%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SWW472^2 : TPTP v6.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n114.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32286.75MB % OS : Linux 2.6.32-431.20.3.el6.x86_64 % CPULimit : 300s % DateTime : Thu Jul 17 13:37:22 EDT 2014 % Result : Timeout 300.02s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----NO SOLUTION OUTPUT BY SYSTEM %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SWW472^2 : TPTP v6.1.0. Released v5.3.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n114.star.cs.uiowa.edu % % Model : x86_64 x86_64 % % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % % Memory : 32286.75MB % % OS : Linux 2.6.32-431.20.3.el6.x86_64 % % CPULimit : 300 % % DateTime : Thu Jul 17 09:16:46 CDT 2014 % % CPUTime : 300.02 % Python 2.7.5 % Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % FOF formula (<kernel.Constant object at 0x1236638>, <kernel.Type object at 0x1237128>) of role type named ty_ty_tc__Com__Ocom % Using role type % Declaring com:Type % FOF formula (<kernel.Constant object at 0x1236dd0>, <kernel.Type object at 0x12373f8>) of role type named ty_ty_tc__Com__Ostate % Using role type % Declaring state:Type % FOF formula (<kernel.Constant object at 0x1236638>, <kernel.Type object at 0x1237b48>) of role type named ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J % Using role type % Declaring hoare_1167836817_state:Type % FOF formula (<kernel.Constant object at 0x1236dd0>, <kernel.Type object at 0x1237488>) of role type named ty_ty_tc__Nat__Onat % Using role type % Declaring nat:Type % FOF formula (<kernel.Constant object at 0x12373f8>, <kernel.DependentProduct object at 0x1237bd8>) of role type named sy_c_All2 % Using role type % Declaring all2:(((hoare_1167836817_state->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x1237248>, <kernel.DependentProduct object at 0x12377e8>) of role type named sy_c_All1 % Using role type % Declaring all1:((Prop->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x1237b90>, <kernel.DependentProduct object at 0x1237bd8>) of role type named sy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_000tc__Hoare____Mirabelle_ % Using role type % Declaring big_co337839062te_nat:((hoare_1167836817_state->nat)->((hoare_1167836817_state->Prop)->nat)) % FOF formula (<kernel.Constant object at 0x12371b8>, <kernel.DependentProduct object at 0x1237098>) of role type named sy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____srushsumbx__O % Using role type % Declaring big_se1603066171_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)) % FOF formula (<kernel.Constant object at 0x1237368>, <kernel.Constant object at 0x1237098>) of role type named sy_c_Com_Ocom_OSKIP % Using role type % Declaring skip:com % FOF formula (<kernel.Constant object at 0x1237b90>, <kernel.DependentProduct object at 0x12371b8>) of role type named sy_c_Com_Ocom_OSemi % Using role type % Declaring semi:(com->(com->com)) % FOF formula (<kernel.Constant object at 0x12377e8>, <kernel.DependentProduct object at 0xe5ab00>) of role type named sy_c_Ex % Using role type % Declaring _TPTP_ex:((hoare_1167836817_state->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x12371b8>, <kernel.DependentProduct object at 0xe5ad88>) of role type named sy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____srushsumbx__Ot % Using role type % Declaring finite1091222817_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->Prop) % FOF formula (<kernel.Constant object at 0x1237b90>, <kernel.DependentProduct object at 0xe5a680>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____srushsumbx__Otrip % Using role type % Declaring finite856902323tate_o:((hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->Prop) % FOF formula (<kernel.Constant object at 0x12371b8>, <kernel.DependentProduct object at 0xe5a680>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____srushsumbx__Otrip_001 % Using role type % Declaring finite1900754844_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->Prop) % FOF formula (<kernel.Constant object at 0x1237b90>, <kernel.DependentProduct object at 0xe5a5f0>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C % Using role type % Declaring finite1084549118_state:((hoare_1167836817_state->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x12377e8>, <kernel.DependentProduct object at 0x1235ea8>) of role type named sy_c_Finite__Set_Ofold1Set_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc_ % Using role type % Declaring finite309220289_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) % FOF formula (<kernel.Constant object at 0x12377e8>, <kernel.DependentProduct object at 0x1235ef0>) of role type named sy_c_Finite__Set_Ofold1_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co % Using role type % Declaring finite1646097201_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->((hoare_1167836817_state->Prop)->hoare_1167836817_state)) % FOF formula (<kernel.Constant object at 0xe5add0>, <kernel.DependentProduct object at 0x1235ea8>) of role type named sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com % Using role type % Declaring finite291020855tate_o:((hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) % FOF formula (<kernel.Constant object at 0xe5ad88>, <kernel.DependentProduct object at 0x1235488>) of role type named sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_002 % Using role type % Declaring finite1731015960_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(hoare_1167836817_state->((hoare_1167836817_state->Prop)->hoare_1167836817_state))) % FOF formula (<kernel.Constant object at 0xe5ab00>, <kernel.DependentProduct object at 0x1235c68>) of role type named sy_c_Finite__Set_Ofold__graph_000tc__Hoare____Mirabelle____srushsumbx__Otriple_I % Using role type % Declaring finite1316643734_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) % FOF formula (<kernel.Constant object at 0xe5ad88>, <kernel.DependentProduct object at 0x1235ef0>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_ % Using role type % Declaring finite1074406356_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)) % FOF formula (<kernel.Constant object at 0xe5ab00>, <kernel.DependentProduct object at 0x1235cb0>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot % Using role type % Declaring finite806517911_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)) % FOF formula (<kernel.Constant object at 0xe5ab00>, <kernel.DependentProduct object at 0x1235ea8>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__ % Using role type % Declaring minus_2107060239tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) % FOF formula (<kernel.Constant object at 0x12357e8>, <kernel.DependentProduct object at 0x1235cb0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_Eo % Using role type % Declaring minus_minus_o:(Prop->(Prop->Prop)) % FOF formula (<kernel.Constant object at 0x1235878>, <kernel.DependentProduct object at 0x12358c0>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat % Using role type % Declaring minus_minus_nat:(nat->(nat->nat)) % FOF formula (<kernel.Constant object at 0x1235ea8>, <kernel.DependentProduct object at 0x1235830>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat % Using role type % Declaring plus_plus_nat:(nat->(nat->nat)) % FOF formula (<kernel.Constant object at 0x1235cb0>, <kernel.DependentProduct object at 0x1235488>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_OMGT % Using role type % Declaring hoare_Mirabelle_MGT:(com->hoare_1167836817_state) % FOF formula (<kernel.Constant object at 0x12358c0>, <kernel.DependentProduct object at 0x1235bd8>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate % Using role type % Declaring hoare_123228589_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x1235830>, <kernel.DependentProduct object at 0x1235440>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate % Using role type % Declaring hoare_529639851_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x12354d0>, <kernel.DependentProduct object at 0x1235cb0>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate % Using role type % Declaring hoare_908217195_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1167836817_state))) % FOF formula (<kernel.Constant object at 0x12357e8>, <kernel.DependentProduct object at 0x1235440>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O % Using role type % Declaring bot_bo70021908tate_o:(hoare_1167836817_state->Prop) % FOF formula (<kernel.Constant object at 0x1235bd8>, <kernel.Sort object at 0xd24128>) of role type named sy_c_Orderings_Obot__class_Obot_000_Eo % Using role type % Declaring bot_bot_o:Prop % FOF formula (<kernel.Constant object at 0x1235488>, <kernel.DependentProduct object at 0x12354d0>) of role type named sy_c_Orderings_Oord_Omax_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_ % Using role type % Declaring max_Ho421493569tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) % FOF formula (<kernel.Constant object at 0x1235c68>, <kernel.DependentProduct object at 0x1235488>) of role type named sy_c_Orderings_Oord_Omax_000_Eo % Using role type % Declaring max_o:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))) % FOF formula (<kernel.Constant object at 0x1235c20>, <kernel.DependentProduct object at 0x1235cf8>) of role type named sy_c_Orderings_Oord_Omin_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_ % Using role type % Declaring min_Ho1955171539tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) % FOF formula (<kernel.Constant object at 0x1235878>, <kernel.DependentProduct object at 0x1235c20>) of role type named sy_c_Orderings_Oord_Omin_000_Eo % Using role type % Declaring min_o:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))) % FOF formula (<kernel.Constant object at 0x12357e8>, <kernel.DependentProduct object at 0x1235c68>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Hoare____Mirabelle____srushsumbx__ % Using role type % Declaring ord_le65125204tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x1235cf8>, <kernel.DependentProduct object at 0x1235c20>) of role type named sy_c_Orderings_Oord__class_Oless_000_Eo % Using role type % Declaring ord_less_o:(Prop->(Prop->Prop)) % FOF formula (<kernel.Constant object at 0x1235fc8>, <kernel.DependentProduct object at 0x1235878>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat % Using role type % Declaring ord_less_nat:(nat->(nat->Prop)) % FOF formula (<kernel.Constant object at 0x1235c68>, <kernel.DependentProduct object at 0x1235710>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____srushsum % Using role type % Declaring ord_le827224136tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x1235c20>, <kernel.DependentProduct object at 0x1235cf8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_Eo % Using role type % Declaring ord_less_eq_o:(Prop->(Prop->Prop)) % FOF formula (<kernel.Constant object at 0x1235fc8>, <kernel.DependentProduct object at 0x1235b90>) of role type named sy_c_Orderings_Oord__class_Omax_000_062_Itc__Hoare____Mirabelle____srushsumbx__O % Using role type % Declaring ord_ma164008317tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) % FOF formula (<kernel.Constant object at 0x1235710>, <kernel.DependentProduct object at 0x1235cf8>) of role type named sy_c_Orderings_Oord__class_Omax_000_Eo % Using role type % Declaring ord_max_o:(Prop->(Prop->Prop)) % FOF formula (<kernel.Constant object at 0x1235c20>, <kernel.DependentProduct object at 0x1235b48>) of role type named sy_c_Orderings_Oord__class_Omin_000_062_Itc__Hoare____Mirabelle____srushsumbx__O % Using role type % Declaring ord_mi1697686287tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) % FOF formula (<kernel.Constant object at 0x1235b90>, <kernel.DependentProduct object at 0x1235cf8>) of role type named sy_c_Orderings_Oord__class_Omin_000_Eo % Using role type % Declaring ord_min_o:(Prop->(Prop->Prop)) % FOF formula (<kernel.Constant object at 0x1235710>, <kernel.DependentProduct object at 0x1235368>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost % Using role type % Declaring collec1027672124_state:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)) % FOF formula (<kernel.Constant object at 0x1235b48>, <kernel.DependentProduct object at 0x12353b0>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta % Using role type % Declaring insert2134838167_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) % FOF formula (<kernel.Constant object at 0x12356c8>, <kernel.DependentProduct object at 0x1235fc8>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O % Using role type % Declaring the_el323660082_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state) % FOF formula (<kernel.Constant object at 0x1235b90>, <kernel.DependentProduct object at 0x12355a8>) of role type named sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J % Using role type % Declaring member2058392318_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x1235cf8>, <kernel.DependentProduct object at 0x1235368>) of role type named sy_v_P % Using role type % Declaring p:(state->(state->Prop)) % FOF formula (<kernel.Constant object at 0x1235fc8>, <kernel.DependentProduct object at 0x1235b48>) of role type named sy_v_Q % Using role type % Declaring q:(state->(state->Prop)) % FOF formula (<kernel.Constant object at 0x12355a8>, <kernel.Constant object at 0x1235b48>) of role type named sy_v_c % Using role type % Declaring c:com % FOF formula (forall (G_29:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_29) bot_bo70021908tate_o)) of role axiom named fact_0_empty % A new axiom: (forall (G_29:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_29) bot_bo70021908tate_o)) % FOF formula (forall (Fun1_2:(state->(state->Prop))) (Com_2:com) (Fun2_2:(state->(state->Prop))) (Fun1_1:(state->(state->Prop))) (Com_1:com) (Fun2_1:(state->(state->Prop))), ((iff (((eq hoare_1167836817_state) (((hoare_908217195_state Fun1_2) Com_2) Fun2_2)) (((hoare_908217195_state Fun1_1) Com_1) Fun2_1))) ((and ((and (((eq (state->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_2) Com_1))) (((eq (state->(state->Prop))) Fun2_2) Fun2_1)))) of role axiom named fact_1_triple_Oinject % A new axiom: (forall (Fun1_2:(state->(state->Prop))) (Com_2:com) (Fun2_2:(state->(state->Prop))) (Fun1_1:(state->(state->Prop))) (Com_1:com) (Fun2_1:(state->(state->Prop))), ((iff (((eq hoare_1167836817_state) (((hoare_908217195_state Fun1_2) Com_2) Fun2_2)) (((hoare_908217195_state Fun1_1) Com_1) Fun2_1))) ((and ((and (((eq (state->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_2) Com_1))) (((eq (state->(state->Prop))) Fun2_2) Fun2_1)))) % FOF formula (forall (G_28:(hoare_1167836817_state->Prop)) (Ts_7:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_28) Ts_7)->((hoare_529639851_state G_28) Ts_7))) of role axiom named fact_2_hoare__sound % A new axiom: (forall (G_28:(hoare_1167836817_state->Prop)) (Ts_7:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_28) Ts_7)->((hoare_529639851_state G_28) Ts_7))) % FOF formula (forall (G_27:(hoare_1167836817_state->Prop)) (G_26:(hoare_1167836817_state->Prop)) (Ts_6:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_26) Ts_6)->(((hoare_123228589_state G_27) G_26)->((hoare_123228589_state G_27) Ts_6)))) of role axiom named fact_3_cut % A new axiom: (forall (G_27:(hoare_1167836817_state->Prop)) (G_26:(hoare_1167836817_state->Prop)) (Ts_6:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_26) Ts_6)->(((hoare_123228589_state G_27) G_26)->((hoare_123228589_state G_27) Ts_6)))) % FOF formula (forall (Ts_5:(hoare_1167836817_state->Prop)) (G_25:(hoare_1167836817_state->Prop)) (T_1:hoare_1167836817_state), (((hoare_123228589_state G_25) ((insert2134838167_state T_1) bot_bo70021908tate_o))->(((hoare_123228589_state G_25) Ts_5)->((hoare_123228589_state G_25) ((insert2134838167_state T_1) Ts_5))))) of role axiom named fact_4_hoare__derivs_Oinsert % A new axiom: (forall (Ts_5:(hoare_1167836817_state->Prop)) (G_25:(hoare_1167836817_state->Prop)) (T_1:hoare_1167836817_state), (((hoare_123228589_state G_25) ((insert2134838167_state T_1) bot_bo70021908tate_o))->(((hoare_123228589_state G_25) Ts_5)->((hoare_123228589_state G_25) ((insert2134838167_state T_1) Ts_5))))) % FOF formula (forall (G_24:(hoare_1167836817_state->Prop)) (T:hoare_1167836817_state) (Ts_4:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_24) ((insert2134838167_state T) Ts_4))->((and ((hoare_123228589_state G_24) ((insert2134838167_state T) bot_bo70021908tate_o))) ((hoare_123228589_state G_24) Ts_4)))) of role axiom named fact_5_derivs__insertD % A new axiom: (forall (G_24:(hoare_1167836817_state->Prop)) (T:hoare_1167836817_state) (Ts_4:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_24) ((insert2134838167_state T) Ts_4))->((and ((hoare_123228589_state G_24) ((insert2134838167_state T) bot_bo70021908tate_o))) ((hoare_123228589_state G_24) Ts_4)))) % FOF formula (forall (Q_11:(state->(state->Prop))) (G_23:(hoare_1167836817_state->Prop)) (P_21:(state->(state->Prop))) (C_39:com) (Q_10:(state->(state->Prop))), (((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_21) C_39) Q_10)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((Q_10 Z_28) S)->((Q_11 Z_28) S)))->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_21) C_39) Q_11)) bot_bo70021908tate_o))))) of role axiom named fact_6_conseq2 % A new axiom: (forall (Q_11:(state->(state->Prop))) (G_23:(hoare_1167836817_state->Prop)) (P_21:(state->(state->Prop))) (C_39:com) (Q_10:(state->(state->Prop))), (((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_21) C_39) Q_10)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((Q_10 Z_28) S)->((Q_11 Z_28) S)))->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_21) C_39) Q_11)) bot_bo70021908tate_o))))) % FOF formula (forall (P_20:(state->(state->Prop))) (G_22:(hoare_1167836817_state->Prop)) (P_19:(state->(state->Prop))) (C_38:com) (Q_9:(state->(state->Prop))), (((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state P_19) C_38) Q_9)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((P_20 Z_28) S)->((P_19 Z_28) S)))->((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state P_20) C_38) Q_9)) bot_bo70021908tate_o))))) of role axiom named fact_7_conseq1 % A new axiom: (forall (P_20:(state->(state->Prop))) (G_22:(hoare_1167836817_state->Prop)) (P_19:(state->(state->Prop))) (C_38:com) (Q_9:(state->(state->Prop))), (((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state P_19) C_38) Q_9)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((P_20 Z_28) S)->((P_19 Z_28) S)))->((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state P_20) C_38) Q_9)) bot_bo70021908tate_o))))) % FOF formula (forall (A_185:hoare_1167836817_state) (B_92:hoare_1167836817_state) (A_184:(hoare_1167836817_state->Prop)), (((member2058392318_state A_185) ((insert2134838167_state B_92) A_184))->((not (((eq hoare_1167836817_state) A_185) B_92))->((member2058392318_state A_185) A_184)))) of role axiom named fact_8_insertE % A new axiom: (forall (A_185:hoare_1167836817_state) (B_92:hoare_1167836817_state) (A_184:(hoare_1167836817_state->Prop)), (((member2058392318_state A_185) ((insert2134838167_state B_92) A_184))->((not (((eq hoare_1167836817_state) A_185) B_92))->((member2058392318_state A_185) A_184)))) % FOF formula (forall (B_91:hoare_1167836817_state) (A_183:hoare_1167836817_state) (B_90:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_183) B_90)->False)->(((eq hoare_1167836817_state) A_183) B_91))->((member2058392318_state A_183) ((insert2134838167_state B_91) B_90)))) of role axiom named fact_9_insertCI % A new axiom: (forall (B_91:hoare_1167836817_state) (A_183:hoare_1167836817_state) (B_90:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_183) B_90)->False)->(((eq hoare_1167836817_state) A_183) B_91))->((member2058392318_state A_183) ((insert2134838167_state B_91) B_90)))) % FOF formula (forall (Q_8:(state->(state->Prop))) (P_18:(state->(state->Prop))) (G_21:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_37:com) (Q_7:(state->(state->Prop))), (((hoare_123228589_state G_21) ((insert2134838167_state (((hoare_908217195_state P_17) C_37) Q_7)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((P_18 Z_28) S)->(forall (S_1:state), ((forall (Z_29:state), (((P_17 Z_29) S)->((Q_7 Z_29) S_1)))->((Q_8 Z_28) S_1)))))->((hoare_123228589_state G_21) ((insert2134838167_state (((hoare_908217195_state P_18) C_37) Q_8)) bot_bo70021908tate_o))))) of role axiom named fact_10_conseq12 % A new axiom: (forall (Q_8:(state->(state->Prop))) (P_18:(state->(state->Prop))) (G_21:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_37:com) (Q_7:(state->(state->Prop))), (((hoare_123228589_state G_21) ((insert2134838167_state (((hoare_908217195_state P_17) C_37) Q_7)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((P_18 Z_28) S)->(forall (S_1:state), ((forall (Z_29:state), (((P_17 Z_29) S)->((Q_7 Z_29) S_1)))->((Q_8 Z_28) S_1)))))->((hoare_123228589_state G_21) ((insert2134838167_state (((hoare_908217195_state P_18) C_37) Q_8)) bot_bo70021908tate_o))))) % FOF formula (forall (A_182:hoare_1167836817_state), (((member2058392318_state A_182) bot_bo70021908tate_o)->False)) of role axiom named fact_11_emptyE % A new axiom: (forall (A_182:hoare_1167836817_state), (((member2058392318_state A_182) bot_bo70021908tate_o)->False)) % FOF formula (forall (A_181:hoare_1167836817_state) (A_180:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_181) A_180)))) of role axiom named fact_12_empty__not__insert % A new axiom: (forall (A_181:hoare_1167836817_state) (A_180:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_181) A_180)))) % FOF formula (forall (A_179:hoare_1167836817_state) (A_178:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_179) A_178)) bot_bo70021908tate_o))) of role axiom named fact_13_insert__not__empty % A new axiom: (forall (A_179:hoare_1167836817_state) (A_178:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_179) A_178)) bot_bo70021908tate_o))) % FOF formula (forall (B_89:hoare_1167836817_state) (A_177:hoare_1167836817_state), ((iff ((member2058392318_state B_89) ((insert2134838167_state A_177) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_89) A_177))) of role axiom named fact_14_singleton__iff % A new axiom: (forall (B_89:hoare_1167836817_state) (A_177:hoare_1167836817_state), ((iff ((member2058392318_state B_89) ((insert2134838167_state A_177) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_89) A_177))) % FOF formula (forall (A_176:hoare_1167836817_state) (B_88:hoare_1167836817_state) (C_36:hoare_1167836817_state) (D_3:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_176) ((insert2134838167_state B_88) bot_bo70021908tate_o))) ((insert2134838167_state C_36) ((insert2134838167_state D_3) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_176) C_36)) (((eq hoare_1167836817_state) B_88) D_3))) ((and (((eq hoare_1167836817_state) A_176) D_3)) (((eq hoare_1167836817_state) B_88) C_36))))) of role axiom named fact_15_doubleton__eq__iff % A new axiom: (forall (A_176:hoare_1167836817_state) (B_88:hoare_1167836817_state) (C_36:hoare_1167836817_state) (D_3:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_176) ((insert2134838167_state B_88) bot_bo70021908tate_o))) ((insert2134838167_state C_36) ((insert2134838167_state D_3) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_176) C_36)) (((eq hoare_1167836817_state) B_88) D_3))) ((and (((eq hoare_1167836817_state) A_176) D_3)) (((eq hoare_1167836817_state) B_88) C_36))))) % FOF formula (forall (A_175:hoare_1167836817_state) (A_174:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_174) bot_bo70021908tate_o)->(((member2058392318_state A_175) A_174)->False))) of role axiom named fact_16_equals0D % A new axiom: (forall (A_175:hoare_1167836817_state) (A_174:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_174) bot_bo70021908tate_o)->(((member2058392318_state A_175) A_174)->False))) % FOF formula (forall (P_16:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_16)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), ((P_16 X)->False)))) of role axiom named fact_17_Collect__empty__eq % A new axiom: (forall (P_16:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_16)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), ((P_16 X)->False)))) % FOF formula (forall (C_35:hoare_1167836817_state), (((member2058392318_state C_35) bot_bo70021908tate_o)->False)) of role axiom named fact_18_empty__iff % A new axiom: (forall (C_35:hoare_1167836817_state), (((member2058392318_state C_35) bot_bo70021908tate_o)->False)) % FOF formula (forall (P_15:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_15))) (forall (X:hoare_1167836817_state), ((P_15 X)->False)))) of role axiom named fact_19_empty__Collect__eq % A new axiom: (forall (P_15:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_15))) (forall (X:hoare_1167836817_state), ((P_15 X)->False)))) % FOF formula (forall (A_173:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((member2058392318_state X) A_173)))) (not (((eq (hoare_1167836817_state->Prop)) A_173) bot_bo70021908tate_o)))) of role axiom named fact_20_ex__in__conv % A new axiom: (forall (A_173:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((member2058392318_state X) A_173)))) (not (((eq (hoare_1167836817_state->Prop)) A_173) bot_bo70021908tate_o)))) % FOF formula (forall (A_172:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_172)->False))) (((eq (hoare_1167836817_state->Prop)) A_172) bot_bo70021908tate_o))) of role axiom named fact_21_all__not__in__conv % A new axiom: (forall (A_172:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_172)->False))) (((eq (hoare_1167836817_state->Prop)) A_172) bot_bo70021908tate_o))) % FOF formula (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X:hoare_1167836817_state)=> False))) of role axiom named fact_22_empty__def % A new axiom: (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X:hoare_1167836817_state)=> False))) % FOF formula (forall (A_171:hoare_1167836817_state) (A_170:(hoare_1167836817_state->Prop)), (((member2058392318_state A_171) A_170)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_171) A_170)) A_170))) of role axiom named fact_23_insert__absorb % A new axiom: (forall (A_171:hoare_1167836817_state) (A_170:(hoare_1167836817_state->Prop)), (((member2058392318_state A_171) A_170)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_171) A_170)) A_170))) % FOF formula (forall (B_87:hoare_1167836817_state) (A_169:hoare_1167836817_state) (B_86:(hoare_1167836817_state->Prop)), (((member2058392318_state A_169) B_86)->((member2058392318_state A_169) ((insert2134838167_state B_87) B_86)))) of role axiom named fact_24_insertI2 % A new axiom: (forall (B_87:hoare_1167836817_state) (A_169:hoare_1167836817_state) (B_86:(hoare_1167836817_state->Prop)), (((member2058392318_state A_169) B_86)->((member2058392318_state A_169) ((insert2134838167_state B_87) B_86)))) % FOF formula (forall (B_85:(hoare_1167836817_state->Prop)) (X_85:hoare_1167836817_state) (A_168:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_85) A_168)->False)->((((member2058392318_state X_85) B_85)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_85) A_168)) ((insert2134838167_state X_85) B_85))) (((eq (hoare_1167836817_state->Prop)) A_168) B_85))))) of role axiom named fact_25_insert__ident % A new axiom: (forall (B_85:(hoare_1167836817_state->Prop)) (X_85:hoare_1167836817_state) (A_168:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_85) A_168)->False)->((((member2058392318_state X_85) B_85)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_85) A_168)) ((insert2134838167_state X_85) B_85))) (((eq (hoare_1167836817_state->Prop)) A_168) B_85))))) % FOF formula (forall (Y_34:hoare_1167836817_state) (A_167:(hoare_1167836817_state->Prop)) (X_84:hoare_1167836817_state), ((iff (((insert2134838167_state Y_34) A_167) X_84)) ((or (((eq hoare_1167836817_state) Y_34) X_84)) (A_167 X_84)))) of role axiom named fact_26_insert__code % A new axiom: (forall (Y_34:hoare_1167836817_state) (A_167:(hoare_1167836817_state->Prop)) (X_84:hoare_1167836817_state), ((iff (((insert2134838167_state Y_34) A_167) X_84)) ((or (((eq hoare_1167836817_state) Y_34) X_84)) (A_167 X_84)))) % FOF formula (forall (A_166:hoare_1167836817_state) (B_84:hoare_1167836817_state) (A_165:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_166) ((insert2134838167_state B_84) A_165))) ((or (((eq hoare_1167836817_state) A_166) B_84)) ((member2058392318_state A_166) A_165)))) of role axiom named fact_27_insert__iff % A new axiom: (forall (A_166:hoare_1167836817_state) (B_84:hoare_1167836817_state) (A_165:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_166) ((insert2134838167_state B_84) A_165))) ((or (((eq hoare_1167836817_state) A_166) B_84)) ((member2058392318_state A_166) A_165)))) % FOF formula (forall (X_83:hoare_1167836817_state) (Y_33:hoare_1167836817_state) (A_164:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_83) ((insert2134838167_state Y_33) A_164))) ((insert2134838167_state Y_33) ((insert2134838167_state X_83) A_164)))) of role axiom named fact_28_insert__commute % A new axiom: (forall (X_83:hoare_1167836817_state) (Y_33:hoare_1167836817_state) (A_164:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_83) ((insert2134838167_state Y_33) A_164))) ((insert2134838167_state Y_33) ((insert2134838167_state X_83) A_164)))) % FOF formula (forall (X_82:hoare_1167836817_state) (A_163:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_82) ((insert2134838167_state X_82) A_163))) ((insert2134838167_state X_82) A_163))) of role axiom named fact_29_insert__absorb2 % A new axiom: (forall (X_82:hoare_1167836817_state) (A_163:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_82) ((insert2134838167_state X_82) A_163))) ((insert2134838167_state X_82) A_163))) % FOF formula (forall (A_162:hoare_1167836817_state) (P_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_162) (collec1027672124_state P_14))) (collec1027672124_state (fun (U:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U) A_162))) (P_14 U)))))) of role axiom named fact_30_insert__Collect % A new axiom: (forall (A_162:hoare_1167836817_state) (P_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_162) (collec1027672124_state P_14))) (collec1027672124_state (fun (U:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U) A_162))) (P_14 U)))))) % FOF formula (forall (A_161:hoare_1167836817_state) (B_83:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_161) B_83)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X) A_161)) ((member2058392318_state X) B_83)))))) of role axiom named fact_31_insert__compr % A new axiom: (forall (A_161:hoare_1167836817_state) (B_83:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_161) B_83)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X) A_161)) ((member2058392318_state X) B_83)))))) % FOF formula (forall (A_160:hoare_1167836817_state) (B_82:(hoare_1167836817_state->Prop)), ((member2058392318_state A_160) ((insert2134838167_state A_160) B_82))) of role axiom named fact_32_insertI1 % A new axiom: (forall (A_160:hoare_1167836817_state) (B_82:(hoare_1167836817_state->Prop)), ((member2058392318_state A_160) ((insert2134838167_state A_160) B_82))) % FOF formula (forall (A_159:hoare_1167836817_state) (B_81:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_159) bot_bo70021908tate_o)) ((insert2134838167_state B_81) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_159) B_81))) of role axiom named fact_33_singleton__inject % A new axiom: (forall (A_159:hoare_1167836817_state) (B_81:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_159) bot_bo70021908tate_o)) ((insert2134838167_state B_81) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_159) B_81))) % FOF formula (forall (B_80:hoare_1167836817_state) (A_158:hoare_1167836817_state), (((member2058392318_state B_80) ((insert2134838167_state A_158) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_80) A_158))) of role axiom named fact_34_singletonE % A new axiom: (forall (B_80:hoare_1167836817_state) (A_158:hoare_1167836817_state), (((member2058392318_state B_80) ((insert2134838167_state A_158) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_80) A_158))) % FOF formula (forall (X_81:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_81) bot_bo70021908tate_o))) X_81)) of role axiom named fact_35_the__elem__eq % A new axiom: (forall (X_81:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_81) bot_bo70021908tate_o))) X_81)) % FOF formula (forall (X_80:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_80)) bot_bot_o)) of role axiom named fact_36_bot__apply % A new axiom: (forall (X_80:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_80)) bot_bot_o)) % FOF formula (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) bot_bot_o)) of role axiom named fact_37_bot__fun__def % A new axiom: (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) bot_bot_o)) % FOF formula (forall (G_20:(hoare_1167836817_state->Prop)) (P_13:(state->(state->Prop))), ((hoare_123228589_state G_20) ((insert2134838167_state (((hoare_908217195_state P_13) skip) P_13)) bot_bo70021908tate_o))) of role axiom named fact_38_hoare__derivs_OSkip % A new axiom: (forall (G_20:(hoare_1167836817_state->Prop)) (P_13:(state->(state->Prop))), ((hoare_123228589_state G_20) ((insert2134838167_state (((hoare_908217195_state P_13) skip) P_13)) bot_bo70021908tate_o))) % FOF formula (forall (D_2:com) (R:(state->(state->Prop))) (G_19:(hoare_1167836817_state->Prop)) (P_12:(state->(state->Prop))) (C_34:com) (Q_6:(state->(state->Prop))), (((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state P_12) C_34) Q_6)) bot_bo70021908tate_o))->(((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state Q_6) D_2) R)) bot_bo70021908tate_o))->((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state P_12) ((semi C_34) D_2)) R)) bot_bo70021908tate_o))))) of role axiom named fact_39_Comp % A new axiom: (forall (D_2:com) (R:(state->(state->Prop))) (G_19:(hoare_1167836817_state->Prop)) (P_12:(state->(state->Prop))) (C_34:com) (Q_6:(state->(state->Prop))), (((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state P_12) C_34) Q_6)) bot_bo70021908tate_o))->(((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state Q_6) D_2) R)) bot_bo70021908tate_o))->((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state P_12) ((semi C_34) D_2)) R)) bot_bo70021908tate_o))))) % FOF formula (forall (Y_32:hoare_1167836817_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_32) (((hoare_908217195_state Fun1) Com) Fun2))))->False)) of role axiom named fact_40_triple_Oexhaust % A new axiom: (forall (Y_32:hoare_1167836817_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_32) (((hoare_908217195_state Fun1) Com) Fun2))))->False)) % FOF formula (forall (X_79:hoare_1167836817_state) (A_157:(hoare_1167836817_state->Prop)), (((member2058392318_state X_79) A_157)->((forall (B_79:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_157) ((insert2134838167_state X_79) B_79))->((member2058392318_state X_79) B_79)))->False))) of role axiom named fact_41_Set_Oset__insert % A new axiom: (forall (X_79:hoare_1167836817_state) (A_157:(hoare_1167836817_state->Prop)), (((member2058392318_state X_79) A_157)->((forall (B_79:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_157) ((insert2134838167_state X_79) B_79))->((member2058392318_state X_79) B_79)))->False))) % FOF formula (forall (A_156:hoare_1167836817_state) (A_155:(hoare_1167836817_state->Prop)), (((member2058392318_state A_156) A_155)->((ex (hoare_1167836817_state->Prop)) (fun (B_79:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_155) ((insert2134838167_state A_156) B_79))) (((member2058392318_state A_156) B_79)->False)))))) of role axiom named fact_42_mk__disjoint__insert % A new axiom: (forall (A_156:hoare_1167836817_state) (A_155:(hoare_1167836817_state->Prop)), (((member2058392318_state A_156) A_155)->((ex (hoare_1167836817_state->Prop)) (fun (B_79:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_155) ((insert2134838167_state A_156) B_79))) (((member2058392318_state A_156) B_79)->False)))))) % FOF formula (forall (A_154:(hoare_1167836817_state->Prop)), ((forall (Y:hoare_1167836817_state), (((member2058392318_state Y) A_154)->False))->(((eq (hoare_1167836817_state->Prop)) A_154) bot_bo70021908tate_o))) of role axiom named fact_43_equals0I % A new axiom: (forall (A_154:(hoare_1167836817_state->Prop)), ((forall (Y:hoare_1167836817_state), (((member2058392318_state Y) A_154)->False))->(((eq (hoare_1167836817_state->Prop)) A_154) bot_bo70021908tate_o))) % FOF formula (forall (Q_4:(state->(state->Prop))) (G_18:(hoare_1167836817_state->Prop)) (C_33:com) (P_10:(state->(state->Prop))), ((forall (Z_28:state) (S:state), (((P_10 Z_28) S)->((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_11) C_33) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((Q_4 Z_28) S_1))))))))))->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_10) C_33) Q_4)) bot_bo70021908tate_o)))) of role axiom named fact_44_conseq % A new axiom: (forall (Q_4:(state->(state->Prop))) (G_18:(hoare_1167836817_state->Prop)) (C_33:com) (P_10:(state->(state->Prop))), ((forall (Z_28:state) (S:state), (((P_10 Z_28) S)->((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_11) C_33) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((Q_4 Z_28) S_1))))))))))->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_10) C_33) Q_4)) bot_bo70021908tate_o)))) % FOF formula (forall (A_153:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_153) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_79:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_153) ((insert2134838167_state X) B_79))) (((member2058392318_state X) B_79)->False)))))))) of role axiom named fact_45_nonempty__iff % A new axiom: (forall (A_153:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_153) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_79:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_153) ((insert2134838167_state X) B_79))) (((member2058392318_state X) B_79)->False)))))))) % FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))) of role axiom named fact_46_com_Osimps_I13_J % A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))) % FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))) of role axiom named fact_47_com_Osimps_I12_J % A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))) % FOF formula (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))) of role axiom named fact_48_com_Osimps_I3_J % A new axiom: (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))) % FOF formula (forall (F_82:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_152:hoare_1167836817_state) (B_78:hoare_1167836817_state), ((iff (((finite309220289_state F_82) ((insert2134838167_state A_152) bot_bo70021908tate_o)) B_78)) (((eq hoare_1167836817_state) A_152) B_78))) of role axiom named fact_49_fold1Set__sing % A new axiom: (forall (F_82:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_152:hoare_1167836817_state) (B_78:hoare_1167836817_state), ((iff (((finite309220289_state F_82) ((insert2134838167_state A_152) bot_bo70021908tate_o)) B_78)) (((eq hoare_1167836817_state) A_152) B_78))) % FOF formula (forall (X_78:hoare_1167836817_state) (F_81:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_80:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_81) F_80)->(((eq hoare_1167836817_state) (F_80 ((insert2134838167_state X_78) bot_bo70021908tate_o))) X_78))) of role axiom named fact_50_folding__one_Osingleton % A new axiom: (forall (X_78:hoare_1167836817_state) (F_81:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_80:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_81) F_80)->(((eq hoare_1167836817_state) (F_80 ((insert2134838167_state X_78) bot_bo70021908tate_o))) X_78))) % FOF formula (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) ((member2058392318_state X) bot_bo70021908tate_o))) of role axiom named fact_51_bot__empty__eq % A new axiom: (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) ((member2058392318_state X) bot_bo70021908tate_o))) % FOF formula (forall (F_79:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_151:hoare_1167836817_state), (((eq hoare_1167836817_state) ((finite1646097201_state F_79) ((insert2134838167_state A_151) bot_bo70021908tate_o))) A_151)) of role axiom named fact_52_fold1__singleton % A new axiom: (forall (F_79:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_151:hoare_1167836817_state), (((eq hoare_1167836817_state) ((finite1646097201_state F_79) ((insert2134838167_state A_151) bot_bo70021908tate_o))) A_151)) % FOF formula (forall (A_150:hoare_1167836817_state) (G_17:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (F_78:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((((eq ((hoare_1167836817_state->Prop)->hoare_1167836817_state)) G_17) (finite1646097201_state F_78))->(((eq hoare_1167836817_state) (G_17 ((insert2134838167_state A_150) bot_bo70021908tate_o))) A_150))) of role axiom named fact_53_fold1__singleton__def % A new axiom: (forall (A_150:hoare_1167836817_state) (G_17:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (F_78:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((((eq ((hoare_1167836817_state->Prop)->hoare_1167836817_state)) G_17) (finite1646097201_state F_78))->(((eq hoare_1167836817_state) (G_17 ((insert2134838167_state A_150) bot_bo70021908tate_o))) A_150))) % FOF formula (forall (F_77:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (X_77:hoare_1167836817_state), ((((finite309220289_state F_77) bot_bo70021908tate_o) X_77)->False)) of role axiom named fact_54_empty__fold1SetE % A new axiom: (forall (F_77:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (X_77:hoare_1167836817_state), ((((finite309220289_state F_77) bot_bo70021908tate_o) X_77)->False)) % FOF formula (forall (F_76:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_149:(hoare_1167836817_state->Prop)) (X_76:hoare_1167836817_state), ((((finite309220289_state F_76) A_149) X_76)->(not (((eq (hoare_1167836817_state->Prop)) A_149) bot_bo70021908tate_o)))) of role axiom named fact_55_fold1Set__nonempty % A new axiom: (forall (F_76:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_149:(hoare_1167836817_state->Prop)) (X_76:hoare_1167836817_state), ((((finite309220289_state F_76) A_149) X_76)->(not (((eq (hoare_1167836817_state->Prop)) A_149) bot_bo70021908tate_o)))) % FOF formula (forall (F_75:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_148:hoare_1167836817_state) (A_147:(hoare_1167836817_state->Prop)) (X_75:hoare_1167836817_state), (((((finite1316643734_state F_75) A_148) A_147) X_75)->((((member2058392318_state A_148) A_147)->False)->(((finite309220289_state F_75) ((insert2134838167_state A_148) A_147)) X_75)))) of role axiom named fact_56_fold1Set_Ointros % A new axiom: (forall (F_75:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_148:hoare_1167836817_state) (A_147:(hoare_1167836817_state->Prop)) (X_75:hoare_1167836817_state), (((((finite1316643734_state F_75) A_148) A_147) X_75)->((((member2058392318_state A_148) A_147)->False)->(((finite309220289_state F_75) ((insert2134838167_state A_148) A_147)) X_75)))) % FOF formula (forall (X_74:hoare_1167836817_state) (A_146:(hoare_1167836817_state->Prop)) (F_74:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_73:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_74) F_73)->((finite1084549118_state A_146)->((((member2058392318_state X_74) A_146)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_146) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_73 ((insert2134838167_state X_74) A_146))) ((F_74 X_74) (F_73 A_146)))))))) of role axiom named fact_57_folding__one_Oinsert % A new axiom: (forall (X_74:hoare_1167836817_state) (A_146:(hoare_1167836817_state->Prop)) (F_74:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_73:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_74) F_73)->((finite1084549118_state A_146)->((((member2058392318_state X_74) A_146)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_146) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_73 ((insert2134838167_state X_74) A_146))) ((F_74 X_74) (F_73 A_146)))))))) % FOF formula (forall (A_145:(hoare_1167836817_state->Prop)) (F_72:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_71:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_72) F_71)->((finite1084549118_state A_145)->(((eq hoare_1167836817_state) (F_71 A_145)) ((finite1646097201_state F_72) A_145))))) of role axiom named fact_58_folding__one_Oeq__fold % A new axiom: (forall (A_145:(hoare_1167836817_state->Prop)) (F_72:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_71:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_72) F_71)->((finite1084549118_state A_145)->(((eq hoare_1167836817_state) (F_71 A_145)) ((finite1646097201_state F_72) A_145))))) % FOF formula (forall (A_144:(hoare_1167836817_state->Prop)) (F_70:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_69:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_70) F_69)->((finite1084549118_state A_144)->((not (((eq (hoare_1167836817_state->Prop)) A_144) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((member2058392318_state ((F_70 X) Y)) ((insert2134838167_state X) ((insert2134838167_state Y) bot_bo70021908tate_o))))->((member2058392318_state (F_69 A_144)) A_144)))))) of role axiom named fact_59_folding__one_Oclosed % A new axiom: (forall (A_144:(hoare_1167836817_state->Prop)) (F_70:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_69:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_70) F_69)->((finite1084549118_state A_144)->((not (((eq (hoare_1167836817_state->Prop)) A_144) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((member2058392318_state ((F_70 X) Y)) ((insert2134838167_state X) ((insert2134838167_state Y) bot_bo70021908tate_o))))->((member2058392318_state (F_69 A_144)) A_144)))))) % FOF formula (forall (F_68:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_143:hoare_1167836817_state) (X_73:(hoare_1167836817_state->Prop)) (X_72:hoare_1167836817_state), ((((finite309220289_state F_68) ((insert2134838167_state A_143) X_73)) X_72)->((forall (A_59:hoare_1167836817_state) (A_58:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_143) X_73)) ((insert2134838167_state A_59) A_58))->(((((finite1316643734_state F_68) A_59) A_58) X_72)->((member2058392318_state A_59) A_58))))->False))) of role axiom named fact_60_insert__fold1SetE % A new axiom: (forall (F_68:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_143:hoare_1167836817_state) (X_73:(hoare_1167836817_state->Prop)) (X_72:hoare_1167836817_state), ((((finite309220289_state F_68) ((insert2134838167_state A_143) X_73)) X_72)->((forall (A_59:hoare_1167836817_state) (A_58:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_143) X_73)) ((insert2134838167_state A_59) A_58))->(((((finite1316643734_state F_68) A_59) A_58) X_72)->((member2058392318_state A_59) A_58))))->False))) % FOF formula (forall (A_142:(hoare_1167836817_state->Prop)) (X_71:hoare_1167836817_state), (((ord_le827224136tate_o A_142) ((insert2134838167_state X_71) bot_bo70021908tate_o))->((or (((eq (hoare_1167836817_state->Prop)) A_142) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_142) ((insert2134838167_state X_71) bot_bo70021908tate_o))))) of role axiom named fact_61_subset__singletonD % A new axiom: (forall (A_142:(hoare_1167836817_state->Prop)) (X_71:hoare_1167836817_state), (((ord_le827224136tate_o A_142) ((insert2134838167_state X_71) bot_bo70021908tate_o))->((or (((eq (hoare_1167836817_state->Prop)) A_142) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_142) ((insert2134838167_state X_71) bot_bo70021908tate_o))))) % FOF formula (forall (X_70:Prop), ((ord_less_eq_o X_70) X_70)) of role axiom named fact_62_order__refl % A new axiom: (forall (X_70:Prop), ((ord_less_eq_o X_70) X_70)) % FOF formula (forall (X_70:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_70) X_70)) of role axiom named fact_63_order__refl % A new axiom: (forall (X_70:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_70) X_70)) % FOF formula (forall (C_32:hoare_1167836817_state) (A_141:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_141) B_77)->(((member2058392318_state C_32) A_141)->((member2058392318_state C_32) B_77)))) of role axiom named fact_64_subsetD % A new axiom: (forall (C_32:hoare_1167836817_state) (A_141:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_141) B_77)->(((member2058392318_state C_32) A_141)->((member2058392318_state C_32) B_77)))) % FOF formula (forall (A_140:(hoare_1167836817_state->Prop)) (B_76:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_140) B_76)->(((ord_le827224136tate_o B_76) A_140)->(((eq (hoare_1167836817_state->Prop)) A_140) B_76)))) of role axiom named fact_65_equalityI % A new axiom: (forall (A_140:(hoare_1167836817_state->Prop)) (B_76:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_140) B_76)->(((ord_le827224136tate_o B_76) A_140)->(((eq (hoare_1167836817_state->Prop)) A_140) B_76)))) % FOF formula (finite1084549118_state bot_bo70021908tate_o) of role axiom named fact_66_finite_OemptyI % A new axiom: (finite1084549118_state bot_bo70021908tate_o) % FOF formula (forall (A_139:hoare_1167836817_state) (A_138:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_138)->(finite1084549118_state ((insert2134838167_state A_139) A_138)))) of role axiom named fact_67_finite_OinsertI % A new axiom: (forall (A_139:hoare_1167836817_state) (A_138:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_138)->(finite1084549118_state ((insert2134838167_state A_139) A_138)))) % FOF formula (forall (A_137:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_137)) of role axiom named fact_68_empty__subsetI % A new axiom: (forall (A_137:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_137)) % FOF formula (forall (Q_3:(hoare_1167836817_state->Prop)) (P_9:(hoare_1167836817_state->Prop)) (X_69:hoare_1167836817_state), ((P_9 X_69)->(((ord_le827224136tate_o P_9) Q_3)->(Q_3 X_69)))) of role axiom named fact_69_rev__predicate1D % A new axiom: (forall (Q_3:(hoare_1167836817_state->Prop)) (P_9:(hoare_1167836817_state->Prop)) (X_69:hoare_1167836817_state), ((P_9 X_69)->(((ord_le827224136tate_o P_9) Q_3)->(Q_3 X_69)))) % FOF formula (forall (X_68:hoare_1167836817_state) (P_8:(hoare_1167836817_state->Prop)) (Q_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o P_8) Q_2)->((P_8 X_68)->(Q_2 X_68)))) of role axiom named fact_70_predicate1D % A new axiom: (forall (X_68:hoare_1167836817_state) (P_8:(hoare_1167836817_state->Prop)) (Q_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o P_8) Q_2)->((P_8 X_68)->(Q_2 X_68)))) % FOF formula (forall (X_67:hoare_1167836817_state) (A_136:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_67) A_136)) (A_136 X_67))) of role axiom named fact_71_mem__def % A new axiom: (forall (X_67:hoare_1167836817_state) (A_136:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_67) A_136)) (A_136 X_67))) % FOF formula (forall (P_7:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_7)) P_7)) of role axiom named fact_72_Collect__def % A new axiom: (forall (P_7:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_7)) P_7)) % FOF formula (forall (A_135:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_135) A_135)) of role axiom named fact_73_subset__refl % A new axiom: (forall (A_135:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_135) A_135)) % FOF formula (forall (A_134:(hoare_1167836817_state->Prop)) (B_75:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) A_134) B_75)) ((and ((ord_le827224136tate_o A_134) B_75)) ((ord_le827224136tate_o B_75) A_134)))) of role axiom named fact_74_set__eq__subset % A new axiom: (forall (A_134:(hoare_1167836817_state->Prop)) (B_75:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) A_134) B_75)) ((and ((ord_le827224136tate_o A_134) B_75)) ((ord_le827224136tate_o B_75) A_134)))) % FOF formula (forall (A_133:(hoare_1167836817_state->Prop)) (B_74:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_133) B_74)->((ord_le827224136tate_o A_133) B_74))) of role axiom named fact_75_equalityD1 % A new axiom: (forall (A_133:(hoare_1167836817_state->Prop)) (B_74:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_133) B_74)->((ord_le827224136tate_o A_133) B_74))) % FOF formula (forall (A_132:(hoare_1167836817_state->Prop)) (B_73:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_132) B_73)->((ord_le827224136tate_o B_73) A_132))) of role axiom named fact_76_equalityD2 % A new axiom: (forall (A_132:(hoare_1167836817_state->Prop)) (B_73:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_132) B_73)->((ord_le827224136tate_o B_73) A_132))) % FOF formula (forall (X_66:hoare_1167836817_state) (A_131:(hoare_1167836817_state->Prop)) (B_72:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_131) B_72)->(((member2058392318_state X_66) A_131)->((member2058392318_state X_66) B_72)))) of role axiom named fact_77_in__mono % A new axiom: (forall (X_66:hoare_1167836817_state) (A_131:(hoare_1167836817_state->Prop)) (B_72:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_131) B_72)->(((member2058392318_state X_66) A_131)->((member2058392318_state X_66) B_72)))) % FOF formula (forall (B_71:(hoare_1167836817_state->Prop)) (X_65:hoare_1167836817_state) (A_130:(hoare_1167836817_state->Prop)), (((member2058392318_state X_65) A_130)->(((ord_le827224136tate_o A_130) B_71)->((member2058392318_state X_65) B_71)))) of role axiom named fact_78_set__rev__mp % A new axiom: (forall (B_71:(hoare_1167836817_state->Prop)) (X_65:hoare_1167836817_state) (A_130:(hoare_1167836817_state->Prop)), (((member2058392318_state X_65) A_130)->(((ord_le827224136tate_o A_130) B_71)->((member2058392318_state X_65) B_71)))) % FOF formula (forall (X_64:hoare_1167836817_state) (A_129:(hoare_1167836817_state->Prop)) (B_70:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_129) B_70)->(((member2058392318_state X_64) A_129)->((member2058392318_state X_64) B_70)))) of role axiom named fact_79_set__mp % A new axiom: (forall (X_64:hoare_1167836817_state) (A_129:(hoare_1167836817_state->Prop)) (B_70:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_129) B_70)->(((member2058392318_state X_64) A_129)->((member2058392318_state X_64) B_70)))) % FOF formula (forall (C_31:(hoare_1167836817_state->Prop)) (A_128:(hoare_1167836817_state->Prop)) (B_69:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_128) B_69)->(((ord_le827224136tate_o B_69) C_31)->((ord_le827224136tate_o A_128) C_31)))) of role axiom named fact_80_subset__trans % A new axiom: (forall (C_31:(hoare_1167836817_state->Prop)) (A_128:(hoare_1167836817_state->Prop)) (B_69:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_128) B_69)->(((ord_le827224136tate_o B_69) C_31)->((ord_le827224136tate_o A_128) C_31)))) % FOF formula (forall (A_127:(hoare_1167836817_state->Prop)) (B_68:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_127) B_68)->((((ord_le827224136tate_o A_127) B_68)->(((ord_le827224136tate_o B_68) A_127)->False))->False))) of role axiom named fact_81_equalityE % A new axiom: (forall (A_127:(hoare_1167836817_state->Prop)) (B_68:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_127) B_68)->((((ord_le827224136tate_o A_127) B_68)->(((ord_le827224136tate_o B_68) A_127)->False))->False))) % FOF formula (forall (F_67:(hoare_1167836817_state->Prop)) (G_16:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o F_67) G_16)) (forall (X:hoare_1167836817_state), ((ord_less_eq_o (F_67 X)) (G_16 X))))) of role axiom named fact_82_le__fun__def % A new axiom: (forall (F_67:(hoare_1167836817_state->Prop)) (G_16:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o F_67) G_16)) (forall (X:hoare_1167836817_state), ((ord_less_eq_o (F_67 X)) (G_16 X))))) % FOF formula (forall (Y_31:Prop) (X_63:Prop), ((iff ((iff X_63) Y_31)) ((and ((ord_less_eq_o X_63) Y_31)) ((ord_less_eq_o Y_31) X_63)))) of role axiom named fact_83_order__eq__iff % A new axiom: (forall (Y_31:Prop) (X_63:Prop), ((iff ((iff X_63) Y_31)) ((and ((ord_less_eq_o X_63) Y_31)) ((ord_less_eq_o Y_31) X_63)))) % FOF formula (forall (X_63:(hoare_1167836817_state->Prop)) (Y_31:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) X_63) Y_31)) ((and ((ord_le827224136tate_o X_63) Y_31)) ((ord_le827224136tate_o Y_31) X_63)))) of role axiom named fact_84_order__eq__iff % A new axiom: (forall (X_63:(hoare_1167836817_state->Prop)) (Y_31:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) X_63) Y_31)) ((and ((ord_le827224136tate_o X_63) Y_31)) ((ord_le827224136tate_o Y_31) X_63)))) % FOF formula (forall (A_126:(hoare_1167836817_state->Prop)) (B_67:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_67)->(((ord_le827224136tate_o A_126) B_67)->(finite1084549118_state A_126)))) of role axiom named fact_85_rev__finite__subset % A new axiom: (forall (A_126:(hoare_1167836817_state->Prop)) (B_67:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_67)->(((ord_le827224136tate_o A_126) B_67)->(finite1084549118_state A_126)))) % FOF formula (forall (Y_30:Prop) (X_62:Prop), (((iff X_62) Y_30)->((ord_less_eq_o X_62) Y_30))) of role axiom named fact_86_order__eq__refl % A new axiom: (forall (Y_30:Prop) (X_62:Prop), (((iff X_62) Y_30)->((ord_less_eq_o X_62) Y_30))) % FOF formula (forall (X_62:(hoare_1167836817_state->Prop)) (Y_30:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) X_62) Y_30)->((ord_le827224136tate_o X_62) Y_30))) of role axiom named fact_87_order__eq__refl % A new axiom: (forall (X_62:(hoare_1167836817_state->Prop)) (Y_30:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) X_62) Y_30)->((ord_le827224136tate_o X_62) Y_30))) % FOF formula (forall (X_61:hoare_1167836817_state) (F_66:(hoare_1167836817_state->Prop)) (G_15:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_66) G_15)->((ord_less_eq_o (F_66 X_61)) (G_15 X_61)))) of role axiom named fact_88_le__funD % A new axiom: (forall (X_61:hoare_1167836817_state) (F_66:(hoare_1167836817_state->Prop)) (G_15:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_66) G_15)->((ord_less_eq_o (F_66 X_61)) (G_15 X_61)))) % FOF formula (forall (Y_29:Prop) (X_60:Prop), (((ord_less_eq_o Y_29) X_60)->((iff ((ord_less_eq_o X_60) Y_29)) ((iff X_60) Y_29)))) of role axiom named fact_89_order__antisym__conv % A new axiom: (forall (Y_29:Prop) (X_60:Prop), (((ord_less_eq_o Y_29) X_60)->((iff ((ord_less_eq_o X_60) Y_29)) ((iff X_60) Y_29)))) % FOF formula (forall (Y_29:(hoare_1167836817_state->Prop)) (X_60:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_29) X_60)->((iff ((ord_le827224136tate_o X_60) Y_29)) (((eq (hoare_1167836817_state->Prop)) X_60) Y_29)))) of role axiom named fact_90_order__antisym__conv % A new axiom: (forall (Y_29:(hoare_1167836817_state->Prop)) (X_60:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_29) X_60)->((iff ((ord_le827224136tate_o X_60) Y_29)) (((eq (hoare_1167836817_state->Prop)) X_60) Y_29)))) % FOF formula (forall (A_125:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_125) B_66)->((finite1084549118_state B_66)->(finite1084549118_state A_125)))) of role axiom named fact_91_finite__subset % A new axiom: (forall (A_125:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_125) B_66)->((finite1084549118_state B_66)->(finite1084549118_state A_125)))) % FOF formula (forall (C_30:Prop) (B_65:Prop) (A_124:Prop), (((iff A_124) B_65)->(((ord_less_eq_o B_65) C_30)->((ord_less_eq_o A_124) C_30)))) of role axiom named fact_92_ord__eq__le__trans % A new axiom: (forall (C_30:Prop) (B_65:Prop) (A_124:Prop), (((iff A_124) B_65)->(((ord_less_eq_o B_65) C_30)->((ord_less_eq_o A_124) C_30)))) % FOF formula (forall (C_30:(hoare_1167836817_state->Prop)) (A_124:(hoare_1167836817_state->Prop)) (B_65:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_124) B_65)->(((ord_le827224136tate_o B_65) C_30)->((ord_le827224136tate_o A_124) C_30)))) of role axiom named fact_93_ord__eq__le__trans % A new axiom: (forall (C_30:(hoare_1167836817_state->Prop)) (A_124:(hoare_1167836817_state->Prop)) (B_65:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_124) B_65)->(((ord_le827224136tate_o B_65) C_30)->((ord_le827224136tate_o A_124) C_30)))) % FOF formula (forall (C_29:Prop) (B_64:Prop) (A_123:Prop), (((iff A_123) B_64)->(((ord_less_eq_o C_29) B_64)->((ord_less_eq_o C_29) A_123)))) of role axiom named fact_94_xt1_I3_J % A new axiom: (forall (C_29:Prop) (B_64:Prop) (A_123:Prop), (((iff A_123) B_64)->(((ord_less_eq_o C_29) B_64)->((ord_less_eq_o C_29) A_123)))) % FOF formula (forall (C_29:(hoare_1167836817_state->Prop)) (A_123:(hoare_1167836817_state->Prop)) (B_64:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_123) B_64)->(((ord_le827224136tate_o C_29) B_64)->((ord_le827224136tate_o C_29) A_123)))) of role axiom named fact_95_xt1_I3_J % A new axiom: (forall (C_29:(hoare_1167836817_state->Prop)) (A_123:(hoare_1167836817_state->Prop)) (B_64:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_123) B_64)->(((ord_le827224136tate_o C_29) B_64)->((ord_le827224136tate_o C_29) A_123)))) % FOF formula (forall (C_28:Prop) (A_122:Prop) (B_63:Prop), (((ord_less_eq_o A_122) B_63)->(((iff B_63) C_28)->((ord_less_eq_o A_122) C_28)))) of role axiom named fact_96_ord__le__eq__trans % A new axiom: (forall (C_28:Prop) (A_122:Prop) (B_63:Prop), (((ord_less_eq_o A_122) B_63)->(((iff B_63) C_28)->((ord_less_eq_o A_122) C_28)))) % FOF formula (forall (C_28:(hoare_1167836817_state->Prop)) (A_122:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_122) B_63)->((((eq (hoare_1167836817_state->Prop)) B_63) C_28)->((ord_le827224136tate_o A_122) C_28)))) of role axiom named fact_97_ord__le__eq__trans % A new axiom: (forall (C_28:(hoare_1167836817_state->Prop)) (A_122:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_122) B_63)->((((eq (hoare_1167836817_state->Prop)) B_63) C_28)->((ord_le827224136tate_o A_122) C_28)))) % FOF formula (forall (C_27:Prop) (B_62:Prop) (A_121:Prop), (((ord_less_eq_o B_62) A_121)->(((iff B_62) C_27)->((ord_less_eq_o C_27) A_121)))) of role axiom named fact_98_xt1_I4_J % A new axiom: (forall (C_27:Prop) (B_62:Prop) (A_121:Prop), (((ord_less_eq_o B_62) A_121)->(((iff B_62) C_27)->((ord_less_eq_o C_27) A_121)))) % FOF formula (forall (C_27:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)) (A_121:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_62) A_121)->((((eq (hoare_1167836817_state->Prop)) B_62) C_27)->((ord_le827224136tate_o C_27) A_121)))) of role axiom named fact_99_xt1_I4_J % A new axiom: (forall (C_27:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)) (A_121:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_62) A_121)->((((eq (hoare_1167836817_state->Prop)) B_62) C_27)->((ord_le827224136tate_o C_27) A_121)))) % FOF formula (forall (X_59:Prop) (Y_28:Prop), (((ord_less_eq_o X_59) Y_28)->(((ord_less_eq_o Y_28) X_59)->((iff X_59) Y_28)))) of role axiom named fact_100_order__antisym % A new axiom: (forall (X_59:Prop) (Y_28:Prop), (((ord_less_eq_o X_59) Y_28)->(((ord_less_eq_o Y_28) X_59)->((iff X_59) Y_28)))) % FOF formula (forall (X_59:(hoare_1167836817_state->Prop)) (Y_28:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_59) Y_28)->(((ord_le827224136tate_o Y_28) X_59)->(((eq (hoare_1167836817_state->Prop)) X_59) Y_28)))) of role axiom named fact_101_order__antisym % A new axiom: (forall (X_59:(hoare_1167836817_state->Prop)) (Y_28:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_59) Y_28)->(((ord_le827224136tate_o Y_28) X_59)->(((eq (hoare_1167836817_state->Prop)) X_59) Y_28)))) % FOF formula (forall (Z_27:Prop) (X_58:Prop) (Y_27:Prop), (((ord_less_eq_o X_58) Y_27)->(((ord_less_eq_o Y_27) Z_27)->((ord_less_eq_o X_58) Z_27)))) of role axiom named fact_102_order__trans % A new axiom: (forall (Z_27:Prop) (X_58:Prop) (Y_27:Prop), (((ord_less_eq_o X_58) Y_27)->(((ord_less_eq_o Y_27) Z_27)->((ord_less_eq_o X_58) Z_27)))) % FOF formula (forall (Z_27:(hoare_1167836817_state->Prop)) (X_58:(hoare_1167836817_state->Prop)) (Y_27:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_58) Y_27)->(((ord_le827224136tate_o Y_27) Z_27)->((ord_le827224136tate_o X_58) Z_27)))) of role axiom named fact_103_order__trans % A new axiom: (forall (Z_27:(hoare_1167836817_state->Prop)) (X_58:(hoare_1167836817_state->Prop)) (Y_27:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_58) Y_27)->(((ord_le827224136tate_o Y_27) Z_27)->((ord_le827224136tate_o X_58) Z_27)))) % FOF formula (forall (Y_26:Prop) (X_57:Prop), (((ord_less_eq_o Y_26) X_57)->(((ord_less_eq_o X_57) Y_26)->((iff X_57) Y_26)))) of role axiom named fact_104_xt1_I5_J % A new axiom: (forall (Y_26:Prop) (X_57:Prop), (((ord_less_eq_o Y_26) X_57)->(((ord_less_eq_o X_57) Y_26)->((iff X_57) Y_26)))) % FOF formula (forall (Y_26:(hoare_1167836817_state->Prop)) (X_57:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_26) X_57)->(((ord_le827224136tate_o X_57) Y_26)->(((eq (hoare_1167836817_state->Prop)) X_57) Y_26)))) of role axiom named fact_105_xt1_I5_J % A new axiom: (forall (Y_26:(hoare_1167836817_state->Prop)) (X_57:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_26) X_57)->(((ord_le827224136tate_o X_57) Y_26)->(((eq (hoare_1167836817_state->Prop)) X_57) Y_26)))) % FOF formula (forall (Z_26:Prop) (Y_25:Prop) (X_56:Prop), (((ord_less_eq_o Y_25) X_56)->(((ord_less_eq_o Z_26) Y_25)->((ord_less_eq_o Z_26) X_56)))) of role axiom named fact_106_xt1_I6_J % A new axiom: (forall (Z_26:Prop) (Y_25:Prop) (X_56:Prop), (((ord_less_eq_o Y_25) X_56)->(((ord_less_eq_o Z_26) Y_25)->((ord_less_eq_o Z_26) X_56)))) % FOF formula (forall (Z_26:(hoare_1167836817_state->Prop)) (Y_25:(hoare_1167836817_state->Prop)) (X_56:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_25) X_56)->(((ord_le827224136tate_o Z_26) Y_25)->((ord_le827224136tate_o Z_26) X_56)))) of role axiom named fact_107_xt1_I6_J % A new axiom: (forall (Z_26:(hoare_1167836817_state->Prop)) (Y_25:(hoare_1167836817_state->Prop)) (X_56:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_25) X_56)->(((ord_le827224136tate_o Z_26) Y_25)->((ord_le827224136tate_o Z_26) X_56)))) % FOF formula (forall (X_55:hoare_1167836817_state) (F_65:(hoare_1167836817_state->Prop)) (G_14:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_65) G_14)->((ord_less_eq_o (F_65 X_55)) (G_14 X_55)))) of role axiom named fact_108_le__funE % A new axiom: (forall (X_55:hoare_1167836817_state) (F_65:(hoare_1167836817_state->Prop)) (G_14:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_65) G_14)->((ord_less_eq_o (F_65 X_55)) (G_14 X_55)))) % FOF formula (forall (A_120:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_120)) of role axiom named fact_109_bot__least % A new axiom: (forall (A_120:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_120)) % FOF formula (forall (A_120:Prop), ((ord_less_eq_o bot_bot_o) A_120)) of role axiom named fact_110_bot__least % A new axiom: (forall (A_120:Prop), ((ord_less_eq_o bot_bot_o) A_120)) % FOF formula (forall (A_119:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_119) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_119) bot_bo70021908tate_o))) of role axiom named fact_111_bot__unique % A new axiom: (forall (A_119:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_119) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_119) bot_bo70021908tate_o))) % FOF formula (forall (A_119:Prop), ((iff ((ord_less_eq_o A_119) bot_bot_o)) ((iff A_119) bot_bot_o))) of role axiom named fact_112_bot__unique % A new axiom: (forall (A_119:Prop), ((iff ((ord_less_eq_o A_119) bot_bot_o)) ((iff A_119) bot_bot_o))) % FOF formula (forall (A_118:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_118) bot_bo70021908tate_o)->(((eq (hoare_1167836817_state->Prop)) A_118) bot_bo70021908tate_o))) of role axiom named fact_113_le__bot % A new axiom: (forall (A_118:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_118) bot_bo70021908tate_o)->(((eq (hoare_1167836817_state->Prop)) A_118) bot_bo70021908tate_o))) % FOF formula (forall (A_118:Prop), (((ord_less_eq_o A_118) bot_bot_o)->((iff A_118) bot_bot_o))) of role axiom named fact_114_le__bot % A new axiom: (forall (A_118:Prop), (((ord_less_eq_o A_118) bot_bot_o)->((iff A_118) bot_bot_o))) % FOF formula (forall (A_117:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_117) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_117) bot_bo70021908tate_o))) of role axiom named fact_115_subset__empty % A new axiom: (forall (A_117:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_117) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_117) bot_bo70021908tate_o))) % FOF formula (forall (B_61:(hoare_1167836817_state->Prop)) (A_116:hoare_1167836817_state), ((ord_le827224136tate_o B_61) ((insert2134838167_state A_116) B_61))) of role axiom named fact_116_subset__insertI % A new axiom: (forall (B_61:(hoare_1167836817_state->Prop)) (A_116:hoare_1167836817_state), ((ord_le827224136tate_o B_61) ((insert2134838167_state A_116) B_61))) % FOF formula (forall (X_54:hoare_1167836817_state) (A_115:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((insert2134838167_state X_54) A_115)) B_60)) ((and ((member2058392318_state X_54) B_60)) ((ord_le827224136tate_o A_115) B_60)))) of role axiom named fact_117_insert__subset % A new axiom: (forall (X_54:hoare_1167836817_state) (A_115:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((insert2134838167_state X_54) A_115)) B_60)) ((and ((member2058392318_state X_54) B_60)) ((ord_le827224136tate_o A_115) B_60)))) % FOF formula (forall (B_59:(hoare_1167836817_state->Prop)) (X_53:hoare_1167836817_state) (A_114:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_53) A_114)->False)->((iff ((ord_le827224136tate_o A_114) ((insert2134838167_state X_53) B_59))) ((ord_le827224136tate_o A_114) B_59)))) of role axiom named fact_118_subset__insert % A new axiom: (forall (B_59:(hoare_1167836817_state->Prop)) (X_53:hoare_1167836817_state) (A_114:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_53) A_114)->False)->((iff ((ord_le827224136tate_o A_114) ((insert2134838167_state X_53) B_59))) ((ord_le827224136tate_o A_114) B_59)))) % FOF formula (forall (B_58:hoare_1167836817_state) (A_113:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_113) B_57)->((ord_le827224136tate_o A_113) ((insert2134838167_state B_58) B_57)))) of role axiom named fact_119_subset__insertI2 % A new axiom: (forall (B_58:hoare_1167836817_state) (A_113:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_113) B_57)->((ord_le827224136tate_o A_113) ((insert2134838167_state B_58) B_57)))) % FOF formula (forall (A_112:hoare_1167836817_state) (C_26:(hoare_1167836817_state->Prop)) (D_1:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_26) D_1)->((ord_le827224136tate_o ((insert2134838167_state A_112) C_26)) ((insert2134838167_state A_112) D_1)))) of role axiom named fact_120_insert__mono % A new axiom: (forall (A_112:hoare_1167836817_state) (C_26:(hoare_1167836817_state->Prop)) (D_1:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_26) D_1)->((ord_le827224136tate_o ((insert2134838167_state A_112) C_26)) ((insert2134838167_state A_112) D_1)))) % FOF formula (forall (A_111:hoare_1167836817_state) (A_110:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_111) A_110))) (finite1084549118_state A_110))) of role axiom named fact_121_finite__insert % A new axiom: (forall (A_111:hoare_1167836817_state) (A_110:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_111) A_110))) (finite1084549118_state A_110))) % FOF formula (forall (Ts_3:(hoare_1167836817_state->Prop)) (G_13:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Ts_3) G_13)->((hoare_123228589_state G_13) Ts_3))) of role axiom named fact_122_asm % A new axiom: (forall (Ts_3:(hoare_1167836817_state->Prop)) (G_13:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Ts_3) G_13)->((hoare_123228589_state G_13) Ts_3))) % FOF formula (forall (Ts_2:(hoare_1167836817_state->Prop)) (G_12:(hoare_1167836817_state->Prop)) (Ts_1:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_12) Ts_1)->(((ord_le827224136tate_o Ts_2) Ts_1)->((hoare_123228589_state G_12) Ts_2)))) of role axiom named fact_123_weaken % A new axiom: (forall (Ts_2:(hoare_1167836817_state->Prop)) (G_12:(hoare_1167836817_state->Prop)) (Ts_1:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_12) Ts_1)->(((ord_le827224136tate_o Ts_2) Ts_1)->((hoare_123228589_state G_12) Ts_2)))) % FOF formula (forall (G_11:(hoare_1167836817_state->Prop)) (G_10:(hoare_1167836817_state->Prop)) (Ts:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_10) Ts)->(((ord_le827224136tate_o G_10) G_11)->((hoare_123228589_state G_11) Ts)))) of role axiom named fact_124_thin % A new axiom: (forall (G_11:(hoare_1167836817_state->Prop)) (G_10:(hoare_1167836817_state->Prop)) (Ts:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_10) Ts)->(((ord_le827224136tate_o G_10) G_11)->((hoare_123228589_state G_11) Ts)))) % FOF formula (forall (F_64:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_25:hoare_1167836817_state), ((((finite1316643734_state F_64) Z_25) bot_bo70021908tate_o) Z_25)) of role axiom named fact_125_fold__graph_OemptyI % A new axiom: (forall (F_64:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_25:hoare_1167836817_state), ((((finite1316643734_state F_64) Z_25) bot_bo70021908tate_o) Z_25)) % FOF formula (forall (F_63:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_24:hoare_1167836817_state) (X_52:hoare_1167836817_state), (((((finite1316643734_state F_63) Z_24) bot_bo70021908tate_o) X_52)->(((eq hoare_1167836817_state) X_52) Z_24))) of role axiom named fact_126_empty__fold__graphE % A new axiom: (forall (F_63:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_24:hoare_1167836817_state) (X_52:hoare_1167836817_state), (((((finite1316643734_state F_63) Z_24) bot_bo70021908tate_o) X_52)->(((eq hoare_1167836817_state) X_52) Z_24))) % FOF formula (forall (F_62:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_23:hoare_1167836817_state) (Y_24:hoare_1167836817_state) (X_51:hoare_1167836817_state) (A_109:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_51) A_109)->False)->(((((finite1316643734_state F_62) Z_23) A_109) Y_24)->((((finite1316643734_state F_62) Z_23) ((insert2134838167_state X_51) A_109)) ((F_62 X_51) Y_24))))) of role axiom named fact_127_fold__graph_OinsertI % A new axiom: (forall (F_62:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_23:hoare_1167836817_state) (Y_24:hoare_1167836817_state) (X_51:hoare_1167836817_state) (A_109:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_51) A_109)->False)->(((((finite1316643734_state F_62) Z_23) A_109) Y_24)->((((finite1316643734_state F_62) Z_23) ((insert2134838167_state X_51) A_109)) ((F_62 X_51) Y_24))))) % FOF formula (forall (P_6:((hoare_1167836817_state->Prop)->Prop)) (A_108:(hoare_1167836817_state->Prop)) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(((ord_le827224136tate_o F_61) A_108)->((P_6 bot_bo70021908tate_o)->((forall (A_59:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->(((member2058392318_state A_59) A_108)->((((member2058392318_state A_59) F_50)->False)->((P_6 F_50)->(P_6 ((insert2134838167_state A_59) F_50)))))))->(P_6 F_61)))))) of role axiom named fact_128_finite__subset__induct % A new axiom: (forall (P_6:((hoare_1167836817_state->Prop)->Prop)) (A_108:(hoare_1167836817_state->Prop)) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(((ord_le827224136tate_o F_61) A_108)->((P_6 bot_bo70021908tate_o)->((forall (A_59:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->(((member2058392318_state A_59) A_108)->((((member2058392318_state A_59) F_50)->False)->((P_6 F_50)->(P_6 ((insert2134838167_state A_59) F_50)))))))->(P_6 F_61)))))) % FOF formula (forall (F_60:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_107:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_107)->((not (((eq (hoare_1167836817_state->Prop)) A_107) bot_bo70021908tate_o))->(_TPTP_ex ((finite309220289_state F_60) A_107))))) of role axiom named fact_129_finite__nonempty__imp__fold1Set % A new axiom: (forall (F_60:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_107:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_107)->((not (((eq (hoare_1167836817_state->Prop)) A_107) bot_bo70021908tate_o))->(_TPTP_ex ((finite309220289_state F_60) A_107))))) % FOF formula (forall (B_56:(hoare_1167836817_state->Prop)) (A_106:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_106)->((member2058392318_state X) B_56)))->((ord_le827224136tate_o A_106) B_56))) of role axiom named fact_130_subsetI % A new axiom: (forall (B_56:(hoare_1167836817_state->Prop)) (A_106:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_106)->((member2058392318_state X) B_56)))->((ord_le827224136tate_o A_106) B_56))) % FOF formula (forall (A_105:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_105)) ((or (((eq (hoare_1167836817_state->Prop)) A_105) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_59:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_105) ((insert2134838167_state A_59) A_58))) (finite1084549118_state A_58))))))))) of role axiom named fact_131_finite_Osimps % A new axiom: (forall (A_105:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_105)) ((or (((eq (hoare_1167836817_state->Prop)) A_105) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_59:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_105) ((insert2134838167_state A_59) A_58))) (finite1084549118_state A_58))))))))) % FOF formula (forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (F_59:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_59)->((P_5 bot_bo70021908tate_o)->((forall (X:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->((((member2058392318_state X) F_50)->False)->((P_5 F_50)->(P_5 ((insert2134838167_state X) F_50))))))->(P_5 F_59))))) of role axiom named fact_132_finite__induct % A new axiom: (forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (F_59:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_59)->((P_5 bot_bo70021908tate_o)->((forall (X:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->((((member2058392318_state X) F_50)->False)->((P_5 F_50)->(P_5 ((insert2134838167_state X) F_50))))))->(P_5 F_59))))) % FOF formula (forall (F_58:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_22:hoare_1167836817_state) (A_104:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_104)->(_TPTP_ex (((finite1316643734_state F_58) Z_22) A_104)))) of role axiom named fact_133_finite__imp__fold__graph % A new axiom: (forall (F_58:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_22:hoare_1167836817_state) (A_104:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_104)->(_TPTP_ex (((finite1316643734_state F_58) Z_22) A_104)))) % FOF formula (forall (F_57:(hoare_1167836817_state->Prop)) (G_9:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((ord_less_eq_o (F_57 X)) (G_9 X)))->((ord_le827224136tate_o F_57) G_9))) of role axiom named fact_134_le__funI % A new axiom: (forall (F_57:(hoare_1167836817_state->Prop)) (G_9:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((ord_less_eq_o (F_57 X)) (G_9 X)))->((ord_le827224136tate_o F_57) G_9))) % FOF formula (forall (F_56:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A1_1:(hoare_1167836817_state->Prop)) (A2_1:hoare_1167836817_state), ((iff (((finite309220289_state F_56) A1_1) A2_1)) ((ex hoare_1167836817_state) (fun (A_59:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((and ((and (((eq (hoare_1167836817_state->Prop)) A1_1) ((insert2134838167_state A_59) A_58))) (((eq hoare_1167836817_state) A2_1) X))) ((((finite1316643734_state F_56) A_59) A_58) X))) (((member2058392318_state A_59) A_58)->False)))))))))) of role axiom named fact_135_fold1Set_Osimps % A new axiom: (forall (F_56:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A1_1:(hoare_1167836817_state->Prop)) (A2_1:hoare_1167836817_state), ((iff (((finite309220289_state F_56) A1_1) A2_1)) ((ex hoare_1167836817_state) (fun (A_59:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((and ((and (((eq (hoare_1167836817_state->Prop)) A1_1) ((insert2134838167_state A_59) A_58))) (((eq hoare_1167836817_state) A2_1) X))) ((((finite1316643734_state F_56) A_59) A_58) X))) (((member2058392318_state A_59) A_58)->False)))))))))) % FOF formula (forall (F_55:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_21:hoare_1167836817_state) (A1:(hoare_1167836817_state->Prop)) (A2:hoare_1167836817_state), ((iff ((((finite1316643734_state F_55) Z_21) A1) A2)) ((or ((and (((eq (hoare_1167836817_state->Prop)) A1) bot_bo70021908tate_o)) (((eq hoare_1167836817_state) A2) Z_21))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (Y:hoare_1167836817_state)=> ((and ((and ((and (((eq (hoare_1167836817_state->Prop)) A1) ((insert2134838167_state X) A_58))) (((eq hoare_1167836817_state) A2) ((F_55 X) Y)))) (((member2058392318_state X) A_58)->False))) ((((finite1316643734_state F_55) Z_21) A_58) Y))))))))))) of role axiom named fact_136_fold__graph_Osimps % A new axiom: (forall (F_55:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_21:hoare_1167836817_state) (A1:(hoare_1167836817_state->Prop)) (A2:hoare_1167836817_state), ((iff ((((finite1316643734_state F_55) Z_21) A1) A2)) ((or ((and (((eq (hoare_1167836817_state->Prop)) A1) bot_bo70021908tate_o)) (((eq hoare_1167836817_state) A2) Z_21))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (Y:hoare_1167836817_state)=> ((and ((and ((and (((eq (hoare_1167836817_state->Prop)) A1) ((insert2134838167_state X) A_58))) (((eq hoare_1167836817_state) A2) ((F_55 X) Y)))) (((member2058392318_state X) A_58)->False))) ((((finite1316643734_state F_55) Z_21) A_58) Y))))))))))) % FOF formula (forall (B_55:(hoare_1167836817_state->Prop)) (A_103:(hoare_1167836817_state->Prop)) (F_54:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_53:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_54) F_53)->((finite1084549118_state A_103)->((not (((eq (hoare_1167836817_state->Prop)) B_55) bot_bo70021908tate_o))->(((ord_le827224136tate_o B_55) A_103)->(((eq hoare_1167836817_state) ((F_54 (F_53 B_55)) (F_53 A_103))) (F_53 A_103))))))) of role axiom named fact_137_folding__one__idem_Osubset__idem % A new axiom: (forall (B_55:(hoare_1167836817_state->Prop)) (A_103:(hoare_1167836817_state->Prop)) (F_54:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_53:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_54) F_53)->((finite1084549118_state A_103)->((not (((eq (hoare_1167836817_state->Prop)) B_55) bot_bo70021908tate_o))->(((ord_le827224136tate_o B_55) A_103)->(((eq hoare_1167836817_state) ((F_54 (F_53 B_55)) (F_53 A_103))) (F_53 A_103))))))) % FOF formula (forall (X_50:hoare_1167836817_state) (A_102:(hoare_1167836817_state->Prop)) (F_52:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_51:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_52) F_51)->((finite1084549118_state A_102)->((not (((eq (hoare_1167836817_state->Prop)) A_102) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_51 ((insert2134838167_state X_50) A_102))) ((F_52 X_50) (F_51 A_102))))))) of role axiom named fact_138_folding__one__idem_Oinsert__idem % A new axiom: (forall (X_50:hoare_1167836817_state) (A_102:(hoare_1167836817_state->Prop)) (F_52:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_51:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_52) F_51)->((finite1084549118_state A_102)->((not (((eq (hoare_1167836817_state->Prop)) A_102) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_51 ((insert2134838167_state X_50) A_102))) ((F_52 X_50) (F_51 A_102))))))) % FOF formula (forall (P_4:((hoare_1167836817_state->Prop)->Prop)) (F_49:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_49)->((not (((eq (hoare_1167836817_state->Prop)) F_49) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (P_4 ((insert2134838167_state X) bot_bo70021908tate_o)))->((forall (X:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->((not (((eq (hoare_1167836817_state->Prop)) F_50) bot_bo70021908tate_o))->((((member2058392318_state X) F_50)->False)->((P_4 F_50)->(P_4 ((insert2134838167_state X) F_50)))))))->(P_4 F_49)))))) of role axiom named fact_139_finite__ne__induct % A new axiom: (forall (P_4:((hoare_1167836817_state->Prop)->Prop)) (F_49:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_49)->((not (((eq (hoare_1167836817_state->Prop)) F_49) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (P_4 ((insert2134838167_state X) bot_bo70021908tate_o)))->((forall (X:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->((not (((eq (hoare_1167836817_state->Prop)) F_50) bot_bo70021908tate_o))->((((member2058392318_state X) F_50)->False)->((P_4 F_50)->(P_4 ((insert2134838167_state X) F_50)))))))->(P_4 F_49)))))) % FOF formula (forall (Q_1:(hoare_1167836817_state->Prop)) (P_3:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((P_3 X)->(Q_1 X)))->((ord_le827224136tate_o (collec1027672124_state P_3)) (collec1027672124_state Q_1)))) of role axiom named fact_140_Collect__mono % A new axiom: (forall (Q_1:(hoare_1167836817_state->Prop)) (P_3:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((P_3 X)->(Q_1 X)))->((ord_le827224136tate_o (collec1027672124_state P_3)) (collec1027672124_state Q_1)))) % FOF formula (forall (X_49:hoare_1167836817_state) (F_48:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_47:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_48) F_47)->(((eq hoare_1167836817_state) ((F_48 X_49) X_49)) X_49))) of role axiom named fact_141_folding__one__idem_Oidem % A new axiom: (forall (X_49:hoare_1167836817_state) (F_48:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_47:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_48) F_47)->(((eq hoare_1167836817_state) ((F_48 X_49) X_49)) X_49))) % FOF formula (forall (X_48:hoare_1167836817_state) (A_101:(hoare_1167836817_state->Prop)) (F_46:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_45:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_46) F_45)->((finite1084549118_state A_101)->(((member2058392318_state X_48) A_101)->(((eq hoare_1167836817_state) ((F_46 X_48) (F_45 A_101))) (F_45 A_101)))))) of role axiom named fact_142_folding__one__idem_Oin__idem % A new axiom: (forall (X_48:hoare_1167836817_state) (A_101:(hoare_1167836817_state->Prop)) (F_46:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_45:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_46) F_45)->((finite1084549118_state A_101)->(((member2058392318_state X_48) A_101)->(((eq hoare_1167836817_state) ((F_46 X_48) (F_45 A_101))) (F_45 A_101)))))) % FOF formula (forall (Q:(hoare_1167836817_state->Prop)) (P_2:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((P_2 X)->(Q X)))->((ord_le827224136tate_o P_2) Q))) of role axiom named fact_143_predicate1I % A new axiom: (forall (Q:(hoare_1167836817_state->Prop)) (P_2:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((P_2 X)->(Q X)))->((ord_le827224136tate_o P_2) Q))) % FOF formula (forall (C_25:Prop) (F_44:((hoare_1167836817_state->Prop)->Prop)) (B_54:(hoare_1167836817_state->Prop)) (A_100:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_54) A_100)->(((ord_less_eq_o C_25) (F_44 B_54))->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F_44 Y)) (F_44 X))))->((ord_less_eq_o C_25) (F_44 A_100)))))) of role axiom named fact_144_xt3 % A new axiom: (forall (C_25:Prop) (F_44:((hoare_1167836817_state->Prop)->Prop)) (B_54:(hoare_1167836817_state->Prop)) (A_100:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_54) A_100)->(((ord_less_eq_o C_25) (F_44 B_54))->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F_44 Y)) (F_44 X))))->((ord_less_eq_o C_25) (F_44 A_100)))))) % FOF formula (forall (C_25:(hoare_1167836817_state->Prop)) (F_44:(Prop->(hoare_1167836817_state->Prop))) (B_54:Prop) (A_100:Prop), (((ord_less_eq_o B_54) A_100)->(((ord_le827224136tate_o C_25) (F_44 B_54))->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F_44 Y)) (F_44 X))))->((ord_le827224136tate_o C_25) (F_44 A_100)))))) of role axiom named fact_145_xt3 % A new axiom: (forall (C_25:(hoare_1167836817_state->Prop)) (F_44:(Prop->(hoare_1167836817_state->Prop))) (B_54:Prop) (A_100:Prop), (((ord_less_eq_o B_54) A_100)->(((ord_le827224136tate_o C_25) (F_44 B_54))->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F_44 Y)) (F_44 X))))->((ord_le827224136tate_o C_25) (F_44 A_100)))))) % FOF formula (forall (C_24:Prop) (F_43:(Prop->Prop)) (B_53:Prop) (A_99:Prop), (((ord_less_eq_o B_53) A_99)->(((iff (F_43 B_53)) C_24)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_less_eq_o (F_43 Y)) (F_43 X))))->((ord_less_eq_o C_24) (F_43 A_99)))))) of role axiom named fact_146_xt1_I16_J % A new axiom: (forall (C_24:Prop) (F_43:(Prop->Prop)) (B_53:Prop) (A_99:Prop), (((ord_less_eq_o B_53) A_99)->(((iff (F_43 B_53)) C_24)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_less_eq_o (F_43 Y)) (F_43 X))))->((ord_less_eq_o C_24) (F_43 A_99)))))) % FOF formula (forall (F_43:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (C_24:(hoare_1167836817_state->Prop)) (B_53:(hoare_1167836817_state->Prop)) (A_99:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_53) A_99)->((((eq (hoare_1167836817_state->Prop)) (F_43 B_53)) C_24)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F_43 Y)) (F_43 X))))->((ord_le827224136tate_o C_24) (F_43 A_99)))))) of role axiom named fact_147_xt1_I16_J % A new axiom: (forall (F_43:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (C_24:(hoare_1167836817_state->Prop)) (B_53:(hoare_1167836817_state->Prop)) (A_99:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_53) A_99)->((((eq (hoare_1167836817_state->Prop)) (F_43 B_53)) C_24)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F_43 Y)) (F_43 X))))->((ord_le827224136tate_o C_24) (F_43 A_99)))))) % FOF formula (forall (C_23:Prop) (F_42:((hoare_1167836817_state->Prop)->Prop)) (A_98:(hoare_1167836817_state->Prop)) (B_52:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_98) B_52)->(((iff (F_42 B_52)) C_23)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_42 X)) (F_42 Y))))->((ord_less_eq_o (F_42 A_98)) C_23))))) of role axiom named fact_148_ord__le__eq__subst % A new axiom: (forall (C_23:Prop) (F_42:((hoare_1167836817_state->Prop)->Prop)) (A_98:(hoare_1167836817_state->Prop)) (B_52:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_98) B_52)->(((iff (F_42 B_52)) C_23)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_42 X)) (F_42 Y))))->((ord_less_eq_o (F_42 A_98)) C_23))))) % FOF formula (forall (F_42:(Prop->(hoare_1167836817_state->Prop))) (C_23:(hoare_1167836817_state->Prop)) (A_98:Prop) (B_52:Prop), (((ord_less_eq_o A_98) B_52)->((((eq (hoare_1167836817_state->Prop)) (F_42 B_52)) C_23)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_42 X)) (F_42 Y))))->((ord_le827224136tate_o (F_42 A_98)) C_23))))) of role axiom named fact_149_ord__le__eq__subst % A new axiom: (forall (F_42:(Prop->(hoare_1167836817_state->Prop))) (C_23:(hoare_1167836817_state->Prop)) (A_98:Prop) (B_52:Prop), (((ord_less_eq_o A_98) B_52)->((((eq (hoare_1167836817_state->Prop)) (F_42 B_52)) C_23)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_42 X)) (F_42 Y))))->((ord_le827224136tate_o (F_42 A_98)) C_23))))) % FOF formula (forall (F_41:((hoare_1167836817_state->Prop)->Prop)) (C_22:Prop) (A_97:(hoare_1167836817_state->Prop)) (B_51:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_97) B_51)->(((ord_less_eq_o (F_41 B_51)) C_22)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_41 X)) (F_41 Y))))->((ord_less_eq_o (F_41 A_97)) C_22))))) of role axiom named fact_150_order__subst2 % A new axiom: (forall (F_41:((hoare_1167836817_state->Prop)->Prop)) (C_22:Prop) (A_97:(hoare_1167836817_state->Prop)) (B_51:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_97) B_51)->(((ord_less_eq_o (F_41 B_51)) C_22)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_41 X)) (F_41 Y))))->((ord_less_eq_o (F_41 A_97)) C_22))))) % FOF formula (forall (F_41:(Prop->(hoare_1167836817_state->Prop))) (C_22:(hoare_1167836817_state->Prop)) (A_97:Prop) (B_51:Prop), (((ord_less_eq_o A_97) B_51)->(((ord_le827224136tate_o (F_41 B_51)) C_22)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_41 X)) (F_41 Y))))->((ord_le827224136tate_o (F_41 A_97)) C_22))))) of role axiom named fact_151_order__subst2 % A new axiom: (forall (F_41:(Prop->(hoare_1167836817_state->Prop))) (C_22:(hoare_1167836817_state->Prop)) (A_97:Prop) (B_51:Prop), (((ord_less_eq_o A_97) B_51)->(((ord_le827224136tate_o (F_41 B_51)) C_22)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_41 X)) (F_41 Y))))->((ord_le827224136tate_o (F_41 A_97)) C_22))))) % FOF formula (forall (C_21:(hoare_1167836817_state->Prop)) (F_40:((hoare_1167836817_state->Prop)->Prop)) (B_50:(hoare_1167836817_state->Prop)) (A_96:Prop), (((iff A_96) (F_40 B_50))->(((ord_le827224136tate_o B_50) C_21)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_40 X)) (F_40 Y))))->((ord_less_eq_o A_96) (F_40 C_21)))))) of role axiom named fact_152_ord__eq__le__subst % A new axiom: (forall (C_21:(hoare_1167836817_state->Prop)) (F_40:((hoare_1167836817_state->Prop)->Prop)) (B_50:(hoare_1167836817_state->Prop)) (A_96:Prop), (((iff A_96) (F_40 B_50))->(((ord_le827224136tate_o B_50) C_21)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_40 X)) (F_40 Y))))->((ord_less_eq_o A_96) (F_40 C_21)))))) % FOF formula (forall (C_21:Prop) (A_96:(hoare_1167836817_state->Prop)) (F_40:(Prop->(hoare_1167836817_state->Prop))) (B_50:Prop), ((((eq (hoare_1167836817_state->Prop)) A_96) (F_40 B_50))->(((ord_less_eq_o B_50) C_21)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_40 X)) (F_40 Y))))->((ord_le827224136tate_o A_96) (F_40 C_21)))))) of role axiom named fact_153_ord__eq__le__subst % A new axiom: (forall (C_21:Prop) (A_96:(hoare_1167836817_state->Prop)) (F_40:(Prop->(hoare_1167836817_state->Prop))) (B_50:Prop), ((((eq (hoare_1167836817_state->Prop)) A_96) (F_40 B_50))->(((ord_less_eq_o B_50) C_21)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_40 X)) (F_40 Y))))->((ord_le827224136tate_o A_96) (F_40 C_21)))))) % FOF formula (forall (C_20:Prop) (F_39:(Prop->(hoare_1167836817_state->Prop))) (B_49:Prop) (A_95:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_39 B_49)) A_95)->(((ord_less_eq_o C_20) B_49)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F_39 Y)) (F_39 X))))->((ord_le827224136tate_o (F_39 C_20)) A_95))))) of role axiom named fact_154_xt2 % A new axiom: (forall (C_20:Prop) (F_39:(Prop->(hoare_1167836817_state->Prop))) (B_49:Prop) (A_95:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_39 B_49)) A_95)->(((ord_less_eq_o C_20) B_49)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F_39 Y)) (F_39 X))))->((ord_le827224136tate_o (F_39 C_20)) A_95))))) % FOF formula (forall (C_20:(hoare_1167836817_state->Prop)) (F_39:((hoare_1167836817_state->Prop)->Prop)) (B_49:(hoare_1167836817_state->Prop)) (A_95:Prop), (((ord_less_eq_o (F_39 B_49)) A_95)->(((ord_le827224136tate_o C_20) B_49)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F_39 Y)) (F_39 X))))->((ord_less_eq_o (F_39 C_20)) A_95))))) of role axiom named fact_155_xt2 % A new axiom: (forall (C_20:(hoare_1167836817_state->Prop)) (F_39:((hoare_1167836817_state->Prop)->Prop)) (B_49:(hoare_1167836817_state->Prop)) (A_95:Prop), (((ord_less_eq_o (F_39 B_49)) A_95)->(((ord_le827224136tate_o C_20) B_49)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F_39 Y)) (F_39 X))))->((ord_less_eq_o (F_39 C_20)) A_95))))) % FOF formula (forall (C_19:Prop) (F_38:(Prop->Prop)) (B_48:Prop) (A_94:Prop), (((iff A_94) (F_38 B_48))->(((ord_less_eq_o C_19) B_48)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_less_eq_o (F_38 Y)) (F_38 X))))->((ord_less_eq_o (F_38 C_19)) A_94))))) of role axiom named fact_156_xt1_I15_J % A new axiom: (forall (C_19:Prop) (F_38:(Prop->Prop)) (B_48:Prop) (A_94:Prop), (((iff A_94) (F_38 B_48))->(((ord_less_eq_o C_19) B_48)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_less_eq_o (F_38 Y)) (F_38 X))))->((ord_less_eq_o (F_38 C_19)) A_94))))) % FOF formula (forall (C_19:(hoare_1167836817_state->Prop)) (A_94:(hoare_1167836817_state->Prop)) (F_38:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_48:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_94) (F_38 B_48))->(((ord_le827224136tate_o C_19) B_48)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F_38 Y)) (F_38 X))))->((ord_le827224136tate_o (F_38 C_19)) A_94))))) of role axiom named fact_157_xt1_I15_J % A new axiom: (forall (C_19:(hoare_1167836817_state->Prop)) (A_94:(hoare_1167836817_state->Prop)) (F_38:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_48:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_94) (F_38 B_48))->(((ord_le827224136tate_o C_19) B_48)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F_38 Y)) (F_38 X))))->((ord_le827224136tate_o (F_38 C_19)) A_94))))) % FOF formula (forall (C_18:Prop) (A_93:(hoare_1167836817_state->Prop)) (F_37:(Prop->(hoare_1167836817_state->Prop))) (B_47:Prop), (((ord_le827224136tate_o A_93) (F_37 B_47))->(((ord_less_eq_o B_47) C_18)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_37 X)) (F_37 Y))))->((ord_le827224136tate_o A_93) (F_37 C_18)))))) of role axiom named fact_158_order__subst1 % A new axiom: (forall (C_18:Prop) (A_93:(hoare_1167836817_state->Prop)) (F_37:(Prop->(hoare_1167836817_state->Prop))) (B_47:Prop), (((ord_le827224136tate_o A_93) (F_37 B_47))->(((ord_less_eq_o B_47) C_18)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_37 X)) (F_37 Y))))->((ord_le827224136tate_o A_93) (F_37 C_18)))))) % FOF formula (forall (C_18:(hoare_1167836817_state->Prop)) (A_93:Prop) (F_37:((hoare_1167836817_state->Prop)->Prop)) (B_47:(hoare_1167836817_state->Prop)), (((ord_less_eq_o A_93) (F_37 B_47))->(((ord_le827224136tate_o B_47) C_18)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_37 X)) (F_37 Y))))->((ord_less_eq_o A_93) (F_37 C_18)))))) of role axiom named fact_159_order__subst1 % A new axiom: (forall (C_18:(hoare_1167836817_state->Prop)) (A_93:Prop) (F_37:((hoare_1167836817_state->Prop)->Prop)) (B_47:(hoare_1167836817_state->Prop)), (((ord_less_eq_o A_93) (F_37 B_47))->(((ord_le827224136tate_o B_47) C_18)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_37 X)) (F_37 Y))))->((ord_less_eq_o A_93) (F_37 C_18)))))) % FOF formula (forall (A_92:(hoare_1167836817_state->Prop)) (F_36:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_35:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((big_se1603066171_state F_36) F_35)->((finite1084549118_state A_92)->(((eq hoare_1167836817_state) (F_35 A_92)) ((finite1646097201_state F_36) A_92))))) of role axiom named fact_160_semilattice__big_OF__eq % A new axiom: (forall (A_92:(hoare_1167836817_state->Prop)) (F_36:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_35:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((big_se1603066171_state F_36) F_35)->((finite1084549118_state A_92)->(((eq hoare_1167836817_state) (F_35 A_92)) ((finite1646097201_state F_36) A_92))))) % FOF formula (forall (X_47:hoare_1167836817_state) (A_91:(hoare_1167836817_state->Prop)) (F_34:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_33:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_34) F_33)->((finite1084549118_state A_91)->(((member2058392318_state X_47) A_91)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_33 A_91)) X_47))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_33 A_91)) ((F_34 X_47) (F_33 ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))))))))))) of role axiom named fact_161_folding__one_Oremove % A new axiom: (forall (X_47:hoare_1167836817_state) (A_91:(hoare_1167836817_state->Prop)) (F_34:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_33:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_34) F_33)->((finite1084549118_state A_91)->(((member2058392318_state X_47) A_91)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_33 A_91)) X_47))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_33 A_91)) ((F_34 X_47) (F_33 ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))))))))))) % FOF formula (forall (X_46:hoare_1167836817_state) (A_90:(hoare_1167836817_state->Prop)) (F_32:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_31:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_32) F_31)->((finite1084549118_state A_90)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_31 ((insert2134838167_state X_46) A_90))) X_46))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_31 ((insert2134838167_state X_46) A_90))) ((F_32 X_46) (F_31 ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o)))))))))) of role axiom named fact_162_folding__one_Oinsert__remove % A new axiom: (forall (X_46:hoare_1167836817_state) (A_90:(hoare_1167836817_state->Prop)) (F_32:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_31:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_32) F_31)->((finite1084549118_state A_90)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_31 ((insert2134838167_state X_46) A_90))) X_46))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_31 ((insert2134838167_state X_46) A_90))) ((F_32 X_46) (F_31 ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o)))))))))) % FOF formula (forall (B_46:(hoare_1167836817_state->Prop)) (C_17:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((member2058392318_state C_17) A_89)->((((member2058392318_state C_17) B_46)->False)->((member2058392318_state C_17) ((minus_2107060239tate_o A_89) B_46))))) of role axiom named fact_163_DiffI % A new axiom: (forall (B_46:(hoare_1167836817_state->Prop)) (C_17:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((member2058392318_state C_17) A_89)->((((member2058392318_state C_17) B_46)->False)->((member2058392318_state C_17) ((minus_2107060239tate_o A_89) B_46))))) % FOF formula (forall (C_16:hoare_1167836817_state) (A_88:(hoare_1167836817_state->Prop)) (B_45:(hoare_1167836817_state->Prop)), (((member2058392318_state C_16) ((minus_2107060239tate_o A_88) B_45))->((((member2058392318_state C_16) A_88)->((member2058392318_state C_16) B_45))->False))) of role axiom named fact_164_DiffE % A new axiom: (forall (C_16:hoare_1167836817_state) (A_88:(hoare_1167836817_state->Prop)) (B_45:(hoare_1167836817_state->Prop)), (((member2058392318_state C_16) ((minus_2107060239tate_o A_88) B_45))->((((member2058392318_state C_16) A_88)->((member2058392318_state C_16) B_45))->False))) % FOF formula (forall (B_44:(hoare_1167836817_state->Prop)) (A_87:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_87)->(finite1084549118_state ((minus_2107060239tate_o A_87) B_44)))) of role axiom named fact_165_finite__Diff % A new axiom: (forall (B_44:(hoare_1167836817_state->Prop)) (A_87:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_87)->(finite1084549118_state ((minus_2107060239tate_o A_87) B_44)))) % FOF formula (forall (A_86:(hoare_1167836817_state->Prop)) (B_43:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_86) B_43)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) A_86)) (not ((member2058392318_state X) B_43))))))) of role axiom named fact_166_set__diff__eq % A new axiom: (forall (A_86:(hoare_1167836817_state->Prop)) (B_43:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_86) B_43)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) A_86)) (not ((member2058392318_state X) B_43))))))) % FOF formula (forall (C_15:hoare_1167836817_state) (A_85:(hoare_1167836817_state->Prop)) (B_42:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_15) ((minus_2107060239tate_o A_85) B_42))) ((and ((member2058392318_state C_15) A_85)) (((member2058392318_state C_15) B_42)->False)))) of role axiom named fact_167_Diff__iff % A new axiom: (forall (C_15:hoare_1167836817_state) (A_85:(hoare_1167836817_state->Prop)) (B_42:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_15) ((minus_2107060239tate_o A_85) B_42))) ((and ((member2058392318_state C_15) A_85)) (((member2058392318_state C_15) B_42)->False)))) % FOF formula (forall (A_84:(hoare_1167836817_state->Prop)) (B_41:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((minus_2107060239tate_o A_84) B_41)) B_41)) ((minus_2107060239tate_o A_84) B_41))) of role axiom named fact_168_Diff__idemp % A new axiom: (forall (A_84:(hoare_1167836817_state->Prop)) (B_41:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((minus_2107060239tate_o A_84) B_41)) B_41)) ((minus_2107060239tate_o A_84) B_41))) % FOF formula (forall (C_14:hoare_1167836817_state) (A_83:(hoare_1167836817_state->Prop)) (B_40:(hoare_1167836817_state->Prop)), (((member2058392318_state C_14) ((minus_2107060239tate_o A_83) B_40))->((member2058392318_state C_14) A_83))) of role axiom named fact_169_DiffD1 % A new axiom: (forall (C_14:hoare_1167836817_state) (A_83:(hoare_1167836817_state->Prop)) (B_40:(hoare_1167836817_state->Prop)), (((member2058392318_state C_14) ((minus_2107060239tate_o A_83) B_40))->((member2058392318_state C_14) A_83))) % FOF formula (forall (C_13:hoare_1167836817_state) (A_82:(hoare_1167836817_state->Prop)) (B_39:(hoare_1167836817_state->Prop)), (((member2058392318_state C_13) ((minus_2107060239tate_o A_82) B_39))->(((member2058392318_state C_13) B_39)->False))) of role axiom named fact_170_DiffD2 % A new axiom: (forall (C_13:hoare_1167836817_state) (A_82:(hoare_1167836817_state->Prop)) (B_39:(hoare_1167836817_state->Prop)), (((member2058392318_state C_13) ((minus_2107060239tate_o A_82) B_39))->(((member2058392318_state C_13) B_39)->False))) % FOF formula (forall (A_81:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o bot_bo70021908tate_o) A_81)) bot_bo70021908tate_o)) of role axiom named fact_171_empty__Diff % A new axiom: (forall (A_81:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o bot_bo70021908tate_o) A_81)) bot_bo70021908tate_o)) % FOF formula (forall (A_80:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_80) bot_bo70021908tate_o)) A_80)) of role axiom named fact_172_Diff__empty % A new axiom: (forall (A_80:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_80) bot_bo70021908tate_o)) A_80)) % FOF formula (forall (A_79:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_79) A_79)) bot_bo70021908tate_o)) of role axiom named fact_173_Diff__cancel % A new axiom: (forall (A_79:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_79) A_79)) bot_bo70021908tate_o)) % FOF formula (forall (A_78:(hoare_1167836817_state->Prop)) (B_38:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_38)->((iff (finite1084549118_state ((minus_2107060239tate_o A_78) B_38))) (finite1084549118_state A_78)))) of role axiom named fact_174_finite__Diff2 % A new axiom: (forall (A_78:(hoare_1167836817_state->Prop)) (B_38:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_38)->((iff (finite1084549118_state ((minus_2107060239tate_o A_78) B_38))) (finite1084549118_state A_78)))) % FOF formula (forall (A_77:(hoare_1167836817_state->Prop)) (X_45:hoare_1167836817_state) (B_37:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state X_45) B_37)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_45) A_77)) B_37)) ((minus_2107060239tate_o A_77) B_37)))) ((((member2058392318_state X_45) B_37)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_45) A_77)) B_37)) ((insert2134838167_state X_45) ((minus_2107060239tate_o A_77) B_37)))))) of role axiom named fact_175_insert__Diff__if % A new axiom: (forall (A_77:(hoare_1167836817_state->Prop)) (X_45:hoare_1167836817_state) (B_37:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state X_45) B_37)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_45) A_77)) B_37)) ((minus_2107060239tate_o A_77) B_37)))) ((((member2058392318_state X_45) B_37)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_45) A_77)) B_37)) ((insert2134838167_state X_45) ((minus_2107060239tate_o A_77) B_37)))))) % FOF formula (forall (A_76:(hoare_1167836817_state->Prop)) (X_44:hoare_1167836817_state) (B_36:(hoare_1167836817_state->Prop)), (((member2058392318_state X_44) B_36)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_44) A_76)) B_36)) ((minus_2107060239tate_o A_76) B_36)))) of role axiom named fact_176_insert__Diff1 % A new axiom: (forall (A_76:(hoare_1167836817_state->Prop)) (X_44:hoare_1167836817_state) (B_36:(hoare_1167836817_state->Prop)), (((member2058392318_state X_44) B_36)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_44) A_76)) B_36)) ((minus_2107060239tate_o A_76) B_36)))) % FOF formula (forall (A_75:(hoare_1167836817_state->Prop)) (B_35:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((minus_2107060239tate_o A_75) B_35)) A_75)) of role axiom named fact_177_Diff__subset % A new axiom: (forall (A_75:(hoare_1167836817_state->Prop)) (B_35:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((minus_2107060239tate_o A_75) B_35)) A_75)) % FOF formula (forall (D:(hoare_1167836817_state->Prop)) (B_34:(hoare_1167836817_state->Prop)) (A_74:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_74) C_12)->(((ord_le827224136tate_o D) B_34)->((ord_le827224136tate_o ((minus_2107060239tate_o A_74) B_34)) ((minus_2107060239tate_o C_12) D))))) of role axiom named fact_178_Diff__mono % A new axiom: (forall (D:(hoare_1167836817_state->Prop)) (B_34:(hoare_1167836817_state->Prop)) (A_74:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_74) C_12)->(((ord_le827224136tate_o D) B_34)->((ord_le827224136tate_o ((minus_2107060239tate_o A_74) B_34)) ((minus_2107060239tate_o C_12) D))))) % FOF formula (forall (C_11:(hoare_1167836817_state->Prop)) (A_73:(hoare_1167836817_state->Prop)) (B_33:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_73) B_33)->(((ord_le827224136tate_o B_33) C_11)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o B_33) ((minus_2107060239tate_o C_11) A_73))) A_73)))) of role axiom named fact_179_double__diff % A new axiom: (forall (C_11:(hoare_1167836817_state->Prop)) (A_73:(hoare_1167836817_state->Prop)) (B_33:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_73) B_33)->(((ord_le827224136tate_o B_33) C_11)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o B_33) ((minus_2107060239tate_o C_11) A_73))) A_73)))) % FOF formula (forall (A_72:(hoare_1167836817_state->Prop)) (A_71:hoare_1167836817_state) (B_32:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_72) ((insert2134838167_state A_71) B_32))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_72) B_32)) ((insert2134838167_state A_71) bot_bo70021908tate_o)))) of role axiom named fact_180_Diff__insert % A new axiom: (forall (A_72:(hoare_1167836817_state->Prop)) (A_71:hoare_1167836817_state) (B_32:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_72) ((insert2134838167_state A_71) B_32))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_72) B_32)) ((insert2134838167_state A_71) bot_bo70021908tate_o)))) % FOF formula (forall (A_70:(hoare_1167836817_state->Prop)) (A_69:hoare_1167836817_state) (B_31:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_70) ((insert2134838167_state A_69) B_31))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_70) ((insert2134838167_state A_69) bot_bo70021908tate_o))) B_31))) of role axiom named fact_181_Diff__insert2 % A new axiom: (forall (A_70:(hoare_1167836817_state->Prop)) (A_69:hoare_1167836817_state) (B_31:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_70) ((insert2134838167_state A_69) B_31))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_70) ((insert2134838167_state A_69) bot_bo70021908tate_o))) B_31))) % FOF formula (forall (A_68:hoare_1167836817_state) (A_67:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_68) ((minus_2107060239tate_o A_67) ((insert2134838167_state A_68) bot_bo70021908tate_o)))) ((insert2134838167_state A_68) A_67))) of role axiom named fact_182_insert__Diff__single % A new axiom: (forall (A_68:hoare_1167836817_state) (A_67:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_68) ((minus_2107060239tate_o A_67) ((insert2134838167_state A_68) bot_bo70021908tate_o)))) ((insert2134838167_state A_68) A_67))) % FOF formula (forall (X_43:hoare_1167836817_state) (A_66:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_43) A_66)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_43) A_66)) ((insert2134838167_state X_43) bot_bo70021908tate_o))) A_66))) of role axiom named fact_183_Diff__insert__absorb % A new axiom: (forall (X_43:hoare_1167836817_state) (A_66:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_43) A_66)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_43) A_66)) ((insert2134838167_state X_43) bot_bo70021908tate_o))) A_66))) % FOF formula (forall (A_65:hoare_1167836817_state) (A_64:(hoare_1167836817_state->Prop)), (((member2058392318_state A_65) A_64)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_65) ((minus_2107060239tate_o A_64) ((insert2134838167_state A_65) bot_bo70021908tate_o)))) A_64))) of role axiom named fact_184_insert__Diff % A new axiom: (forall (A_65:hoare_1167836817_state) (A_64:(hoare_1167836817_state->Prop)), (((member2058392318_state A_65) A_64)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_65) ((minus_2107060239tate_o A_64) ((insert2134838167_state A_65) bot_bo70021908tate_o)))) A_64))) % FOF formula (forall (A_63:(hoare_1167836817_state->Prop)) (A_62:hoare_1167836817_state) (B_30:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((minus_2107060239tate_o A_63) ((insert2134838167_state A_62) B_30)))) (finite1084549118_state ((minus_2107060239tate_o A_63) B_30)))) of role axiom named fact_185_finite__Diff__insert % A new axiom: (forall (A_63:(hoare_1167836817_state->Prop)) (A_62:hoare_1167836817_state) (B_30:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((minus_2107060239tate_o A_63) ((insert2134838167_state A_62) B_30)))) (finite1084549118_state ((minus_2107060239tate_o A_63) B_30)))) % FOF formula (forall (A_61:(hoare_1167836817_state->Prop)) (X_42:hoare_1167836817_state) (B_29:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_61) ((insert2134838167_state X_42) B_29))) ((and (((member2058392318_state X_42) A_61)->((ord_le827224136tate_o ((minus_2107060239tate_o A_61) ((insert2134838167_state X_42) bot_bo70021908tate_o))) B_29))) ((((member2058392318_state X_42) A_61)->False)->((ord_le827224136tate_o A_61) B_29))))) of role axiom named fact_186_subset__insert__iff % A new axiom: (forall (A_61:(hoare_1167836817_state->Prop)) (X_42:hoare_1167836817_state) (B_29:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_61) ((insert2134838167_state X_42) B_29))) ((and (((member2058392318_state X_42) A_61)->((ord_le827224136tate_o ((minus_2107060239tate_o A_61) ((insert2134838167_state X_42) bot_bo70021908tate_o))) B_29))) ((((member2058392318_state X_42) A_61)->False)->((ord_le827224136tate_o A_61) B_29))))) % FOF formula (forall (A_60:(hoare_1167836817_state->Prop)) (X_41:hoare_1167836817_state) (B_28:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o ((minus_2107060239tate_o A_60) ((insert2134838167_state X_41) bot_bo70021908tate_o))) B_28)->(((member2058392318_state X_41) A_60)->((ord_le827224136tate_o A_60) ((insert2134838167_state X_41) B_28))))) of role axiom named fact_187_diff__single__insert % A new axiom: (forall (A_60:(hoare_1167836817_state->Prop)) (X_41:hoare_1167836817_state) (B_28:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o ((minus_2107060239tate_o A_60) ((insert2134838167_state X_41) bot_bo70021908tate_o))) B_28)->(((member2058392318_state X_41) A_60)->((ord_le827224136tate_o A_60) ((insert2134838167_state X_41) B_28))))) % FOF formula (forall (P_1:((hoare_1167836817_state->Prop)->Prop)) (A_57:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_57)->((P_1 A_57)->((forall (A_59:hoare_1167836817_state) (A_58:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_58)->(((member2058392318_state A_59) A_58)->((P_1 A_58)->(P_1 ((minus_2107060239tate_o A_58) ((insert2134838167_state A_59) bot_bo70021908tate_o)))))))->(P_1 bot_bo70021908tate_o))))) of role axiom named fact_188_finite__empty__induct % A new axiom: (forall (P_1:((hoare_1167836817_state->Prop)->Prop)) (A_57:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_57)->((P_1 A_57)->((forall (A_59:hoare_1167836817_state) (A_58:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_58)->(((member2058392318_state A_59) A_58)->((P_1 A_58)->(P_1 ((minus_2107060239tate_o A_58) ((insert2134838167_state A_59) bot_bo70021908tate_o)))))))->(P_1 bot_bo70021908tate_o))))) % FOF formula (forall (A_56:(hoare_1167836817_state->Prop)) (B_27:(hoare_1167836817_state->Prop)) (X_40:hoare_1167836817_state), ((iff (((minus_2107060239tate_o A_56) B_27) X_40)) ((minus_minus_o (A_56 X_40)) (B_27 X_40)))) of role axiom named fact_189_minus__apply % A new axiom: (forall (A_56:(hoare_1167836817_state->Prop)) (B_27:(hoare_1167836817_state->Prop)) (X_40:hoare_1167836817_state), ((iff (((minus_2107060239tate_o A_56) B_27) X_40)) ((minus_minus_o (A_56 X_40)) (B_27 X_40)))) % FOF formula (forall (A_55:(hoare_1167836817_state->Prop)) (B_26:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), ((iff (((minus_2107060239tate_o A_55) B_26) X)) ((minus_minus_o (A_55 X)) (B_26 X)))) of role axiom named fact_190_fun__diff__def % A new axiom: (forall (A_55:(hoare_1167836817_state->Prop)) (B_26:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), ((iff (((minus_2107060239tate_o A_55) B_26) X)) ((minus_minus_o (A_55 X)) (B_26 X)))) % FOF formula (forall (A_54:hoare_1167836817_state) (Z_20:hoare_1167836817_state) (A_53:(hoare_1167836817_state->Prop)) (Y_22:hoare_1167836817_state) (F_30:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_30)->(((((finite1316643734_state F_30) Z_20) A_53) Y_22)->(((member2058392318_state A_54) A_53)->((ex hoare_1167836817_state) (fun (Y_23:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) Y_22) ((F_30 A_54) Y_23))) ((((finite1316643734_state F_30) Z_20) ((minus_2107060239tate_o A_53) ((insert2134838167_state A_54) bot_bo70021908tate_o))) Y_23)))))))) of role axiom named fact_191_comp__fun__commute_Ofold__graph__insertE__aux % A new axiom: (forall (A_54:hoare_1167836817_state) (Z_20:hoare_1167836817_state) (A_53:(hoare_1167836817_state->Prop)) (Y_22:hoare_1167836817_state) (F_30:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_30)->(((((finite1316643734_state F_30) Z_20) A_53) Y_22)->(((member2058392318_state A_54) A_53)->((ex hoare_1167836817_state) (fun (Y_23:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) Y_22) ((F_30 A_54) Y_23))) ((((finite1316643734_state F_30) Z_20) ((minus_2107060239tate_o A_53) ((insert2134838167_state A_54) bot_bo70021908tate_o))) Y_23)))))))) % FOF formula (forall (X_39:hoare_1167836817_state) (Y_21:hoare_1167836817_state) (Z_19:hoare_1167836817_state) (F_29:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_29)->(((eq hoare_1167836817_state) ((F_29 X_39) ((F_29 Y_21) Z_19))) ((F_29 Y_21) ((F_29 X_39) Z_19))))) of role axiom named fact_192_comp__fun__commute_Ofun__left__comm % A new axiom: (forall (X_39:hoare_1167836817_state) (Y_21:hoare_1167836817_state) (Z_19:hoare_1167836817_state) (F_29:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_29)->(((eq hoare_1167836817_state) ((F_29 X_39) ((F_29 Y_21) Z_19))) ((F_29 Y_21) ((F_29 X_39) Z_19))))) % FOF formula (forall (Y_20:hoare_1167836817_state) (Z_18:hoare_1167836817_state) (A_52:(hoare_1167836817_state->Prop)) (X_38:hoare_1167836817_state) (F_28:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_28)->(((((finite1316643734_state F_28) Z_18) A_52) X_38)->(((((finite1316643734_state F_28) Z_18) A_52) Y_20)->(((eq hoare_1167836817_state) Y_20) X_38))))) of role axiom named fact_193_comp__fun__commute_Ofold__graph__determ % A new axiom: (forall (Y_20:hoare_1167836817_state) (Z_18:hoare_1167836817_state) (A_52:(hoare_1167836817_state->Prop)) (X_38:hoare_1167836817_state) (F_28:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_28)->(((((finite1316643734_state F_28) Z_18) A_52) X_38)->(((((finite1316643734_state F_28) Z_18) A_52) Y_20)->(((eq hoare_1167836817_state) Y_20) X_38))))) % FOF formula (forall (Z_17:hoare_1167836817_state) (X_37:hoare_1167836817_state) (A_51:(hoare_1167836817_state->Prop)) (V:hoare_1167836817_state) (F_27:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_27)->(((((finite1316643734_state F_27) Z_17) ((insert2134838167_state X_37) A_51)) V)->((((member2058392318_state X_37) A_51)->False)->((forall (Y:hoare_1167836817_state), ((((eq hoare_1167836817_state) V) ((F_27 X_37) Y))->(((((finite1316643734_state F_27) Z_17) A_51) Y)->False)))->False))))) of role axiom named fact_194_comp__fun__commute_Ofold__graph__insertE % A new axiom: (forall (Z_17:hoare_1167836817_state) (X_37:hoare_1167836817_state) (A_51:(hoare_1167836817_state->Prop)) (V:hoare_1167836817_state) (F_27:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_27)->(((((finite1316643734_state F_27) Z_17) ((insert2134838167_state X_37) A_51)) V)->((((member2058392318_state X_37) A_51)->False)->((forall (Y:hoare_1167836817_state), ((((eq hoare_1167836817_state) V) ((F_27 X_37) Y))->(((((finite1316643734_state F_27) Z_17) A_51) Y)->False)))->False))))) % FOF formula (forall (X_36:Prop) (Least_3:Prop), ((all1 (ord_less_eq_o Least_3))->((iff ((ord_min_o X_36) Least_3)) Least_3))) of role axiom named fact_195_min__leastR % A new axiom: (forall (X_36:Prop) (Least_3:Prop), ((all1 (ord_less_eq_o Least_3))->((iff ((ord_min_o X_36) Least_3)) Least_3))) % FOF formula (forall (X_36:(hoare_1167836817_state->Prop)) (Least_3:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_3))->(((eq (hoare_1167836817_state->Prop)) ((ord_mi1697686287tate_o X_36) Least_3)) Least_3))) of role axiom named fact_196_min__leastR % A new axiom: (forall (X_36:(hoare_1167836817_state->Prop)) (Least_3:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_3))->(((eq (hoare_1167836817_state->Prop)) ((ord_mi1697686287tate_o X_36) Least_3)) Least_3))) % FOF formula (forall (X_35:Prop) (Least_2:Prop), ((all1 (ord_less_eq_o Least_2))->((iff ((ord_min_o Least_2) X_35)) Least_2))) of role axiom named fact_197_min__leastL % A new axiom: (forall (X_35:Prop) (Least_2:Prop), ((all1 (ord_less_eq_o Least_2))->((iff ((ord_min_o Least_2) X_35)) Least_2))) % FOF formula (forall (X_35:(hoare_1167836817_state->Prop)) (Least_2:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_2))->(((eq (hoare_1167836817_state->Prop)) ((ord_mi1697686287tate_o Least_2) X_35)) Least_2))) of role axiom named fact_198_min__leastL % A new axiom: (forall (X_35:(hoare_1167836817_state->Prop)) (Least_2:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_2))->(((eq (hoare_1167836817_state->Prop)) ((ord_mi1697686287tate_o Least_2) X_35)) Least_2))) % FOF formula (((eq (Prop->(Prop->Prop))) ord_min_o) (min_o ord_less_eq_o)) of role axiom named fact_199_min__ord__min % A new axiom: (((eq (Prop->(Prop->Prop))) ord_min_o) (min_o ord_less_eq_o)) % FOF formula (((eq ((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) ord_mi1697686287tate_o) (min_Ho1955171539tate_o ord_le827224136tate_o)) of role axiom named fact_200_min__ord__min % A new axiom: (((eq ((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) ord_mi1697686287tate_o) (min_Ho1955171539tate_o ord_le827224136tate_o)) % FOF formula (forall (Z_16:hoare_1167836817_state) (X_34:hoare_1167836817_state) (A_50:(hoare_1167836817_state->Prop)) (F_26:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_26)->((finite1084549118_state A_50)->(((eq hoare_1167836817_state) (((finite1731015960_state F_26) Z_16) ((insert2134838167_state X_34) A_50))) ((F_26 X_34) (((finite1731015960_state F_26) Z_16) ((minus_2107060239tate_o A_50) ((insert2134838167_state X_34) bot_bo70021908tate_o)))))))) of role axiom named fact_201_comp__fun__commute_Ofold__insert__remove % A new axiom: (forall (Z_16:hoare_1167836817_state) (X_34:hoare_1167836817_state) (A_50:(hoare_1167836817_state->Prop)) (F_26:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_26)->((finite1084549118_state A_50)->(((eq hoare_1167836817_state) (((finite1731015960_state F_26) Z_16) ((insert2134838167_state X_34) A_50))) ((F_26 X_34) (((finite1731015960_state F_26) Z_16) ((minus_2107060239tate_o A_50) ((insert2134838167_state X_34) bot_bo70021908tate_o)))))))) % FOF formula (forall (Z_15:hoare_1167836817_state) (X_33:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (F_25:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_25)->((finite1084549118_state A_49)->(((member2058392318_state X_33) A_49)->(((eq hoare_1167836817_state) (((finite1731015960_state F_25) Z_15) A_49)) ((F_25 X_33) (((finite1731015960_state F_25) Z_15) ((minus_2107060239tate_o A_49) ((insert2134838167_state X_33) bot_bo70021908tate_o))))))))) of role axiom named fact_202_comp__fun__commute_Ofold__rec % A new axiom: (forall (Z_15:hoare_1167836817_state) (X_33:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (F_25:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_25)->((finite1084549118_state A_49)->(((member2058392318_state X_33) A_49)->(((eq hoare_1167836817_state) (((finite1731015960_state F_25) Z_15) A_49)) ((F_25 X_33) (((finite1731015960_state F_25) Z_15) ((minus_2107060239tate_o A_49) ((insert2134838167_state X_33) bot_bo70021908tate_o))))))))) % FOF formula (forall (F_24:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_14:hoare_1167836817_state), (((eq hoare_1167836817_state) (((finite1731015960_state F_24) Z_14) bot_bo70021908tate_o)) Z_14)) of role axiom named fact_203_fold__empty % A new axiom: (forall (F_24:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_14:hoare_1167836817_state), (((eq hoare_1167836817_state) (((finite1731015960_state F_24) Z_14) bot_bo70021908tate_o)) Z_14)) % FOF formula (forall (X_32:hoare_1167836817_state) (Z_13:hoare_1167836817_state) (A_48:(hoare_1167836817_state->Prop)) (F_23:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_23)->((finite1084549118_state A_48)->(((eq hoare_1167836817_state) ((F_23 X_32) (((finite1731015960_state F_23) Z_13) A_48))) (((finite1731015960_state F_23) ((F_23 X_32) Z_13)) A_48))))) of role axiom named fact_204_comp__fun__commute_Ofold__fun__comm % A new axiom: (forall (X_32:hoare_1167836817_state) (Z_13:hoare_1167836817_state) (A_48:(hoare_1167836817_state->Prop)) (F_23:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_23)->((finite1084549118_state A_48)->(((eq hoare_1167836817_state) ((F_23 X_32) (((finite1731015960_state F_23) Z_13) A_48))) (((finite1731015960_state F_23) ((F_23 X_32) Z_13)) A_48))))) % FOF formula (forall (Z_12:hoare_1167836817_state) (A_47:(hoare_1167836817_state->Prop)) (Y_19:hoare_1167836817_state) (F_22:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_22)->(((((finite1316643734_state F_22) Z_12) A_47) Y_19)->(((eq hoare_1167836817_state) (((finite1731015960_state F_22) Z_12) A_47)) Y_19)))) of role axiom named fact_205_comp__fun__commute_Ofold__equality % A new axiom: (forall (Z_12:hoare_1167836817_state) (A_47:(hoare_1167836817_state->Prop)) (Y_19:hoare_1167836817_state) (F_22:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_22)->(((((finite1316643734_state F_22) Z_12) A_47) Y_19)->(((eq hoare_1167836817_state) (((finite1731015960_state F_22) Z_12) A_47)) Y_19)))) % FOF formula (forall (Z_11:hoare_1167836817_state) (X_31:hoare_1167836817_state) (A_46:(hoare_1167836817_state->Prop)) (F_21:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_21)->((finite1084549118_state A_46)->((((member2058392318_state X_31) A_46)->False)->(((eq hoare_1167836817_state) (((finite1731015960_state F_21) Z_11) ((insert2134838167_state X_31) A_46))) (((finite1731015960_state F_21) ((F_21 X_31) Z_11)) A_46)))))) of role axiom named fact_206_comp__fun__commute_Ofold__insert2 % A new axiom: (forall (Z_11:hoare_1167836817_state) (X_31:hoare_1167836817_state) (A_46:(hoare_1167836817_state->Prop)) (F_21:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_21)->((finite1084549118_state A_46)->((((member2058392318_state X_31) A_46)->False)->(((eq hoare_1167836817_state) (((finite1731015960_state F_21) Z_11) ((insert2134838167_state X_31) A_46))) (((finite1731015960_state F_21) ((F_21 X_31) Z_11)) A_46)))))) % FOF formula (forall (Z_10:hoare_1167836817_state) (X_30:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)) (F_20:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_20)->((finite1084549118_state A_45)->((((member2058392318_state X_30) A_45)->False)->(((eq hoare_1167836817_state) (((finite1731015960_state F_20) Z_10) ((insert2134838167_state X_30) A_45))) ((F_20 X_30) (((finite1731015960_state F_20) Z_10) A_45))))))) of role axiom named fact_207_comp__fun__commute_Ofold__insert % A new axiom: (forall (Z_10:hoare_1167836817_state) (X_30:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)) (F_20:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_20)->((finite1084549118_state A_45)->((((member2058392318_state X_30) A_45)->False)->(((eq hoare_1167836817_state) (((finite1731015960_state F_20) Z_10) ((insert2134838167_state X_30) A_45))) ((F_20 X_30) (((finite1731015960_state F_20) Z_10) A_45))))))) % FOF formula (forall (X_29:hoare_1167836817_state) (A_44:(hoare_1167836817_state->Prop)) (F_19:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_18:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_19) F_18)->((finite1084549118_state A_44)->((((member2058392318_state X_29) A_44)->False)->(((eq hoare_1167836817_state) (F_18 ((insert2134838167_state X_29) A_44))) (((finite1731015960_state F_19) X_29) A_44)))))) of role axiom named fact_208_folding__one_Oeq__fold_H % A new axiom: (forall (X_29:hoare_1167836817_state) (A_44:(hoare_1167836817_state->Prop)) (F_19:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_18:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_19) F_18)->((finite1084549118_state A_44)->((((member2058392318_state X_29) A_44)->False)->(((eq hoare_1167836817_state) (F_18 ((insert2134838167_state X_29) A_44))) (((finite1731015960_state F_19) X_29) A_44)))))) % FOF formula (forall (A_43:hoare_1167836817_state) (A_42:(hoare_1167836817_state->Prop)) (F_17:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_16:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_17) F_16)->((finite1084549118_state A_42)->(((eq hoare_1167836817_state) (F_16 ((insert2134838167_state A_43) A_42))) (((finite1731015960_state F_17) A_43) A_42))))) of role axiom named fact_209_folding__one__idem_Oeq__fold__idem_H % A new axiom: (forall (A_43:hoare_1167836817_state) (A_42:(hoare_1167836817_state->Prop)) (F_17:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_16:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_17) F_16)->((finite1084549118_state A_42)->(((eq hoare_1167836817_state) (F_16 ((insert2134838167_state A_43) A_42))) (((finite1731015960_state F_17) A_43) A_42))))) % FOF formula (forall (Z_9:hoare_1167836817_state) (A_41:(hoare_1167836817_state->Prop)) (F_15:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_15)->((finite1084549118_state A_41)->((((finite1316643734_state F_15) Z_9) A_41) (((finite1731015960_state F_15) Z_9) A_41))))) of role axiom named fact_210_comp__fun__commute_Ofold__graph__fold % A new axiom: (forall (Z_9:hoare_1167836817_state) (A_41:(hoare_1167836817_state->Prop)) (F_15:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_15)->((finite1084549118_state A_41)->((((finite1316643734_state F_15) Z_9) A_41) (((finite1731015960_state F_15) Z_9) A_41))))) % FOF formula (forall (Z_8:hoare_1167836817_state) (X_28:hoare_1167836817_state) (A_40:(hoare_1167836817_state->Prop)) (F_14:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1900754844_state F_14)->((finite1084549118_state A_40)->(((eq hoare_1167836817_state) (((finite1731015960_state F_14) Z_8) ((insert2134838167_state X_28) A_40))) ((F_14 X_28) (((finite1731015960_state F_14) Z_8) A_40)))))) of role axiom named fact_211_comp__fun__idem_Ofold__insert__idem % A new axiom: (forall (Z_8:hoare_1167836817_state) (X_28:hoare_1167836817_state) (A_40:(hoare_1167836817_state->Prop)) (F_14:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1900754844_state F_14)->((finite1084549118_state A_40)->(((eq hoare_1167836817_state) (((finite1731015960_state F_14) Z_8) ((insert2134838167_state X_28) A_40))) ((F_14 X_28) (((finite1731015960_state F_14) Z_8) A_40)))))) % FOF formula (forall (Z_8:(hoare_1167836817_state->Prop)) (X_28:hoare_1167836817_state) (A_40:(hoare_1167836817_state->Prop)) (F_14:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_14)->((finite1084549118_state A_40)->(((eq (hoare_1167836817_state->Prop)) (((finite291020855tate_o F_14) Z_8) ((insert2134838167_state X_28) A_40))) ((F_14 X_28) (((finite291020855tate_o F_14) Z_8) A_40)))))) of role axiom named fact_212_comp__fun__idem_Ofold__insert__idem % A new axiom: (forall (Z_8:(hoare_1167836817_state->Prop)) (X_28:hoare_1167836817_state) (A_40:(hoare_1167836817_state->Prop)) (F_14:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_14)->((finite1084549118_state A_40)->(((eq (hoare_1167836817_state->Prop)) (((finite291020855tate_o F_14) Z_8) ((insert2134838167_state X_28) A_40))) ((F_14 X_28) (((finite291020855tate_o F_14) Z_8) A_40)))))) % FOF formula (forall (Z_7:hoare_1167836817_state) (X_27:hoare_1167836817_state) (A_39:(hoare_1167836817_state->Prop)) (F_13:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1900754844_state F_13)->((finite1084549118_state A_39)->(((eq hoare_1167836817_state) (((finite1731015960_state F_13) Z_7) ((insert2134838167_state X_27) A_39))) (((finite1731015960_state F_13) ((F_13 X_27) Z_7)) A_39))))) of role axiom named fact_213_comp__fun__idem_Ofold__insert__idem2 % A new axiom: (forall (Z_7:hoare_1167836817_state) (X_27:hoare_1167836817_state) (A_39:(hoare_1167836817_state->Prop)) (F_13:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1900754844_state F_13)->((finite1084549118_state A_39)->(((eq hoare_1167836817_state) (((finite1731015960_state F_13) Z_7) ((insert2134838167_state X_27) A_39))) (((finite1731015960_state F_13) ((F_13 X_27) Z_7)) A_39))))) % FOF formula (forall (Z_7:(hoare_1167836817_state->Prop)) (X_27:hoare_1167836817_state) (A_39:(hoare_1167836817_state->Prop)) (F_13:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_13)->((finite1084549118_state A_39)->(((eq (hoare_1167836817_state->Prop)) (((finite291020855tate_o F_13) Z_7) ((insert2134838167_state X_27) A_39))) (((finite291020855tate_o F_13) ((F_13 X_27) Z_7)) A_39))))) of role axiom named fact_214_comp__fun__idem_Ofold__insert__idem2 % A new axiom: (forall (Z_7:(hoare_1167836817_state->Prop)) (X_27:hoare_1167836817_state) (A_39:(hoare_1167836817_state->Prop)) (F_13:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_13)->((finite1084549118_state A_39)->(((eq (hoare_1167836817_state->Prop)) (((finite291020855tate_o F_13) Z_7) ((insert2134838167_state X_27) A_39))) (((finite291020855tate_o F_13) ((F_13 X_27) Z_7)) A_39))))) % FOF formula (forall (X_26:hoare_1167836817_state) (Z_6:(hoare_1167836817_state->Prop)) (F_12:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_12)->(((eq (hoare_1167836817_state->Prop)) ((F_12 X_26) ((F_12 X_26) Z_6))) ((F_12 X_26) Z_6)))) of role axiom named fact_215_comp__fun__idem_Ofun__left__idem % A new axiom: (forall (X_26:hoare_1167836817_state) (Z_6:(hoare_1167836817_state->Prop)) (F_12:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_12)->(((eq (hoare_1167836817_state->Prop)) ((F_12 X_26) ((F_12 X_26) Z_6))) ((F_12 X_26) Z_6)))) % FOF formula (finite856902323tate_o insert2134838167_state) of role axiom named fact_216_comp__fun__idem__insert % A new axiom: (finite856902323tate_o insert2134838167_state) % FOF formula (forall (F_11:(hoare_1167836817_state->nat)) (A_38:hoare_1167836817_state) (A_37:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_38) A_37)->(((eq nat) ((big_co337839062te_nat F_11) ((minus_2107060239tate_o A_37) ((insert2134838167_state A_38) bot_bo70021908tate_o)))) ((minus_minus_nat ((big_co337839062te_nat F_11) A_37)) (F_11 A_38))))) ((((member2058392318_state A_38) A_37)->False)->(((eq nat) ((big_co337839062te_nat F_11) ((minus_2107060239tate_o A_37) ((insert2134838167_state A_38) bot_bo70021908tate_o)))) ((big_co337839062te_nat F_11) A_37))))) of role axiom named fact_217_setsum__diff1__nat % A new axiom: (forall (F_11:(hoare_1167836817_state->nat)) (A_38:hoare_1167836817_state) (A_37:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_38) A_37)->(((eq nat) ((big_co337839062te_nat F_11) ((minus_2107060239tate_o A_37) ((insert2134838167_state A_38) bot_bo70021908tate_o)))) ((minus_minus_nat ((big_co337839062te_nat F_11) A_37)) (F_11 A_38))))) ((((member2058392318_state A_38) A_37)->False)->(((eq nat) ((big_co337839062te_nat F_11) ((minus_2107060239tate_o A_37) ((insert2134838167_state A_38) bot_bo70021908tate_o)))) ((big_co337839062te_nat F_11) A_37))))) % FOF formula (forall (F_10:(hoare_1167836817_state->nat)) (A_36:(hoare_1167836817_state->Prop)) (B_25:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_25)->(((ord_le827224136tate_o B_25) A_36)->(((eq nat) ((big_co337839062te_nat F_10) ((minus_2107060239tate_o A_36) B_25))) ((minus_minus_nat ((big_co337839062te_nat F_10) A_36)) ((big_co337839062te_nat F_10) B_25)))))) of role axiom named fact_218_setsum__diff__nat % A new axiom: (forall (F_10:(hoare_1167836817_state->nat)) (A_36:(hoare_1167836817_state->Prop)) (B_25:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_25)->(((ord_le827224136tate_o B_25) A_36)->(((eq nat) ((big_co337839062te_nat F_10) ((minus_2107060239tate_o A_36) B_25))) ((minus_minus_nat ((big_co337839062te_nat F_10) A_36)) ((big_co337839062te_nat F_10) B_25)))))) % FOF formula (forall (G_8:(hoare_1167836817_state->nat)) (H_1:(hoare_1167836817_state->nat)) (A_35:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_35)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_35)->(((eq nat) (G_8 X)) (H_1 X))))->(((eq nat) ((big_co337839062te_nat G_8) A_35)) ((big_co337839062te_nat H_1) A_35))))) of role axiom named fact_219_setsum_Ocong % A new axiom: (forall (G_8:(hoare_1167836817_state->nat)) (H_1:(hoare_1167836817_state->nat)) (A_35:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_35)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_35)->(((eq nat) (G_8 X)) (H_1 X))))->(((eq nat) ((big_co337839062te_nat G_8) A_35)) ((big_co337839062te_nat H_1) A_35))))) % FOF formula (forall (X_25:Prop) (Least_1:Prop), ((all1 (ord_less_eq_o Least_1))->((iff ((ord_max_o X_25) Least_1)) X_25))) of role axiom named fact_220_max__leastR % A new axiom: (forall (X_25:Prop) (Least_1:Prop), ((all1 (ord_less_eq_o Least_1))->((iff ((ord_max_o X_25) Least_1)) X_25))) % FOF formula (forall (X_25:(hoare_1167836817_state->Prop)) (Least_1:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_1))->(((eq (hoare_1167836817_state->Prop)) ((ord_ma164008317tate_o X_25) Least_1)) X_25))) of role axiom named fact_221_max__leastR % A new axiom: (forall (X_25:(hoare_1167836817_state->Prop)) (Least_1:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_1))->(((eq (hoare_1167836817_state->Prop)) ((ord_ma164008317tate_o X_25) Least_1)) X_25))) % FOF formula (forall (X_24:Prop) (Least:Prop), ((all1 (ord_less_eq_o Least))->((iff ((ord_max_o Least) X_24)) X_24))) of role axiom named fact_222_max__leastL % A new axiom: (forall (X_24:Prop) (Least:Prop), ((all1 (ord_less_eq_o Least))->((iff ((ord_max_o Least) X_24)) X_24))) % FOF formula (forall (X_24:(hoare_1167836817_state->Prop)) (Least:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least))->(((eq (hoare_1167836817_state->Prop)) ((ord_ma164008317tate_o Least) X_24)) X_24))) of role axiom named fact_223_max__leastL % A new axiom: (forall (X_24:(hoare_1167836817_state->Prop)) (Least:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least))->(((eq (hoare_1167836817_state->Prop)) ((ord_ma164008317tate_o Least) X_24)) X_24))) % FOF formula (((eq (Prop->(Prop->Prop))) ord_max_o) (max_o ord_less_eq_o)) of role axiom named fact_224_max__ord__max % A new axiom: (((eq (Prop->(Prop->Prop))) ord_max_o) (max_o ord_less_eq_o)) % FOF formula (((eq ((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) ord_ma164008317tate_o) (max_Ho421493569tate_o ord_le827224136tate_o)) of role axiom named fact_225_max__ord__max % A new axiom: (((eq ((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) ord_ma164008317tate_o) (max_Ho421493569tate_o ord_le827224136tate_o)) % FOF formula (forall (G_7:(hoare_1167836817_state->nat)) (X_23:hoare_1167836817_state) (A_34:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_34)->(((member2058392318_state X_23) A_34)->(((eq nat) ((big_co337839062te_nat G_7) A_34)) ((plus_plus_nat (G_7 X_23)) ((big_co337839062te_nat G_7) ((minus_2107060239tate_o A_34) ((insert2134838167_state X_23) bot_bo70021908tate_o)))))))) of role axiom named fact_226_setsum_Oremove % A new axiom: (forall (G_7:(hoare_1167836817_state->nat)) (X_23:hoare_1167836817_state) (A_34:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_34)->(((member2058392318_state X_23) A_34)->(((eq nat) ((big_co337839062te_nat G_7) A_34)) ((plus_plus_nat (G_7 X_23)) ((big_co337839062te_nat G_7) ((minus_2107060239tate_o A_34) ((insert2134838167_state X_23) bot_bo70021908tate_o)))))))) % FOF formula (forall (F_9:(hoare_1167836817_state->nat)) (A_33:hoare_1167836817_state) (A_32:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_32)->(((member2058392318_state A_33) A_32)->(((eq nat) ((big_co337839062te_nat F_9) A_32)) ((plus_plus_nat (F_9 A_33)) ((big_co337839062te_nat F_9) ((minus_2107060239tate_o A_32) ((insert2134838167_state A_33) bot_bo70021908tate_o)))))))) of role axiom named fact_227_setsum__diff1_H % A new axiom: (forall (F_9:(hoare_1167836817_state->nat)) (A_33:hoare_1167836817_state) (A_32:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_32)->(((member2058392318_state A_33) A_32)->(((eq nat) ((big_co337839062te_nat F_9) A_32)) ((plus_plus_nat (F_9 A_33)) ((big_co337839062te_nat F_9) ((minus_2107060239tate_o A_32) ((insert2134838167_state A_33) bot_bo70021908tate_o)))))))) % FOF formula (forall (G_6:(hoare_1167836817_state->nat)) (X_22:hoare_1167836817_state) (A_31:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_31)->((((member2058392318_state X_22) A_31)->False)->(((eq nat) ((big_co337839062te_nat G_6) ((insert2134838167_state X_22) A_31))) ((plus_plus_nat (G_6 X_22)) ((big_co337839062te_nat G_6) A_31)))))) of role axiom named fact_228_setsum_Oinsert % A new axiom: (forall (G_6:(hoare_1167836817_state->nat)) (X_22:hoare_1167836817_state) (A_31:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_31)->((((member2058392318_state X_22) A_31)->False)->(((eq nat) ((big_co337839062te_nat G_6) ((insert2134838167_state X_22) A_31))) ((plus_plus_nat (G_6 X_22)) ((big_co337839062te_nat G_6) A_31)))))) % FOF formula (forall (F_8:(hoare_1167836817_state->nat)) (A_30:hoare_1167836817_state) (F_7:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_7)->((((member2058392318_state A_30) F_7)->False)->(((eq nat) ((big_co337839062te_nat F_8) ((insert2134838167_state A_30) F_7))) ((plus_plus_nat (F_8 A_30)) ((big_co337839062te_nat F_8) F_7)))))) of role axiom named fact_229_setsum__insert % A new axiom: (forall (F_8:(hoare_1167836817_state->nat)) (A_30:hoare_1167836817_state) (F_7:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_7)->((((member2058392318_state A_30) F_7)->False)->(((eq nat) ((big_co337839062te_nat F_8) ((insert2134838167_state A_30) F_7))) ((plus_plus_nat (F_8 A_30)) ((big_co337839062te_nat F_8) F_7)))))) % FOF formula (forall (G_5:(hoare_1167836817_state->nat)) (X_21:hoare_1167836817_state) (A_29:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_29)->(((eq nat) ((big_co337839062te_nat G_5) ((insert2134838167_state X_21) A_29))) ((plus_plus_nat (G_5 X_21)) ((big_co337839062te_nat G_5) ((minus_2107060239tate_o A_29) ((insert2134838167_state X_21) bot_bo70021908tate_o))))))) of role axiom named fact_230_setsum_Oinsert__remove % A new axiom: (forall (G_5:(hoare_1167836817_state->nat)) (X_21:hoare_1167836817_state) (A_29:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_29)->(((eq nat) ((big_co337839062te_nat G_5) ((insert2134838167_state X_21) A_29))) ((plus_plus_nat (G_5 X_21)) ((big_co337839062te_nat G_5) ((minus_2107060239tate_o A_29) ((insert2134838167_state X_21) bot_bo70021908tate_o))))))) % FOF formula (forall (F_6:(hoare_1167836817_state->nat)) (G_4:(hoare_1167836817_state->nat)) (A_28:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_28)->(((eq nat) (F_6 X)) (G_4 X))))->(((eq nat) ((big_co337839062te_nat F_6) A_28)) ((big_co337839062te_nat G_4) A_28)))) of role axiom named fact_231_setsum__cong2 % A new axiom: (forall (F_6:(hoare_1167836817_state->nat)) (G_4:(hoare_1167836817_state->nat)) (A_28:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_28)->(((eq nat) (F_6 X)) (G_4 X))))->(((eq nat) ((big_co337839062te_nat F_6) A_28)) ((big_co337839062te_nat G_4) A_28)))) % FOF formula (forall (F_5:(hoare_1167836817_state->nat)) (G_3:(hoare_1167836817_state->nat)) (A_27:(hoare_1167836817_state->Prop)) (B_24:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_27) B_24)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) B_24)->(((eq nat) (F_5 X)) (G_3 X))))->(((eq nat) ((big_co337839062te_nat F_5) A_27)) ((big_co337839062te_nat G_3) B_24))))) of role axiom named fact_232_setsum__cong % A new axiom: (forall (F_5:(hoare_1167836817_state->nat)) (G_3:(hoare_1167836817_state->nat)) (A_27:(hoare_1167836817_state->Prop)) (B_24:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_27) B_24)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) B_24)->(((eq nat) (F_5 X)) (G_3 X))))->(((eq nat) ((big_co337839062te_nat F_5) A_27)) ((big_co337839062te_nat G_3) B_24))))) % FOF formula (forall (H:(hoare_1167836817_state->nat)) (G_2:(hoare_1167836817_state->nat)) (A_26:(hoare_1167836817_state->Prop)) (B_23:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_26) B_23)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) B_23)->(((eq nat) (H X)) (G_2 X))))->(((eq nat) ((big_co337839062te_nat H) A_26)) ((big_co337839062te_nat G_2) B_23))))) of role axiom named fact_233_setsum_OF__cong % A new axiom: (forall (H:(hoare_1167836817_state->nat)) (G_2:(hoare_1167836817_state->nat)) (A_26:(hoare_1167836817_state->Prop)) (B_23:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_26) B_23)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) B_23)->(((eq nat) (H X)) (G_2 X))))->(((eq nat) ((big_co337839062te_nat H) A_26)) ((big_co337839062te_nat G_2) B_23))))) % FOF formula (forall (A_25:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_25) bot_bo70021908tate_o)->False)) of role axiom named fact_234_not__less__bot % A new axiom: (forall (A_25:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_25) bot_bo70021908tate_o)->False)) % FOF formula (forall (A_25:Prop), (((ord_less_o A_25) bot_bot_o)->False)) of role axiom named fact_235_not__less__bot % A new axiom: (forall (A_25:Prop), (((ord_less_o A_25) bot_bot_o)->False)) % FOF formula (forall (A_24:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_24) bot_bo70021908tate_o))) ((ord_le65125204tate_o bot_bo70021908tate_o) A_24))) of role axiom named fact_236_bot__less % A new axiom: (forall (A_24:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_24) bot_bo70021908tate_o))) ((ord_le65125204tate_o bot_bo70021908tate_o) A_24))) % FOF formula (forall (A_24:Prop), ((iff (((iff A_24) bot_bot_o)->False)) ((ord_less_o bot_bot_o) A_24))) of role axiom named fact_237_bot__less % A new axiom: (forall (A_24:Prop), ((iff (((iff A_24) bot_bot_o)->False)) ((ord_less_o bot_bot_o) A_24))) % FOF formula (forall (A_23:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_23) bot_bo70021908tate_o)->False)) of role axiom named fact_238_not__psubset__empty % A new axiom: (forall (A_23:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_23) bot_bo70021908tate_o)->False)) % FOF formula (forall (A_22:(hoare_1167836817_state->Prop)) (B_22:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o A_22) B_22)) ((and ((ord_le827224136tate_o A_22) B_22)) (not (((eq (hoare_1167836817_state->Prop)) A_22) B_22))))) of role axiom named fact_239_psubset__eq % A new axiom: (forall (A_22:(hoare_1167836817_state->Prop)) (B_22:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o A_22) B_22)) ((and ((ord_le827224136tate_o A_22) B_22)) (not (((eq (hoare_1167836817_state->Prop)) A_22) B_22))))) % FOF formula (forall (A_21:(hoare_1167836817_state->Prop)) (B_21:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_21) B_21)) ((or ((ord_le65125204tate_o A_21) B_21)) (((eq (hoare_1167836817_state->Prop)) A_21) B_21)))) of role axiom named fact_240_subset__iff__psubset__eq % A new axiom: (forall (A_21:(hoare_1167836817_state->Prop)) (B_21:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_21) B_21)) ((or ((ord_le65125204tate_o A_21) B_21)) (((eq (hoare_1167836817_state->Prop)) A_21) B_21)))) % FOF formula (forall (A_20:(hoare_1167836817_state->Prop)) (B_20:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_20) B_20)->((ord_le827224136tate_o A_20) B_20))) of role axiom named fact_241_psubset__imp__subset % A new axiom: (forall (A_20:(hoare_1167836817_state->Prop)) (B_20:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_20) B_20)->((ord_le827224136tate_o A_20) B_20))) % FOF formula (forall (C_10:(hoare_1167836817_state->Prop)) (A_19:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_19) B_19)->(((ord_le827224136tate_o B_19) C_10)->((ord_le65125204tate_o A_19) C_10)))) of role axiom named fact_242_psubset__subset__trans % A new axiom: (forall (C_10:(hoare_1167836817_state->Prop)) (A_19:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_19) B_19)->(((ord_le827224136tate_o B_19) C_10)->((ord_le65125204tate_o A_19) C_10)))) % FOF formula (forall (C_9:(hoare_1167836817_state->Prop)) (A_18:(hoare_1167836817_state->Prop)) (B_18:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_18) B_18)->(((ord_le65125204tate_o B_18) C_9)->((ord_le65125204tate_o A_18) C_9)))) of role axiom named fact_243_subset__psubset__trans % A new axiom: (forall (C_9:(hoare_1167836817_state->Prop)) (A_18:(hoare_1167836817_state->Prop)) (B_18:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_18) B_18)->(((ord_le65125204tate_o B_18) C_9)->((ord_le65125204tate_o A_18) C_9)))) % FOF formula (forall (X_20:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_20) Y_18)->(((ord_le65125204tate_o Y_18) X_20)->False))) of role axiom named fact_244_order__less__asym % A new axiom: (forall (X_20:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_20) Y_18)->(((ord_le65125204tate_o Y_18) X_20)->False))) % FOF formula (forall (X_20:Prop) (Y_18:Prop), (((ord_less_o X_20) Y_18)->(((ord_less_o Y_18) X_20)->False))) of role axiom named fact_245_order__less__asym % A new axiom: (forall (X_20:Prop) (Y_18:Prop), (((ord_less_o X_20) Y_18)->(((ord_less_o Y_18) X_20)->False))) % FOF formula (forall (Z_5:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)) (X_19:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y_17) X_19)->(((ord_le65125204tate_o Z_5) Y_17)->((ord_le65125204tate_o Z_5) X_19)))) of role axiom named fact_246_xt1_I10_J % A new axiom: (forall (Z_5:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)) (X_19:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y_17) X_19)->(((ord_le65125204tate_o Z_5) Y_17)->((ord_le65125204tate_o Z_5) X_19)))) % FOF formula (forall (Z_5:Prop) (Y_17:Prop) (X_19:Prop), (((ord_less_o Y_17) X_19)->(((ord_less_o Z_5) Y_17)->((ord_less_o Z_5) X_19)))) of role axiom named fact_247_xt1_I10_J % A new axiom: (forall (Z_5:Prop) (Y_17:Prop) (X_19:Prop), (((ord_less_o Y_17) X_19)->(((ord_less_o Z_5) Y_17)->((ord_less_o Z_5) X_19)))) % FOF formula (forall (Z_4:(hoare_1167836817_state->Prop)) (X_18:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_18) Y_16)->(((ord_le65125204tate_o Y_16) Z_4)->((ord_le65125204tate_o X_18) Z_4)))) of role axiom named fact_248_order__less__trans % A new axiom: (forall (Z_4:(hoare_1167836817_state->Prop)) (X_18:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_18) Y_16)->(((ord_le65125204tate_o Y_16) Z_4)->((ord_le65125204tate_o X_18) Z_4)))) % FOF formula (forall (Z_4:Prop) (X_18:Prop) (Y_16:Prop), (((ord_less_o X_18) Y_16)->(((ord_less_o Y_16) Z_4)->((ord_less_o X_18) Z_4)))) of role axiom named fact_249_order__less__trans % A new axiom: (forall (Z_4:Prop) (X_18:Prop) (Y_16:Prop), (((ord_less_o X_18) Y_16)->(((ord_less_o Y_16) Z_4)->((ord_less_o X_18) Z_4)))) % FOF formula (forall (C_8:(hoare_1167836817_state->Prop)) (B_17:(hoare_1167836817_state->Prop)) (A_17:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_17) A_17)->((((eq (hoare_1167836817_state->Prop)) B_17) C_8)->((ord_le65125204tate_o C_8) A_17)))) of role axiom named fact_250_xt1_I2_J % A new axiom: (forall (C_8:(hoare_1167836817_state->Prop)) (B_17:(hoare_1167836817_state->Prop)) (A_17:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_17) A_17)->((((eq (hoare_1167836817_state->Prop)) B_17) C_8)->((ord_le65125204tate_o C_8) A_17)))) % FOF formula (forall (C_8:Prop) (B_17:Prop) (A_17:Prop), (((ord_less_o B_17) A_17)->(((iff B_17) C_8)->((ord_less_o C_8) A_17)))) of role axiom named fact_251_xt1_I2_J % A new axiom: (forall (C_8:Prop) (B_17:Prop) (A_17:Prop), (((ord_less_o B_17) A_17)->(((iff B_17) C_8)->((ord_less_o C_8) A_17)))) % FOF formula (forall (C_7:(hoare_1167836817_state->Prop)) (A_16:(hoare_1167836817_state->Prop)) (B_16:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_16) B_16)->((((eq (hoare_1167836817_state->Prop)) B_16) C_7)->((ord_le65125204tate_o A_16) C_7)))) of role axiom named fact_252_ord__less__eq__trans % A new axiom: (forall (C_7:(hoare_1167836817_state->Prop)) (A_16:(hoare_1167836817_state->Prop)) (B_16:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_16) B_16)->((((eq (hoare_1167836817_state->Prop)) B_16) C_7)->((ord_le65125204tate_o A_16) C_7)))) % FOF formula (forall (C_7:Prop) (A_16:Prop) (B_16:Prop), (((ord_less_o A_16) B_16)->(((iff B_16) C_7)->((ord_less_o A_16) C_7)))) of role axiom named fact_253_ord__less__eq__trans % A new axiom: (forall (C_7:Prop) (A_16:Prop) (B_16:Prop), (((ord_less_o A_16) B_16)->(((iff B_16) C_7)->((ord_less_o A_16) C_7)))) % FOF formula (forall (C_6:(hoare_1167836817_state->Prop)) (A_15:(hoare_1167836817_state->Prop)) (B_15:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_15) B_15)->(((ord_le65125204tate_o C_6) B_15)->((ord_le65125204tate_o C_6) A_15)))) of role axiom named fact_254_xt1_I1_J % A new axiom: (forall (C_6:(hoare_1167836817_state->Prop)) (A_15:(hoare_1167836817_state->Prop)) (B_15:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_15) B_15)->(((ord_le65125204tate_o C_6) B_15)->((ord_le65125204tate_o C_6) A_15)))) % FOF formula (forall (C_6:Prop) (B_15:Prop) (A_15:Prop), (((iff A_15) B_15)->(((ord_less_o C_6) B_15)->((ord_less_o C_6) A_15)))) of role axiom named fact_255_xt1_I1_J % A new axiom: (forall (C_6:Prop) (B_15:Prop) (A_15:Prop), (((iff A_15) B_15)->(((ord_less_o C_6) B_15)->((ord_less_o C_6) A_15)))) % FOF formula (forall (C_5:(hoare_1167836817_state->Prop)) (A_14:(hoare_1167836817_state->Prop)) (B_14:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_14) B_14)->(((ord_le65125204tate_o B_14) C_5)->((ord_le65125204tate_o A_14) C_5)))) of role axiom named fact_256_ord__eq__less__trans % A new axiom: (forall (C_5:(hoare_1167836817_state->Prop)) (A_14:(hoare_1167836817_state->Prop)) (B_14:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_14) B_14)->(((ord_le65125204tate_o B_14) C_5)->((ord_le65125204tate_o A_14) C_5)))) % FOF formula (forall (C_5:Prop) (B_14:Prop) (A_14:Prop), (((iff A_14) B_14)->(((ord_less_o B_14) C_5)->((ord_less_o A_14) C_5)))) of role axiom named fact_257_ord__eq__less__trans % A new axiom: (forall (C_5:Prop) (B_14:Prop) (A_14:Prop), (((iff A_14) B_14)->(((ord_less_o B_14) C_5)->((ord_less_o A_14) C_5)))) % FOF formula (forall (B_13:(hoare_1167836817_state->Prop)) (A_13:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_13) A_13)->(((ord_le65125204tate_o A_13) B_13)->False))) of role axiom named fact_258_xt1_I9_J % A new axiom: (forall (B_13:(hoare_1167836817_state->Prop)) (A_13:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_13) A_13)->(((ord_le65125204tate_o A_13) B_13)->False))) % FOF formula (forall (B_13:Prop) (A_13:Prop), (((ord_less_o B_13) A_13)->(((ord_less_o A_13) B_13)->False))) of role axiom named fact_259_xt1_I9_J % A new axiom: (forall (B_13:Prop) (A_13:Prop), (((ord_less_o B_13) A_13)->(((ord_less_o A_13) B_13)->False))) % FOF formula (forall (A_12:(hoare_1167836817_state->Prop)) (B_12:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_12) B_12)->(((ord_le65125204tate_o B_12) A_12)->False))) of role axiom named fact_260_order__less__asym_H % A new axiom: (forall (A_12:(hoare_1167836817_state->Prop)) (B_12:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_12) B_12)->(((ord_le65125204tate_o B_12) A_12)->False))) % FOF formula (forall (A_12:Prop) (B_12:Prop), (((ord_less_o A_12) B_12)->(((ord_less_o B_12) A_12)->False))) of role axiom named fact_261_order__less__asym_H % A new axiom: (forall (A_12:Prop) (B_12:Prop), (((ord_less_o A_12) B_12)->(((ord_less_o B_12) A_12)->False))) % FOF formula (forall (P:Prop) (X_17:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_17) Y_15)->(((ord_le65125204tate_o Y_15) X_17)->P))) of role axiom named fact_262_order__less__imp__triv % A new axiom: (forall (P:Prop) (X_17:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_17) Y_15)->(((ord_le65125204tate_o Y_15) X_17)->P))) % FOF formula (forall (P:Prop) (X_17:Prop) (Y_15:Prop), (((ord_less_o X_17) Y_15)->(((ord_less_o Y_15) X_17)->P))) of role axiom named fact_263_order__less__imp__triv % A new axiom: (forall (P:Prop) (X_17:Prop) (Y_15:Prop), (((ord_less_o X_17) Y_15)->(((ord_less_o Y_15) X_17)->P))) % FOF formula (forall (X_16:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_16) Y_14)->(not (((eq (hoare_1167836817_state->Prop)) Y_14) X_16)))) of role axiom named fact_264_order__less__imp__not__eq2 % A new axiom: (forall (X_16:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_16) Y_14)->(not (((eq (hoare_1167836817_state->Prop)) Y_14) X_16)))) % FOF formula (forall (X_16:Prop) (Y_14:Prop), (((ord_less_o X_16) Y_14)->((iff Y_14) (X_16->False)))) of role axiom named fact_265_order__less__imp__not__eq2 % A new axiom: (forall (X_16:Prop) (Y_14:Prop), (((ord_less_o X_16) Y_14)->((iff Y_14) (X_16->False)))) % FOF formula (forall (X_15:(hoare_1167836817_state->Prop)) (Y_13:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_15) Y_13)->(not (((eq (hoare_1167836817_state->Prop)) X_15) Y_13)))) of role axiom named fact_266_order__less__imp__not__eq % A new axiom: (forall (X_15:(hoare_1167836817_state->Prop)) (Y_13:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_15) Y_13)->(not (((eq (hoare_1167836817_state->Prop)) X_15) Y_13)))) % FOF formula (forall (X_15:Prop) (Y_13:Prop), (((ord_less_o X_15) Y_13)->((iff X_15) (Y_13->False)))) of role axiom named fact_267_order__less__imp__not__eq % A new axiom: (forall (X_15:Prop) (Y_13:Prop), (((ord_less_o X_15) Y_13)->((iff X_15) (Y_13->False)))) % FOF formula (forall (X_14:(hoare_1167836817_state->Prop)) (Y_12:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_14) Y_12)->(((ord_le65125204tate_o Y_12) X_14)->False))) of role axiom named fact_268_order__less__imp__not__less % A new axiom: (forall (X_14:(hoare_1167836817_state->Prop)) (Y_12:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_14) Y_12)->(((ord_le65125204tate_o Y_12) X_14)->False))) % FOF formula (forall (X_14:Prop) (Y_12:Prop), (((ord_less_o X_14) Y_12)->(((ord_less_o Y_12) X_14)->False))) of role axiom named fact_269_order__less__imp__not__less % A new axiom: (forall (X_14:Prop) (Y_12:Prop), (((ord_less_o X_14) Y_12)->(((ord_less_o Y_12) X_14)->False))) % FOF formula (forall (X_13:(hoare_1167836817_state->Prop)) (Y_11:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_13) Y_11)->(((ord_le65125204tate_o Y_11) X_13)->False))) of role axiom named fact_270_order__less__not__sym % A new axiom: (forall (X_13:(hoare_1167836817_state->Prop)) (Y_11:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_13) Y_11)->(((ord_le65125204tate_o Y_11) X_13)->False))) % FOF formula (forall (X_13:Prop) (Y_11:Prop), (((ord_less_o X_13) Y_11)->(((ord_less_o Y_11) X_13)->False))) of role axiom named fact_271_order__less__not__sym % A new axiom: (forall (X_13:Prop) (Y_11:Prop), (((ord_less_o X_13) Y_11)->(((ord_less_o Y_11) X_13)->False))) % FOF formula (forall (X_12:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_12) Y_10)->(not (((eq (hoare_1167836817_state->Prop)) X_12) Y_10)))) of role axiom named fact_272_less__imp__neq % A new axiom: (forall (X_12:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_12) Y_10)->(not (((eq (hoare_1167836817_state->Prop)) X_12) Y_10)))) % FOF formula (forall (X_12:Prop) (Y_10:Prop), (((ord_less_o X_12) Y_10)->(((iff X_12) Y_10)->False))) of role axiom named fact_273_less__imp__neq % A new axiom: (forall (X_12:Prop) (Y_10:Prop), (((ord_less_o X_12) Y_10)->(((iff X_12) Y_10)->False))) % FOF formula (forall (X_11:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_11) X_11)->False)) of role axiom named fact_274_order__less__irrefl % A new axiom: (forall (X_11:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_11) X_11)->False)) % FOF formula (forall (X_11:Prop), (((ord_less_o X_11) X_11)->False)) of role axiom named fact_275_order__less__irrefl % A new axiom: (forall (X_11:Prop), (((ord_less_o X_11) X_11)->False)) % FOF formula (forall (X_10:Prop) (Y_9:Prop), ((iff ((ord_less_o X_10) Y_9)) ((and ((ord_less_eq_o X_10) Y_9)) (((iff X_10) Y_9)->False)))) of role axiom named fact_276_order__less__le % A new axiom: (forall (X_10:Prop) (Y_9:Prop), ((iff ((ord_less_o X_10) Y_9)) ((and ((ord_less_eq_o X_10) Y_9)) (((iff X_10) Y_9)->False)))) % FOF formula (forall (X_10:(hoare_1167836817_state->Prop)) (Y_9:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o X_10) Y_9)) ((and ((ord_le827224136tate_o X_10) Y_9)) (not (((eq (hoare_1167836817_state->Prop)) X_10) Y_9))))) of role axiom named fact_277_order__less__le % A new axiom: (forall (X_10:(hoare_1167836817_state->Prop)) (Y_9:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o X_10) Y_9)) ((and ((ord_le827224136tate_o X_10) Y_9)) (not (((eq (hoare_1167836817_state->Prop)) X_10) Y_9))))) % FOF formula (forall (X_9:Prop) (Y_8:Prop), ((iff ((ord_less_o X_9) Y_8)) ((and ((ord_less_eq_o X_9) Y_8)) (((ord_less_eq_o Y_8) X_9)->False)))) of role axiom named fact_278_less__le__not__le % A new axiom: (forall (X_9:Prop) (Y_8:Prop), ((iff ((ord_less_o X_9) Y_8)) ((and ((ord_less_eq_o X_9) Y_8)) (((ord_less_eq_o Y_8) X_9)->False)))) % FOF formula (forall (X_9:(hoare_1167836817_state->Prop)) (Y_8:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o X_9) Y_8)) ((and ((ord_le827224136tate_o X_9) Y_8)) (((ord_le827224136tate_o Y_8) X_9)->False)))) of role axiom named fact_279_less__le__not__le % A new axiom: (forall (X_9:(hoare_1167836817_state->Prop)) (Y_8:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o X_9) Y_8)) ((and ((ord_le827224136tate_o X_9) Y_8)) (((ord_le827224136tate_o Y_8) X_9)->False)))) % FOF formula (forall (X_8:Prop) (Y_7:Prop), ((iff ((ord_less_eq_o X_8) Y_7)) ((or ((ord_less_o X_8) Y_7)) ((iff X_8) Y_7)))) of role axiom named fact_280_order__le__less % A new axiom: (forall (X_8:Prop) (Y_7:Prop), ((iff ((ord_less_eq_o X_8) Y_7)) ((or ((ord_less_o X_8) Y_7)) ((iff X_8) Y_7)))) % FOF formula (forall (X_8:(hoare_1167836817_state->Prop)) (Y_7:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_8) Y_7)) ((or ((ord_le65125204tate_o X_8) Y_7)) (((eq (hoare_1167836817_state->Prop)) X_8) Y_7)))) of role axiom named fact_281_order__le__less % A new axiom: (forall (X_8:(hoare_1167836817_state->Prop)) (Y_7:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_8) Y_7)) ((or ((ord_le65125204tate_o X_8) Y_7)) (((eq (hoare_1167836817_state->Prop)) X_8) Y_7)))) % FOF formula (forall (B_11:Prop) (A_11:Prop), ((((iff A_11) B_11)->False)->(((ord_less_eq_o A_11) B_11)->((ord_less_o A_11) B_11)))) of role axiom named fact_282_order__neq__le__trans % A new axiom: (forall (B_11:Prop) (A_11:Prop), ((((iff A_11) B_11)->False)->(((ord_less_eq_o A_11) B_11)->((ord_less_o A_11) B_11)))) % FOF formula (forall (A_11:(hoare_1167836817_state->Prop)) (B_11:(hoare_1167836817_state->Prop)), ((not (((eq (hoare_1167836817_state->Prop)) A_11) B_11))->(((ord_le827224136tate_o A_11) B_11)->((ord_le65125204tate_o A_11) B_11)))) of role axiom named fact_283_order__neq__le__trans % A new axiom: (forall (A_11:(hoare_1167836817_state->Prop)) (B_11:(hoare_1167836817_state->Prop)), ((not (((eq (hoare_1167836817_state->Prop)) A_11) B_11))->(((ord_le827224136tate_o A_11) B_11)->((ord_le65125204tate_o A_11) B_11)))) % FOF formula (forall (B_10:Prop) (A_10:Prop), ((((iff A_10) B_10)->False)->(((ord_less_eq_o B_10) A_10)->((ord_less_o B_10) A_10)))) of role axiom named fact_284_xt1_I12_J % A new axiom: (forall (B_10:Prop) (A_10:Prop), ((((iff A_10) B_10)->False)->(((ord_less_eq_o B_10) A_10)->((ord_less_o B_10) A_10)))) % FOF formula (forall (A_10:(hoare_1167836817_state->Prop)) (B_10:(hoare_1167836817_state->Prop)), ((not (((eq (hoare_1167836817_state->Prop)) A_10) B_10))->(((ord_le827224136tate_o B_10) A_10)->((ord_le65125204tate_o B_10) A_10)))) of role axiom named fact_285_xt1_I12_J % A new axiom: (forall (A_10:(hoare_1167836817_state->Prop)) (B_10:(hoare_1167836817_state->Prop)), ((not (((eq (hoare_1167836817_state->Prop)) A_10) B_10))->(((ord_le827224136tate_o B_10) A_10)->((ord_le65125204tate_o B_10) A_10)))) % FOF formula (forall (X_7:Prop) (Y_6:Prop), (((ord_less_o X_7) Y_6)->((ord_less_eq_o X_7) Y_6))) of role axiom named fact_286_order__less__imp__le % A new axiom: (forall (X_7:Prop) (Y_6:Prop), (((ord_less_o X_7) Y_6)->((ord_less_eq_o X_7) Y_6))) % FOF formula (forall (X_7:(hoare_1167836817_state->Prop)) (Y_6:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_7) Y_6)->((ord_le827224136tate_o X_7) Y_6))) of role axiom named fact_287_order__less__imp__le % A new axiom: (forall (X_7:(hoare_1167836817_state->Prop)) (Y_6:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_7) Y_6)->((ord_le827224136tate_o X_7) Y_6))) % FOF formula (forall (X_6:Prop) (Y_5:Prop), (((ord_less_eq_o X_6) Y_5)->((or ((ord_less_o X_6) Y_5)) ((iff X_6) Y_5)))) of role axiom named fact_288_order__le__imp__less__or__eq % A new axiom: (forall (X_6:Prop) (Y_5:Prop), (((ord_less_eq_o X_6) Y_5)->((or ((ord_less_o X_6) Y_5)) ((iff X_6) Y_5)))) % FOF formula (forall (X_6:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_6) Y_5)->((or ((ord_le65125204tate_o X_6) Y_5)) (((eq (hoare_1167836817_state->Prop)) X_6) Y_5)))) of role axiom named fact_289_order__le__imp__less__or__eq % A new axiom: (forall (X_6:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_6) Y_5)->((or ((ord_le65125204tate_o X_6) Y_5)) (((eq (hoare_1167836817_state->Prop)) X_6) Y_5)))) % FOF formula (forall (A_9:Prop) (B_9:Prop), (((ord_less_eq_o A_9) B_9)->((((iff A_9) B_9)->False)->((ord_less_o A_9) B_9)))) of role axiom named fact_290_order__le__neq__trans % A new axiom: (forall (A_9:Prop) (B_9:Prop), (((ord_less_eq_o A_9) B_9)->((((iff A_9) B_9)->False)->((ord_less_o A_9) B_9)))) % FOF formula (forall (A_9:(hoare_1167836817_state->Prop)) (B_9:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_9) B_9)->((not (((eq (hoare_1167836817_state->Prop)) A_9) B_9))->((ord_le65125204tate_o A_9) B_9)))) of role axiom named fact_291_order__le__neq__trans % A new axiom: (forall (A_9:(hoare_1167836817_state->Prop)) (B_9:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_9) B_9)->((not (((eq (hoare_1167836817_state->Prop)) A_9) B_9))->((ord_le65125204tate_o A_9) B_9)))) % FOF formula (forall (B_8:Prop) (A_8:Prop), (((ord_less_eq_o B_8) A_8)->((((iff A_8) B_8)->False)->((ord_less_o B_8) A_8)))) of role axiom named fact_292_xt1_I11_J % A new axiom: (forall (B_8:Prop) (A_8:Prop), (((ord_less_eq_o B_8) A_8)->((((iff A_8) B_8)->False)->((ord_less_o B_8) A_8)))) % FOF formula (forall (B_8:(hoare_1167836817_state->Prop)) (A_8:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_8) A_8)->((not (((eq (hoare_1167836817_state->Prop)) A_8) B_8))->((ord_le65125204tate_o B_8) A_8)))) of role axiom named fact_293_xt1_I11_J % A new axiom: (forall (B_8:(hoare_1167836817_state->Prop)) (A_8:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_8) A_8)->((not (((eq (hoare_1167836817_state->Prop)) A_8) B_8))->((ord_le65125204tate_o B_8) A_8)))) % FOF formula (forall (Z_3:Prop) (X_5:Prop) (Y_4:Prop), (((ord_less_o X_5) Y_4)->(((ord_less_eq_o Y_4) Z_3)->((ord_less_o X_5) Z_3)))) of role axiom named fact_294_order__less__le__trans % A new axiom: (forall (Z_3:Prop) (X_5:Prop) (Y_4:Prop), (((ord_less_o X_5) Y_4)->(((ord_less_eq_o Y_4) Z_3)->((ord_less_o X_5) Z_3)))) % FOF formula (forall (Z_3:(hoare_1167836817_state->Prop)) (X_5:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_5) Y_4)->(((ord_le827224136tate_o Y_4) Z_3)->((ord_le65125204tate_o X_5) Z_3)))) of role axiom named fact_295_order__less__le__trans % A new axiom: (forall (Z_3:(hoare_1167836817_state->Prop)) (X_5:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_5) Y_4)->(((ord_le827224136tate_o Y_4) Z_3)->((ord_le65125204tate_o X_5) Z_3)))) % FOF formula (forall (Z_2:Prop) (Y_3:Prop) (X_4:Prop), (((ord_less_o Y_3) X_4)->(((ord_less_eq_o Z_2) Y_3)->((ord_less_o Z_2) X_4)))) of role axiom named fact_296_xt1_I7_J % A new axiom: (forall (Z_2:Prop) (Y_3:Prop) (X_4:Prop), (((ord_less_o Y_3) X_4)->(((ord_less_eq_o Z_2) Y_3)->((ord_less_o Z_2) X_4)))) % FOF formula (forall (Z_2:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (X_4:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y_3) X_4)->(((ord_le827224136tate_o Z_2) Y_3)->((ord_le65125204tate_o Z_2) X_4)))) of role axiom named fact_297_xt1_I7_J % A new axiom: (forall (Z_2:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (X_4:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y_3) X_4)->(((ord_le827224136tate_o Z_2) Y_3)->((ord_le65125204tate_o Z_2) X_4)))) % FOF formula (forall (Z_1:Prop) (X_3:Prop) (Y_2:Prop), (((ord_less_eq_o X_3) Y_2)->(((ord_less_o Y_2) Z_1)->((ord_less_o X_3) Z_1)))) of role axiom named fact_298_order__le__less__trans % A new axiom: (forall (Z_1:Prop) (X_3:Prop) (Y_2:Prop), (((ord_less_eq_o X_3) Y_2)->(((ord_less_o Y_2) Z_1)->((ord_less_o X_3) Z_1)))) % FOF formula (forall (Z_1:(hoare_1167836817_state->Prop)) (X_3:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_3) Y_2)->(((ord_le65125204tate_o Y_2) Z_1)->((ord_le65125204tate_o X_3) Z_1)))) of role axiom named fact_299_order__le__less__trans % A new axiom: (forall (Z_1:(hoare_1167836817_state->Prop)) (X_3:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_3) Y_2)->(((ord_le65125204tate_o Y_2) Z_1)->((ord_le65125204tate_o X_3) Z_1)))) % FOF formula (forall (Z:Prop) (Y_1:Prop) (X_2:Prop), (((ord_less_eq_o Y_1) X_2)->(((ord_less_o Z) Y_1)->((ord_less_o Z) X_2)))) of role axiom named fact_300_xt1_I8_J % A new axiom: (forall (Z:Prop) (Y_1:Prop) (X_2:Prop), (((ord_less_eq_o Y_1) X_2)->(((ord_less_o Z) Y_1)->((ord_less_o Z) X_2)))) % FOF formula (forall (Z:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (X_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_1) X_2)->(((ord_le65125204tate_o Z) Y_1)->((ord_le65125204tate_o Z) X_2)))) of role axiom named fact_301_xt1_I8_J % A new axiom: (forall (Z:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (X_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_1) X_2)->(((ord_le65125204tate_o Z) Y_1)->((ord_le65125204tate_o Z) X_2)))) % FOF formula (forall (F_4:(hoare_1167836817_state->Prop)) (G_1:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o F_4) G_1)) ((and ((ord_le827224136tate_o F_4) G_1)) (((ord_le827224136tate_o G_1) F_4)->False)))) of role axiom named fact_302_less__fun__def % A new axiom: (forall (F_4:(hoare_1167836817_state->Prop)) (G_1:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o F_4) G_1)) ((and ((ord_le827224136tate_o F_4) G_1)) (((ord_le827224136tate_o G_1) F_4)->False)))) % FOF formula (forall (A_7:(hoare_1167836817_state->Prop)) (X_1:hoare_1167836817_state) (B_7:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o A_7) ((insert2134838167_state X_1) B_7))) ((and (((member2058392318_state X_1) B_7)->((ord_le65125204tate_o A_7) B_7))) ((((member2058392318_state X_1) B_7)->False)->((and (((member2058392318_state X_1) A_7)->((ord_le65125204tate_o ((minus_2107060239tate_o A_7) ((insert2134838167_state X_1) bot_bo70021908tate_o))) B_7))) ((((member2058392318_state X_1) A_7)->False)->((ord_le827224136tate_o A_7) B_7))))))) of role axiom named fact_303_psubset__insert__iff % A new axiom: (forall (A_7:(hoare_1167836817_state->Prop)) (X_1:hoare_1167836817_state) (B_7:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o A_7) ((insert2134838167_state X_1) B_7))) ((and (((member2058392318_state X_1) B_7)->((ord_le65125204tate_o A_7) B_7))) ((((member2058392318_state X_1) B_7)->False)->((and (((member2058392318_state X_1) A_7)->((ord_le65125204tate_o ((minus_2107060239tate_o A_7) ((insert2134838167_state X_1) bot_bo70021908tate_o))) B_7))) ((((member2058392318_state X_1) A_7)->False)->((ord_le827224136tate_o A_7) B_7))))))) % FOF formula (forall (F_3:(hoare_1167836817_state->nat)) (G:(hoare_1167836817_state->nat)) (A_6:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_6)->((not (((eq (hoare_1167836817_state->Prop)) A_6) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_6)->((ord_less_nat (F_3 X)) (G X))))->((ord_less_nat ((big_co337839062te_nat F_3) A_6)) ((big_co337839062te_nat G) A_6)))))) of role axiom named fact_304_setsum__strict__mono % A new axiom: (forall (F_3:(hoare_1167836817_state->nat)) (G:(hoare_1167836817_state->nat)) (A_6:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_6)->((not (((eq (hoare_1167836817_state->Prop)) A_6) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_6)->((ord_less_nat (F_3 X)) (G X))))->((ord_less_nat ((big_co337839062te_nat F_3) A_6)) ((big_co337839062te_nat G) A_6)))))) % FOF formula (forall (C_4:(hoare_1167836817_state->Prop)) (A_5:(hoare_1167836817_state->Prop)) (B_6:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_5) B_6)->(((ord_le65125204tate_o B_6) C_4)->((ord_le65125204tate_o A_5) C_4)))) of role axiom named fact_305_psubset__trans % A new axiom: (forall (C_4:(hoare_1167836817_state->Prop)) (A_5:(hoare_1167836817_state->Prop)) (B_6:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_5) B_6)->(((ord_le65125204tate_o B_6) C_4)->((ord_le65125204tate_o A_5) C_4)))) % FOF formula (forall (C_3:hoare_1167836817_state) (A_4:(hoare_1167836817_state->Prop)) (B_5:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_4) B_5)->(((member2058392318_state C_3) A_4)->((member2058392318_state C_3) B_5)))) of role axiom named fact_306_psubsetD % A new axiom: (forall (C_3:hoare_1167836817_state) (A_4:(hoare_1167836817_state->Prop)) (B_5:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_4) B_5)->(((member2058392318_state C_3) A_4)->((member2058392318_state C_3) B_5)))) % FOF formula (forall (A_3:(hoare_1167836817_state->Prop)) (B_3:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_3) B_3)->((ex hoare_1167836817_state) (fun (B_4:hoare_1167836817_state)=> ((member2058392318_state B_4) ((minus_2107060239tate_o B_3) A_3)))))) of role axiom named fact_307_psubset__imp__ex__mem % A new axiom: (forall (A_3:(hoare_1167836817_state->Prop)) (B_3:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_3) B_3)->((ex hoare_1167836817_state) (fun (B_4:hoare_1167836817_state)=> ((member2058392318_state B_4) ((minus_2107060239tate_o B_3) A_3)))))) % FOF formula (forall (C_2:(hoare_1167836817_state->Prop)) (F_2:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_2:(hoare_1167836817_state->Prop)) (A_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_2 B_2)) A_2)->(((ord_le65125204tate_o C_2) B_2)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y) X)->((ord_le65125204tate_o (F_2 Y)) (F_2 X))))->((ord_le65125204tate_o (F_2 C_2)) A_2))))) of role axiom named fact_308_xt6 % A new axiom: (forall (C_2:(hoare_1167836817_state->Prop)) (F_2:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_2:(hoare_1167836817_state->Prop)) (A_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_2 B_2)) A_2)->(((ord_le65125204tate_o C_2) B_2)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y) X)->((ord_le65125204tate_o (F_2 Y)) (F_2 X))))->((ord_le65125204tate_o (F_2 C_2)) A_2))))) % FOF formula (forall (C_2:Prop) (F_2:(Prop->(hoare_1167836817_state->Prop))) (B_2:Prop) (A_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_2 B_2)) A_2)->(((ord_less_o C_2) B_2)->((forall (X:Prop) (Y:Prop), (((ord_less_o Y) X)->((ord_le65125204tate_o (F_2 Y)) (F_2 X))))->((ord_le65125204tate_o (F_2 C_2)) A_2))))) of role axiom named fact_309_xt6 % A new axiom: (forall (C_2:Prop) (F_2:(Prop->(hoare_1167836817_state->Prop))) (B_2:Prop) (A_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_2 B_2)) A_2)->(((ord_less_o C_2) B_2)->((forall (X:Prop) (Y:Prop), (((ord_less_o Y) X)->((ord_le65125204tate_o (F_2 Y)) (F_2 X))))->((ord_le65125204tate_o (F_2 C_2)) A_2))))) % FOF formula (forall (C_1:(hoare_1167836817_state->Prop)) (F_1:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_1:(hoare_1167836817_state->Prop)) (A_1:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_1) A_1)->(((ord_le827224136tate_o C_1) (F_1 B_1))->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y) X)->((ord_le65125204tate_o (F_1 Y)) (F_1 X))))->((ord_le65125204tate_o C_1) (F_1 A_1)))))) of role axiom named fact_310_xt5 % A new axiom: (forall (C_1:(hoare_1167836817_state->Prop)) (F_1:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_1:(hoare_1167836817_state->Prop)) (A_1:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_1) A_1)->(((ord_le827224136tate_o C_1) (F_1 B_1))->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y) X)->((ord_le65125204tate_o (F_1 Y)) (F_1 X))))->((ord_le65125204tate_o C_1) (F_1 A_1)))))) % FOF formula (forall (C_1:(hoare_1167836817_state->Prop)) (F_1:(Prop->(hoare_1167836817_state->Prop))) (B_1:Prop) (A_1:Prop), (((ord_less_o B_1) A_1)->(((ord_le827224136tate_o C_1) (F_1 B_1))->((forall (X:Prop) (Y:Prop), (((ord_less_o Y) X)->((ord_le65125204tate_o (F_1 Y)) (F_1 X))))->((ord_le65125204tate_o C_1) (F_1 A_1)))))) of role axiom named fact_311_xt5 % A new axiom: (forall (C_1:(hoare_1167836817_state->Prop)) (F_1:(Prop->(hoare_1167836817_state->Prop))) (B_1:Prop) (A_1:Prop), (((ord_less_o B_1) A_1)->(((ord_le827224136tate_o C_1) (F_1 B_1))->((forall (X:Prop) (Y:Prop), (((ord_less_o Y) X)->((ord_le65125204tate_o (F_1 Y)) (F_1 X))))->((ord_le65125204tate_o C_1) (F_1 A_1)))))) % FOF formula (forall (C:(hoare_1167836817_state->Prop)) (F:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B:(hoare_1167836817_state->Prop)) (A:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o (F B)) A)->(((ord_le827224136tate_o C) B)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F Y)) (F X))))->((ord_le65125204tate_o (F C)) A))))) of role axiom named fact_312_xt4 % A new axiom: (forall (C:(hoare_1167836817_state->Prop)) (F:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B:(hoare_1167836817_state->Prop)) (A:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o (F B)) A)->(((ord_le827224136tate_o C) B)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F Y)) (F X))))->((ord_le65125204tate_o (F C)) A))))) % FOF formula (forall (C:(hoare_1167836817_state->Prop)) (F:((hoare_1167836817_state->Prop)->Prop)) (B:(hoare_1167836817_state->Prop)) (A:Prop), (((ord_less_o (F B)) A)->(((ord_le827224136tate_o C) B)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F Y)) (F X))))->((ord_less_o (F C)) A))))) of role axiom named fact_313_xt4 % A new axiom: (forall (C:(hoare_1167836817_state->Prop)) (F:((hoare_1167836817_state->Prop)->Prop)) (B:(hoare_1167836817_state->Prop)) (A:Prop), (((ord_less_o (F B)) A)->(((ord_le827224136tate_o C) B)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F Y)) (F X))))->((ord_less_o (F C)) A))))) % FOF formula (forall (C:Prop) (F:(Prop->(hoare_1167836817_state->Prop))) (B:Prop) (A:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o (F B)) A)->(((ord_less_eq_o C) B)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F Y)) (F X))))->((ord_le65125204tate_o (F C)) A))))) of role axiom named fact_314_xt4 % A new axiom: (forall (C:Prop) (F:(Prop->(hoare_1167836817_state->Prop))) (B:Prop) (A:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o (F B)) A)->(((ord_less_eq_o C) B)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F Y)) (F X))))->((ord_le65125204tate_o (F C)) A))))) % FOF formula ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) of role hypothesis named conj_0 % A new axiom: ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) % FOF formula ((hoare_529639851_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) of role hypothesis named conj_1 % A new axiom: ((hoare_529639851_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % FOF formula ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) of role conjecture named conj_2 % Conjecture to prove = ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)):Prop % Parameter state_DUMMY:state. % Parameter hoare_1167836817_state_DUMMY:hoare_1167836817_state. % Parameter nat_DUMMY:nat. % We need to prove ['((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o))'] % Parameter com:Type. % Parameter state:Type. % Parameter hoare_1167836817_state:Type. % Parameter nat:Type. % Parameter all2:(((hoare_1167836817_state->Prop)->Prop)->Prop). % Parameter all1:((Prop->Prop)->Prop). % Parameter big_co337839062te_nat:((hoare_1167836817_state->nat)->((hoare_1167836817_state->Prop)->nat)). % Parameter big_se1603066171_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)). % Parameter skip:com. % Parameter semi:(com->(com->com)). % Parameter _TPTP_ex:((hoare_1167836817_state->Prop)->Prop). % Parameter finite1091222817_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->Prop). % Parameter finite856902323tate_o:((hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->Prop). % Parameter finite1900754844_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->Prop). % Parameter finite1084549118_state:((hoare_1167836817_state->Prop)->Prop). % Parameter finite309220289_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))). % Parameter finite1646097201_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->((hoare_1167836817_state->Prop)->hoare_1167836817_state)). % Parameter finite291020855tate_o:((hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))). % Parameter finite1731015960_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(hoare_1167836817_state->((hoare_1167836817_state->Prop)->hoare_1167836817_state))). % Parameter finite1316643734_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))). % Parameter finite1074406356_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)). % Parameter finite806517911_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)). % Parameter minus_2107060239tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))). % Parameter minus_minus_o:(Prop->(Prop->Prop)). % Parameter minus_minus_nat:(nat->(nat->nat)). % Parameter plus_plus_nat:(nat->(nat->nat)). % Parameter hoare_Mirabelle_MGT:(com->hoare_1167836817_state). % Parameter hoare_123228589_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)). % Parameter hoare_529639851_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)). % Parameter hoare_908217195_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1167836817_state))). % Parameter bot_bo70021908tate_o:(hoare_1167836817_state->Prop). % Parameter bot_bot_o:Prop. % Parameter max_Ho421493569tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))). % Parameter max_o:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))). % Parameter min_Ho1955171539tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))). % Parameter min_o:((Prop->(Prop->Prop))->(Prop->(Prop->Prop))). % Parameter ord_le65125204tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)). % Parameter ord_less_o:(Prop->(Prop->Prop)). % Parameter ord_less_nat:(nat->(nat->Prop)). % Parameter ord_le827224136tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)). % Parameter ord_less_eq_o:(Prop->(Prop->Prop)). % Parameter ord_ma164008317tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))). % Parameter ord_max_o:(Prop->(Prop->Prop)). % Parameter ord_mi1697686287tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))). % Parameter ord_min_o:(Prop->(Prop->Prop)). % Parameter collec1027672124_state:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)). % Parameter insert2134838167_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))). % Parameter the_el323660082_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state). % Parameter member2058392318_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->Prop)). % Parameter p:(state->(state->Prop)). % Parameter q:(state->(state->Prop)). % Parameter c:com. % Axiom fact_0_empty:(forall (G_29:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_29) bot_bo70021908tate_o)). % Axiom fact_1_triple_Oinject:(forall (Fun1_2:(state->(state->Prop))) (Com_2:com) (Fun2_2:(state->(state->Prop))) (Fun1_1:(state->(state->Prop))) (Com_1:com) (Fun2_1:(state->(state->Prop))), ((iff (((eq hoare_1167836817_state) (((hoare_908217195_state Fun1_2) Com_2) Fun2_2)) (((hoare_908217195_state Fun1_1) Com_1) Fun2_1))) ((and ((and (((eq (state->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_2) Com_1))) (((eq (state->(state->Prop))) Fun2_2) Fun2_1)))). % Axiom fact_2_hoare__sound:(forall (G_28:(hoare_1167836817_state->Prop)) (Ts_7:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_28) Ts_7)->((hoare_529639851_state G_28) Ts_7))). % Axiom fact_3_cut:(forall (G_27:(hoare_1167836817_state->Prop)) (G_26:(hoare_1167836817_state->Prop)) (Ts_6:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_26) Ts_6)->(((hoare_123228589_state G_27) G_26)->((hoare_123228589_state G_27) Ts_6)))). % Axiom fact_4_hoare__derivs_Oinsert:(forall (Ts_5:(hoare_1167836817_state->Prop)) (G_25:(hoare_1167836817_state->Prop)) (T_1:hoare_1167836817_state), (((hoare_123228589_state G_25) ((insert2134838167_state T_1) bot_bo70021908tate_o))->(((hoare_123228589_state G_25) Ts_5)->((hoare_123228589_state G_25) ((insert2134838167_state T_1) Ts_5))))). % Axiom fact_5_derivs__insertD:(forall (G_24:(hoare_1167836817_state->Prop)) (T:hoare_1167836817_state) (Ts_4:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_24) ((insert2134838167_state T) Ts_4))->((and ((hoare_123228589_state G_24) ((insert2134838167_state T) bot_bo70021908tate_o))) ((hoare_123228589_state G_24) Ts_4)))). % Axiom fact_6_conseq2:(forall (Q_11:(state->(state->Prop))) (G_23:(hoare_1167836817_state->Prop)) (P_21:(state->(state->Prop))) (C_39:com) (Q_10:(state->(state->Prop))), (((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_21) C_39) Q_10)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((Q_10 Z_28) S)->((Q_11 Z_28) S)))->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_21) C_39) Q_11)) bot_bo70021908tate_o))))). % Axiom fact_7_conseq1:(forall (P_20:(state->(state->Prop))) (G_22:(hoare_1167836817_state->Prop)) (P_19:(state->(state->Prop))) (C_38:com) (Q_9:(state->(state->Prop))), (((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state P_19) C_38) Q_9)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((P_20 Z_28) S)->((P_19 Z_28) S)))->((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state P_20) C_38) Q_9)) bot_bo70021908tate_o))))). % Axiom fact_8_insertE:(forall (A_185:hoare_1167836817_state) (B_92:hoare_1167836817_state) (A_184:(hoare_1167836817_state->Prop)), (((member2058392318_state A_185) ((insert2134838167_state B_92) A_184))->((not (((eq hoare_1167836817_state) A_185) B_92))->((member2058392318_state A_185) A_184)))). % Axiom fact_9_insertCI:(forall (B_91:hoare_1167836817_state) (A_183:hoare_1167836817_state) (B_90:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_183) B_90)->False)->(((eq hoare_1167836817_state) A_183) B_91))->((member2058392318_state A_183) ((insert2134838167_state B_91) B_90)))). % Axiom fact_10_conseq12:(forall (Q_8:(state->(state->Prop))) (P_18:(state->(state->Prop))) (G_21:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_37:com) (Q_7:(state->(state->Prop))), (((hoare_123228589_state G_21) ((insert2134838167_state (((hoare_908217195_state P_17) C_37) Q_7)) bot_bo70021908tate_o))->((forall (Z_28:state) (S:state), (((P_18 Z_28) S)->(forall (S_1:state), ((forall (Z_29:state), (((P_17 Z_29) S)->((Q_7 Z_29) S_1)))->((Q_8 Z_28) S_1)))))->((hoare_123228589_state G_21) ((insert2134838167_state (((hoare_908217195_state P_18) C_37) Q_8)) bot_bo70021908tate_o))))). % Axiom fact_11_emptyE:(forall (A_182:hoare_1167836817_state), (((member2058392318_state A_182) bot_bo70021908tate_o)->False)). % Axiom fact_12_empty__not__insert:(forall (A_181:hoare_1167836817_state) (A_180:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_181) A_180)))). % Axiom fact_13_insert__not__empty:(forall (A_179:hoare_1167836817_state) (A_178:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_179) A_178)) bot_bo70021908tate_o))). % Axiom fact_14_singleton__iff:(forall (B_89:hoare_1167836817_state) (A_177:hoare_1167836817_state), ((iff ((member2058392318_state B_89) ((insert2134838167_state A_177) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_89) A_177))). % Axiom fact_15_doubleton__eq__iff:(forall (A_176:hoare_1167836817_state) (B_88:hoare_1167836817_state) (C_36:hoare_1167836817_state) (D_3:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_176) ((insert2134838167_state B_88) bot_bo70021908tate_o))) ((insert2134838167_state C_36) ((insert2134838167_state D_3) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_176) C_36)) (((eq hoare_1167836817_state) B_88) D_3))) ((and (((eq hoare_1167836817_state) A_176) D_3)) (((eq hoare_1167836817_state) B_88) C_36))))). % Axiom fact_16_equals0D:(forall (A_175:hoare_1167836817_state) (A_174:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_174) bot_bo70021908tate_o)->(((member2058392318_state A_175) A_174)->False))). % Axiom fact_17_Collect__empty__eq:(forall (P_16:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_16)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), ((P_16 X)->False)))). % Axiom fact_18_empty__iff:(forall (C_35:hoare_1167836817_state), (((member2058392318_state C_35) bot_bo70021908tate_o)->False)). % Axiom fact_19_empty__Collect__eq:(forall (P_15:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_15))) (forall (X:hoare_1167836817_state), ((P_15 X)->False)))). % Axiom fact_20_ex__in__conv:(forall (A_173:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((member2058392318_state X) A_173)))) (not (((eq (hoare_1167836817_state->Prop)) A_173) bot_bo70021908tate_o)))). % Axiom fact_21_all__not__in__conv:(forall (A_172:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_172)->False))) (((eq (hoare_1167836817_state->Prop)) A_172) bot_bo70021908tate_o))). % Axiom fact_22_empty__def:(((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X:hoare_1167836817_state)=> False))). % Axiom fact_23_insert__absorb:(forall (A_171:hoare_1167836817_state) (A_170:(hoare_1167836817_state->Prop)), (((member2058392318_state A_171) A_170)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_171) A_170)) A_170))). % Axiom fact_24_insertI2:(forall (B_87:hoare_1167836817_state) (A_169:hoare_1167836817_state) (B_86:(hoare_1167836817_state->Prop)), (((member2058392318_state A_169) B_86)->((member2058392318_state A_169) ((insert2134838167_state B_87) B_86)))). % Axiom fact_25_insert__ident:(forall (B_85:(hoare_1167836817_state->Prop)) (X_85:hoare_1167836817_state) (A_168:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_85) A_168)->False)->((((member2058392318_state X_85) B_85)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_85) A_168)) ((insert2134838167_state X_85) B_85))) (((eq (hoare_1167836817_state->Prop)) A_168) B_85))))). % Axiom fact_26_insert__code:(forall (Y_34:hoare_1167836817_state) (A_167:(hoare_1167836817_state->Prop)) (X_84:hoare_1167836817_state), ((iff (((insert2134838167_state Y_34) A_167) X_84)) ((or (((eq hoare_1167836817_state) Y_34) X_84)) (A_167 X_84)))). % Axiom fact_27_insert__iff:(forall (A_166:hoare_1167836817_state) (B_84:hoare_1167836817_state) (A_165:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_166) ((insert2134838167_state B_84) A_165))) ((or (((eq hoare_1167836817_state) A_166) B_84)) ((member2058392318_state A_166) A_165)))). % Axiom fact_28_insert__commute:(forall (X_83:hoare_1167836817_state) (Y_33:hoare_1167836817_state) (A_164:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_83) ((insert2134838167_state Y_33) A_164))) ((insert2134838167_state Y_33) ((insert2134838167_state X_83) A_164)))). % Axiom fact_29_insert__absorb2:(forall (X_82:hoare_1167836817_state) (A_163:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_82) ((insert2134838167_state X_82) A_163))) ((insert2134838167_state X_82) A_163))). % Axiom fact_30_insert__Collect:(forall (A_162:hoare_1167836817_state) (P_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_162) (collec1027672124_state P_14))) (collec1027672124_state (fun (U:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U) A_162))) (P_14 U)))))). % Axiom fact_31_insert__compr:(forall (A_161:hoare_1167836817_state) (B_83:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_161) B_83)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X) A_161)) ((member2058392318_state X) B_83)))))). % Axiom fact_32_insertI1:(forall (A_160:hoare_1167836817_state) (B_82:(hoare_1167836817_state->Prop)), ((member2058392318_state A_160) ((insert2134838167_state A_160) B_82))). % Axiom fact_33_singleton__inject:(forall (A_159:hoare_1167836817_state) (B_81:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_159) bot_bo70021908tate_o)) ((insert2134838167_state B_81) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_159) B_81))). % Axiom fact_34_singletonE:(forall (B_80:hoare_1167836817_state) (A_158:hoare_1167836817_state), (((member2058392318_state B_80) ((insert2134838167_state A_158) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_80) A_158))). % Axiom fact_35_the__elem__eq:(forall (X_81:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_81) bot_bo70021908tate_o))) X_81)). % Axiom fact_36_bot__apply:(forall (X_80:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_80)) bot_bot_o)). % Axiom fact_37_bot__fun__def:(forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) bot_bot_o)). % Axiom fact_38_hoare__derivs_OSkip:(forall (G_20:(hoare_1167836817_state->Prop)) (P_13:(state->(state->Prop))), ((hoare_123228589_state G_20) ((insert2134838167_state (((hoare_908217195_state P_13) skip) P_13)) bot_bo70021908tate_o))). % Axiom fact_39_Comp:(forall (D_2:com) (R:(state->(state->Prop))) (G_19:(hoare_1167836817_state->Prop)) (P_12:(state->(state->Prop))) (C_34:com) (Q_6:(state->(state->Prop))), (((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state P_12) C_34) Q_6)) bot_bo70021908tate_o))->(((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state Q_6) D_2) R)) bot_bo70021908tate_o))->((hoare_123228589_state G_19) ((insert2134838167_state (((hoare_908217195_state P_12) ((semi C_34) D_2)) R)) bot_bo70021908tate_o))))). % Axiom fact_40_triple_Oexhaust:(forall (Y_32:hoare_1167836817_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_32) (((hoare_908217195_state Fun1) Com) Fun2))))->False)). % Axiom fact_41_Set_Oset__insert:(forall (X_79:hoare_1167836817_state) (A_157:(hoare_1167836817_state->Prop)), (((member2058392318_state X_79) A_157)->((forall (B_79:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_157) ((insert2134838167_state X_79) B_79))->((member2058392318_state X_79) B_79)))->False))). % Axiom fact_42_mk__disjoint__insert:(forall (A_156:hoare_1167836817_state) (A_155:(hoare_1167836817_state->Prop)), (((member2058392318_state A_156) A_155)->((ex (hoare_1167836817_state->Prop)) (fun (B_79:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_155) ((insert2134838167_state A_156) B_79))) (((member2058392318_state A_156) B_79)->False)))))). % Axiom fact_43_equals0I:(forall (A_154:(hoare_1167836817_state->Prop)), ((forall (Y:hoare_1167836817_state), (((member2058392318_state Y) A_154)->False))->(((eq (hoare_1167836817_state->Prop)) A_154) bot_bo70021908tate_o))). % Axiom fact_44_conseq:(forall (Q_4:(state->(state->Prop))) (G_18:(hoare_1167836817_state->Prop)) (C_33:com) (P_10:(state->(state->Prop))), ((forall (Z_28:state) (S:state), (((P_10 Z_28) S)->((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_11) C_33) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((Q_4 Z_28) S_1))))))))))->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_10) C_33) Q_4)) bot_bo70021908tate_o)))). % Axiom fact_45_nonempty__iff:(forall (A_153:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_153) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_79:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_153) ((insert2134838167_state X) B_79))) (((member2058392318_state X) B_79)->False)))))))). % Axiom fact_46_com_Osimps_I13_J:(forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))). % Axiom fact_47_com_Osimps_I12_J:(forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))). % Axiom fact_48_com_Osimps_I3_J:(forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))). % Axiom fact_49_fold1Set__sing:(forall (F_82:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_152:hoare_1167836817_state) (B_78:hoare_1167836817_state), ((iff (((finite309220289_state F_82) ((insert2134838167_state A_152) bot_bo70021908tate_o)) B_78)) (((eq hoare_1167836817_state) A_152) B_78))). % Axiom fact_50_folding__one_Osingleton:(forall (X_78:hoare_1167836817_state) (F_81:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_80:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_81) F_80)->(((eq hoare_1167836817_state) (F_80 ((insert2134838167_state X_78) bot_bo70021908tate_o))) X_78))). % Axiom fact_51_bot__empty__eq:(forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) ((member2058392318_state X) bot_bo70021908tate_o))). % Axiom fact_52_fold1__singleton:(forall (F_79:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_151:hoare_1167836817_state), (((eq hoare_1167836817_state) ((finite1646097201_state F_79) ((insert2134838167_state A_151) bot_bo70021908tate_o))) A_151)). % Axiom fact_53_fold1__singleton__def:(forall (A_150:hoare_1167836817_state) (G_17:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (F_78:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((((eq ((hoare_1167836817_state->Prop)->hoare_1167836817_state)) G_17) (finite1646097201_state F_78))->(((eq hoare_1167836817_state) (G_17 ((insert2134838167_state A_150) bot_bo70021908tate_o))) A_150))). % Axiom fact_54_empty__fold1SetE:(forall (F_77:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (X_77:hoare_1167836817_state), ((((finite309220289_state F_77) bot_bo70021908tate_o) X_77)->False)). % Axiom fact_55_fold1Set__nonempty:(forall (F_76:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_149:(hoare_1167836817_state->Prop)) (X_76:hoare_1167836817_state), ((((finite309220289_state F_76) A_149) X_76)->(not (((eq (hoare_1167836817_state->Prop)) A_149) bot_bo70021908tate_o)))). % Axiom fact_56_fold1Set_Ointros:(forall (F_75:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_148:hoare_1167836817_state) (A_147:(hoare_1167836817_state->Prop)) (X_75:hoare_1167836817_state), (((((finite1316643734_state F_75) A_148) A_147) X_75)->((((member2058392318_state A_148) A_147)->False)->(((finite309220289_state F_75) ((insert2134838167_state A_148) A_147)) X_75)))). % Axiom fact_57_folding__one_Oinsert:(forall (X_74:hoare_1167836817_state) (A_146:(hoare_1167836817_state->Prop)) (F_74:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_73:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_74) F_73)->((finite1084549118_state A_146)->((((member2058392318_state X_74) A_146)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_146) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_73 ((insert2134838167_state X_74) A_146))) ((F_74 X_74) (F_73 A_146)))))))). % Axiom fact_58_folding__one_Oeq__fold:(forall (A_145:(hoare_1167836817_state->Prop)) (F_72:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_71:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_72) F_71)->((finite1084549118_state A_145)->(((eq hoare_1167836817_state) (F_71 A_145)) ((finite1646097201_state F_72) A_145))))). % Axiom fact_59_folding__one_Oclosed:(forall (A_144:(hoare_1167836817_state->Prop)) (F_70:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_69:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_70) F_69)->((finite1084549118_state A_144)->((not (((eq (hoare_1167836817_state->Prop)) A_144) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((member2058392318_state ((F_70 X) Y)) ((insert2134838167_state X) ((insert2134838167_state Y) bot_bo70021908tate_o))))->((member2058392318_state (F_69 A_144)) A_144)))))). % Axiom fact_60_insert__fold1SetE:(forall (F_68:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_143:hoare_1167836817_state) (X_73:(hoare_1167836817_state->Prop)) (X_72:hoare_1167836817_state), ((((finite309220289_state F_68) ((insert2134838167_state A_143) X_73)) X_72)->((forall (A_59:hoare_1167836817_state) (A_58:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_143) X_73)) ((insert2134838167_state A_59) A_58))->(((((finite1316643734_state F_68) A_59) A_58) X_72)->((member2058392318_state A_59) A_58))))->False))). % Axiom fact_61_subset__singletonD:(forall (A_142:(hoare_1167836817_state->Prop)) (X_71:hoare_1167836817_state), (((ord_le827224136tate_o A_142) ((insert2134838167_state X_71) bot_bo70021908tate_o))->((or (((eq (hoare_1167836817_state->Prop)) A_142) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_142) ((insert2134838167_state X_71) bot_bo70021908tate_o))))). % Axiom fact_62_order__refl:(forall (X_70:Prop), ((ord_less_eq_o X_70) X_70)). % Axiom fact_63_order__refl:(forall (X_70:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_70) X_70)). % Axiom fact_64_subsetD:(forall (C_32:hoare_1167836817_state) (A_141:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_141) B_77)->(((member2058392318_state C_32) A_141)->((member2058392318_state C_32) B_77)))). % Axiom fact_65_equalityI:(forall (A_140:(hoare_1167836817_state->Prop)) (B_76:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_140) B_76)->(((ord_le827224136tate_o B_76) A_140)->(((eq (hoare_1167836817_state->Prop)) A_140) B_76)))). % Axiom fact_66_finite_OemptyI:(finite1084549118_state bot_bo70021908tate_o). % Axiom fact_67_finite_OinsertI:(forall (A_139:hoare_1167836817_state) (A_138:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_138)->(finite1084549118_state ((insert2134838167_state A_139) A_138)))). % Axiom fact_68_empty__subsetI:(forall (A_137:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_137)). % Axiom fact_69_rev__predicate1D:(forall (Q_3:(hoare_1167836817_state->Prop)) (P_9:(hoare_1167836817_state->Prop)) (X_69:hoare_1167836817_state), ((P_9 X_69)->(((ord_le827224136tate_o P_9) Q_3)->(Q_3 X_69)))). % Axiom fact_70_predicate1D:(forall (X_68:hoare_1167836817_state) (P_8:(hoare_1167836817_state->Prop)) (Q_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o P_8) Q_2)->((P_8 X_68)->(Q_2 X_68)))). % Axiom fact_71_mem__def:(forall (X_67:hoare_1167836817_state) (A_136:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_67) A_136)) (A_136 X_67))). % Axiom fact_72_Collect__def:(forall (P_7:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_7)) P_7)). % Axiom fact_73_subset__refl:(forall (A_135:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_135) A_135)). % Axiom fact_74_set__eq__subset:(forall (A_134:(hoare_1167836817_state->Prop)) (B_75:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) A_134) B_75)) ((and ((ord_le827224136tate_o A_134) B_75)) ((ord_le827224136tate_o B_75) A_134)))). % Axiom fact_75_equalityD1:(forall (A_133:(hoare_1167836817_state->Prop)) (B_74:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_133) B_74)->((ord_le827224136tate_o A_133) B_74))). % Axiom fact_76_equalityD2:(forall (A_132:(hoare_1167836817_state->Prop)) (B_73:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_132) B_73)->((ord_le827224136tate_o B_73) A_132))). % Axiom fact_77_in__mono:(forall (X_66:hoare_1167836817_state) (A_131:(hoare_1167836817_state->Prop)) (B_72:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_131) B_72)->(((member2058392318_state X_66) A_131)->((member2058392318_state X_66) B_72)))). % Axiom fact_78_set__rev__mp:(forall (B_71:(hoare_1167836817_state->Prop)) (X_65:hoare_1167836817_state) (A_130:(hoare_1167836817_state->Prop)), (((member2058392318_state X_65) A_130)->(((ord_le827224136tate_o A_130) B_71)->((member2058392318_state X_65) B_71)))). % Axiom fact_79_set__mp:(forall (X_64:hoare_1167836817_state) (A_129:(hoare_1167836817_state->Prop)) (B_70:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_129) B_70)->(((member2058392318_state X_64) A_129)->((member2058392318_state X_64) B_70)))). % Axiom fact_80_subset__trans:(forall (C_31:(hoare_1167836817_state->Prop)) (A_128:(hoare_1167836817_state->Prop)) (B_69:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_128) B_69)->(((ord_le827224136tate_o B_69) C_31)->((ord_le827224136tate_o A_128) C_31)))). % Axiom fact_81_equalityE:(forall (A_127:(hoare_1167836817_state->Prop)) (B_68:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_127) B_68)->((((ord_le827224136tate_o A_127) B_68)->(((ord_le827224136tate_o B_68) A_127)->False))->False))). % Axiom fact_82_le__fun__def:(forall (F_67:(hoare_1167836817_state->Prop)) (G_16:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o F_67) G_16)) (forall (X:hoare_1167836817_state), ((ord_less_eq_o (F_67 X)) (G_16 X))))). % Axiom fact_83_order__eq__iff:(forall (Y_31:Prop) (X_63:Prop), ((iff ((iff X_63) Y_31)) ((and ((ord_less_eq_o X_63) Y_31)) ((ord_less_eq_o Y_31) X_63)))). % Axiom fact_84_order__eq__iff:(forall (X_63:(hoare_1167836817_state->Prop)) (Y_31:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) X_63) Y_31)) ((and ((ord_le827224136tate_o X_63) Y_31)) ((ord_le827224136tate_o Y_31) X_63)))). % Axiom fact_85_rev__finite__subset:(forall (A_126:(hoare_1167836817_state->Prop)) (B_67:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_67)->(((ord_le827224136tate_o A_126) B_67)->(finite1084549118_state A_126)))). % Axiom fact_86_order__eq__refl:(forall (Y_30:Prop) (X_62:Prop), (((iff X_62) Y_30)->((ord_less_eq_o X_62) Y_30))). % Axiom fact_87_order__eq__refl:(forall (X_62:(hoare_1167836817_state->Prop)) (Y_30:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) X_62) Y_30)->((ord_le827224136tate_o X_62) Y_30))). % Axiom fact_88_le__funD:(forall (X_61:hoare_1167836817_state) (F_66:(hoare_1167836817_state->Prop)) (G_15:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_66) G_15)->((ord_less_eq_o (F_66 X_61)) (G_15 X_61)))). % Axiom fact_89_order__antisym__conv:(forall (Y_29:Prop) (X_60:Prop), (((ord_less_eq_o Y_29) X_60)->((iff ((ord_less_eq_o X_60) Y_29)) ((iff X_60) Y_29)))). % Axiom fact_90_order__antisym__conv:(forall (Y_29:(hoare_1167836817_state->Prop)) (X_60:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_29) X_60)->((iff ((ord_le827224136tate_o X_60) Y_29)) (((eq (hoare_1167836817_state->Prop)) X_60) Y_29)))). % Axiom fact_91_finite__subset:(forall (A_125:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_125) B_66)->((finite1084549118_state B_66)->(finite1084549118_state A_125)))). % Axiom fact_92_ord__eq__le__trans:(forall (C_30:Prop) (B_65:Prop) (A_124:Prop), (((iff A_124) B_65)->(((ord_less_eq_o B_65) C_30)->((ord_less_eq_o A_124) C_30)))). % Axiom fact_93_ord__eq__le__trans:(forall (C_30:(hoare_1167836817_state->Prop)) (A_124:(hoare_1167836817_state->Prop)) (B_65:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_124) B_65)->(((ord_le827224136tate_o B_65) C_30)->((ord_le827224136tate_o A_124) C_30)))). % Axiom fact_94_xt1_I3_J:(forall (C_29:Prop) (B_64:Prop) (A_123:Prop), (((iff A_123) B_64)->(((ord_less_eq_o C_29) B_64)->((ord_less_eq_o C_29) A_123)))). % Axiom fact_95_xt1_I3_J:(forall (C_29:(hoare_1167836817_state->Prop)) (A_123:(hoare_1167836817_state->Prop)) (B_64:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_123) B_64)->(((ord_le827224136tate_o C_29) B_64)->((ord_le827224136tate_o C_29) A_123)))). % Axiom fact_96_ord__le__eq__trans:(forall (C_28:Prop) (A_122:Prop) (B_63:Prop), (((ord_less_eq_o A_122) B_63)->(((iff B_63) C_28)->((ord_less_eq_o A_122) C_28)))). % Axiom fact_97_ord__le__eq__trans:(forall (C_28:(hoare_1167836817_state->Prop)) (A_122:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_122) B_63)->((((eq (hoare_1167836817_state->Prop)) B_63) C_28)->((ord_le827224136tate_o A_122) C_28)))). % Axiom fact_98_xt1_I4_J:(forall (C_27:Prop) (B_62:Prop) (A_121:Prop), (((ord_less_eq_o B_62) A_121)->(((iff B_62) C_27)->((ord_less_eq_o C_27) A_121)))). % Axiom fact_99_xt1_I4_J:(forall (C_27:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)) (A_121:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_62) A_121)->((((eq (hoare_1167836817_state->Prop)) B_62) C_27)->((ord_le827224136tate_o C_27) A_121)))). % Axiom fact_100_order__antisym:(forall (X_59:Prop) (Y_28:Prop), (((ord_less_eq_o X_59) Y_28)->(((ord_less_eq_o Y_28) X_59)->((iff X_59) Y_28)))). % Axiom fact_101_order__antisym:(forall (X_59:(hoare_1167836817_state->Prop)) (Y_28:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_59) Y_28)->(((ord_le827224136tate_o Y_28) X_59)->(((eq (hoare_1167836817_state->Prop)) X_59) Y_28)))). % Axiom fact_102_order__trans:(forall (Z_27:Prop) (X_58:Prop) (Y_27:Prop), (((ord_less_eq_o X_58) Y_27)->(((ord_less_eq_o Y_27) Z_27)->((ord_less_eq_o X_58) Z_27)))). % Axiom fact_103_order__trans:(forall (Z_27:(hoare_1167836817_state->Prop)) (X_58:(hoare_1167836817_state->Prop)) (Y_27:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_58) Y_27)->(((ord_le827224136tate_o Y_27) Z_27)->((ord_le827224136tate_o X_58) Z_27)))). % Axiom fact_104_xt1_I5_J:(forall (Y_26:Prop) (X_57:Prop), (((ord_less_eq_o Y_26) X_57)->(((ord_less_eq_o X_57) Y_26)->((iff X_57) Y_26)))). % Axiom fact_105_xt1_I5_J:(forall (Y_26:(hoare_1167836817_state->Prop)) (X_57:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_26) X_57)->(((ord_le827224136tate_o X_57) Y_26)->(((eq (hoare_1167836817_state->Prop)) X_57) Y_26)))). % Axiom fact_106_xt1_I6_J:(forall (Z_26:Prop) (Y_25:Prop) (X_56:Prop), (((ord_less_eq_o Y_25) X_56)->(((ord_less_eq_o Z_26) Y_25)->((ord_less_eq_o Z_26) X_56)))). % Axiom fact_107_xt1_I6_J:(forall (Z_26:(hoare_1167836817_state->Prop)) (Y_25:(hoare_1167836817_state->Prop)) (X_56:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_25) X_56)->(((ord_le827224136tate_o Z_26) Y_25)->((ord_le827224136tate_o Z_26) X_56)))). % Axiom fact_108_le__funE:(forall (X_55:hoare_1167836817_state) (F_65:(hoare_1167836817_state->Prop)) (G_14:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_65) G_14)->((ord_less_eq_o (F_65 X_55)) (G_14 X_55)))). % Axiom fact_109_bot__least:(forall (A_120:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_120)). % Axiom fact_110_bot__least:(forall (A_120:Prop), ((ord_less_eq_o bot_bot_o) A_120)). % Axiom fact_111_bot__unique:(forall (A_119:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_119) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_119) bot_bo70021908tate_o))). % Axiom fact_112_bot__unique:(forall (A_119:Prop), ((iff ((ord_less_eq_o A_119) bot_bot_o)) ((iff A_119) bot_bot_o))). % Axiom fact_113_le__bot:(forall (A_118:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_118) bot_bo70021908tate_o)->(((eq (hoare_1167836817_state->Prop)) A_118) bot_bo70021908tate_o))). % Axiom fact_114_le__bot:(forall (A_118:Prop), (((ord_less_eq_o A_118) bot_bot_o)->((iff A_118) bot_bot_o))). % Axiom fact_115_subset__empty:(forall (A_117:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_117) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_117) bot_bo70021908tate_o))). % Axiom fact_116_subset__insertI:(forall (B_61:(hoare_1167836817_state->Prop)) (A_116:hoare_1167836817_state), ((ord_le827224136tate_o B_61) ((insert2134838167_state A_116) B_61))). % Axiom fact_117_insert__subset:(forall (X_54:hoare_1167836817_state) (A_115:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((insert2134838167_state X_54) A_115)) B_60)) ((and ((member2058392318_state X_54) B_60)) ((ord_le827224136tate_o A_115) B_60)))). % Axiom fact_118_subset__insert:(forall (B_59:(hoare_1167836817_state->Prop)) (X_53:hoare_1167836817_state) (A_114:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_53) A_114)->False)->((iff ((ord_le827224136tate_o A_114) ((insert2134838167_state X_53) B_59))) ((ord_le827224136tate_o A_114) B_59)))). % Axiom fact_119_subset__insertI2:(forall (B_58:hoare_1167836817_state) (A_113:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_113) B_57)->((ord_le827224136tate_o A_113) ((insert2134838167_state B_58) B_57)))). % Axiom fact_120_insert__mono:(forall (A_112:hoare_1167836817_state) (C_26:(hoare_1167836817_state->Prop)) (D_1:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_26) D_1)->((ord_le827224136tate_o ((insert2134838167_state A_112) C_26)) ((insert2134838167_state A_112) D_1)))). % Axiom fact_121_finite__insert:(forall (A_111:hoare_1167836817_state) (A_110:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_111) A_110))) (finite1084549118_state A_110))). % Axiom fact_122_asm:(forall (Ts_3:(hoare_1167836817_state->Prop)) (G_13:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Ts_3) G_13)->((hoare_123228589_state G_13) Ts_3))). % Axiom fact_123_weaken:(forall (Ts_2:(hoare_1167836817_state->Prop)) (G_12:(hoare_1167836817_state->Prop)) (Ts_1:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_12) Ts_1)->(((ord_le827224136tate_o Ts_2) Ts_1)->((hoare_123228589_state G_12) Ts_2)))). % Axiom fact_124_thin:(forall (G_11:(hoare_1167836817_state->Prop)) (G_10:(hoare_1167836817_state->Prop)) (Ts:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_10) Ts)->(((ord_le827224136tate_o G_10) G_11)->((hoare_123228589_state G_11) Ts)))). % Axiom fact_125_fold__graph_OemptyI:(forall (F_64:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_25:hoare_1167836817_state), ((((finite1316643734_state F_64) Z_25) bot_bo70021908tate_o) Z_25)). % Axiom fact_126_empty__fold__graphE:(forall (F_63:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_24:hoare_1167836817_state) (X_52:hoare_1167836817_state), (((((finite1316643734_state F_63) Z_24) bot_bo70021908tate_o) X_52)->(((eq hoare_1167836817_state) X_52) Z_24))). % Axiom fact_127_fold__graph_OinsertI:(forall (F_62:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_23:hoare_1167836817_state) (Y_24:hoare_1167836817_state) (X_51:hoare_1167836817_state) (A_109:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_51) A_109)->False)->(((((finite1316643734_state F_62) Z_23) A_109) Y_24)->((((finite1316643734_state F_62) Z_23) ((insert2134838167_state X_51) A_109)) ((F_62 X_51) Y_24))))). % Axiom fact_128_finite__subset__induct:(forall (P_6:((hoare_1167836817_state->Prop)->Prop)) (A_108:(hoare_1167836817_state->Prop)) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(((ord_le827224136tate_o F_61) A_108)->((P_6 bot_bo70021908tate_o)->((forall (A_59:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->(((member2058392318_state A_59) A_108)->((((member2058392318_state A_59) F_50)->False)->((P_6 F_50)->(P_6 ((insert2134838167_state A_59) F_50)))))))->(P_6 F_61)))))). % Axiom fact_129_finite__nonempty__imp__fold1Set:(forall (F_60:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A_107:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_107)->((not (((eq (hoare_1167836817_state->Prop)) A_107) bot_bo70021908tate_o))->(_TPTP_ex ((finite309220289_state F_60) A_107))))). % Axiom fact_130_subsetI:(forall (B_56:(hoare_1167836817_state->Prop)) (A_106:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_106)->((member2058392318_state X) B_56)))->((ord_le827224136tate_o A_106) B_56))). % Axiom fact_131_finite_Osimps:(forall (A_105:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_105)) ((or (((eq (hoare_1167836817_state->Prop)) A_105) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_59:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_105) ((insert2134838167_state A_59) A_58))) (finite1084549118_state A_58))))))))). % Axiom fact_132_finite__induct:(forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (F_59:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_59)->((P_5 bot_bo70021908tate_o)->((forall (X:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->((((member2058392318_state X) F_50)->False)->((P_5 F_50)->(P_5 ((insert2134838167_state X) F_50))))))->(P_5 F_59))))). % Axiom fact_133_finite__imp__fold__graph:(forall (F_58:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_22:hoare_1167836817_state) (A_104:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_104)->(_TPTP_ex (((finite1316643734_state F_58) Z_22) A_104)))). % Axiom fact_134_le__funI:(forall (F_57:(hoare_1167836817_state->Prop)) (G_9:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((ord_less_eq_o (F_57 X)) (G_9 X)))->((ord_le827224136tate_o F_57) G_9))). % Axiom fact_135_fold1Set_Osimps:(forall (F_56:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (A1_1:(hoare_1167836817_state->Prop)) (A2_1:hoare_1167836817_state), ((iff (((finite309220289_state F_56) A1_1) A2_1)) ((ex hoare_1167836817_state) (fun (A_59:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((and ((and (((eq (hoare_1167836817_state->Prop)) A1_1) ((insert2134838167_state A_59) A_58))) (((eq hoare_1167836817_state) A2_1) X))) ((((finite1316643734_state F_56) A_59) A_58) X))) (((member2058392318_state A_59) A_58)->False)))))))))). % Axiom fact_136_fold__graph_Osimps:(forall (F_55:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_21:hoare_1167836817_state) (A1:(hoare_1167836817_state->Prop)) (A2:hoare_1167836817_state), ((iff ((((finite1316643734_state F_55) Z_21) A1) A2)) ((or ((and (((eq (hoare_1167836817_state->Prop)) A1) bot_bo70021908tate_o)) (((eq hoare_1167836817_state) A2) Z_21))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (Y:hoare_1167836817_state)=> ((and ((and ((and (((eq (hoare_1167836817_state->Prop)) A1) ((insert2134838167_state X) A_58))) (((eq hoare_1167836817_state) A2) ((F_55 X) Y)))) (((member2058392318_state X) A_58)->False))) ((((finite1316643734_state F_55) Z_21) A_58) Y))))))))))). % Axiom fact_137_folding__one__idem_Osubset__idem:(forall (B_55:(hoare_1167836817_state->Prop)) (A_103:(hoare_1167836817_state->Prop)) (F_54:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_53:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_54) F_53)->((finite1084549118_state A_103)->((not (((eq (hoare_1167836817_state->Prop)) B_55) bot_bo70021908tate_o))->(((ord_le827224136tate_o B_55) A_103)->(((eq hoare_1167836817_state) ((F_54 (F_53 B_55)) (F_53 A_103))) (F_53 A_103))))))). % Axiom fact_138_folding__one__idem_Oinsert__idem:(forall (X_50:hoare_1167836817_state) (A_102:(hoare_1167836817_state->Prop)) (F_52:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_51:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_52) F_51)->((finite1084549118_state A_102)->((not (((eq (hoare_1167836817_state->Prop)) A_102) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_51 ((insert2134838167_state X_50) A_102))) ((F_52 X_50) (F_51 A_102))))))). % Axiom fact_139_finite__ne__induct:(forall (P_4:((hoare_1167836817_state->Prop)->Prop)) (F_49:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_49)->((not (((eq (hoare_1167836817_state->Prop)) F_49) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (P_4 ((insert2134838167_state X) bot_bo70021908tate_o)))->((forall (X:hoare_1167836817_state) (F_50:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_50)->((not (((eq (hoare_1167836817_state->Prop)) F_50) bot_bo70021908tate_o))->((((member2058392318_state X) F_50)->False)->((P_4 F_50)->(P_4 ((insert2134838167_state X) F_50)))))))->(P_4 F_49)))))). % Axiom fact_140_Collect__mono:(forall (Q_1:(hoare_1167836817_state->Prop)) (P_3:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((P_3 X)->(Q_1 X)))->((ord_le827224136tate_o (collec1027672124_state P_3)) (collec1027672124_state Q_1)))). % Axiom fact_141_folding__one__idem_Oidem:(forall (X_49:hoare_1167836817_state) (F_48:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_47:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_48) F_47)->(((eq hoare_1167836817_state) ((F_48 X_49) X_49)) X_49))). % Axiom fact_142_folding__one__idem_Oin__idem:(forall (X_48:hoare_1167836817_state) (A_101:(hoare_1167836817_state->Prop)) (F_46:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_45:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_46) F_45)->((finite1084549118_state A_101)->(((member2058392318_state X_48) A_101)->(((eq hoare_1167836817_state) ((F_46 X_48) (F_45 A_101))) (F_45 A_101)))))). % Axiom fact_143_predicate1I:(forall (Q:(hoare_1167836817_state->Prop)) (P_2:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), ((P_2 X)->(Q X)))->((ord_le827224136tate_o P_2) Q))). % Axiom fact_144_xt3:(forall (C_25:Prop) (F_44:((hoare_1167836817_state->Prop)->Prop)) (B_54:(hoare_1167836817_state->Prop)) (A_100:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_54) A_100)->(((ord_less_eq_o C_25) (F_44 B_54))->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F_44 Y)) (F_44 X))))->((ord_less_eq_o C_25) (F_44 A_100)))))). % Axiom fact_145_xt3:(forall (C_25:(hoare_1167836817_state->Prop)) (F_44:(Prop->(hoare_1167836817_state->Prop))) (B_54:Prop) (A_100:Prop), (((ord_less_eq_o B_54) A_100)->(((ord_le827224136tate_o C_25) (F_44 B_54))->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F_44 Y)) (F_44 X))))->((ord_le827224136tate_o C_25) (F_44 A_100)))))). % Axiom fact_146_xt1_I16_J:(forall (C_24:Prop) (F_43:(Prop->Prop)) (B_53:Prop) (A_99:Prop), (((ord_less_eq_o B_53) A_99)->(((iff (F_43 B_53)) C_24)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_less_eq_o (F_43 Y)) (F_43 X))))->((ord_less_eq_o C_24) (F_43 A_99)))))). % Axiom fact_147_xt1_I16_J:(forall (F_43:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (C_24:(hoare_1167836817_state->Prop)) (B_53:(hoare_1167836817_state->Prop)) (A_99:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_53) A_99)->((((eq (hoare_1167836817_state->Prop)) (F_43 B_53)) C_24)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F_43 Y)) (F_43 X))))->((ord_le827224136tate_o C_24) (F_43 A_99)))))). % Axiom fact_148_ord__le__eq__subst:(forall (C_23:Prop) (F_42:((hoare_1167836817_state->Prop)->Prop)) (A_98:(hoare_1167836817_state->Prop)) (B_52:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_98) B_52)->(((iff (F_42 B_52)) C_23)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_42 X)) (F_42 Y))))->((ord_less_eq_o (F_42 A_98)) C_23))))). % Axiom fact_149_ord__le__eq__subst:(forall (F_42:(Prop->(hoare_1167836817_state->Prop))) (C_23:(hoare_1167836817_state->Prop)) (A_98:Prop) (B_52:Prop), (((ord_less_eq_o A_98) B_52)->((((eq (hoare_1167836817_state->Prop)) (F_42 B_52)) C_23)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_42 X)) (F_42 Y))))->((ord_le827224136tate_o (F_42 A_98)) C_23))))). % Axiom fact_150_order__subst2:(forall (F_41:((hoare_1167836817_state->Prop)->Prop)) (C_22:Prop) (A_97:(hoare_1167836817_state->Prop)) (B_51:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_97) B_51)->(((ord_less_eq_o (F_41 B_51)) C_22)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_41 X)) (F_41 Y))))->((ord_less_eq_o (F_41 A_97)) C_22))))). % Axiom fact_151_order__subst2:(forall (F_41:(Prop->(hoare_1167836817_state->Prop))) (C_22:(hoare_1167836817_state->Prop)) (A_97:Prop) (B_51:Prop), (((ord_less_eq_o A_97) B_51)->(((ord_le827224136tate_o (F_41 B_51)) C_22)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_41 X)) (F_41 Y))))->((ord_le827224136tate_o (F_41 A_97)) C_22))))). % Axiom fact_152_ord__eq__le__subst:(forall (C_21:(hoare_1167836817_state->Prop)) (F_40:((hoare_1167836817_state->Prop)->Prop)) (B_50:(hoare_1167836817_state->Prop)) (A_96:Prop), (((iff A_96) (F_40 B_50))->(((ord_le827224136tate_o B_50) C_21)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_40 X)) (F_40 Y))))->((ord_less_eq_o A_96) (F_40 C_21)))))). % Axiom fact_153_ord__eq__le__subst:(forall (C_21:Prop) (A_96:(hoare_1167836817_state->Prop)) (F_40:(Prop->(hoare_1167836817_state->Prop))) (B_50:Prop), ((((eq (hoare_1167836817_state->Prop)) A_96) (F_40 B_50))->(((ord_less_eq_o B_50) C_21)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_40 X)) (F_40 Y))))->((ord_le827224136tate_o A_96) (F_40 C_21)))))). % Axiom fact_154_xt2:(forall (C_20:Prop) (F_39:(Prop->(hoare_1167836817_state->Prop))) (B_49:Prop) (A_95:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_39 B_49)) A_95)->(((ord_less_eq_o C_20) B_49)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F_39 Y)) (F_39 X))))->((ord_le827224136tate_o (F_39 C_20)) A_95))))). % Axiom fact_155_xt2:(forall (C_20:(hoare_1167836817_state->Prop)) (F_39:((hoare_1167836817_state->Prop)->Prop)) (B_49:(hoare_1167836817_state->Prop)) (A_95:Prop), (((ord_less_eq_o (F_39 B_49)) A_95)->(((ord_le827224136tate_o C_20) B_49)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F_39 Y)) (F_39 X))))->((ord_less_eq_o (F_39 C_20)) A_95))))). % Axiom fact_156_xt1_I15_J:(forall (C_19:Prop) (F_38:(Prop->Prop)) (B_48:Prop) (A_94:Prop), (((iff A_94) (F_38 B_48))->(((ord_less_eq_o C_19) B_48)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_less_eq_o (F_38 Y)) (F_38 X))))->((ord_less_eq_o (F_38 C_19)) A_94))))). % Axiom fact_157_xt1_I15_J:(forall (C_19:(hoare_1167836817_state->Prop)) (A_94:(hoare_1167836817_state->Prop)) (F_38:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_48:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_94) (F_38 B_48))->(((ord_le827224136tate_o C_19) B_48)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F_38 Y)) (F_38 X))))->((ord_le827224136tate_o (F_38 C_19)) A_94))))). % Axiom fact_158_order__subst1:(forall (C_18:Prop) (A_93:(hoare_1167836817_state->Prop)) (F_37:(Prop->(hoare_1167836817_state->Prop))) (B_47:Prop), (((ord_le827224136tate_o A_93) (F_37 B_47))->(((ord_less_eq_o B_47) C_18)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o X) Y)->((ord_le827224136tate_o (F_37 X)) (F_37 Y))))->((ord_le827224136tate_o A_93) (F_37 C_18)))))). % Axiom fact_159_order__subst1:(forall (C_18:(hoare_1167836817_state->Prop)) (A_93:Prop) (F_37:((hoare_1167836817_state->Prop)->Prop)) (B_47:(hoare_1167836817_state->Prop)), (((ord_less_eq_o A_93) (F_37 B_47))->(((ord_le827224136tate_o B_47) C_18)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X) Y)->((ord_less_eq_o (F_37 X)) (F_37 Y))))->((ord_less_eq_o A_93) (F_37 C_18)))))). % Axiom fact_160_semilattice__big_OF__eq:(forall (A_92:(hoare_1167836817_state->Prop)) (F_36:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_35:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((big_se1603066171_state F_36) F_35)->((finite1084549118_state A_92)->(((eq hoare_1167836817_state) (F_35 A_92)) ((finite1646097201_state F_36) A_92))))). % Axiom fact_161_folding__one_Oremove:(forall (X_47:hoare_1167836817_state) (A_91:(hoare_1167836817_state->Prop)) (F_34:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_33:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_34) F_33)->((finite1084549118_state A_91)->(((member2058392318_state X_47) A_91)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_33 A_91)) X_47))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_33 A_91)) ((F_34 X_47) (F_33 ((minus_2107060239tate_o A_91) ((insert2134838167_state X_47) bot_bo70021908tate_o))))))))))). % Axiom fact_162_folding__one_Oinsert__remove:(forall (X_46:hoare_1167836817_state) (A_90:(hoare_1167836817_state->Prop)) (F_32:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_31:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_32) F_31)->((finite1084549118_state A_90)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_31 ((insert2134838167_state X_46) A_90))) X_46))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_31 ((insert2134838167_state X_46) A_90))) ((F_32 X_46) (F_31 ((minus_2107060239tate_o A_90) ((insert2134838167_state X_46) bot_bo70021908tate_o)))))))))). % Axiom fact_163_DiffI:(forall (B_46:(hoare_1167836817_state->Prop)) (C_17:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((member2058392318_state C_17) A_89)->((((member2058392318_state C_17) B_46)->False)->((member2058392318_state C_17) ((minus_2107060239tate_o A_89) B_46))))). % Axiom fact_164_DiffE:(forall (C_16:hoare_1167836817_state) (A_88:(hoare_1167836817_state->Prop)) (B_45:(hoare_1167836817_state->Prop)), (((member2058392318_state C_16) ((minus_2107060239tate_o A_88) B_45))->((((member2058392318_state C_16) A_88)->((member2058392318_state C_16) B_45))->False))). % Axiom fact_165_finite__Diff:(forall (B_44:(hoare_1167836817_state->Prop)) (A_87:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_87)->(finite1084549118_state ((minus_2107060239tate_o A_87) B_44)))). % Axiom fact_166_set__diff__eq:(forall (A_86:(hoare_1167836817_state->Prop)) (B_43:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_86) B_43)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) A_86)) (not ((member2058392318_state X) B_43))))))). % Axiom fact_167_Diff__iff:(forall (C_15:hoare_1167836817_state) (A_85:(hoare_1167836817_state->Prop)) (B_42:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_15) ((minus_2107060239tate_o A_85) B_42))) ((and ((member2058392318_state C_15) A_85)) (((member2058392318_state C_15) B_42)->False)))). % Axiom fact_168_Diff__idemp:(forall (A_84:(hoare_1167836817_state->Prop)) (B_41:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((minus_2107060239tate_o A_84) B_41)) B_41)) ((minus_2107060239tate_o A_84) B_41))). % Axiom fact_169_DiffD1:(forall (C_14:hoare_1167836817_state) (A_83:(hoare_1167836817_state->Prop)) (B_40:(hoare_1167836817_state->Prop)), (((member2058392318_state C_14) ((minus_2107060239tate_o A_83) B_40))->((member2058392318_state C_14) A_83))). % Axiom fact_170_DiffD2:(forall (C_13:hoare_1167836817_state) (A_82:(hoare_1167836817_state->Prop)) (B_39:(hoare_1167836817_state->Prop)), (((member2058392318_state C_13) ((minus_2107060239tate_o A_82) B_39))->(((member2058392318_state C_13) B_39)->False))). % Axiom fact_171_empty__Diff:(forall (A_81:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o bot_bo70021908tate_o) A_81)) bot_bo70021908tate_o)). % Axiom fact_172_Diff__empty:(forall (A_80:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_80) bot_bo70021908tate_o)) A_80)). % Axiom fact_173_Diff__cancel:(forall (A_79:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_79) A_79)) bot_bo70021908tate_o)). % Axiom fact_174_finite__Diff2:(forall (A_78:(hoare_1167836817_state->Prop)) (B_38:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_38)->((iff (finite1084549118_state ((minus_2107060239tate_o A_78) B_38))) (finite1084549118_state A_78)))). % Axiom fact_175_insert__Diff__if:(forall (A_77:(hoare_1167836817_state->Prop)) (X_45:hoare_1167836817_state) (B_37:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state X_45) B_37)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_45) A_77)) B_37)) ((minus_2107060239tate_o A_77) B_37)))) ((((member2058392318_state X_45) B_37)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_45) A_77)) B_37)) ((insert2134838167_state X_45) ((minus_2107060239tate_o A_77) B_37)))))). % Axiom fact_176_insert__Diff1:(forall (A_76:(hoare_1167836817_state->Prop)) (X_44:hoare_1167836817_state) (B_36:(hoare_1167836817_state->Prop)), (((member2058392318_state X_44) B_36)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_44) A_76)) B_36)) ((minus_2107060239tate_o A_76) B_36)))). % Axiom fact_177_Diff__subset:(forall (A_75:(hoare_1167836817_state->Prop)) (B_35:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((minus_2107060239tate_o A_75) B_35)) A_75)). % Axiom fact_178_Diff__mono:(forall (D:(hoare_1167836817_state->Prop)) (B_34:(hoare_1167836817_state->Prop)) (A_74:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_74) C_12)->(((ord_le827224136tate_o D) B_34)->((ord_le827224136tate_o ((minus_2107060239tate_o A_74) B_34)) ((minus_2107060239tate_o C_12) D))))). % Axiom fact_179_double__diff:(forall (C_11:(hoare_1167836817_state->Prop)) (A_73:(hoare_1167836817_state->Prop)) (B_33:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_73) B_33)->(((ord_le827224136tate_o B_33) C_11)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o B_33) ((minus_2107060239tate_o C_11) A_73))) A_73)))). % Axiom fact_180_Diff__insert:(forall (A_72:(hoare_1167836817_state->Prop)) (A_71:hoare_1167836817_state) (B_32:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_72) ((insert2134838167_state A_71) B_32))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_72) B_32)) ((insert2134838167_state A_71) bot_bo70021908tate_o)))). % Axiom fact_181_Diff__insert2:(forall (A_70:(hoare_1167836817_state->Prop)) (A_69:hoare_1167836817_state) (B_31:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_70) ((insert2134838167_state A_69) B_31))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_70) ((insert2134838167_state A_69) bot_bo70021908tate_o))) B_31))). % Axiom fact_182_insert__Diff__single:(forall (A_68:hoare_1167836817_state) (A_67:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_68) ((minus_2107060239tate_o A_67) ((insert2134838167_state A_68) bot_bo70021908tate_o)))) ((insert2134838167_state A_68) A_67))). % Axiom fact_183_Diff__insert__absorb:(forall (X_43:hoare_1167836817_state) (A_66:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_43) A_66)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_43) A_66)) ((insert2134838167_state X_43) bot_bo70021908tate_o))) A_66))). % Axiom fact_184_insert__Diff:(forall (A_65:hoare_1167836817_state) (A_64:(hoare_1167836817_state->Prop)), (((member2058392318_state A_65) A_64)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_65) ((minus_2107060239tate_o A_64) ((insert2134838167_state A_65) bot_bo70021908tate_o)))) A_64))). % Axiom fact_185_finite__Diff__insert:(forall (A_63:(hoare_1167836817_state->Prop)) (A_62:hoare_1167836817_state) (B_30:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((minus_2107060239tate_o A_63) ((insert2134838167_state A_62) B_30)))) (finite1084549118_state ((minus_2107060239tate_o A_63) B_30)))). % Axiom fact_186_subset__insert__iff:(forall (A_61:(hoare_1167836817_state->Prop)) (X_42:hoare_1167836817_state) (B_29:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_61) ((insert2134838167_state X_42) B_29))) ((and (((member2058392318_state X_42) A_61)->((ord_le827224136tate_o ((minus_2107060239tate_o A_61) ((insert2134838167_state X_42) bot_bo70021908tate_o))) B_29))) ((((member2058392318_state X_42) A_61)->False)->((ord_le827224136tate_o A_61) B_29))))). % Axiom fact_187_diff__single__insert:(forall (A_60:(hoare_1167836817_state->Prop)) (X_41:hoare_1167836817_state) (B_28:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o ((minus_2107060239tate_o A_60) ((insert2134838167_state X_41) bot_bo70021908tate_o))) B_28)->(((member2058392318_state X_41) A_60)->((ord_le827224136tate_o A_60) ((insert2134838167_state X_41) B_28))))). % Axiom fact_188_finite__empty__induct:(forall (P_1:((hoare_1167836817_state->Prop)->Prop)) (A_57:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_57)->((P_1 A_57)->((forall (A_59:hoare_1167836817_state) (A_58:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_58)->(((member2058392318_state A_59) A_58)->((P_1 A_58)->(P_1 ((minus_2107060239tate_o A_58) ((insert2134838167_state A_59) bot_bo70021908tate_o)))))))->(P_1 bot_bo70021908tate_o))))). % Axiom fact_189_minus__apply:(forall (A_56:(hoare_1167836817_state->Prop)) (B_27:(hoare_1167836817_state->Prop)) (X_40:hoare_1167836817_state), ((iff (((minus_2107060239tate_o A_56) B_27) X_40)) ((minus_minus_o (A_56 X_40)) (B_27 X_40)))). % Axiom fact_190_fun__diff__def:(forall (A_55:(hoare_1167836817_state->Prop)) (B_26:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), ((iff (((minus_2107060239tate_o A_55) B_26) X)) ((minus_minus_o (A_55 X)) (B_26 X)))). % Axiom fact_191_comp__fun__commute_Ofold__graph__insertE__aux:(forall (A_54:hoare_1167836817_state) (Z_20:hoare_1167836817_state) (A_53:(hoare_1167836817_state->Prop)) (Y_22:hoare_1167836817_state) (F_30:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_30)->(((((finite1316643734_state F_30) Z_20) A_53) Y_22)->(((member2058392318_state A_54) A_53)->((ex hoare_1167836817_state) (fun (Y_23:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) Y_22) ((F_30 A_54) Y_23))) ((((finite1316643734_state F_30) Z_20) ((minus_2107060239tate_o A_53) ((insert2134838167_state A_54) bot_bo70021908tate_o))) Y_23)))))))). % Axiom fact_192_comp__fun__commute_Ofun__left__comm:(forall (X_39:hoare_1167836817_state) (Y_21:hoare_1167836817_state) (Z_19:hoare_1167836817_state) (F_29:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_29)->(((eq hoare_1167836817_state) ((F_29 X_39) ((F_29 Y_21) Z_19))) ((F_29 Y_21) ((F_29 X_39) Z_19))))). % Axiom fact_193_comp__fun__commute_Ofold__graph__determ:(forall (Y_20:hoare_1167836817_state) (Z_18:hoare_1167836817_state) (A_52:(hoare_1167836817_state->Prop)) (X_38:hoare_1167836817_state) (F_28:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_28)->(((((finite1316643734_state F_28) Z_18) A_52) X_38)->(((((finite1316643734_state F_28) Z_18) A_52) Y_20)->(((eq hoare_1167836817_state) Y_20) X_38))))). % Axiom fact_194_comp__fun__commute_Ofold__graph__insertE:(forall (Z_17:hoare_1167836817_state) (X_37:hoare_1167836817_state) (A_51:(hoare_1167836817_state->Prop)) (V:hoare_1167836817_state) (F_27:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_27)->(((((finite1316643734_state F_27) Z_17) ((insert2134838167_state X_37) A_51)) V)->((((member2058392318_state X_37) A_51)->False)->((forall (Y:hoare_1167836817_state), ((((eq hoare_1167836817_state) V) ((F_27 X_37) Y))->(((((finite1316643734_state F_27) Z_17) A_51) Y)->False)))->False))))). % Axiom fact_195_min__leastR:(forall (X_36:Prop) (Least_3:Prop), ((all1 (ord_less_eq_o Least_3))->((iff ((ord_min_o X_36) Least_3)) Least_3))). % Axiom fact_196_min__leastR:(forall (X_36:(hoare_1167836817_state->Prop)) (Least_3:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_3))->(((eq (hoare_1167836817_state->Prop)) ((ord_mi1697686287tate_o X_36) Least_3)) Least_3))). % Axiom fact_197_min__leastL:(forall (X_35:Prop) (Least_2:Prop), ((all1 (ord_less_eq_o Least_2))->((iff ((ord_min_o Least_2) X_35)) Least_2))). % Axiom fact_198_min__leastL:(forall (X_35:(hoare_1167836817_state->Prop)) (Least_2:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_2))->(((eq (hoare_1167836817_state->Prop)) ((ord_mi1697686287tate_o Least_2) X_35)) Least_2))). % Axiom fact_199_min__ord__min:(((eq (Prop->(Prop->Prop))) ord_min_o) (min_o ord_less_eq_o)). % Axiom fact_200_min__ord__min:(((eq ((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) ord_mi1697686287tate_o) (min_Ho1955171539tate_o ord_le827224136tate_o)). % Axiom fact_201_comp__fun__commute_Ofold__insert__remove:(forall (Z_16:hoare_1167836817_state) (X_34:hoare_1167836817_state) (A_50:(hoare_1167836817_state->Prop)) (F_26:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_26)->((finite1084549118_state A_50)->(((eq hoare_1167836817_state) (((finite1731015960_state F_26) Z_16) ((insert2134838167_state X_34) A_50))) ((F_26 X_34) (((finite1731015960_state F_26) Z_16) ((minus_2107060239tate_o A_50) ((insert2134838167_state X_34) bot_bo70021908tate_o)))))))). % Axiom fact_202_comp__fun__commute_Ofold__rec:(forall (Z_15:hoare_1167836817_state) (X_33:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (F_25:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_25)->((finite1084549118_state A_49)->(((member2058392318_state X_33) A_49)->(((eq hoare_1167836817_state) (((finite1731015960_state F_25) Z_15) A_49)) ((F_25 X_33) (((finite1731015960_state F_25) Z_15) ((minus_2107060239tate_o A_49) ((insert2134838167_state X_33) bot_bo70021908tate_o))))))))). % Axiom fact_203_fold__empty:(forall (F_24:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (Z_14:hoare_1167836817_state), (((eq hoare_1167836817_state) (((finite1731015960_state F_24) Z_14) bot_bo70021908tate_o)) Z_14)). % Axiom fact_204_comp__fun__commute_Ofold__fun__comm:(forall (X_32:hoare_1167836817_state) (Z_13:hoare_1167836817_state) (A_48:(hoare_1167836817_state->Prop)) (F_23:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_23)->((finite1084549118_state A_48)->(((eq hoare_1167836817_state) ((F_23 X_32) (((finite1731015960_state F_23) Z_13) A_48))) (((finite1731015960_state F_23) ((F_23 X_32) Z_13)) A_48))))). % Axiom fact_205_comp__fun__commute_Ofold__equality:(forall (Z_12:hoare_1167836817_state) (A_47:(hoare_1167836817_state->Prop)) (Y_19:hoare_1167836817_state) (F_22:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_22)->(((((finite1316643734_state F_22) Z_12) A_47) Y_19)->(((eq hoare_1167836817_state) (((finite1731015960_state F_22) Z_12) A_47)) Y_19)))). % Axiom fact_206_comp__fun__commute_Ofold__insert2:(forall (Z_11:hoare_1167836817_state) (X_31:hoare_1167836817_state) (A_46:(hoare_1167836817_state->Prop)) (F_21:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_21)->((finite1084549118_state A_46)->((((member2058392318_state X_31) A_46)->False)->(((eq hoare_1167836817_state) (((finite1731015960_state F_21) Z_11) ((insert2134838167_state X_31) A_46))) (((finite1731015960_state F_21) ((F_21 X_31) Z_11)) A_46)))))). % Axiom fact_207_comp__fun__commute_Ofold__insert:(forall (Z_10:hoare_1167836817_state) (X_30:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)) (F_20:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_20)->((finite1084549118_state A_45)->((((member2058392318_state X_30) A_45)->False)->(((eq hoare_1167836817_state) (((finite1731015960_state F_20) Z_10) ((insert2134838167_state X_30) A_45))) ((F_20 X_30) (((finite1731015960_state F_20) Z_10) A_45))))))). % Axiom fact_208_folding__one_Oeq__fold_H:(forall (X_29:hoare_1167836817_state) (A_44:(hoare_1167836817_state->Prop)) (F_19:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_18:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_19) F_18)->((finite1084549118_state A_44)->((((member2058392318_state X_29) A_44)->False)->(((eq hoare_1167836817_state) (F_18 ((insert2134838167_state X_29) A_44))) (((finite1731015960_state F_19) X_29) A_44)))))). % Axiom fact_209_folding__one__idem_Oeq__fold__idem_H:(forall (A_43:hoare_1167836817_state) (A_42:(hoare_1167836817_state->Prop)) (F_17:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_16:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_17) F_16)->((finite1084549118_state A_42)->(((eq hoare_1167836817_state) (F_16 ((insert2134838167_state A_43) A_42))) (((finite1731015960_state F_17) A_43) A_42))))). % Axiom fact_210_comp__fun__commute_Ofold__graph__fold:(forall (Z_9:hoare_1167836817_state) (A_41:(hoare_1167836817_state->Prop)) (F_15:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1091222817_state F_15)->((finite1084549118_state A_41)->((((finite1316643734_state F_15) Z_9) A_41) (((finite1731015960_state F_15) Z_9) A_41))))). % Axiom fact_211_comp__fun__idem_Ofold__insert__idem:(forall (Z_8:hoare_1167836817_state) (X_28:hoare_1167836817_state) (A_40:(hoare_1167836817_state->Prop)) (F_14:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1900754844_state F_14)->((finite1084549118_state A_40)->(((eq hoare_1167836817_state) (((finite1731015960_state F_14) Z_8) ((insert2134838167_state X_28) A_40))) ((F_14 X_28) (((finite1731015960_state F_14) Z_8) A_40)))))). % Axiom fact_212_comp__fun__idem_Ofold__insert__idem:(forall (Z_8:(hoare_1167836817_state->Prop)) (X_28:hoare_1167836817_state) (A_40:(hoare_1167836817_state->Prop)) (F_14:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_14)->((finite1084549118_state A_40)->(((eq (hoare_1167836817_state->Prop)) (((finite291020855tate_o F_14) Z_8) ((insert2134838167_state X_28) A_40))) ((F_14 X_28) (((finite291020855tate_o F_14) Z_8) A_40)))))). % Axiom fact_213_comp__fun__idem_Ofold__insert__idem2:(forall (Z_7:hoare_1167836817_state) (X_27:hoare_1167836817_state) (A_39:(hoare_1167836817_state->Prop)) (F_13:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))), ((finite1900754844_state F_13)->((finite1084549118_state A_39)->(((eq hoare_1167836817_state) (((finite1731015960_state F_13) Z_7) ((insert2134838167_state X_27) A_39))) (((finite1731015960_state F_13) ((F_13 X_27) Z_7)) A_39))))). % Axiom fact_214_comp__fun__idem_Ofold__insert__idem2:(forall (Z_7:(hoare_1167836817_state->Prop)) (X_27:hoare_1167836817_state) (A_39:(hoare_1167836817_state->Prop)) (F_13:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_13)->((finite1084549118_state A_39)->(((eq (hoare_1167836817_state->Prop)) (((finite291020855tate_o F_13) Z_7) ((insert2134838167_state X_27) A_39))) (((finite291020855tate_o F_13) ((F_13 X_27) Z_7)) A_39))))). % Axiom fact_215_comp__fun__idem_Ofun__left__idem:(forall (X_26:hoare_1167836817_state) (Z_6:(hoare_1167836817_state->Prop)) (F_12:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))), ((finite856902323tate_o F_12)->(((eq (hoare_1167836817_state->Prop)) ((F_12 X_26) ((F_12 X_26) Z_6))) ((F_12 X_26) Z_6)))). % Axiom fact_216_comp__fun__idem__insert:(finite856902323tate_o insert2134838167_state). % Axiom fact_217_setsum__diff1__nat:(forall (F_11:(hoare_1167836817_state->nat)) (A_38:hoare_1167836817_state) (A_37:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_38) A_37)->(((eq nat) ((big_co337839062te_nat F_11) ((minus_2107060239tate_o A_37) ((insert2134838167_state A_38) bot_bo70021908tate_o)))) ((minus_minus_nat ((big_co337839062te_nat F_11) A_37)) (F_11 A_38))))) ((((member2058392318_state A_38) A_37)->False)->(((eq nat) ((big_co337839062te_nat F_11) ((minus_2107060239tate_o A_37) ((insert2134838167_state A_38) bot_bo70021908tate_o)))) ((big_co337839062te_nat F_11) A_37))))). % Axiom fact_218_setsum__diff__nat:(forall (F_10:(hoare_1167836817_state->nat)) (A_36:(hoare_1167836817_state->Prop)) (B_25:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_25)->(((ord_le827224136tate_o B_25) A_36)->(((eq nat) ((big_co337839062te_nat F_10) ((minus_2107060239tate_o A_36) B_25))) ((minus_minus_nat ((big_co337839062te_nat F_10) A_36)) ((big_co337839062te_nat F_10) B_25)))))). % Axiom fact_219_setsum_Ocong:(forall (G_8:(hoare_1167836817_state->nat)) (H_1:(hoare_1167836817_state->nat)) (A_35:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_35)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_35)->(((eq nat) (G_8 X)) (H_1 X))))->(((eq nat) ((big_co337839062te_nat G_8) A_35)) ((big_co337839062te_nat H_1) A_35))))). % Axiom fact_220_max__leastR:(forall (X_25:Prop) (Least_1:Prop), ((all1 (ord_less_eq_o Least_1))->((iff ((ord_max_o X_25) Least_1)) X_25))). % Axiom fact_221_max__leastR:(forall (X_25:(hoare_1167836817_state->Prop)) (Least_1:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least_1))->(((eq (hoare_1167836817_state->Prop)) ((ord_ma164008317tate_o X_25) Least_1)) X_25))). % Axiom fact_222_max__leastL:(forall (X_24:Prop) (Least:Prop), ((all1 (ord_less_eq_o Least))->((iff ((ord_max_o Least) X_24)) X_24))). % Axiom fact_223_max__leastL:(forall (X_24:(hoare_1167836817_state->Prop)) (Least:(hoare_1167836817_state->Prop)), ((all2 (ord_le827224136tate_o Least))->(((eq (hoare_1167836817_state->Prop)) ((ord_ma164008317tate_o Least) X_24)) X_24))). % Axiom fact_224_max__ord__max:(((eq (Prop->(Prop->Prop))) ord_max_o) (max_o ord_less_eq_o)). % Axiom fact_225_max__ord__max:(((eq ((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) ord_ma164008317tate_o) (max_Ho421493569tate_o ord_le827224136tate_o)). % Axiom fact_226_setsum_Oremove:(forall (G_7:(hoare_1167836817_state->nat)) (X_23:hoare_1167836817_state) (A_34:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_34)->(((member2058392318_state X_23) A_34)->(((eq nat) ((big_co337839062te_nat G_7) A_34)) ((plus_plus_nat (G_7 X_23)) ((big_co337839062te_nat G_7) ((minus_2107060239tate_o A_34) ((insert2134838167_state X_23) bot_bo70021908tate_o)))))))). % Axiom fact_227_setsum__diff1_H:(forall (F_9:(hoare_1167836817_state->nat)) (A_33:hoare_1167836817_state) (A_32:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_32)->(((member2058392318_state A_33) A_32)->(((eq nat) ((big_co337839062te_nat F_9) A_32)) ((plus_plus_nat (F_9 A_33)) ((big_co337839062te_nat F_9) ((minus_2107060239tate_o A_32) ((insert2134838167_state A_33) bot_bo70021908tate_o)))))))). % Axiom fact_228_setsum_Oinsert:(forall (G_6:(hoare_1167836817_state->nat)) (X_22:hoare_1167836817_state) (A_31:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_31)->((((member2058392318_state X_22) A_31)->False)->(((eq nat) ((big_co337839062te_nat G_6) ((insert2134838167_state X_22) A_31))) ((plus_plus_nat (G_6 X_22)) ((big_co337839062te_nat G_6) A_31)))))). % Axiom fact_229_setsum__insert:(forall (F_8:(hoare_1167836817_state->nat)) (A_30:hoare_1167836817_state) (F_7:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_7)->((((member2058392318_state A_30) F_7)->False)->(((eq nat) ((big_co337839062te_nat F_8) ((insert2134838167_state A_30) F_7))) ((plus_plus_nat (F_8 A_30)) ((big_co337839062te_nat F_8) F_7)))))). % Axiom fact_230_setsum_Oinsert__remove:(forall (G_5:(hoare_1167836817_state->nat)) (X_21:hoare_1167836817_state) (A_29:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_29)->(((eq nat) ((big_co337839062te_nat G_5) ((insert2134838167_state X_21) A_29))) ((plus_plus_nat (G_5 X_21)) ((big_co337839062te_nat G_5) ((minus_2107060239tate_o A_29) ((insert2134838167_state X_21) bot_bo70021908tate_o))))))). % Axiom fact_231_setsum__cong2:(forall (F_6:(hoare_1167836817_state->nat)) (G_4:(hoare_1167836817_state->nat)) (A_28:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_28)->(((eq nat) (F_6 X)) (G_4 X))))->(((eq nat) ((big_co337839062te_nat F_6) A_28)) ((big_co337839062te_nat G_4) A_28)))). % Axiom fact_232_setsum__cong:(forall (F_5:(hoare_1167836817_state->nat)) (G_3:(hoare_1167836817_state->nat)) (A_27:(hoare_1167836817_state->Prop)) (B_24:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_27) B_24)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) B_24)->(((eq nat) (F_5 X)) (G_3 X))))->(((eq nat) ((big_co337839062te_nat F_5) A_27)) ((big_co337839062te_nat G_3) B_24))))). % Axiom fact_233_setsum_OF__cong:(forall (H:(hoare_1167836817_state->nat)) (G_2:(hoare_1167836817_state->nat)) (A_26:(hoare_1167836817_state->Prop)) (B_23:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_26) B_23)->((forall (X:hoare_1167836817_state), (((member2058392318_state X) B_23)->(((eq nat) (H X)) (G_2 X))))->(((eq nat) ((big_co337839062te_nat H) A_26)) ((big_co337839062te_nat G_2) B_23))))). % Axiom fact_234_not__less__bot:(forall (A_25:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_25) bot_bo70021908tate_o)->False)). % Axiom fact_235_not__less__bot:(forall (A_25:Prop), (((ord_less_o A_25) bot_bot_o)->False)). % Axiom fact_236_bot__less:(forall (A_24:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_24) bot_bo70021908tate_o))) ((ord_le65125204tate_o bot_bo70021908tate_o) A_24))). % Axiom fact_237_bot__less:(forall (A_24:Prop), ((iff (((iff A_24) bot_bot_o)->False)) ((ord_less_o bot_bot_o) A_24))). % Axiom fact_238_not__psubset__empty:(forall (A_23:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_23) bot_bo70021908tate_o)->False)). % Axiom fact_239_psubset__eq:(forall (A_22:(hoare_1167836817_state->Prop)) (B_22:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o A_22) B_22)) ((and ((ord_le827224136tate_o A_22) B_22)) (not (((eq (hoare_1167836817_state->Prop)) A_22) B_22))))). % Axiom fact_240_subset__iff__psubset__eq:(forall (A_21:(hoare_1167836817_state->Prop)) (B_21:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_21) B_21)) ((or ((ord_le65125204tate_o A_21) B_21)) (((eq (hoare_1167836817_state->Prop)) A_21) B_21)))). % Axiom fact_241_psubset__imp__subset:(forall (A_20:(hoare_1167836817_state->Prop)) (B_20:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_20) B_20)->((ord_le827224136tate_o A_20) B_20))). % Axiom fact_242_psubset__subset__trans:(forall (C_10:(hoare_1167836817_state->Prop)) (A_19:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_19) B_19)->(((ord_le827224136tate_o B_19) C_10)->((ord_le65125204tate_o A_19) C_10)))). % Axiom fact_243_subset__psubset__trans:(forall (C_9:(hoare_1167836817_state->Prop)) (A_18:(hoare_1167836817_state->Prop)) (B_18:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_18) B_18)->(((ord_le65125204tate_o B_18) C_9)->((ord_le65125204tate_o A_18) C_9)))). % Axiom fact_244_order__less__asym:(forall (X_20:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_20) Y_18)->(((ord_le65125204tate_o Y_18) X_20)->False))). % Axiom fact_245_order__less__asym:(forall (X_20:Prop) (Y_18:Prop), (((ord_less_o X_20) Y_18)->(((ord_less_o Y_18) X_20)->False))). % Axiom fact_246_xt1_I10_J:(forall (Z_5:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)) (X_19:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y_17) X_19)->(((ord_le65125204tate_o Z_5) Y_17)->((ord_le65125204tate_o Z_5) X_19)))). % Axiom fact_247_xt1_I10_J:(forall (Z_5:Prop) (Y_17:Prop) (X_19:Prop), (((ord_less_o Y_17) X_19)->(((ord_less_o Z_5) Y_17)->((ord_less_o Z_5) X_19)))). % Axiom fact_248_order__less__trans:(forall (Z_4:(hoare_1167836817_state->Prop)) (X_18:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_18) Y_16)->(((ord_le65125204tate_o Y_16) Z_4)->((ord_le65125204tate_o X_18) Z_4)))). % Axiom fact_249_order__less__trans:(forall (Z_4:Prop) (X_18:Prop) (Y_16:Prop), (((ord_less_o X_18) Y_16)->(((ord_less_o Y_16) Z_4)->((ord_less_o X_18) Z_4)))). % Axiom fact_250_xt1_I2_J:(forall (C_8:(hoare_1167836817_state->Prop)) (B_17:(hoare_1167836817_state->Prop)) (A_17:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_17) A_17)->((((eq (hoare_1167836817_state->Prop)) B_17) C_8)->((ord_le65125204tate_o C_8) A_17)))). % Axiom fact_251_xt1_I2_J:(forall (C_8:Prop) (B_17:Prop) (A_17:Prop), (((ord_less_o B_17) A_17)->(((iff B_17) C_8)->((ord_less_o C_8) A_17)))). % Axiom fact_252_ord__less__eq__trans:(forall (C_7:(hoare_1167836817_state->Prop)) (A_16:(hoare_1167836817_state->Prop)) (B_16:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_16) B_16)->((((eq (hoare_1167836817_state->Prop)) B_16) C_7)->((ord_le65125204tate_o A_16) C_7)))). % Axiom fact_253_ord__less__eq__trans:(forall (C_7:Prop) (A_16:Prop) (B_16:Prop), (((ord_less_o A_16) B_16)->(((iff B_16) C_7)->((ord_less_o A_16) C_7)))). % Axiom fact_254_xt1_I1_J:(forall (C_6:(hoare_1167836817_state->Prop)) (A_15:(hoare_1167836817_state->Prop)) (B_15:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_15) B_15)->(((ord_le65125204tate_o C_6) B_15)->((ord_le65125204tate_o C_6) A_15)))). % Axiom fact_255_xt1_I1_J:(forall (C_6:Prop) (B_15:Prop) (A_15:Prop), (((iff A_15) B_15)->(((ord_less_o C_6) B_15)->((ord_less_o C_6) A_15)))). % Axiom fact_256_ord__eq__less__trans:(forall (C_5:(hoare_1167836817_state->Prop)) (A_14:(hoare_1167836817_state->Prop)) (B_14:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_14) B_14)->(((ord_le65125204tate_o B_14) C_5)->((ord_le65125204tate_o A_14) C_5)))). % Axiom fact_257_ord__eq__less__trans:(forall (C_5:Prop) (B_14:Prop) (A_14:Prop), (((iff A_14) B_14)->(((ord_less_o B_14) C_5)->((ord_less_o A_14) C_5)))). % Axiom fact_258_xt1_I9_J:(forall (B_13:(hoare_1167836817_state->Prop)) (A_13:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_13) A_13)->(((ord_le65125204tate_o A_13) B_13)->False))). % Axiom fact_259_xt1_I9_J:(forall (B_13:Prop) (A_13:Prop), (((ord_less_o B_13) A_13)->(((ord_less_o A_13) B_13)->False))). % Axiom fact_260_order__less__asym_H:(forall (A_12:(hoare_1167836817_state->Prop)) (B_12:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_12) B_12)->(((ord_le65125204tate_o B_12) A_12)->False))). % Axiom fact_261_order__less__asym_H:(forall (A_12:Prop) (B_12:Prop), (((ord_less_o A_12) B_12)->(((ord_less_o B_12) A_12)->False))). % Axiom fact_262_order__less__imp__triv:(forall (P:Prop) (X_17:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_17) Y_15)->(((ord_le65125204tate_o Y_15) X_17)->P))). % Axiom fact_263_order__less__imp__triv:(forall (P:Prop) (X_17:Prop) (Y_15:Prop), (((ord_less_o X_17) Y_15)->(((ord_less_o Y_15) X_17)->P))). % Axiom fact_264_order__less__imp__not__eq2:(forall (X_16:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_16) Y_14)->(not (((eq (hoare_1167836817_state->Prop)) Y_14) X_16)))). % Axiom fact_265_order__less__imp__not__eq2:(forall (X_16:Prop) (Y_14:Prop), (((ord_less_o X_16) Y_14)->((iff Y_14) (X_16->False)))). % Axiom fact_266_order__less__imp__not__eq:(forall (X_15:(hoare_1167836817_state->Prop)) (Y_13:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_15) Y_13)->(not (((eq (hoare_1167836817_state->Prop)) X_15) Y_13)))). % Axiom fact_267_order__less__imp__not__eq:(forall (X_15:Prop) (Y_13:Prop), (((ord_less_o X_15) Y_13)->((iff X_15) (Y_13->False)))). % Axiom fact_268_order__less__imp__not__less:(forall (X_14:(hoare_1167836817_state->Prop)) (Y_12:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_14) Y_12)->(((ord_le65125204tate_o Y_12) X_14)->False))). % Axiom fact_269_order__less__imp__not__less:(forall (X_14:Prop) (Y_12:Prop), (((ord_less_o X_14) Y_12)->(((ord_less_o Y_12) X_14)->False))). % Axiom fact_270_order__less__not__sym:(forall (X_13:(hoare_1167836817_state->Prop)) (Y_11:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_13) Y_11)->(((ord_le65125204tate_o Y_11) X_13)->False))). % Axiom fact_271_order__less__not__sym:(forall (X_13:Prop) (Y_11:Prop), (((ord_less_o X_13) Y_11)->(((ord_less_o Y_11) X_13)->False))). % Axiom fact_272_less__imp__neq:(forall (X_12:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_12) Y_10)->(not (((eq (hoare_1167836817_state->Prop)) X_12) Y_10)))). % Axiom fact_273_less__imp__neq:(forall (X_12:Prop) (Y_10:Prop), (((ord_less_o X_12) Y_10)->(((iff X_12) Y_10)->False))). % Axiom fact_274_order__less__irrefl:(forall (X_11:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_11) X_11)->False)). % Axiom fact_275_order__less__irrefl:(forall (X_11:Prop), (((ord_less_o X_11) X_11)->False)). % Axiom fact_276_order__less__le:(forall (X_10:Prop) (Y_9:Prop), ((iff ((ord_less_o X_10) Y_9)) ((and ((ord_less_eq_o X_10) Y_9)) (((iff X_10) Y_9)->False)))). % Axiom fact_277_order__less__le:(forall (X_10:(hoare_1167836817_state->Prop)) (Y_9:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o X_10) Y_9)) ((and ((ord_le827224136tate_o X_10) Y_9)) (not (((eq (hoare_1167836817_state->Prop)) X_10) Y_9))))). % Axiom fact_278_less__le__not__le:(forall (X_9:Prop) (Y_8:Prop), ((iff ((ord_less_o X_9) Y_8)) ((and ((ord_less_eq_o X_9) Y_8)) (((ord_less_eq_o Y_8) X_9)->False)))). % Axiom fact_279_less__le__not__le:(forall (X_9:(hoare_1167836817_state->Prop)) (Y_8:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o X_9) Y_8)) ((and ((ord_le827224136tate_o X_9) Y_8)) (((ord_le827224136tate_o Y_8) X_9)->False)))). % Axiom fact_280_order__le__less:(forall (X_8:Prop) (Y_7:Prop), ((iff ((ord_less_eq_o X_8) Y_7)) ((or ((ord_less_o X_8) Y_7)) ((iff X_8) Y_7)))). % Axiom fact_281_order__le__less:(forall (X_8:(hoare_1167836817_state->Prop)) (Y_7:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_8) Y_7)) ((or ((ord_le65125204tate_o X_8) Y_7)) (((eq (hoare_1167836817_state->Prop)) X_8) Y_7)))). % Axiom fact_282_order__neq__le__trans:(forall (B_11:Prop) (A_11:Prop), ((((iff A_11) B_11)->False)->(((ord_less_eq_o A_11) B_11)->((ord_less_o A_11) B_11)))). % Axiom fact_283_order__neq__le__trans:(forall (A_11:(hoare_1167836817_state->Prop)) (B_11:(hoare_1167836817_state->Prop)), ((not (((eq (hoare_1167836817_state->Prop)) A_11) B_11))->(((ord_le827224136tate_o A_11) B_11)->((ord_le65125204tate_o A_11) B_11)))). % Axiom fact_284_xt1_I12_J:(forall (B_10:Prop) (A_10:Prop), ((((iff A_10) B_10)->False)->(((ord_less_eq_o B_10) A_10)->((ord_less_o B_10) A_10)))). % Axiom fact_285_xt1_I12_J:(forall (A_10:(hoare_1167836817_state->Prop)) (B_10:(hoare_1167836817_state->Prop)), ((not (((eq (hoare_1167836817_state->Prop)) A_10) B_10))->(((ord_le827224136tate_o B_10) A_10)->((ord_le65125204tate_o B_10) A_10)))). % Axiom fact_286_order__less__imp__le:(forall (X_7:Prop) (Y_6:Prop), (((ord_less_o X_7) Y_6)->((ord_less_eq_o X_7) Y_6))). % Axiom fact_287_order__less__imp__le:(forall (X_7:(hoare_1167836817_state->Prop)) (Y_6:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_7) Y_6)->((ord_le827224136tate_o X_7) Y_6))). % Axiom fact_288_order__le__imp__less__or__eq:(forall (X_6:Prop) (Y_5:Prop), (((ord_less_eq_o X_6) Y_5)->((or ((ord_less_o X_6) Y_5)) ((iff X_6) Y_5)))). % Axiom fact_289_order__le__imp__less__or__eq:(forall (X_6:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_6) Y_5)->((or ((ord_le65125204tate_o X_6) Y_5)) (((eq (hoare_1167836817_state->Prop)) X_6) Y_5)))). % Axiom fact_290_order__le__neq__trans:(forall (A_9:Prop) (B_9:Prop), (((ord_less_eq_o A_9) B_9)->((((iff A_9) B_9)->False)->((ord_less_o A_9) B_9)))). % Axiom fact_291_order__le__neq__trans:(forall (A_9:(hoare_1167836817_state->Prop)) (B_9:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_9) B_9)->((not (((eq (hoare_1167836817_state->Prop)) A_9) B_9))->((ord_le65125204tate_o A_9) B_9)))). % Axiom fact_292_xt1_I11_J:(forall (B_8:Prop) (A_8:Prop), (((ord_less_eq_o B_8) A_8)->((((iff A_8) B_8)->False)->((ord_less_o B_8) A_8)))). % Axiom fact_293_xt1_I11_J:(forall (B_8:(hoare_1167836817_state->Prop)) (A_8:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_8) A_8)->((not (((eq (hoare_1167836817_state->Prop)) A_8) B_8))->((ord_le65125204tate_o B_8) A_8)))). % Axiom fact_294_order__less__le__trans:(forall (Z_3:Prop) (X_5:Prop) (Y_4:Prop), (((ord_less_o X_5) Y_4)->(((ord_less_eq_o Y_4) Z_3)->((ord_less_o X_5) Z_3)))). % Axiom fact_295_order__less__le__trans:(forall (Z_3:(hoare_1167836817_state->Prop)) (X_5:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o X_5) Y_4)->(((ord_le827224136tate_o Y_4) Z_3)->((ord_le65125204tate_o X_5) Z_3)))). % Axiom fact_296_xt1_I7_J:(forall (Z_2:Prop) (Y_3:Prop) (X_4:Prop), (((ord_less_o Y_3) X_4)->(((ord_less_eq_o Z_2) Y_3)->((ord_less_o Z_2) X_4)))). % Axiom fact_297_xt1_I7_J:(forall (Z_2:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (X_4:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y_3) X_4)->(((ord_le827224136tate_o Z_2) Y_3)->((ord_le65125204tate_o Z_2) X_4)))). % Axiom fact_298_order__le__less__trans:(forall (Z_1:Prop) (X_3:Prop) (Y_2:Prop), (((ord_less_eq_o X_3) Y_2)->(((ord_less_o Y_2) Z_1)->((ord_less_o X_3) Z_1)))). % Axiom fact_299_order__le__less__trans:(forall (Z_1:(hoare_1167836817_state->Prop)) (X_3:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_3) Y_2)->(((ord_le65125204tate_o Y_2) Z_1)->((ord_le65125204tate_o X_3) Z_1)))). % Axiom fact_300_xt1_I8_J:(forall (Z:Prop) (Y_1:Prop) (X_2:Prop), (((ord_less_eq_o Y_1) X_2)->(((ord_less_o Z) Y_1)->((ord_less_o Z) X_2)))). % Axiom fact_301_xt1_I8_J:(forall (Z:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (X_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_1) X_2)->(((ord_le65125204tate_o Z) Y_1)->((ord_le65125204tate_o Z) X_2)))). % Axiom fact_302_less__fun__def:(forall (F_4:(hoare_1167836817_state->Prop)) (G_1:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o F_4) G_1)) ((and ((ord_le827224136tate_o F_4) G_1)) (((ord_le827224136tate_o G_1) F_4)->False)))). % Axiom fact_303_psubset__insert__iff:(forall (A_7:(hoare_1167836817_state->Prop)) (X_1:hoare_1167836817_state) (B_7:(hoare_1167836817_state->Prop)), ((iff ((ord_le65125204tate_o A_7) ((insert2134838167_state X_1) B_7))) ((and (((member2058392318_state X_1) B_7)->((ord_le65125204tate_o A_7) B_7))) ((((member2058392318_state X_1) B_7)->False)->((and (((member2058392318_state X_1) A_7)->((ord_le65125204tate_o ((minus_2107060239tate_o A_7) ((insert2134838167_state X_1) bot_bo70021908tate_o))) B_7))) ((((member2058392318_state X_1) A_7)->False)->((ord_le827224136tate_o A_7) B_7))))))). % Axiom fact_304_setsum__strict__mono:(forall (F_3:(hoare_1167836817_state->nat)) (G:(hoare_1167836817_state->nat)) (A_6:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_6)->((not (((eq (hoare_1167836817_state->Prop)) A_6) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (((member2058392318_state X) A_6)->((ord_less_nat (F_3 X)) (G X))))->((ord_less_nat ((big_co337839062te_nat F_3) A_6)) ((big_co337839062te_nat G) A_6)))))). % Axiom fact_305_psubset__trans:(forall (C_4:(hoare_1167836817_state->Prop)) (A_5:(hoare_1167836817_state->Prop)) (B_6:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_5) B_6)->(((ord_le65125204tate_o B_6) C_4)->((ord_le65125204tate_o A_5) C_4)))). % Axiom fact_306_psubsetD:(forall (C_3:hoare_1167836817_state) (A_4:(hoare_1167836817_state->Prop)) (B_5:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_4) B_5)->(((member2058392318_state C_3) A_4)->((member2058392318_state C_3) B_5)))). % Axiom fact_307_psubset__imp__ex__mem:(forall (A_3:(hoare_1167836817_state->Prop)) (B_3:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o A_3) B_3)->((ex hoare_1167836817_state) (fun (B_4:hoare_1167836817_state)=> ((member2058392318_state B_4) ((minus_2107060239tate_o B_3) A_3)))))). % Axiom fact_308_xt6:(forall (C_2:(hoare_1167836817_state->Prop)) (F_2:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_2:(hoare_1167836817_state->Prop)) (A_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_2 B_2)) A_2)->(((ord_le65125204tate_o C_2) B_2)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y) X)->((ord_le65125204tate_o (F_2 Y)) (F_2 X))))->((ord_le65125204tate_o (F_2 C_2)) A_2))))). % Axiom fact_309_xt6:(forall (C_2:Prop) (F_2:(Prop->(hoare_1167836817_state->Prop))) (B_2:Prop) (A_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o (F_2 B_2)) A_2)->(((ord_less_o C_2) B_2)->((forall (X:Prop) (Y:Prop), (((ord_less_o Y) X)->((ord_le65125204tate_o (F_2 Y)) (F_2 X))))->((ord_le65125204tate_o (F_2 C_2)) A_2))))). % Axiom fact_310_xt5:(forall (C_1:(hoare_1167836817_state->Prop)) (F_1:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_1:(hoare_1167836817_state->Prop)) (A_1:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o B_1) A_1)->(((ord_le827224136tate_o C_1) (F_1 B_1))->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o Y) X)->((ord_le65125204tate_o (F_1 Y)) (F_1 X))))->((ord_le65125204tate_o C_1) (F_1 A_1)))))). % Axiom fact_311_xt5:(forall (C_1:(hoare_1167836817_state->Prop)) (F_1:(Prop->(hoare_1167836817_state->Prop))) (B_1:Prop) (A_1:Prop), (((ord_less_o B_1) A_1)->(((ord_le827224136tate_o C_1) (F_1 B_1))->((forall (X:Prop) (Y:Prop), (((ord_less_o Y) X)->((ord_le65125204tate_o (F_1 Y)) (F_1 X))))->((ord_le65125204tate_o C_1) (F_1 A_1)))))). % Axiom fact_312_xt4:(forall (C:(hoare_1167836817_state->Prop)) (F:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B:(hoare_1167836817_state->Prop)) (A:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o (F B)) A)->(((ord_le827224136tate_o C) B)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_le827224136tate_o (F Y)) (F X))))->((ord_le65125204tate_o (F C)) A))))). % Axiom fact_313_xt4:(forall (C:(hoare_1167836817_state->Prop)) (F:((hoare_1167836817_state->Prop)->Prop)) (B:(hoare_1167836817_state->Prop)) (A:Prop), (((ord_less_o (F B)) A)->(((ord_le827224136tate_o C) B)->((forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y) X)->((ord_less_eq_o (F Y)) (F X))))->((ord_less_o (F C)) A))))). % Axiom fact_314_xt4:(forall (C:Prop) (F:(Prop->(hoare_1167836817_state->Prop))) (B:Prop) (A:(hoare_1167836817_state->Prop)), (((ord_le65125204tate_o (F B)) A)->(((ord_less_eq_o C) B)->((forall (X:Prop) (Y:Prop), (((ord_less_eq_o Y) X)->((ord_le827224136tate_o (F Y)) (F X))))->((ord_le65125204tate_o (F C)) A))))). % Axiom conj_0:((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)). % Axiom conj_1:((hoare_529639851_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)). % Trying to prove ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found conj_0:((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) % Instantiate: G_26:=((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o):(hoare_1167836817_state->Prop) % Found conj_0 as proof of ((hoare_123228589_state bot_bo70021908tate_o) G_26) % Found x:((Q_10 Z_28) S) % Found x as proof of ((q Z_28) S) % Found (fun (x:((Q_10 Z_28) S))=> x) as proof of ((q Z_28) S) % Found (fun (S:state) (x:((Q_10 Z_28) S))=> x) as proof of (((Q_10 Z_28) S)->((q Z_28) S)) % Found (fun (Z_28:state) (S:state) (x:((Q_10 Z_28) S))=> x) as proof of (forall (S:state), (((Q_10 Z_28) S)->((q Z_28) S))) % Found (fun (Z_28:state) (S:state) (x:((Q_10 Z_28) S))=> x) as proof of (forall (Z_28:state) (S:state), (((Q_10 Z_28) S)->((q Z_28) S))) % Found x:((p Z_28) S) % Instantiate: P_19:=p:(state->(state->Prop)) % Found (fun (x:((p Z_28) S))=> x) as proof of ((P_19 Z_28) S) % Found (fun (S:state) (x:((p Z_28) S))=> x) as proof of (((p Z_28) S)->((P_19 Z_28) S)) % Found (fun (Z_28:state) (S:state) (x:((p Z_28) S))=> x) as proof of (forall (S:state), (((p Z_28) S)->((P_19 Z_28) S))) % Found (fun (Z_28:state) (S:state) (x:((p Z_28) S))=> x) as proof of (forall (Z_28:state) (S:state), (((p Z_28) S)->((P_19 Z_28) S))) % Found fact_0_empty0:=(fact_0_empty bot_bo70021908tate_o):((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_0_empty bot_bo70021908tate_o) as proof of ((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_0_empty bot_bo70021908tate_o) as proof of ((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found conj_0:((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) % Instantiate: Ts_1:=((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o):(hoare_1167836817_state->Prop) % Found conj_0 as proof of ((hoare_123228589_state bot_bo70021908tate_o) Ts_1) % Found fact_63_order__refl0:=(fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)):((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) Ts_1) % Found (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) Ts_1) % Found (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) Ts_1) % Found fact_66_finite_OemptyI:(finite1084549118_state bot_bo70021908tate_o) % Instantiate: A_57:=bot_bo70021908tate_o:(hoare_1167836817_state->Prop) % Found fact_66_finite_OemptyI as proof of (finite1084549118_state A_57) % Found fact_68_empty__subsetI0:=(fact_68_empty__subsetI bot_bo70021908tate_o):((ord_le827224136tate_o bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_68_empty__subsetI bot_bo70021908tate_o) as proof of ((ord_le827224136tate_o G_10) bot_bo70021908tate_o) % Found (fact_68_empty__subsetI bot_bo70021908tate_o) as proof of ((ord_le827224136tate_o G_10) bot_bo70021908tate_o) % Found (fact_68_empty__subsetI bot_bo70021908tate_o) as proof of ((ord_le827224136tate_o G_10) bot_bo70021908tate_o) % Found conj_0:((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) % Instantiate: G_26:=((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o):(hoare_1167836817_state->Prop) % Found conj_0 as proof of ((hoare_123228589_state bot_bo70021908tate_o) G_26) % Found x:((P_19 Z_28) S) % Found x as proof of ((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_11) c) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((q Z_28) S_1)))))))) % Found (fun (x:((P_19 Z_28) S))=> x) as proof of ((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_11) c) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((q Z_28) S_1)))))))) % Found (fun (S:state) (x:((P_19 Z_28) S))=> x) as proof of (((P_19 Z_28) S)->((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_11) c) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((q Z_28) S_1))))))))) % Found (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x) as proof of (forall (S:state), (((P_19 Z_28) S)->((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_11) c) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((q Z_28) S_1)))))))))) % Found (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x) as proof of (forall (Z_28:state) (S:state), (((P_19 Z_28) S)->((ex (state->(state->Prop))) (fun (P_11:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_5:(state->(state->Prop)))=> ((and ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_11) c) Q_5)) bot_bo70021908tate_o))) (forall (S_1:state), ((forall (Z_29:state), (((P_11 Z_29) S)->((Q_5 Z_29) S_1)))->((q Z_28) S_1)))))))))) % Found (fact_44_conseq0000 (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x)) as proof of ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_19) c) q)) bot_bo70021908tate_o)) % Found ((fact_44_conseq000 P_19) (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x)) as proof of ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_19) c) q)) bot_bo70021908tate_o)) % Found (((fact_44_conseq00 c) P_19) (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x)) as proof of ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_19) c) q)) bot_bo70021908tate_o)) % Found ((((fact_44_conseq0 bot_bo70021908tate_o) c) P_19) (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x)) as proof of ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_19) c) q)) bot_bo70021908tate_o)) % Found (((((fact_44_conseq q) bot_bo70021908tate_o) c) P_19) (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x)) as proof of ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_19) c) q)) bot_bo70021908tate_o)) % Found (((((fact_44_conseq q) bot_bo70021908tate_o) c) P_19) (fun (Z_28:state) (S:state) (x:((P_19 Z_28) S))=> x)) as proof of ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P_19) c) q)) bot_bo70021908tate_o)) % Found fact_67_finite_OinsertI000:=(fact_67_finite_OinsertI00 fact_66_finite_OemptyI):(finite1084549118_state ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (fact_67_finite_OinsertI00 fact_66_finite_OemptyI) as proof of (finite1084549118_state ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found ((fact_67_finite_OinsertI0 bot_bo70021908tate_o) fact_66_finite_OemptyI) as proof of (finite1084549118_state ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (((fact_67_finite_OinsertI (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o) fact_66_finite_OemptyI) as proof of (finite1084549118_state ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (((fact_67_finite_OinsertI (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o) fact_66_finite_OemptyI) as proof of (finite1084549118_state ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found x1:((hoare_123228589_state bot_bo70021908tate_o) F_50) % Found x1 as proof of ((hoare_123228589_state bot_bo70021908tate_o) F_50) % Found fact_66_finite_OemptyI:(finite1084549118_state bot_bo70021908tate_o) % Instantiate: A_57:=bot_bo70021908tate_o:(hoare_1167836817_state->Prop) % Found fact_66_finite_OemptyI as proof of (finite1084549118_state A_57) % Found x1:((hoare_123228589_state bot_bo70021908tate_o) F_50) % Instantiate: G_26:=F_50:(hoare_1167836817_state->Prop) % Found x1 as proof of ((hoare_123228589_state bot_bo70021908tate_o) G_26) % Found fact_68_empty__subsetI0:=(fact_68_empty__subsetI (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))):((ord_le827224136tate_o bot_bo70021908tate_o) (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) % Found (fact_68_empty__subsetI (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) as proof of ((ord_le827224136tate_o P_8) (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) % Found (fact_68_empty__subsetI (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) as proof of ((ord_le827224136tate_o P_8) (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) % Found (fact_68_empty__subsetI (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) as proof of ((ord_le827224136tate_o P_8) (fun (x4:hoare_1167836817_state)=> ((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state x4) F_50)))) % Found fact_13_insert__not__empty00:=(fact_13_insert__not__empty0 F_50):(not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) F_50)) bot_bo70021908tate_o)) % Found (fact_13_insert__not__empty0 F_50) as proof of (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) F_50)) bot_bo70021908tate_o)) % Found ((fact_13_insert__not__empty X) F_50) as proof of (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) F_50)) bot_bo70021908tate_o)) % Found ((fact_13_insert__not__empty X) F_50) as proof of (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) F_50)) bot_bo70021908tate_o)) % Found fact_0_empty0:=(fact_0_empty bot_bo70021908tate_o):((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_0_empty bot_bo70021908tate_o) as proof of ((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_0_empty bot_bo70021908tate_o) as proof of ((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found fact_63_order__refl0:=(fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)):((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) G_26) % Found (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) G_26) % Found (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) G_26) % Found (fact_122_asm00 (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o))) as proof of ((hoare_123228589_state G_26) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found ((fact_122_asm0 G_26) (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o))) as proof of ((hoare_123228589_state G_26) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (((fact_122_asm ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) G_26) (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o))) as proof of ((hoare_123228589_state G_26) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (((fact_122_asm ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) G_26) (fact_63_order__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o))) as proof of ((hoare_123228589_state G_26) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found conj_0:((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) % Instantiate: G_26:=((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o):(hoare_1167836817_state->Prop) % Found conj_0 as proof of ((hoare_123228589_state bot_bo70021908tate_o) G_26) % Found conj_0:((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o)) % Instantiate: G_26:=((insert2134838167_state (hoare_Mirabelle_MGT c)) bot_bo70021908tate_o):(hoare_1167836817_state->Prop) % Found conj_0 as proof of ((hoare_123228589_state bot_bo70021908tate_o) G_26) % Found fact_0_empty0:=(fact_0_empty bot_bo70021908tate_o):((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_0_empty bot_bo70021908tate_o) as proof of ((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found (fact_0_empty bot_bo70021908tate_o) as proof of ((hoare_123228589_state bot_bo70021908tate_o) bot_bo70021908tate_o) % Found fact_73_subset__refl0:=(fact_73_subset__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)):((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) % Found (fact_73_subset__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) A_108) % Found (fact_73_subset__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) A_108) % Found (fact_73_subset__refl ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (((hoare_908217195_state p) c) q)) bot_bo70021908tate_o)) A_108) % Found fact_0_empty0:=(fact_0_empty bot_bo70021908tate_o):((hoare_123228589_state % EOF %------------------------------------------------------------------------------