_1,X_2,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1)))
<=> ( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))
=> ( ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))),B_1)) )
& ( ~ hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) ) ) ) ) ) ).
fof(fact_304_setsum__strict__mono,axiom,
! [F,G,A_1] :
( hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))
=> ( A_1 != bot_bo1055319631e_bool
=> ( ! [X_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))
=> hBOOL(hAPP_nat_bool(ord_less_nat(hAPP_H716259088te_nat(F,X_1)),hAPP_H716259088te_nat(G,X_1))) )
=> hBOOL(hAPP_nat_bool(ord_less_nat(big_co272093296te_nat(F,A_1)),big_co272093296te_nat(G,A_1))) ) ) ) ).
fof(fact_305_psubset__trans,axiom,
! [C,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B_1),C))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),C)) ) ) ).
fof(fact_306_psubsetD,axiom,
! [Ca,A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)) ) ) ).
fof(fact_307_psubset__imp__ex__mem,axiom,
! [A_1,B_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))
=> ? [B_2] : hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_2),hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),A_1))) ) ).
fof(fact_308_xt6,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,B)),A))
=> ( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),B))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))) )
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Ca)),A)) ) ) ) ).
fof(fact_309_xt6,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,B)),A))
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Ca),B))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Ca)),A)) ) ) ) ).
fof(fact_310_xt5,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_f921536533e_bool(F,B)))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))) )
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),hAPP_f921536533e_bool(F,A))) ) ) ) ).
fof(fact_311_xt5,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_bool_bool(ord_less_bool(B),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_b1245957081e_bool(F,B)))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(ord_less_bool(Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),hAPP_b1245957081e_bool(F,A))) ) ) ) ).
fof(fact_312_xt4,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,B)),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B))
=> ( ! [X_1,Y_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,hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))) )
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Ca)),A)) ) ) ) ).
fof(fact_313_xt4,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_bool_bool(ord_less_bool(hAPP_f1760790145l_bool(F,B)),A))
=> ( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B))
=> ( ! [X_1,Y_1] :
( hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Y_1)),hAPP_f1760790145l_bool(F,X_1))) )
=> hBOOL(hAPP_bool_bool(ord_less_bool(hAPP_f1760790145l_bool(F,Ca)),A)) ) ) ) ).
fof(fact_314_xt4,axiom,
! [Ca,F,B,A] :
( hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,B)),A))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B))
=> ( ! [X_1,Y_1] :
( ( is_bool(X_1)
& is_bool(Y_1) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
=> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1))) ) )
=> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Ca)),A)) ) ) ) ).
%----Helper facts (21)
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(hAPP_bool_bool(fNot,P))
| ~ hBOOL(P) ) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(fNot,P)) ) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(P) ) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(Q) ) ).
fof(help_fdisj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
fof(help_fdisj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
fof(help_fdisj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
| hBOOL(P)
| hBOOL(Q) ) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse) ).
fof(help_fFalse_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fimplies_1_1_U,axiom,
! [Q,P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
fof(help_fimplies_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
fof(help_fimplies_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
| ~ hBOOL(P)
| hBOOL(Q) ) ).
fof(help_fequal_1_1_fequal_000tc__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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_H513860823e_bool(hAPP_b1245957081e_bool(cOMBK_1079618832_state,P),Q) = P ) ).
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(cOMBS_1248383340l_bool(P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_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_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_H1645666623e_bool(cOMBC_1424981238e_bool(P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___002,axiom,
! [P,Q,R] : hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBC_764456866l_bool(P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q) ).
%----Conjectures (3)
fof(conj_0,hypothesis,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_Mirabelle_MGT(c)),bot_bo1055319631e_bool))) ).
fof(conj_1,hypothesis,
hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(p,c,q)),bot_bo1055319631e_bool))) ).
fof(conj_2,conjecture,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(p,c,q)),bot_bo1055319631e_bool))) ).
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