TSTP Solution File: ITP120^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP120^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:24:14 EDT 2021
% 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
% 0.03/0.12 % Problem : ITP120^1 : TPTP v7.5.0. Released v7.5.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Fri Mar 19 06:01:56 EDT 2021
% 0.12/0.34 % CPUTime :
% 0.12/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 0.41/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b368>, <kernel.Type object at 0x169b128>) of role type named ty_n_t__Set__Oset_Itf__a_J
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring set_a:Type
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169fef0>, <kernel.Type object at 0x169b1b8>) of role type named ty_n_tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring a:Type
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b878>, <kernel.DependentProduct object at 0x169b998>) of role type named sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring condit1627435690bove_a:((a->(a->Prop))->(set_a->Prop))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b6c8>, <kernel.DependentProduct object at 0x169b488>) of role type named sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring condit1001553558elow_a:((a->(a->Prop))->(set_a->Prop))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b518>, <kernel.DependentProduct object at 0x1678bd8>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring finite40241356em_a_a:((a->(a->a))->Prop)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b908>, <kernel.DependentProduct object at 0x1678c20>) of role type named sy_c_Finite__Set_Ofinite_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring finite_finite_a:(set_a->Prop)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b878>, <kernel.DependentProduct object at 0x1678998>) of role type named sy_c_Groups_Oabel__semigroup_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring abel_semigroup_a:((a->(a->a))->Prop)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b488>, <kernel.DependentProduct object at 0x1678ea8>) of role type named sy_c_Groups_Osemigroup_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring semigroup_a:((a->(a->a))->Prop)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b6c8>, <kernel.DependentProduct object at 0x1678c20>) of role type named sy_c_If_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring if_a:(Prop->(a->(a->a)))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b488>, <kernel.DependentProduct object at 0x1678ab8>) of role type named sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring inf_inf_set_a:(set_a->(set_a->set_a))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b488>, <kernel.DependentProduct object at 0x1678ea8>) of role type named sy_c_Lattices_Osemilattice_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring semilattice_a:((a->(a->a))->Prop)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x169b488>, <kernel.DependentProduct object at 0x1678998>) of role type named sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring sup_sup_set_a:(set_a->(set_a->set_a))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1678ab8>, <kernel.DependentProduct object at 0x16785f0>) of role type named sy_c_Lattices__Big_Osemilattice__set_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring lattic1885654924_set_a:((a->(a->a))->Prop)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1678a28>, <kernel.DependentProduct object at 0x1678ea8>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring modula17988509_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x2b556a01efc8>, <kernel.DependentProduct object at 0x1678c68>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring modula1373251614_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x2b556a01efc8>, <kernel.DependentProduct object at 0x1678c68>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring modula581031071_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1678950>, <kernel.DependentProduct object at 0x16785f0>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring modula1936294176_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678ea8>, <kernel.DependentProduct object at 0x1678908>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring modula1144073633_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678a28>, <kernel.DependentProduct object at 0x1678950>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring modula1727524044comp_a:((a->(a->Prop))->(a->(a->Prop)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678c20>, <kernel.DependentProduct object at 0x2b5562546e60>) of role type named sy_c_Orderings_Oord_OLeast_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring least_a:((a->(a->Prop))->((a->Prop)->a))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x16785f0>, <kernel.DependentProduct object at 0x2b5562546f80>) of role type named sy_c_Orderings_Oord_Omax_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring max_a:((a->(a->Prop))->(a->(a->a)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678a28>, <kernel.DependentProduct object at 0x2b5562546d88>) of role type named sy_c_Orderings_Oord_Omin_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring min_a:((a->(a->Prop))->(a->(a->a)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678ea8>, <kernel.DependentProduct object at 0x2b5562546ea8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_less_eq_set_a:(set_a->(set_a->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678950>, <kernel.DependentProduct object at 0x2b5562546f38>) of role type named sy_c_Orderings_Oorder_OGreatest_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring greatest_a:((a->(a->Prop))->((a->Prop)->a))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678a28>, <kernel.DependentProduct object at 0x2b5562546fc8>) of role type named sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring antimono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x1678a28>, <kernel.DependentProduct object at 0x2b5562546cf8>) of role type named sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546ef0>, <kernel.DependentProduct object at 0x2b5562546f38>) of role type named sy_c_Set_OCollect_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring collect_a:((a->Prop)->set_a)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546ea8>, <kernel.DependentProduct object at 0x2b5562546dd0>) of role type named sy_c_member_001tf__a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring member_a:(a->(set_a->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546e18>, <kernel.Constant object at 0x2b5562546dd0>) of role type named sy_v_a
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring a2:a
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546ef0>, <kernel.Constant object at 0x2b5562546dd0>) of role type named sy_v_b
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring b:a
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546ea8>, <kernel.Constant object at 0x2b5562546dd0>) of role type named sy_v_c
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c:a
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546e18>, <kernel.DependentProduct object at 0x2b5562546b90>) of role type named sy_v_inf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring inf:(a->(a->a))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546cb0>, <kernel.DependentProduct object at 0x2b5562546b48>) of role type named sy_v_less__eq
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring less_eq:(a->(a->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b5562546dd0>, <kernel.DependentProduct object at 0x2b5562546bd8>) of role type named sy_v_sup
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring sup:(a->(a->a))
% 0.47/0.63 FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y)))) of role axiom named fact_0_local_Oantisym
% 0.47/0.63 A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y))))
% 0.47/0.63 FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))) of role axiom named fact_1_local_Oantisym__conv
% 0.47/0.65 A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y))))
% 0.47/0.65 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B)))) of role axiom named fact_2_local_Odual__order_Oantisym
% 0.47/0.65 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B))))
% 0.47/0.65 FOF formula (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq B2) A2)) ((less_eq A2) B2)))) of role axiom named fact_3_local_Odual__order_Oeq__iff
% 0.47/0.65 A new axiom: (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq B2) A2)) ((less_eq A2) B2))))
% 0.47/0.65 FOF formula (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A)))) of role axiom named fact_4_local_Odual__order_Otrans
% 0.47/0.65 A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A))))
% 0.47/0.65 FOF formula (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (X2:a) (Y3:a)=> ((and ((less_eq X2) Y3)) ((less_eq Y3) X2)))) of role axiom named fact_5_local_Oeq__iff
% 0.47/0.65 A new axiom: (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (X2:a) (Y3:a)=> ((and ((less_eq X2) Y3)) ((less_eq Y3) X2))))
% 0.47/0.65 FOF formula (forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y))) of role axiom named fact_6_local_Oeq__refl
% 0.47/0.65 A new axiom: (forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y)))
% 0.47/0.65 FOF formula (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C)))) of role axiom named fact_7_local_Oord__eq__le__trans
% 0.47/0.65 A new axiom: (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C))))
% 0.47/0.65 FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C)))) of role axiom named fact_8_local_Oord__le__eq__trans
% 0.47/0.65 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C))))
% 0.47/0.65 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B)))) of role axiom named fact_9_local_Oorder_Oantisym
% 0.47/0.65 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B))))
% 0.47/0.65 FOF formula (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq A2) B2)) ((less_eq B2) A2)))) of role axiom named fact_10_local_Oorder_Oeq__iff
% 0.47/0.65 A new axiom: (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq A2) B2)) ((less_eq B2) A2))))
% 0.47/0.65 FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C)))) of role axiom named fact_11_local_Oorder_Otrans
% 0.47/0.65 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C))))
% 0.47/0.65 FOF formula (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq Y) Z2)->((less_eq X) Z2)))) of role axiom named fact_12_local_Oorder__trans
% 0.47/0.65 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq Y) Z2)->((less_eq X) Z2))))
% 0.47/0.65 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C)))) of role axiom named fact_13_local_Oinf_Oassoc
% 0.47/0.65 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C))))
% 0.47/0.65 FOF formula (forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A))) of role axiom named fact_14_local_Oinf_Ocommute
% 0.47/0.65 A new axiom: (forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A)))
% 0.47/0.65 FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C)))) of role axiom named fact_15_local_Oinf_Oleft__commute
% 0.47/0.65 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C))))
% 0.47/0.65 FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf ((inf X) Y)) Z2)) ((inf X) ((inf Y) Z2)))) of role axiom named fact_16_local_Oinf__assoc
% 0.47/0.65 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf ((inf X) Y)) Z2)) ((inf X) ((inf Y) Z2))))
% 0.47/0.65 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X))) of role axiom named fact_17_local_Oinf__commute
% 0.47/0.65 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X)))
% 0.47/0.65 FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf X) ((inf Y) Z2))) ((inf Y) ((inf X) Z2)))) of role axiom named fact_18_local_Oinf__left__commute
% 0.49/0.67 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf X) ((inf Y) Z2))) ((inf Y) ((inf X) Z2))))
% 0.49/0.67 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C)))) of role axiom named fact_19_local_Osup_Oassoc
% 0.49/0.67 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C))))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A))) of role axiom named fact_20_local_Osup_Ocommute
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A)))
% 0.49/0.67 FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C)))) of role axiom named fact_21_local_Osup_Oleft__commute
% 0.49/0.67 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C))))
% 0.49/0.67 FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup ((sup X) Y)) Z2)) ((sup X) ((sup Y) Z2)))) of role axiom named fact_22_local_Osup__assoc
% 0.49/0.67 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup ((sup X) Y)) Z2)) ((sup X) ((sup Y) Z2))))
% 0.49/0.67 FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X))) of role axiom named fact_23_local_Osup__commute
% 0.49/0.67 A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X)))
% 0.49/0.67 FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup X) ((sup Y) Z2))) ((sup Y) ((sup X) Z2)))) of role axiom named fact_24_local_Osup__left__commute
% 0.49/0.67 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup X) ((sup Y) Z2))) ((sup Y) ((sup X) Z2))))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A))) of role axiom named fact_25_local_Oinf_Oabsorb1
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A)))
% 0.49/0.67 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B))) of role axiom named fact_26_local_Oinf_Oabsorb2
% 0.49/0.67 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B)))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A))) of role axiom named fact_27_local_Oinf_Oabsorb__iff1
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A)))
% 0.49/0.67 FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B))) of role axiom named fact_28_local_Oinf_Oabsorb__iff2
% 0.49/0.67 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B)))
% 0.49/0.67 FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) ((inf B) C))->((((less_eq A) B)->(((less_eq A) C)->False))->False))) of role axiom named fact_29_local_Oinf_OboundedE
% 0.49/0.67 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) ((inf B) C))->((((less_eq A) B)->(((less_eq A) C)->False))->False)))
% 0.49/0.67 FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C))))) of role axiom named fact_30_local_Oinf_OboundedI
% 0.49/0.67 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C)))))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), ((less_eq ((inf A) B)) A)) of role axiom named fact_31_local_Oinf_Ocobounded1
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), ((less_eq ((inf A) B)) A))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), ((less_eq ((inf A) B)) B)) of role axiom named fact_32_local_Oinf_Ocobounded2
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), ((less_eq ((inf A) B)) B))
% 0.49/0.67 FOF formula (forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C))) of role axiom named fact_33_local_Oinf_OcoboundedI1
% 0.49/0.67 A new axiom: (forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C)))
% 0.49/0.67 FOF formula (forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C))) of role axiom named fact_34_local_Oinf_OcoboundedI2
% 0.49/0.67 A new axiom: (forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C)))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B)))) of role axiom named fact_35_local_Oinf_OorderE
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B))))
% 0.49/0.67 FOF formula (forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B))) of role axiom named fact_36_local_Oinf_OorderI
% 0.49/0.67 A new axiom: (forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B)))
% 0.49/0.69 FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B)))) of role axiom named fact_37_local_Oinf_Oorder__iff
% 0.49/0.69 A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B))))
% 0.49/0.69 FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X))) of role axiom named fact_38_local_Oinf__absorb1
% 0.49/0.69 A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X)))
% 0.49/0.69 FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y))) of role axiom named fact_39_local_Oinf__absorb2
% 0.49/0.69 A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y)))
% 0.49/0.69 FOF formula (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq X) Z2)->((less_eq X) ((inf Y) Z2))))) of role axiom named fact_40_local_Oinf__greatest
% 0.49/0.69 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq X) Z2)->((less_eq X) ((inf Y) Z2)))))
% 0.49/0.69 FOF formula (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X)) of role axiom named fact_41_local_Oinf__le1
% 0.49/0.69 A new axiom: (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X))
% 0.49/0.69 FOF formula (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y)) of role axiom named fact_42_local_Oinf__le2
% 0.49/0.69 A new axiom: (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y))
% 0.49/0.69 FOF formula (forall (A:a) (C:a) (B:a) (D:a), (((less_eq A) C)->(((less_eq B) D)->((less_eq ((inf A) B)) ((inf C) D))))) of role axiom named fact_43_local_Oinf__mono
% 0.49/0.69 A new axiom: (forall (A:a) (C:a) (B:a) (D:a), (((less_eq A) C)->(((less_eq B) D)->((less_eq ((inf A) B)) ((inf C) D)))))
% 0.49/0.69 FOF formula (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) X3))->((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) Y4))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq X3) Y4)->(((less_eq X3) Z3)->((less_eq X3) ((F Y4) Z3)))))->(((eq a) ((inf X) Y)) ((F X) Y)))))) of role axiom named fact_44_local_Oinf__unique
% 0.49/0.69 A new axiom: (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) X3))->((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) Y4))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq X3) Y4)->(((less_eq X3) Z3)->((less_eq X3) ((F Y4) Z3)))))->(((eq a) ((inf X) Y)) ((F X) Y))))))
% 0.49/0.69 FOF formula (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))) of role axiom named fact_45_mem__Collect__eq
% 0.49/0.69 A new axiom: (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A)))
% 0.49/0.69 FOF formula (forall (A3:set_a), (((eq set_a) (collect_a (fun (X2:a)=> ((member_a X2) A3)))) A3)) of role axiom named fact_46_Collect__mem__eq
% 0.49/0.69 A new axiom: (forall (A3:set_a), (((eq set_a) (collect_a (fun (X2:a)=> ((member_a X2) A3)))) A3))
% 0.49/0.69 FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), (((eq Prop) (P X3)) (Q X3)))->(((eq set_a) (collect_a P)) (collect_a Q)))) of role axiom named fact_47_Collect__cong
% 0.49/0.69 A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), (((eq Prop) (P X3)) (Q X3)))->(((eq set_a) (collect_a P)) (collect_a Q))))
% 0.49/0.69 FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X))) of role axiom named fact_48_local_Ole__iff__inf
% 0.49/0.69 A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X)))
% 0.49/0.69 FOF formula (forall (X:a) (A:a) (B:a), (((less_eq X) ((inf A) B))->((((less_eq X) A)->(((less_eq X) B)->False))->False))) of role axiom named fact_49_local_Ole__infE
% 0.49/0.69 A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) ((inf A) B))->((((less_eq X) A)->(((less_eq X) B)->False))->False)))
% 0.49/0.69 FOF formula (forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B))))) of role axiom named fact_50_local_Ole__infI
% 0.49/0.69 A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B)))))
% 0.49/0.69 FOF formula (forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X))) of role axiom named fact_51_local_Ole__infI1
% 0.49/0.69 A new axiom: (forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X)))
% 0.49/0.69 FOF formula (forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X))) of role axiom named fact_52_local_Ole__infI2
% 0.49/0.71 A new axiom: (forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X)))
% 0.49/0.71 FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y))) of role axiom named fact_53_local_Ole__iff__sup
% 0.49/0.71 A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y)))
% 0.49/0.71 FOF formula (forall (A:a) (B:a) (X:a), (((less_eq ((sup A) B)) X)->((((less_eq A) X)->(((less_eq B) X)->False))->False))) of role axiom named fact_54_local_Ole__supE
% 0.49/0.71 A new axiom: (forall (A:a) (B:a) (X:a), (((less_eq ((sup A) B)) X)->((((less_eq A) X)->(((less_eq B) X)->False))->False)))
% 0.49/0.71 FOF formula (forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X)))) of role axiom named fact_55_local_Ole__supI
% 0.49/0.71 A new axiom: (forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X))))
% 0.49/0.71 FOF formula (forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B)))) of role axiom named fact_56_local_Ole__supI1
% 0.49/0.71 A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B))))
% 0.49/0.71 FOF formula (forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B)))) of role axiom named fact_57_local_Ole__supI2
% 0.49/0.71 A new axiom: (forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B))))
% 0.49/0.71 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A))) of role axiom named fact_58_local_Osup_Oabsorb1
% 0.49/0.71 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A)))
% 0.49/0.71 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B))) of role axiom named fact_59_local_Osup_Oabsorb2
% 0.49/0.71 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B)))
% 0.49/0.71 FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A))) of role axiom named fact_60_local_Osup_Oabsorb__iff1
% 0.49/0.71 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A)))
% 0.49/0.71 FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B))) of role axiom named fact_61_local_Osup_Oabsorb__iff2
% 0.49/0.71 A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B)))
% 0.49/0.71 FOF formula (forall (B:a) (C:a) (A:a), (((less_eq ((sup B) C)) A)->((((less_eq B) A)->(((less_eq C) A)->False))->False))) of role axiom named fact_62_local_Osup_OboundedE
% 0.49/0.71 A new axiom: (forall (B:a) (C:a) (A:a), (((less_eq ((sup B) C)) A)->((((less_eq B) A)->(((less_eq C) A)->False))->False)))
% 0.49/0.71 FOF formula (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A)))) of role axiom named fact_63_local_Osup_OboundedI
% 0.49/0.71 A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A))))
% 0.49/0.71 FOF formula (forall (A:a) (B:a), ((less_eq A) ((sup A) B))) of role axiom named fact_64_local_Osup_Ocobounded1
% 0.49/0.71 A new axiom: (forall (A:a) (B:a), ((less_eq A) ((sup A) B)))
% 0.49/0.71 FOF formula (forall (B:a) (A:a), ((less_eq B) ((sup A) B))) of role axiom named fact_65_local_Osup_Ocobounded2
% 0.49/0.71 A new axiom: (forall (B:a) (A:a), ((less_eq B) ((sup A) B)))
% 0.49/0.71 FOF formula (forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B)))) of role axiom named fact_66_local_Osup_OcoboundedI1
% 0.49/0.71 A new axiom: (forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B))))
% 0.49/0.71 FOF formula (forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B)))) of role axiom named fact_67_local_Osup_OcoboundedI2
% 0.49/0.71 A new axiom: (forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B))))
% 0.49/0.71 FOF formula (forall (C:a) (A:a) (D:a) (B:a), (((less_eq C) A)->(((less_eq D) B)->((less_eq ((sup C) D)) ((sup A) B))))) of role axiom named fact_68_local_Osup_Omono
% 0.49/0.71 A new axiom: (forall (C:a) (A:a) (D:a) (B:a), (((less_eq C) A)->(((less_eq D) B)->((less_eq ((sup C) D)) ((sup A) B)))))
% 0.49/0.71 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B)))) of role axiom named fact_69_local_Osup_OorderE
% 0.49/0.71 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B))))
% 0.49/0.71 FOF formula (forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A))) of role axiom named fact_70_local_Osup_OorderI
% 0.56/0.73 A new axiom: (forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A)))
% 0.56/0.73 FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B)))) of role axiom named fact_71_local_Osup_Oorder__iff
% 0.56/0.73 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B))))
% 0.56/0.73 FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X))) of role axiom named fact_72_local_Osup__absorb1
% 0.56/0.73 A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X)))
% 0.56/0.73 FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y))) of role axiom named fact_73_local_Osup__absorb2
% 0.56/0.73 A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y)))
% 0.56/0.73 FOF formula (forall (X:a) (Y:a), ((less_eq X) ((sup X) Y))) of role axiom named fact_74_local_Osup__ge1
% 0.56/0.73 A new axiom: (forall (X:a) (Y:a), ((less_eq X) ((sup X) Y)))
% 0.56/0.73 FOF formula (forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y))) of role axiom named fact_75_local_Osup__ge2
% 0.56/0.73 A new axiom: (forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y)))
% 0.56/0.73 FOF formula (forall (Y:a) (X:a) (Z2:a), (((less_eq Y) X)->(((less_eq Z2) X)->((less_eq ((sup Y) Z2)) X)))) of role axiom named fact_76_local_Osup__least
% 0.56/0.73 A new axiom: (forall (Y:a) (X:a) (Z2:a), (((less_eq Y) X)->(((less_eq Z2) X)->((less_eq ((sup Y) Z2)) X))))
% 0.56/0.73 FOF formula (forall (A:a) (C:a) (B:a) (D:a), (((less_eq A) C)->(((less_eq B) D)->((less_eq ((sup A) B)) ((sup C) D))))) of role axiom named fact_77_local_Osup__mono
% 0.56/0.73 A new axiom: (forall (A:a) (C:a) (B:a) (D:a), (((less_eq A) C)->(((less_eq B) D)->((less_eq ((sup A) B)) ((sup C) D)))))
% 0.56/0.73 FOF formula (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq X3) ((F X3) Y4)))->((forall (X3:a) (Y4:a), ((less_eq Y4) ((F X3) Y4)))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq Y4) X3)->(((less_eq Z3) X3)->((less_eq ((F Y4) Z3)) X3))))->(((eq a) ((sup X) Y)) ((F X) Y)))))) of role axiom named fact_78_local_Osup__unique
% 0.56/0.73 A new axiom: (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq X3) ((F X3) Y4)))->((forall (X3:a) (Y4:a), ((less_eq Y4) ((F X3) Y4)))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq Y4) X3)->(((less_eq Z3) X3)->((less_eq ((F Y4) Z3)) X3))))->(((eq a) ((sup X) Y)) ((F X) Y))))))
% 0.56/0.73 FOF formula (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((inf X3) ((sup Y4) Z3))) ((sup ((inf X3) Y4)) ((inf X3) Z3))))->(((eq a) ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2))))) of role axiom named fact_79_local_Odistrib__imp1
% 0.56/0.73 A new axiom: (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((inf X3) ((sup Y4) Z3))) ((sup ((inf X3) Y4)) ((inf X3) Z3))))->(((eq a) ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2)))))
% 0.56/0.73 FOF formula (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((sup X3) ((inf Y4) Z3))) ((inf ((sup X3) Y4)) ((sup X3) Z3))))->(((eq a) ((inf X) ((sup Y) Z2))) ((sup ((inf X) Y)) ((inf X) Z2))))) of role axiom named fact_80_local_Odistrib__imp2
% 0.56/0.73 A new axiom: (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((sup X3) ((inf Y4) Z3))) ((inf ((sup X3) Y4)) ((sup X3) Z3))))->(((eq a) ((inf X) ((sup Y) Z2))) ((sup ((inf X) Y)) ((inf X) Z2)))))
% 0.56/0.73 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((sup A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup A) ((inf B) C)))) of role axiom named fact_81_local_Oa__join__d
% 0.56/0.73 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((sup A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup A) ((inf B) C))))
% 0.56/0.73 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf A) B)) ((inf C) A)))) of role axiom named fact_82_a__meet__d
% 0.56/0.73 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf A) B)) ((inf C) A))))
% 0.56/0.73 FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup B) ((inf C) A)))) of role axiom named fact_83_local_Ob__join__d
% 0.56/0.73 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup B) ((inf C) A))))
% 0.56/0.75 FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf B) C)) ((inf A) B)))) of role axiom named fact_84_b__meet__d
% 0.56/0.75 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf B) C)) ((inf A) B))))
% 0.56/0.75 FOF formula (forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf C) A)) ((inf B) C)))) of role axiom named fact_85_c__meet__d
% 0.56/0.75 A new axiom: (forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf C) A)) ((inf B) C))))
% 0.56/0.75 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1936294176_aux_a inf) sup) A) B) C)) ((sup ((sup ((inf A) B)) ((inf B) C))) ((inf C) A)))) of role axiom named fact_86_local_Od__aux__def
% 0.56/0.75 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1936294176_aux_a inf) sup) A) B) C)) ((sup ((sup ((inf A) B)) ((inf B) C))) ((inf C) A))))
% 0.56/0.75 FOF formula (forall (B:a) (C:a) (A:a), (((eq a) (((((modula1936294176_aux_a inf) sup) B) C) A)) (((((modula1936294176_aux_a inf) sup) A) B) C))) of role axiom named fact_87_local_Od__b__c__a
% 0.56/0.75 A new axiom: (forall (B:a) (C:a) (A:a), (((eq a) (((((modula1936294176_aux_a inf) sup) B) C) A)) (((((modula1936294176_aux_a inf) sup) A) B) C)))
% 0.56/0.75 FOF formula (forall (C:a) (A:a) (B:a), (((eq a) (((((modula1936294176_aux_a inf) sup) C) A) B)) (((((modula1936294176_aux_a inf) sup) A) B) C))) of role axiom named fact_88_local_Od__c__a__b
% 0.56/0.75 A new axiom: (forall (C:a) (A:a) (B:a), (((eq a) (((((modula1936294176_aux_a inf) sup) C) A) B)) (((((modula1936294176_aux_a inf) sup) A) B) C)))
% 0.56/0.75 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf A) ((sup B) C)))) of role axiom named fact_89_local_Oa__meet__e
% 0.56/0.75 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf A) ((sup B) C))))
% 0.56/0.75 FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf B) ((sup C) A)))) of role axiom named fact_90_local_Ob__meet__e
% 0.56/0.75 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf B) ((sup C) A))))
% 0.56/0.75 FOF formula (forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf C) ((sup A) B)))) of role axiom named fact_91_local_Oc__meet__e
% 0.56/0.75 A new axiom: (forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf C) ((sup A) B))))
% 0.56/0.75 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1144073633_aux_a inf) sup) A) B) C)) ((inf ((inf ((sup A) B)) ((sup B) C))) ((sup C) A)))) of role axiom named fact_92_local_Oe__aux__def
% 0.56/0.75 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1144073633_aux_a inf) sup) A) B) C)) ((inf ((inf ((sup A) B)) ((sup B) C))) ((sup C) A))))
% 0.56/0.75 FOF formula (forall (B:a) (C:a) (A:a), (((eq a) (((((modula1144073633_aux_a inf) sup) B) C) A)) (((((modula1144073633_aux_a inf) sup) A) B) C))) of role axiom named fact_93_local_Oe__b__c__a
% 0.56/0.75 A new axiom: (forall (B:a) (C:a) (A:a), (((eq a) (((((modula1144073633_aux_a inf) sup) B) C) A)) (((((modula1144073633_aux_a inf) sup) A) B) C)))
% 0.56/0.75 FOF formula (forall (C:a) (A:a) (B:a), (((eq a) (((((modula1144073633_aux_a inf) sup) C) A) B)) (((((modula1144073633_aux_a inf) sup) A) B) C))) of role axiom named fact_94_local_Oe__c__a__b
% 0.56/0.75 A new axiom: (forall (C:a) (A:a) (B:a), (((eq a) (((((modula1144073633_aux_a inf) sup) C) A) B)) (((((modula1144073633_aux_a inf) sup) A) B) C)))
% 0.56/0.75 FOF formula (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z2))) ((inf X) ((sup Y) Z2)))) of role axiom named fact_95_local_Odistrib__inf__le
% 0.56/0.75 A new axiom: (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z2))) ((inf X) ((sup Y) Z2))))
% 0.56/0.75 FOF formula (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2)))) of role axiom named fact_96_local_Odistrib__sup__le
% 0.60/0.76 A new axiom: (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2))))
% 0.60/0.76 FOF formula (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((eq a) ((sup X) ((inf Y) Z2))) ((inf Y) ((sup X) Z2))))) of role axiom named fact_97_local_Omodular
% 0.60/0.76 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((eq a) ((sup X) ((inf Y) Z2))) ((inf Y) ((sup X) Z2)))))
% 0.60/0.76 FOF formula (forall (X:a) (Y:a), (((eq Prop) (((modula1727524044comp_a less_eq) X) Y)) ((and (((less_eq X) Y)->False)) (((less_eq Y) X)->False)))) of role axiom named fact_98_local_Oincomp__def
% 0.60/0.76 A new axiom: (forall (X:a) (Y:a), (((eq Prop) (((modula1727524044comp_a less_eq) X) Y)) ((and (((less_eq X) Y)->False)) (((less_eq Y) X)->False))))
% 0.60/0.76 FOF formula (forall (A:a), ((less_eq A) A)) of role axiom named fact_99_local_Oorder_Orefl
% 0.60/0.76 A new axiom: (forall (A:a), ((less_eq A) A))
% 0.60/0.76 FOF formula (forall (X:a), ((less_eq X) X)) of role axiom named fact_100_local_Oorder__refl
% 0.60/0.76 A new axiom: (forall (X:a), ((less_eq X) X))
% 0.60/0.76 FOF formula (forall (A:a), (((eq a) ((inf A) A)) A)) of role axiom named fact_101_local_Oinf_Oidem
% 0.60/0.76 A new axiom: (forall (A:a), (((eq a) ((inf A) A)) A))
% 0.60/0.76 FOF formula (forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B))) of role axiom named fact_102_local_Oinf_Oleft__idem
% 0.60/0.76 A new axiom: (forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B)))
% 0.60/0.76 FOF formula (forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B))) of role axiom named fact_103_local_Oinf_Oright__idem
% 0.60/0.76 A new axiom: (forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B)))
% 0.60/0.76 FOF formula (forall (X:a), (((eq a) ((inf X) X)) X)) of role axiom named fact_104_local_Oinf__idem
% 0.60/0.76 A new axiom: (forall (X:a), (((eq a) ((inf X) X)) X))
% 0.60/0.76 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y))) of role axiom named fact_105_local_Oinf__left__idem
% 0.60/0.76 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y)))
% 0.60/0.76 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y))) of role axiom named fact_106_local_Oinf__right__idem
% 0.60/0.76 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y)))
% 0.60/0.76 FOF formula (forall (A:a), (((eq a) ((sup A) A)) A)) of role axiom named fact_107_local_Osup_Oidem
% 0.60/0.76 A new axiom: (forall (A:a), (((eq a) ((sup A) A)) A))
% 0.60/0.76 FOF formula (forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B))) of role axiom named fact_108_local_Osup_Oleft__idem
% 0.60/0.76 A new axiom: (forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B)))
% 0.60/0.76 FOF formula (forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B))) of role axiom named fact_109_local_Osup_Oright__idem
% 0.60/0.76 A new axiom: (forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B)))
% 0.60/0.76 FOF formula (forall (X:a), (((eq a) ((sup X) X)) X)) of role axiom named fact_110_local_Osup__idem
% 0.60/0.76 A new axiom: (forall (X:a), (((eq a) ((sup X) X)) X))
% 0.60/0.76 FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y))) of role axiom named fact_111_local_Osup__left__idem
% 0.60/0.76 A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y)))
% 0.60/0.76 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) C) A) B))) of role axiom named fact_112_local_Oc__a
% 0.60/0.76 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) C) A) B)))
% 0.60/0.76 FOF formula (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X3)))->(Q X3))))->(Q ((greatest_a less_eq) P)))))) of role axiom named fact_113_local_OGreatestI2__order
% 0.60/0.76 A new axiom: (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X3)))->(Q X3))))->(Q ((greatest_a less_eq) P))))))
% 0.60/0.76 FOF formula (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->(((eq a) ((greatest_a less_eq) P)) X)))) of role axiom named fact_114_local_OGreatest__equality
% 0.60/0.78 A new axiom: (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->(((eq a) ((greatest_a less_eq) P)) X))))
% 0.60/0.78 FOF formula (forall (A:a) (B:a), ((and (((less_eq A) B)->(((eq a) (((max_a less_eq) A) B)) B))) ((((less_eq A) B)->False)->(((eq a) (((max_a less_eq) A) B)) A)))) of role axiom named fact_115_local_Omax__def
% 0.60/0.78 A new axiom: (forall (A:a) (B:a), ((and (((less_eq A) B)->(((eq a) (((max_a less_eq) A) B)) B))) ((((less_eq A) B)->False)->(((eq a) (((max_a less_eq) A) B)) A))))
% 0.60/0.78 FOF formula (forall (A:a) (B:a), ((and (((less_eq A) B)->(((eq a) (((min_a less_eq) A) B)) A))) ((((less_eq A) B)->False)->(((eq a) (((min_a less_eq) A) B)) B)))) of role axiom named fact_116_local_Omin__def
% 0.60/0.78 A new axiom: (forall (A:a) (B:a), ((and (((less_eq A) B)->(((eq a) (((min_a less_eq) A) B)) A))) ((((less_eq A) B)->False)->(((eq a) (((min_a less_eq) A) B)) B))))
% 0.60/0.78 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula17988509_aux_a inf) sup) A) B) C)) ((sup ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_117_local_Oa__aux__def
% 0.60/0.78 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula17988509_aux_a inf) sup) A) B) C)) ((sup ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.60/0.78 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) ((sup ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_118_local_Oc__aux__def
% 0.60/0.78 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) ((sup ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.60/0.78 FOF formula (forall (A:a) (B:a) (C:a), (((eq Prop) ((less_eq A) ((inf B) C))) ((and ((less_eq A) B)) ((less_eq A) C)))) of role axiom named fact_119_local_Oinf_Obounded__iff
% 0.60/0.78 A new axiom: (forall (A:a) (B:a) (C:a), (((eq Prop) ((less_eq A) ((inf B) C))) ((and ((less_eq A) B)) ((less_eq A) C))))
% 0.60/0.78 FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq X) ((inf Y) Z2))) ((and ((less_eq X) Y)) ((less_eq X) Z2)))) of role axiom named fact_120_local_Ole__inf__iff
% 0.60/0.78 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq X) ((inf Y) Z2))) ((and ((less_eq X) Y)) ((less_eq X) Z2))))
% 0.60/0.78 FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq ((sup X) Y)) Z2)) ((and ((less_eq X) Z2)) ((less_eq Y) Z2)))) of role axiom named fact_121_local_Ole__sup__iff
% 0.60/0.78 A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq ((sup X) Y)) Z2)) ((and ((less_eq X) Z2)) ((less_eq Y) Z2))))
% 0.60/0.78 FOF formula (forall (B:a) (C:a) (A:a), (((eq Prop) ((less_eq ((sup B) C)) A)) ((and ((less_eq B) A)) ((less_eq C) A)))) of role axiom named fact_122_local_Osup_Obounded__iff
% 0.60/0.78 A new axiom: (forall (B:a) (C:a) (A:a), (((eq Prop) ((less_eq ((sup B) C)) A)) ((and ((less_eq B) A)) ((less_eq C) A))))
% 0.60/0.78 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X)) of role axiom named fact_123_local_Oinf__sup__absorb
% 0.60/0.78 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X))
% 0.60/0.78 FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X)) of role axiom named fact_124_local_Osup__inf__absorb
% 0.60/0.78 A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X))
% 0.60/0.78 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) B) C) A))) of role axiom named fact_125_local_Ob__a
% 0.60/0.78 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) B) C) A)))
% 0.60/0.78 FOF formula (forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->(P ((least_a less_eq) P)))) of role axiom named fact_126_local_OLeast1I
% 0.60/0.78 A new axiom: (forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->(P ((least_a less_eq) P))))
% 0.60/0.79 FOF formula (forall (P:(a->Prop)) (Z2:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->((P Z2)->((less_eq ((least_a less_eq) P)) Z2)))) of role axiom named fact_127_local_OLeast1__le
% 0.60/0.79 A new axiom: (forall (P:(a->Prop)) (Z2:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->((P Z2)->((less_eq ((least_a less_eq) P)) Z2))))
% 0.60/0.79 FOF formula (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq X3) Y5)))->(Q X3))))->(Q ((least_a less_eq) P)))))) of role axiom named fact_128_local_OLeastI2__order
% 0.60/0.79 A new axiom: (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq X3) Y5)))->(Q X3))))->(Q ((least_a less_eq) P))))))
% 0.60/0.79 FOF formula (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->(((eq a) ((least_a less_eq) P)) X)))) of role axiom named fact_129_local_OLeast__equality
% 0.60/0.79 A new axiom: (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->(((eq a) ((least_a less_eq) P)) X))))
% 0.60/0.79 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) ((sup ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_130_local_Ob__aux__def
% 0.60/0.79 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) ((sup ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.60/0.79 FOF formula (forall (A:a) (B:a) (C:a), (((less_eq (((((modula1936294176_aux_a inf) sup) A) B) C)) (((((modula1144073633_aux_a inf) sup) A) B) C))->(((eq a) ((inf (((((modula17988509_aux_a inf) sup) A) B) C)) (((((modula1373251614_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_131_a__meet__b__eq__d
% 0.60/0.79 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq (((((modula1936294176_aux_a inf) sup) A) B) C)) (((((modula1144073633_aux_a inf) sup) A) B) C))->(((eq a) ((inf (((((modula17988509_aux_a inf) sup) A) B) C)) (((((modula1373251614_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.60/0.79 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula17988509_aux_a) modula17988509_aux_a) of role axiom named fact_132_lattice_Oa__aux_Ocong
% 0.60/0.79 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula17988509_aux_a) modula17988509_aux_a)
% 0.60/0.79 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula581031071_aux_a) modula581031071_aux_a) of role axiom named fact_133_lattice_Oc__aux_Ocong
% 0.60/0.79 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula581031071_aux_a) modula581031071_aux_a)
% 0.60/0.79 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a) of role axiom named fact_134_lattice_Od__aux_Ocong
% 0.60/0.79 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a)
% 0.60/0.79 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a) of role axiom named fact_135_lattice_Oe__aux_Ocong
% 0.60/0.79 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a)
% 0.60/0.79 FOF formula (finite40241356em_a_a sup) of role axiom named fact_136_local_Ocomp__fun__idem__sup
% 0.60/0.79 A new axiom: (finite40241356em_a_a sup)
% 0.60/0.79 FOF formula (finite40241356em_a_a inf) of role axiom named fact_137_local_Ocomp__fun__idem__inf
% 0.60/0.80 A new axiom: (finite40241356em_a_a inf)
% 0.60/0.80 FOF formula (semigroup_a sup) of role axiom named fact_138_local_Osup_Osemigroup__axioms
% 0.60/0.80 A new axiom: (semigroup_a sup)
% 0.60/0.80 FOF formula (semigroup_a inf) of role axiom named fact_139_local_Oinf_Osemigroup__axioms
% 0.60/0.80 A new axiom: (semigroup_a inf)
% 0.60/0.80 FOF formula (semilattice_a sup) of role axiom named fact_140_local_Osup_Osemilattice__axioms
% 0.60/0.80 A new axiom: (semilattice_a sup)
% 0.60/0.80 FOF formula (semilattice_a inf) of role axiom named fact_141_local_Oinf_Osemilattice__axioms
% 0.60/0.80 A new axiom: (semilattice_a inf)
% 0.60/0.80 FOF formula (abel_semigroup_a sup) of role axiom named fact_142_local_Osup_Oabel__semigroup__axioms
% 0.60/0.80 A new axiom: (abel_semigroup_a sup)
% 0.60/0.80 FOF formula (abel_semigroup_a inf) of role axiom named fact_143_local_Oinf_Oabel__semigroup__axioms
% 0.60/0.80 A new axiom: (abel_semigroup_a inf)
% 0.60/0.80 FOF formula (lattic1885654924_set_a sup) of role axiom named fact_144_local_OSup__fin_Osemilattice__set__axioms
% 0.60/0.80 A new axiom: (lattic1885654924_set_a sup)
% 0.60/0.80 FOF formula (lattic1885654924_set_a inf) of role axiom named fact_145_local_OInf__fin_Osemilattice__set__axioms
% 0.60/0.80 A new axiom: (lattic1885654924_set_a inf)
% 0.60/0.80 FOF formula (forall (A3:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A3)) ((ex a) (fun (M:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq X2) M))))))) of role axiom named fact_146_local_Obdd__above__def
% 0.60/0.80 A new axiom: (forall (A3:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A3)) ((ex a) (fun (M:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq X2) M)))))))
% 0.60/0.80 FOF formula (forall (A3:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A3)) ((ex a) (fun (M2:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq M2) X2))))))) of role axiom named fact_147_local_Obdd__below__def
% 0.60/0.80 A new axiom: (forall (A3:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A3)) ((ex a) (fun (M2:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq M2) X2)))))))
% 0.60/0.80 FOF formula (forall (A3:set_a) (M3:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq M3) X3)))->((condit1001553558elow_a less_eq) A3))) of role axiom named fact_148_local_Obdd__belowI
% 0.60/0.80 A new axiom: (forall (A3:set_a) (M3:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq M3) X3)))->((condit1001553558elow_a less_eq) A3)))
% 0.60/0.80 FOF formula (forall (A3:set_a) (M4:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq X3) M4)))->((condit1627435690bove_a less_eq) A3))) of role axiom named fact_149_local_Obdd__aboveI
% 0.60/0.80 A new axiom: (forall (A3:set_a) (M4:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq X3) M4)))->((condit1627435690bove_a less_eq) A3)))
% 0.60/0.80 FOF formula (((eq ((a->(a->Prop))->(a->(a->Prop)))) modula1727524044comp_a) modula1727524044comp_a) of role axiom named fact_150_lattice_Oincomp_Ocong
% 0.60/0.80 A new axiom: (((eq ((a->(a->Prop))->(a->(a->Prop)))) modula1727524044comp_a) modula1727524044comp_a)
% 0.60/0.80 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1373251614_aux_a) modula1373251614_aux_a) of role axiom named fact_151_lattice_Ob__aux_Ocong
% 0.60/0.80 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1373251614_aux_a) modula1373251614_aux_a)
% 0.60/0.80 FOF formula (forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F))) of role axiom named fact_152_abel__semigroup_Oaxioms_I1_J
% 0.60/0.80 A new axiom: (forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F)))
% 0.60/0.80 FOF formula (((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a) of role axiom named fact_153_semilattice__set__def
% 0.60/0.80 A new axiom: (((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a)
% 0.60/0.80 FOF formula (forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F))) of role axiom named fact_154_semilattice__set_Ointro
% 0.60/0.80 A new axiom: (forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F)))
% 0.60/0.80 FOF formula (forall (F:(a->(a->a))) (B:a) (A:a) (C:a), ((abel_semigroup_a F)->(((eq a) ((F B) ((F A) C))) ((F A) ((F B) C))))) of role axiom named fact_155_abel__semigroup_Oleft__commute
% 0.60/0.80 A new axiom: (forall (F:(a->(a->a))) (B:a) (A:a) (C:a), ((abel_semigroup_a F)->(((eq a) ((F B) ((F A) C))) ((F A) ((F B) C)))))
% 0.60/0.80 FOF formula (forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A)))) of role axiom named fact_156_abel__semigroup_Ocommute
% 0.60/0.82 A new axiom: (forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A))))
% 0.60/0.82 FOF formula (forall (F:(a->(a->a))), ((forall (A4:a) (B3:a) (C2:a), (((eq a) ((F ((F A4) B3)) C2)) ((F A4) ((F B3) C2))))->(semigroup_a F))) of role axiom named fact_157_semigroup_Ointro
% 0.60/0.82 A new axiom: (forall (F:(a->(a->a))), ((forall (A4:a) (B3:a) (C2:a), (((eq a) ((F ((F A4) B3)) C2)) ((F A4) ((F B3) C2))))->(semigroup_a F)))
% 0.60/0.82 FOF formula (forall (F:(a->(a->a))) (A:a) (B:a) (C:a), ((semigroup_a F)->(((eq a) ((F ((F A) B)) C)) ((F A) ((F B) C))))) of role axiom named fact_158_semigroup_Oassoc
% 0.60/0.82 A new axiom: (forall (F:(a->(a->a))) (A:a) (B:a) (C:a), ((semigroup_a F)->(((eq a) ((F ((F A) B)) C)) ((F A) ((F B) C)))))
% 0.60/0.82 FOF formula (((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A2:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A2) B2)) C3)) ((F2 A2) ((F2 B2) C3)))))) of role axiom named fact_159_semigroup__def
% 0.60/0.82 A new axiom: (((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A2:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A2) B2)) C3)) ((F2 A2) ((F2 B2) C3))))))
% 0.60/0.82 FOF formula (forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F))) of role axiom named fact_160_semilattice__set_Oaxioms
% 0.60/0.82 A new axiom: (forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F)))
% 0.60/0.82 FOF formula (forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F))) of role axiom named fact_161_semilattice_Oaxioms_I1_J
% 0.60/0.82 A new axiom: (forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F)))
% 0.60/0.82 FOF formula (forall (B4:set_a) (A3:set_a), (((condit1627435690bove_a less_eq) B4)->(((ord_less_eq_set_a A3) B4)->((condit1627435690bove_a less_eq) A3)))) of role axiom named fact_162_local_Obdd__above__mono
% 0.60/0.82 A new axiom: (forall (B4:set_a) (A3:set_a), (((condit1627435690bove_a less_eq) B4)->(((ord_less_eq_set_a A3) B4)->((condit1627435690bove_a less_eq) A3))))
% 0.60/0.82 FOF formula (forall (B4:set_a) (A3:set_a), (((condit1001553558elow_a less_eq) B4)->(((ord_less_eq_set_a A3) B4)->((condit1001553558elow_a less_eq) A3)))) of role axiom named fact_163_local_Obdd__below__mono
% 0.60/0.82 A new axiom: (forall (B4:set_a) (A3:set_a), (((condit1001553558elow_a less_eq) B4)->(((ord_less_eq_set_a A3) B4)->((condit1001553558elow_a less_eq) A3))))
% 0.60/0.82 FOF formula (forall (F:(a->set_a)), (((eq Prop) ((antimono_a_set_a less_eq) F)) (forall (X2:a) (Y3:a), (((less_eq X2) Y3)->((ord_less_eq_set_a (F Y3)) (F X2)))))) of role axiom named fact_164_local_Oantimono__def
% 0.60/0.82 A new axiom: (forall (F:(a->set_a)), (((eq Prop) ((antimono_a_set_a less_eq) F)) (forall (X2:a) (Y3:a), (((less_eq X2) Y3)->((ord_less_eq_set_a (F Y3)) (F X2))))))
% 0.60/0.82 FOF formula (forall (F:(a->set_a)), ((forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F Y4)) (F X3))))->((antimono_a_set_a less_eq) F))) of role axiom named fact_165_local_OantimonoI
% 0.60/0.82 A new axiom: (forall (F:(a->set_a)), ((forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F Y4)) (F X3))))->((antimono_a_set_a less_eq) F)))
% 0.60/0.82 FOF formula (forall (F:(a->set_a)) (X:a) (Y:a), (((antimono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F Y)) (F X))))) of role axiom named fact_166_local_OantimonoE
% 0.60/0.82 A new axiom: (forall (F:(a->set_a)) (X:a) (Y:a), (((antimono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F Y)) (F X)))))
% 0.60/0.82 FOF formula (forall (F:(a->set_a)) (X:a) (Y:a), (((antimono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F Y)) (F X))))) of role axiom named fact_167_local_OantimonoD
% 0.60/0.82 A new axiom: (forall (F:(a->set_a)) (X:a) (Y:a), (((antimono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F Y)) (F X)))))
% 0.60/0.82 FOF formula (forall (F:(a->set_a)) (X:a) (Y:a), (((mono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F X)) (F Y))))) of role axiom named fact_168_local_OmonoD
% 0.60/0.82 A new axiom: (forall (F:(a->set_a)) (X:a) (Y:a), (((mono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F X)) (F Y)))))
% 0.60/0.82 FOF formula (forall (F:(a->set_a)) (X:a) (Y:a), (((mono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F X)) (F Y))))) of role axiom named fact_169_local_OmonoE
% 0.60/0.83 A new axiom: (forall (F:(a->set_a)) (X:a) (Y:a), (((mono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F X)) (F Y)))))
% 0.60/0.83 FOF formula (forall (F:(a->set_a)), ((forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((mono_a_set_a less_eq) F))) of role axiom named fact_170_local_OmonoI
% 0.60/0.83 A new axiom: (forall (F:(a->set_a)), ((forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((mono_a_set_a less_eq) F)))
% 0.60/0.83 FOF formula (forall (F:(a->set_a)), (((eq Prop) ((mono_a_set_a less_eq) F)) (forall (X2:a) (Y3:a), (((less_eq X2) Y3)->((ord_less_eq_set_a (F X2)) (F Y3)))))) of role axiom named fact_171_local_Omono__def
% 0.60/0.83 A new axiom: (forall (F:(a->set_a)), (((eq Prop) ((mono_a_set_a less_eq) F)) (forall (X2:a) (Y3:a), (((less_eq X2) Y3)->((ord_less_eq_set_a (F X2)) (F Y3))))))
% 0.60/0.83 FOF formula (forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A))) of role axiom named fact_172_semilattice_Oidem
% 0.60/0.83 A new axiom: (forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A)))
% 0.60/0.83 FOF formula (forall (F:(a->(a->a))) (A:a) (B:a), ((semilattice_a F)->(((eq a) ((F A) ((F A) B))) ((F A) B)))) of role axiom named fact_173_semilattice_Oleft__idem
% 0.60/0.83 A new axiom: (forall (F:(a->(a->a))) (A:a) (B:a), ((semilattice_a F)->(((eq a) ((F A) ((F A) B))) ((F A) B))))
% 0.60/0.83 FOF formula (forall (F:(a->(a->a))) (A:a) (B:a), ((semilattice_a F)->(((eq a) ((F ((F A) B)) B)) ((F A) B)))) of role axiom named fact_174_semilattice_Oright__idem
% 0.60/0.83 A new axiom: (forall (F:(a->(a->a))) (A:a) (B:a), ((semilattice_a F)->(((eq a) ((F ((F A) B)) B)) ((F A) B))))
% 0.60/0.83 FOF formula (forall (A3:set_a) (B4:set_a), ((forall (X3:a), (((member_a X3) A3)->((member_a X3) B4)))->((ord_less_eq_set_a A3) B4))) of role axiom named fact_175_subsetI
% 0.60/0.83 A new axiom: (forall (A3:set_a) (B4:set_a), ((forall (X3:a), (((member_a X3) A3)->((member_a X3) B4)))->((ord_less_eq_set_a A3) B4)))
% 0.60/0.83 FOF formula (forall (A3:set_a) (B4:set_a), (((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) A3)->(((eq set_a) A3) B4)))) of role axiom named fact_176_subset__antisym
% 0.60/0.83 A new axiom: (forall (A3:set_a) (B4:set_a), (((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) A3)->(((eq set_a) A3) B4))))
% 0.60/0.83 FOF formula (forall (X:set_a), ((ord_less_eq_set_a X) X)) of role axiom named fact_177_preorder__class_Oorder__refl
% 0.60/0.83 A new axiom: (forall (X:set_a), ((ord_less_eq_set_a X) X))
% 0.60/0.83 FOF formula (((eq ((a->(a->Prop))->((a->set_a)->Prop))) antimono_a_set_a) antimono_a_set_a) of role axiom named fact_178_order_Oantimono_Ocong
% 0.60/0.83 A new axiom: (((eq ((a->(a->Prop))->((a->set_a)->Prop))) antimono_a_set_a) antimono_a_set_a)
% 0.60/0.83 FOF formula (((eq ((a->(a->Prop))->((a->set_a)->Prop))) mono_a_set_a) mono_a_set_a) of role axiom named fact_179_order_Omono_Ocong
% 0.60/0.83 A new axiom: (((eq ((a->(a->Prop))->((a->set_a)->Prop))) mono_a_set_a) mono_a_set_a)
% 0.60/0.83 FOF formula (forall (B:set_a) (A:set_a), (((ord_less_eq_set_a B) A)->(((ord_less_eq_set_a A) B)->(((eq set_a) A) B)))) of role axiom named fact_180_order__class_Odual__order_Oantisym
% 0.60/0.83 A new axiom: (forall (B:set_a) (A:set_a), (((ord_less_eq_set_a B) A)->(((ord_less_eq_set_a A) B)->(((eq set_a) A) B))))
% 0.60/0.83 FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A2:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a B2) A2)) ((ord_less_eq_set_a A2) B2)))) of role axiom named fact_181_order__class_Odual__order_Oeq__iff
% 0.60/0.83 A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A2:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a B2) A2)) ((ord_less_eq_set_a A2) B2))))
% 0.60/0.83 FOF formula (forall (B:set_a) (A:set_a) (C:set_a), (((ord_less_eq_set_a B) A)->(((ord_less_eq_set_a C) B)->((ord_less_eq_set_a C) A)))) of role axiom named fact_182_order__class_Odual__order_Otrans
% 0.60/0.83 A new axiom: (forall (B:set_a) (A:set_a) (C:set_a), (((ord_less_eq_set_a B) A)->(((ord_less_eq_set_a C) B)->((ord_less_eq_set_a C) A))))
% 0.60/0.83 FOF formula (forall (A:set_a), ((ord_less_eq_set_a A) A)) of role axiom named fact_183_order__class_Odual__order_Orefl
% 0.67/0.84 A new axiom: (forall (A:set_a), ((ord_less_eq_set_a A) A))
% 0.67/0.84 FOF formula (forall (X:set_a) (Y:set_a) (Z2:set_a), (((ord_less_eq_set_a X) Y)->(((ord_less_eq_set_a Y) Z2)->((ord_less_eq_set_a X) Z2)))) of role axiom named fact_184_preorder__class_Oorder__trans
% 0.67/0.84 A new axiom: (forall (X:set_a) (Y:set_a) (Z2:set_a), (((ord_less_eq_set_a X) Y)->(((ord_less_eq_set_a Y) Z2)->((ord_less_eq_set_a X) Z2))))
% 0.67/0.84 FOF formula (forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->(((eq set_a) A) B)))) of role axiom named fact_185_order__class_Oorder_Oantisym
% 0.67/0.84 A new axiom: (forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->(((eq set_a) A) B))))
% 0.67/0.84 FOF formula (forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->((((eq set_a) B) C)->((ord_less_eq_set_a A) C)))) of role axiom named fact_186_ord__class_Oord__le__eq__trans
% 0.67/0.84 A new axiom: (forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->((((eq set_a) B) C)->((ord_less_eq_set_a A) C))))
% 0.67/0.84 FOF formula (forall (A:set_a) (B:set_a) (C:set_a), ((((eq set_a) A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C)))) of role axiom named fact_187_ord__class_Oord__eq__le__trans
% 0.67/0.84 A new axiom: (forall (A:set_a) (B:set_a) (C:set_a), ((((eq set_a) A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C))))
% 0.67/0.84 FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A2:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a A2) B2)) ((ord_less_eq_set_a B2) A2)))) of role axiom named fact_188_order__class_Oorder_Oeq__iff
% 0.67/0.84 A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A2:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a A2) B2)) ((ord_less_eq_set_a B2) A2))))
% 0.67/0.84 FOF formula (forall (Y:set_a) (X:set_a), (((ord_less_eq_set_a Y) X)->(((eq Prop) ((ord_less_eq_set_a X) Y)) (((eq set_a) X) Y)))) of role axiom named fact_189_order__class_Oantisym__conv
% 0.67/0.84 A new axiom: (forall (Y:set_a) (X:set_a), (((ord_less_eq_set_a Y) X)->(((eq Prop) ((ord_less_eq_set_a X) Y)) (((eq set_a) X) Y))))
% 0.67/0.84 FOF formula (forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C)))) of role axiom named fact_190_order__class_Oorder_Otrans
% 0.67/0.84 A new axiom: (forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C))))
% 0.67/0.84 FOF formula (forall (X:set_a) (Y:set_a), ((((eq set_a) X) Y)->((ord_less_eq_set_a X) Y))) of role axiom named fact_191_preorder__class_Oeq__refl
% 0.67/0.84 A new axiom: (forall (X:set_a) (Y:set_a), ((((eq set_a) X) Y)->((ord_less_eq_set_a X) Y)))
% 0.67/0.84 FOF formula (forall (X:set_a) (Y:set_a), (((ord_less_eq_set_a X) Y)->(((ord_less_eq_set_a Y) X)->(((eq set_a) X) Y)))) of role axiom named fact_192_order__class_Oantisym
% 0.67/0.84 A new axiom: (forall (X:set_a) (Y:set_a), (((ord_less_eq_set_a X) Y)->(((ord_less_eq_set_a Y) X)->(((eq set_a) X) Y))))
% 0.67/0.84 FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (X2:set_a) (Y3:set_a)=> ((and ((ord_less_eq_set_a X2) Y3)) ((ord_less_eq_set_a Y3) X2)))) of role axiom named fact_193_order__class_Oeq__iff
% 0.67/0.84 A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (X2:set_a) (Y3:set_a)=> ((and ((ord_less_eq_set_a X2) Y3)) ((ord_less_eq_set_a Y3) X2))))
% 0.67/0.84 FOF formula (forall (A:set_a) (B:set_a) (F:(set_a->set_a)) (C:set_a), (((ord_less_eq_set_a A) B)->((((eq set_a) (F B)) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a (F A)) C))))) of role axiom named fact_194_ord__le__eq__subst
% 0.67/0.84 A new axiom: (forall (A:set_a) (B:set_a) (F:(set_a->set_a)) (C:set_a), (((ord_less_eq_set_a A) B)->((((eq set_a) (F B)) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a (F A)) C)))))
% 0.67/0.84 FOF formula (forall (A:set_a) (F:(set_a->set_a)) (B:set_a) (C:set_a), ((((eq set_a) A) (F B))->(((ord_less_eq_set_a B) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a A) (F C)))))) of role axiom named fact_195_ord__eq__le__subst
% 0.67/0.85 A new axiom: (forall (A:set_a) (F:(set_a->set_a)) (B:set_a) (C:set_a), ((((eq set_a) A) (F B))->(((ord_less_eq_set_a B) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a A) (F C))))))
% 0.67/0.85 FOF formula (forall (A:set_a) (B:set_a) (F:(set_a->set_a)) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a (F B)) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a (F A)) C))))) of role axiom named fact_196_order__subst2
% 0.67/0.85 A new axiom: (forall (A:set_a) (B:set_a) (F:(set_a->set_a)) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a (F B)) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a (F A)) C)))))
% 0.67/0.85 FOF formula (forall (A:set_a) (F:(set_a->set_a)) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) (F B))->(((ord_less_eq_set_a B) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a A) (F C)))))) of role axiom named fact_197_order__subst1
% 0.67/0.85 A new axiom: (forall (A:set_a) (F:(set_a->set_a)) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) (F B))->(((ord_less_eq_set_a B) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a A) (F C))))))
% 0.67/0.85 FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X2:a), ((P X2)->(Q X2))))) of role axiom named fact_198_Collect__mono__iff
% 0.67/0.85 A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X2:a), ((P X2)->(Q X2)))))
% 0.67/0.85 FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A5:set_a) (B5:set_a)=> ((and ((ord_less_eq_set_a A5) B5)) ((ord_less_eq_set_a B5) A5)))) of role axiom named fact_199_set__eq__subset
% 0.67/0.85 A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A5:set_a) (B5:set_a)=> ((and ((ord_less_eq_set_a A5) B5)) ((ord_less_eq_set_a B5) A5))))
% 0.67/0.85 FOF formula (forall (A3:set_a) (B4:set_a) (C4:set_a), (((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) C4)->((ord_less_eq_set_a A3) C4)))) of role axiom named fact_200_subset__trans
% 0.67/0.85 A new axiom: (forall (A3:set_a) (B4:set_a) (C4:set_a), (((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) C4)->((ord_less_eq_set_a A3) C4))))
% 0.67/0.85 FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), ((P X3)->(Q X3)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q)))) of role axiom named fact_201_Collect__mono
% 0.67/0.85 A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), ((P X3)->(Q X3)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q))))
% 0.67/0.85 FOF formula (forall (A3:set_a), ((ord_less_eq_set_a A3) A3)) of role axiom named fact_202_subset__refl
% 0.67/0.85 A new axiom: (forall (A3:set_a), ((ord_less_eq_set_a A3) A3))
% 0.67/0.85 FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B5:set_a)=> (forall (T:a), (((member_a T) A5)->((member_a T) B5))))) of role axiom named fact_203_subset__iff
% 0.67/0.85 A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B5:set_a)=> (forall (T:a), (((member_a T) A5)->((member_a T) B5)))))
% 0.67/0.85 FOF formula (forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((ord_less_eq_set_a B4) A3))) of role axiom named fact_204_equalityD2
% 0.67/0.85 A new axiom: (forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((ord_less_eq_set_a B4) A3)))
% 0.67/0.85 FOF formula (forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((ord_less_eq_set_a A3) B4))) of role axiom named fact_205_equalityD1
% 0.67/0.85 A new axiom: (forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((ord_less_eq_set_a A3) B4)))
% 0.67/0.85 FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B5:set_a)=> (forall (X2:a), (((member_a X2) A5)->((member_a X2) B5))))) of role axiom named fact_206_subset__eq
% 0.67/0.86 A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B5:set_a)=> (forall (X2:a), (((member_a X2) A5)->((member_a X2) B5)))))
% 0.67/0.86 FOF formula (forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) A3)->False))->False))) of role axiom named fact_207_equalityE
% 0.67/0.86 A new axiom: (forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) A3)->False))->False)))
% 0.67/0.86 FOF formula (forall (A3:set_a) (B4:set_a) (C:a), (((ord_less_eq_set_a A3) B4)->(((member_a C) A3)->((member_a C) B4)))) of role axiom named fact_208_subsetD
% 0.67/0.86 A new axiom: (forall (A3:set_a) (B4:set_a) (C:a), (((ord_less_eq_set_a A3) B4)->(((member_a C) A3)->((member_a C) B4))))
% 0.67/0.86 FOF formula (forall (A3:set_a) (B4:set_a) (X:a), (((ord_less_eq_set_a A3) B4)->(((member_a X) A3)->((member_a X) B4)))) of role axiom named fact_209_in__mono
% 0.67/0.86 A new axiom: (forall (A3:set_a) (B4:set_a) (X:a), (((ord_less_eq_set_a A3) B4)->(((member_a X) A3)->((member_a X) B4))))
% 0.67/0.86 FOF formula (((eq ((a->(a->Prop))->((a->Prop)->a))) least_a) least_a) of role axiom named fact_210_ord_OLeast_Ocong
% 0.67/0.86 A new axiom: (((eq ((a->(a->Prop))->((a->Prop)->a))) least_a) least_a)
% 0.67/0.86 FOF formula (((eq ((a->(a->Prop))->((a->Prop)->a))) greatest_a) greatest_a) of role axiom named fact_211_order_OGreatest_Ocong
% 0.67/0.86 A new axiom: (((eq ((a->(a->Prop))->((a->Prop)->a))) greatest_a) greatest_a)
% 0.67/0.86 FOF formula (((eq ((a->(a->Prop))->(a->(a->a)))) min_a) min_a) of role axiom named fact_212_ord_Omin_Ocong
% 0.67/0.86 A new axiom: (((eq ((a->(a->Prop))->(a->(a->a)))) min_a) min_a)
% 0.67/0.86 FOF formula (((eq ((a->(a->Prop))->(a->(a->a)))) max_a) max_a) of role axiom named fact_213_ord_Omax_Ocong
% 0.67/0.86 A new axiom: (((eq ((a->(a->Prop))->(a->(a->a)))) max_a) max_a)
% 0.67/0.86 FOF formula (((eq ((a->(a->Prop))->(a->(a->a)))) min_a) (fun (Less_eq:(a->(a->Prop))) (A2:a) (B2:a)=> (((if_a ((Less_eq A2) B2)) A2) B2))) of role axiom named fact_214_ord_Omin__def
% 0.67/0.86 A new axiom: (((eq ((a->(a->Prop))->(a->(a->a)))) min_a) (fun (Less_eq:(a->(a->Prop))) (A2:a) (B2:a)=> (((if_a ((Less_eq A2) B2)) A2) B2)))
% 0.67/0.86 FOF formula (((eq ((a->(a->Prop))->(a->(a->a)))) max_a) (fun (Less_eq:(a->(a->Prop))) (A2:a) (B2:a)=> (((if_a ((Less_eq A2) B2)) B2) A2))) of role axiom named fact_215_ord_Omax__def
% 0.67/0.86 A new axiom: (((eq ((a->(a->Prop))->(a->(a->a)))) max_a) (fun (Less_eq:(a->(a->Prop))) (A2:a) (B2:a)=> (((if_a ((Less_eq A2) B2)) B2) A2)))
% 0.67/0.86 FOF formula (forall (F:(a->set_a)) (A3:a) (B4:a), (((mono_a_set_a less_eq) F)->((ord_less_eq_set_a (F ((inf A3) B4))) ((inf_inf_set_a (F A3)) (F B4))))) of role axiom named fact_216_local_Omono__inf
% 0.67/0.86 A new axiom: (forall (F:(a->set_a)) (A3:a) (B4:a), (((mono_a_set_a less_eq) F)->((ord_less_eq_set_a (F ((inf A3) B4))) ((inf_inf_set_a (F A3)) (F B4)))))
% 0.67/0.86 FOF formula (forall (F:(a->set_a)) (A3:a) (B4:a), (((mono_a_set_a less_eq) F)->((ord_less_eq_set_a ((sup_sup_set_a (F A3)) (F B4))) (F ((sup A3) B4))))) of role axiom named fact_217_local_Omono__sup
% 0.67/0.86 A new axiom: (forall (F:(a->set_a)) (A3:a) (B4:a), (((mono_a_set_a less_eq) F)->((ord_less_eq_set_a ((sup_sup_set_a (F A3)) (F B4))) (F ((sup A3) B4)))))
% 0.67/0.86 FOF formula (forall (A3:set_a), ((finite_finite_a A3)->((condit1627435690bove_a less_eq) A3))) of role axiom named fact_218_local_Obdd__above__finite
% 0.67/0.86 A new axiom: (forall (A3:set_a), ((finite_finite_a A3)->((condit1627435690bove_a less_eq) A3)))
% 0.67/0.86 FOF formula (forall (A3:set_a) (A:a), ((finite_finite_a A3)->(((member_a A) A3)->((ex a) (fun (X3:a)=> ((and ((and ((member_a X3) A3)) ((less_eq X3) A))) (forall (Xa:a), (((member_a Xa) A3)->(((less_eq Xa) X3)->(((eq a) X3) Xa)))))))))) of role axiom named fact_219_local_Ofinite__has__minimal2
% 0.67/0.86 A new axiom: (forall (A3:set_a) (A:a), ((finite_finite_a A3)->(((member_a A) A3)->((ex a) (fun (X3:a)=> ((and ((and ((member_a X3) A3)) ((less_eq X3) A))) (forall (Xa:a), (((member_a Xa) A3)->(((less_eq Xa) X3)->(((eq a) X3) Xa))))))))))
% 0.67/0.86 FOF formula (forall (A3:set_a) (A:a), ((finite_finite_a A3)->(((member_a A) A3)->((ex a) (fun (X3:a)=> ((and ((and ((member_a X3) A3)) ((less_eq A) X3))) (forall (Xa:a), (((member_a Xa) A3)->(((less_eq X3) Xa)->(((eq a) X3) Xa)))))))))) of role axiom named fact_220_local_Ofinite__has__maximal2
% 0.67/0.87 A new axiom: (forall (A3:set_a) (A:a), ((finite_finite_a A3)->(((member_a A) A3)->((ex a) (fun (X3:a)=> ((and ((and ((member_a X3) A3)) ((less_eq A) X3))) (forall (Xa:a), (((member_a Xa) A3)->(((less_eq X3) Xa)->(((eq a) X3) Xa))))))))))
% 0.67/0.87 FOF formula (forall (B4:set_a) (A3:set_a), (((condit1001553558elow_a less_eq) B4)->((condit1001553558elow_a less_eq) ((inf_inf_set_a A3) B4)))) of role axiom named fact_221_local_Obdd__below__Int2
% 0.67/0.87 A new axiom: (forall (B4:set_a) (A3:set_a), (((condit1001553558elow_a less_eq) B4)->((condit1001553558elow_a less_eq) ((inf_inf_set_a A3) B4))))
% 0.67/0.87 FOF formula (forall (A3:set_a) (B4:set_a), (((condit1001553558elow_a less_eq) A3)->((condit1001553558elow_a less_eq) ((inf_inf_set_a A3) B4)))) of role axiom named fact_222_local_Obdd__below__Int1
% 0.67/0.87 A new axiom: (forall (A3:set_a) (B4:set_a), (((condit1001553558elow_a less_eq) A3)->((condit1001553558elow_a less_eq) ((inf_inf_set_a A3) B4))))
% 0.67/0.87 FOF formula (forall (B4:set_a) (A3:set_a), (((condit1627435690bove_a less_eq) B4)->((condit1627435690bove_a less_eq) ((inf_inf_set_a A3) B4)))) of role axiom named fact_223_local_Obdd__above__Int2
% 0.67/0.87 A new axiom: (forall (B4:set_a) (A3:set_a), (((condit1627435690bove_a less_eq) B4)->((condit1627435690bove_a less_eq) ((inf_inf_set_a A3) B4))))
% 0.67/0.87 FOF formula (forall (A3:set_a) (B4:set_a), (((condit1627435690bove_a less_eq) A3)->((condit1627435690bove_a less_eq) ((inf_inf_set_a A3) B4)))) of role axiom named fact_224_local_Obdd__above__Int1
% 0.67/0.87 A new axiom: (forall (A3:set_a) (B4:set_a), (((condit1627435690bove_a less_eq) A3)->((condit1627435690bove_a less_eq) ((inf_inf_set_a A3) B4))))
% 0.67/0.87 FOF formula (forall (A3:set_a), ((finite_finite_a A3)->((condit1001553558elow_a less_eq) A3))) of role axiom named fact_225_local_Obdd__below__finite
% 0.67/0.87 A new axiom: (forall (A3:set_a), ((finite_finite_a A3)->((condit1001553558elow_a less_eq) A3)))
% 0.67/0.87 FOF formula (forall (A3:set_a) (B4:set_a) (C4:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a A3) B4)) C4)) ((and ((ord_less_eq_set_a A3) C4)) ((ord_less_eq_set_a B4) C4)))) of role axiom named fact_226_Un__subset__iff
% 0.67/0.87 A new axiom: (forall (A3:set_a) (B4:set_a) (C4:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a A3) B4)) C4)) ((and ((ord_less_eq_set_a A3) C4)) ((ord_less_eq_set_a B4) C4))))
% 0.67/0.87 FOF formula (forall (C4:set_a) (A3:set_a) (B4:set_a), (((eq Prop) ((ord_less_eq_set_a C4) ((inf_inf_set_a A3) B4))) ((and ((ord_less_eq_set_a C4) A3)) ((ord_less_eq_set_a C4) B4)))) of role axiom named fact_227_Int__subset__iff
% 0.67/0.87 A new axiom: (forall (C4:set_a) (A3:set_a) (B4:set_a), (((eq Prop) ((ord_less_eq_set_a C4) ((inf_inf_set_a A3) B4))) ((and ((ord_less_eq_set_a C4) A3)) ((ord_less_eq_set_a C4) B4))))
% 0.67/0.87 FOF formula (forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a ((inf_inf_set_a X) Y)) Y)) ((inf_inf_set_a X) Y))) of role axiom named fact_228_semilattice__inf__class_Oinf__right__idem
% 0.67/0.87 A new axiom: (forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a ((inf_inf_set_a X) Y)) Y)) ((inf_inf_set_a X) Y)))
% 0.67/0.87 FOF formula (forall (A:set_a) (B:set_a), (((eq set_a) ((inf_inf_set_a ((inf_inf_set_a A) B)) B)) ((inf_inf_set_a A) B))) of role axiom named fact_229_semilattice__inf__class_Oinf_Oright__idem
% 0.67/0.87 A new axiom: (forall (A:set_a) (B:set_a), (((eq set_a) ((inf_inf_set_a ((inf_inf_set_a A) B)) B)) ((inf_inf_set_a A) B)))
% 0.67/0.87 FOF formula (forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a X) ((inf_inf_set_a X) Y))) ((inf_inf_set_a X) Y))) of role axiom named fact_230_semilattice__inf__class_Oinf__left__idem
% 0.67/0.87 A new axiom: (forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a X) ((inf_inf_set_a X) Y))) ((inf_inf_set_a X) Y)))
% 0.67/0.87 FOF formula (forall (A:set_a) (B:set_a), (((eq set_a) ((inf_inf_set_a A) ((inf_inf_set_a A) B))) ((inf_inf_set_a A) B))) of role axiom named fact_231_semilattice__inf__class_Oinf_Oleft__idem
% 0.67/0.87 A new axiom: (forall (A:set_a) (B:set_a), (((eq set_a) ((inf_inf_set_a A) ((inf_inf_set_a A) B))) ((inf_inf_set_a A) B)))
% 0.70/0.88 FOF formula (forall (X:set_a), (((eq set_a) ((inf_inf_set_a X) X)) X)) of role axiom named fact_232_semilattice__inf__class_Oinf__idem
% 0.70/0.88 A new axiom: (forall (X:set_a), (((eq set_a) ((inf_inf_set_a X) X)) X))
% 0.70/0.88 FOF formula (forall (A:set_a), (((eq set_a) ((inf_inf_set_a A) A)) A)) of role axiom named fact_233_semilattice__inf__class_Oinf_Oidem
% 0.70/0.88 A new axiom: (forall (A:set_a), (((eq set_a) ((inf_inf_set_a A) A)) A))
% 0.70/0.88 FOF formula (forall (A:set_a) (B:set_a), (((eq set_a) ((sup_sup_set_a ((sup_sup_set_a A) B)) B)) ((sup_sup_set_a A) B))) of role axiom named fact_234_semilattice__sup__class_Osup_Oright__idem
% 0.70/0.88 A new axiom: (forall (A:set_a) (B:set_a), (((eq set_a) ((sup_sup_set_a ((sup_sup_set_a A) B)) B)) ((sup_sup_set_a A) B)))
% 0.70/0.88 FOF formula (forall (X:set_a) (Y:set_a), (((eq set_a) ((sup_sup_set_a X) ((sup_sup_set_a X) Y))) ((sup_sup_set_a X) Y))) of role axiom named fact_235_semilattice__sup__class_Osup__left__idem
% 0.70/0.88 A new axiom: (forall (X:set_a) (Y:set_a), (((eq set_a) ((sup_sup_set_a X) ((sup_sup_set_a X) Y))) ((sup_sup_set_a X) Y)))
% 0.70/0.88 FOF formula (forall (A:set_a) (B:set_a), (((eq set_a) ((sup_sup_set_a A) ((sup_sup_set_a A) B))) ((sup_sup_set_a A) B))) of role axiom named fact_236_semilattice__sup__class_Osup_Oleft__idem
% 0.70/0.88 A new axiom: (forall (A:set_a) (B:set_a), (((eq set_a) ((sup_sup_set_a A) ((sup_sup_set_a A) B))) ((sup_sup_set_a A) B)))
% 0.70/0.88 FOF formula (forall (X:set_a), (((eq set_a) ((sup_sup_set_a X) X)) X)) of role axiom named fact_237_semilattice__sup__class_Osup__idem
% 0.70/0.88 A new axiom: (forall (X:set_a), (((eq set_a) ((sup_sup_set_a X) X)) X))
% 0.70/0.88 FOF formula (forall (A:set_a), (((eq set_a) ((sup_sup_set_a A) A)) A)) of role axiom named fact_238_semilattice__sup__class_Osup_Oidem
% 0.70/0.88 A new axiom: (forall (A:set_a), (((eq set_a) ((sup_sup_set_a A) A)) A))
% 0.70/0.88 FOF formula (forall (X:set_a) (Y:set_a) (Z2:set_a), (((eq Prop) ((ord_less_eq_set_a X) ((inf_inf_set_a Y) Z2))) ((and ((ord_less_eq_set_a X) Y)) ((ord_less_eq_set_a X) Z2)))) of role axiom named fact_239_semilattice__inf__class_Ole__inf__iff
% 0.70/0.88 A new axiom: (forall (X:set_a) (Y:set_a) (Z2:set_a), (((eq Prop) ((ord_less_eq_set_a X) ((inf_inf_set_a Y) Z2))) ((and ((ord_less_eq_set_a X) Y)) ((ord_less_eq_set_a X) Z2))))
% 0.70/0.88 FOF formula (forall (A:set_a) (B:set_a) (C:set_a), (((eq Prop) ((ord_less_eq_set_a A) ((inf_inf_set_a B) C))) ((and ((ord_less_eq_set_a A) B)) ((ord_less_eq_set_a A) C)))) of role axiom named fact_240_semilattice__inf__class_Oinf_Obounded__iff
% 0.70/0.88 A new axiom: (forall (A:set_a) (B:set_a) (C:set_a), (((eq Prop) ((ord_less_eq_set_a A) ((inf_inf_set_a B) C))) ((and ((ord_less_eq_set_a A) B)) ((ord_less_eq_set_a A) C))))
% 0.70/0.88 FOF formula (forall (X:set_a) (Y:set_a) (Z2:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a X) Y)) Z2)) ((and ((ord_less_eq_set_a X) Z2)) ((ord_less_eq_set_a Y) Z2)))) of role axiom named fact_241_semilattice__sup__class_Ole__sup__iff
% 0.70/0.88 A new axiom: (forall (X:set_a) (Y:set_a) (Z2:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a X) Y)) Z2)) ((and ((ord_less_eq_set_a X) Z2)) ((ord_less_eq_set_a Y) Z2))))
% 0.70/0.88 FOF formula (forall (B:set_a) (C:set_a) (A:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a B) C)) A)) ((and ((ord_less_eq_set_a B) A)) ((ord_less_eq_set_a C) A)))) of role axiom named fact_242_semilattice__sup__class_Osup_Obounded__iff
% 0.70/0.88 A new axiom: (forall (B:set_a) (C:set_a) (A:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a B) C)) A)) ((and ((ord_less_eq_set_a B) A)) ((ord_less_eq_set_a C) A))))
% 0.70/0.88 FOF formula (forall (X:set_a) (Y:set_a), (((eq set_a) ((sup_sup_set_a X) ((inf_inf_set_a X) Y))) X)) of role axiom named fact_243_lattice__class_Osup__inf__absorb
% 0.70/0.88 A new axiom: (forall (X:set_a) (Y:set_a), (((eq set_a) ((sup_sup_set_a X) ((inf_inf_set_a X) Y))) X))
% 0.70/0.88 FOF formula (forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a X) ((sup_sup_set_a X) Y))) X)) of role axiom named fact_244_lattice__class_Oinf__sup__absorb
% 0.70/0.88 A new axiom: (forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a X) ((sup_sup_set_a X) Y))) X))
% 0.70/0.88 FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_001tf__a_T
% 0.70/0.88 A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% 0.70/0.88 FOF formula (forall (X:a) (Y:a), (((eq a) (((if_a False) X) Y)) Y)) of role axiom named help_If_2_1_If_001tf__a_T
% 0.70/0.88 A new axiom: (forall (X:a) (Y:a), (((eq a) (((if_a False) X) Y)) Y))
% 0.70/0.88 FOF formula (forall (X:a) (Y:a), (((eq a) (((if_a True) X) Y)) X)) of role axiom named help_If_1_1_If_001tf__a_T
% 0.70/0.88 A new axiom: (forall (X:a) (Y:a), (((eq a) (((if_a True) X) Y)) X))
% 0.70/0.88 FOF formula ((less_eq (((((modula1936294176_aux_a inf) sup) a2) b) c)) (((((modula1144073633_aux_a inf) sup) a2) b) c)) of role hypothesis named conj_0
% 0.70/0.88 A new axiom: ((less_eq (((((modula1936294176_aux_a inf) sup) a2) b) c)) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 0.70/0.88 FOF formula (((eq a) ((inf (((((modula17988509_aux_a inf) sup) b) c) a2)) (((((modula581031071_aux_a inf) sup) a2) b) c))) (((((modula1936294176_aux_a inf) sup) a2) b) c)) of role conjecture named conj_1
% 0.70/0.88 Conjecture to prove = (((eq a) ((inf (((((modula17988509_aux_a inf) sup) b) c) a2)) (((((modula581031071_aux_a inf) sup) a2) b) c))) (((((modula1936294176_aux_a inf) sup) a2) b) c)):Prop
% 0.70/0.88 Parameter set_a_DUMMY:set_a.
% 0.70/0.88 We need to prove ['(((eq a) ((inf (((((modula17988509_aux_a inf) sup) b) c) a2)) (((((modula581031071_aux_a inf) sup) a2) b) c))) (((((modula1936294176_aux_a inf) sup) a2) b) c))']
% 0.70/0.88 Parameter set_a:Type.
% 0.70/0.88 Parameter a:Type.
% 0.70/0.88 Parameter condit1627435690bove_a:((a->(a->Prop))->(set_a->Prop)).
% 0.70/0.88 Parameter condit1001553558elow_a:((a->(a->Prop))->(set_a->Prop)).
% 0.70/0.88 Parameter finite40241356em_a_a:((a->(a->a))->Prop).
% 0.70/0.88 Parameter finite_finite_a:(set_a->Prop).
% 0.70/0.88 Parameter abel_semigroup_a:((a->(a->a))->Prop).
% 0.70/0.88 Parameter semigroup_a:((a->(a->a))->Prop).
% 0.70/0.88 Parameter if_a:(Prop->(a->(a->a))).
% 0.70/0.88 Parameter inf_inf_set_a:(set_a->(set_a->set_a)).
% 0.70/0.88 Parameter semilattice_a:((a->(a->a))->Prop).
% 0.70/0.88 Parameter sup_sup_set_a:(set_a->(set_a->set_a)).
% 0.70/0.88 Parameter lattic1885654924_set_a:((a->(a->a))->Prop).
% 0.70/0.88 Parameter modula17988509_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.70/0.88 Parameter modula1373251614_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.70/0.88 Parameter modula581031071_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.70/0.88 Parameter modula1936294176_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.70/0.88 Parameter modula1144073633_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.70/0.88 Parameter modula1727524044comp_a:((a->(a->Prop))->(a->(a->Prop))).
% 0.70/0.88 Parameter least_a:((a->(a->Prop))->((a->Prop)->a)).
% 0.70/0.88 Parameter max_a:((a->(a->Prop))->(a->(a->a))).
% 0.70/0.88 Parameter min_a:((a->(a->Prop))->(a->(a->a))).
% 0.70/0.88 Parameter ord_less_eq_set_a:(set_a->(set_a->Prop)).
% 0.70/0.88 Parameter greatest_a:((a->(a->Prop))->((a->Prop)->a)).
% 0.70/0.88 Parameter antimono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop)).
% 0.70/0.88 Parameter mono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop)).
% 0.70/0.88 Parameter collect_a:((a->Prop)->set_a).
% 0.70/0.88 Parameter member_a:(a->(set_a->Prop)).
% 0.70/0.88 Parameter a2:a.
% 0.70/0.88 Parameter b:a.
% 0.70/0.88 Parameter c:a.
% 0.70/0.88 Parameter inf:(a->(a->a)).
% 0.70/0.88 Parameter less_eq:(a->(a->Prop)).
% 0.70/0.88 Parameter sup:(a->(a->a)).
% 0.70/0.88 Axiom fact_0_local_Oantisym:(forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y)))).
% 0.70/0.88 Axiom fact_1_local_Oantisym__conv:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))).
% 0.70/0.88 Axiom fact_2_local_Odual__order_Oantisym:(forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B)))).
% 0.70/0.88 Axiom fact_3_local_Odual__order_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq B2) A2)) ((less_eq A2) B2)))).
% 0.70/0.88 Axiom fact_4_local_Odual__order_Otrans:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A)))).
% 0.70/0.88 Axiom fact_5_local_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (X2:a) (Y3:a)=> ((and ((less_eq X2) Y3)) ((less_eq Y3) X2)))).
% 0.70/0.88 Axiom fact_6_local_Oeq__refl:(forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y))).
% 0.70/0.88 Axiom fact_7_local_Oord__eq__le__trans:(forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C)))).
% 0.70/0.88 Axiom fact_8_local_Oord__le__eq__trans:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C)))).
% 0.70/0.88 Axiom fact_9_local_Oorder_Oantisym:(forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B)))).
% 0.70/0.88 Axiom fact_10_local_Oorder_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq A2) B2)) ((less_eq B2) A2)))).
% 0.70/0.88 Axiom fact_11_local_Oorder_Otrans:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C)))).
% 0.70/0.88 Axiom fact_12_local_Oorder__trans:(forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq Y) Z2)->((less_eq X) Z2)))).
% 0.70/0.88 Axiom fact_13_local_Oinf_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C)))).
% 0.70/0.88 Axiom fact_14_local_Oinf_Ocommute:(forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A))).
% 0.70/0.88 Axiom fact_15_local_Oinf_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C)))).
% 0.70/0.88 Axiom fact_16_local_Oinf__assoc:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf ((inf X) Y)) Z2)) ((inf X) ((inf Y) Z2)))).
% 0.70/0.88 Axiom fact_17_local_Oinf__commute:(forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X))).
% 0.70/0.88 Axiom fact_18_local_Oinf__left__commute:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf X) ((inf Y) Z2))) ((inf Y) ((inf X) Z2)))).
% 0.70/0.88 Axiom fact_19_local_Osup_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C)))).
% 0.70/0.88 Axiom fact_20_local_Osup_Ocommute:(forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A))).
% 0.70/0.88 Axiom fact_21_local_Osup_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C)))).
% 0.70/0.88 Axiom fact_22_local_Osup__assoc:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup ((sup X) Y)) Z2)) ((sup X) ((sup Y) Z2)))).
% 0.70/0.88 Axiom fact_23_local_Osup__commute:(forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X))).
% 0.70/0.88 Axiom fact_24_local_Osup__left__commute:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup X) ((sup Y) Z2))) ((sup Y) ((sup X) Z2)))).
% 0.70/0.88 Axiom fact_25_local_Oinf_Oabsorb1:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A))).
% 0.70/0.88 Axiom fact_26_local_Oinf_Oabsorb2:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B))).
% 0.70/0.88 Axiom fact_27_local_Oinf_Oabsorb__iff1:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A))).
% 0.70/0.88 Axiom fact_28_local_Oinf_Oabsorb__iff2:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B))).
% 0.70/0.88 Axiom fact_29_local_Oinf_OboundedE:(forall (A:a) (B:a) (C:a), (((less_eq A) ((inf B) C))->((((less_eq A) B)->(((less_eq A) C)->False))->False))).
% 0.70/0.88 Axiom fact_30_local_Oinf_OboundedI:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C))))).
% 0.70/0.88 Axiom fact_31_local_Oinf_Ocobounded1:(forall (A:a) (B:a), ((less_eq ((inf A) B)) A)).
% 0.70/0.88 Axiom fact_32_local_Oinf_Ocobounded2:(forall (A:a) (B:a), ((less_eq ((inf A) B)) B)).
% 0.70/0.88 Axiom fact_33_local_Oinf_OcoboundedI1:(forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C))).
% 0.70/0.88 Axiom fact_34_local_Oinf_OcoboundedI2:(forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C))).
% 0.70/0.88 Axiom fact_35_local_Oinf_OorderE:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B)))).
% 0.70/0.88 Axiom fact_36_local_Oinf_OorderI:(forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B))).
% 0.70/0.88 Axiom fact_37_local_Oinf_Oorder__iff:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B)))).
% 0.70/0.88 Axiom fact_38_local_Oinf__absorb1:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X))).
% 0.70/0.88 Axiom fact_39_local_Oinf__absorb2:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y))).
% 0.70/0.88 Axiom fact_40_local_Oinf__greatest:(forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq X) Z2)->((less_eq X) ((inf Y) Z2))))).
% 0.70/0.88 Axiom fact_41_local_Oinf__le1:(forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X)).
% 0.70/0.88 Axiom fact_42_local_Oinf__le2:(forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y)).
% 0.70/0.88 Axiom fact_43_local_Oinf__mono:(forall (A:a) (C:a) (B:a) (D:a), (((less_eq A) C)->(((less_eq B) D)->((less_eq ((inf A) B)) ((inf C) D))))).
% 0.70/0.88 Axiom fact_44_local_Oinf__unique:(forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) X3))->((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) Y4))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq X3) Y4)->(((less_eq X3) Z3)->((less_eq X3) ((F Y4) Z3)))))->(((eq a) ((inf X) Y)) ((F X) Y)))))).
% 0.70/0.89 Axiom fact_45_mem__Collect__eq:(forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))).
% 0.70/0.89 Axiom fact_46_Collect__mem__eq:(forall (A3:set_a), (((eq set_a) (collect_a (fun (X2:a)=> ((member_a X2) A3)))) A3)).
% 0.70/0.89 Axiom fact_47_Collect__cong:(forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), (((eq Prop) (P X3)) (Q X3)))->(((eq set_a) (collect_a P)) (collect_a Q)))).
% 0.70/0.89 Axiom fact_48_local_Ole__iff__inf:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X))).
% 0.70/0.89 Axiom fact_49_local_Ole__infE:(forall (X:a) (A:a) (B:a), (((less_eq X) ((inf A) B))->((((less_eq X) A)->(((less_eq X) B)->False))->False))).
% 0.70/0.89 Axiom fact_50_local_Ole__infI:(forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B))))).
% 0.70/0.89 Axiom fact_51_local_Ole__infI1:(forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X))).
% 0.70/0.89 Axiom fact_52_local_Ole__infI2:(forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X))).
% 0.70/0.89 Axiom fact_53_local_Ole__iff__sup:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y))).
% 0.70/0.89 Axiom fact_54_local_Ole__supE:(forall (A:a) (B:a) (X:a), (((less_eq ((sup A) B)) X)->((((less_eq A) X)->(((less_eq B) X)->False))->False))).
% 0.70/0.89 Axiom fact_55_local_Ole__supI:(forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X)))).
% 0.70/0.89 Axiom fact_56_local_Ole__supI1:(forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B)))).
% 0.70/0.89 Axiom fact_57_local_Ole__supI2:(forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B)))).
% 0.70/0.89 Axiom fact_58_local_Osup_Oabsorb1:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A))).
% 0.70/0.89 Axiom fact_59_local_Osup_Oabsorb2:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B))).
% 0.70/0.89 Axiom fact_60_local_Osup_Oabsorb__iff1:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A))).
% 0.70/0.89 Axiom fact_61_local_Osup_Oabsorb__iff2:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B))).
% 0.70/0.89 Axiom fact_62_local_Osup_OboundedE:(forall (B:a) (C:a) (A:a), (((less_eq ((sup B) C)) A)->((((less_eq B) A)->(((less_eq C) A)->False))->False))).
% 0.70/0.89 Axiom fact_63_local_Osup_OboundedI:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A)))).
% 0.70/0.89 Axiom fact_64_local_Osup_Ocobounded1:(forall (A:a) (B:a), ((less_eq A) ((sup A) B))).
% 0.70/0.89 Axiom fact_65_local_Osup_Ocobounded2:(forall (B:a) (A:a), ((less_eq B) ((sup A) B))).
% 0.70/0.89 Axiom fact_66_local_Osup_OcoboundedI1:(forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B)))).
% 0.70/0.89 Axiom fact_67_local_Osup_OcoboundedI2:(forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B)))).
% 0.70/0.89 Axiom fact_68_local_Osup_Omono:(forall (C:a) (A:a) (D:a) (B:a), (((less_eq C) A)->(((less_eq D) B)->((less_eq ((sup C) D)) ((sup A) B))))).
% 0.70/0.89 Axiom fact_69_local_Osup_OorderE:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B)))).
% 0.70/0.89 Axiom fact_70_local_Osup_OorderI:(forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A))).
% 0.70/0.89 Axiom fact_71_local_Osup_Oorder__iff:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B)))).
% 0.70/0.89 Axiom fact_72_local_Osup__absorb1:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X))).
% 0.70/0.89 Axiom fact_73_local_Osup__absorb2:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y))).
% 0.70/0.89 Axiom fact_74_local_Osup__ge1:(forall (X:a) (Y:a), ((less_eq X) ((sup X) Y))).
% 0.70/0.89 Axiom fact_75_local_Osup__ge2:(forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y))).
% 0.70/0.89 Axiom fact_76_local_Osup__least:(forall (Y:a) (X:a) (Z2:a), (((less_eq Y) X)->(((less_eq Z2) X)->((less_eq ((sup Y) Z2)) X)))).
% 0.70/0.89 Axiom fact_77_local_Osup__mono:(forall (A:a) (C:a) (B:a) (D:a), (((less_eq A) C)->(((less_eq B) D)->((less_eq ((sup A) B)) ((sup C) D))))).
% 0.70/0.89 Axiom fact_78_local_Osup__unique:(forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq X3) ((F X3) Y4)))->((forall (X3:a) (Y4:a), ((less_eq Y4) ((F X3) Y4)))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq Y4) X3)->(((less_eq Z3) X3)->((less_eq ((F Y4) Z3)) X3))))->(((eq a) ((sup X) Y)) ((F X) Y)))))).
% 0.70/0.89 Axiom fact_79_local_Odistrib__imp1:(forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((inf X3) ((sup Y4) Z3))) ((sup ((inf X3) Y4)) ((inf X3) Z3))))->(((eq a) ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2))))).
% 0.70/0.89 Axiom fact_80_local_Odistrib__imp2:(forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((sup X3) ((inf Y4) Z3))) ((inf ((sup X3) Y4)) ((sup X3) Z3))))->(((eq a) ((inf X) ((sup Y) Z2))) ((sup ((inf X) Y)) ((inf X) Z2))))).
% 0.70/0.89 Axiom fact_81_local_Oa__join__d:(forall (A:a) (B:a) (C:a), (((eq a) ((sup A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup A) ((inf B) C)))).
% 0.70/0.89 Axiom fact_82_a__meet__d:(forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf A) B)) ((inf C) A)))).
% 0.70/0.89 Axiom fact_83_local_Ob__join__d:(forall (B:a) (A:a) (C:a), (((eq a) ((sup B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup B) ((inf C) A)))).
% 0.70/0.89 Axiom fact_84_b__meet__d:(forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf B) C)) ((inf A) B)))).
% 0.70/0.89 Axiom fact_85_c__meet__d:(forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup ((inf C) A)) ((inf B) C)))).
% 0.70/0.89 Axiom fact_86_local_Od__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1936294176_aux_a inf) sup) A) B) C)) ((sup ((sup ((inf A) B)) ((inf B) C))) ((inf C) A)))).
% 0.70/0.89 Axiom fact_87_local_Od__b__c__a:(forall (B:a) (C:a) (A:a), (((eq a) (((((modula1936294176_aux_a inf) sup) B) C) A)) (((((modula1936294176_aux_a inf) sup) A) B) C))).
% 0.70/0.89 Axiom fact_88_local_Od__c__a__b:(forall (C:a) (A:a) (B:a), (((eq a) (((((modula1936294176_aux_a inf) sup) C) A) B)) (((((modula1936294176_aux_a inf) sup) A) B) C))).
% 0.70/0.89 Axiom fact_89_local_Oa__meet__e:(forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf A) ((sup B) C)))).
% 0.70/0.89 Axiom fact_90_local_Ob__meet__e:(forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf B) ((sup C) A)))).
% 0.70/0.89 Axiom fact_91_local_Oc__meet__e:(forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf C) ((sup A) B)))).
% 0.70/0.89 Axiom fact_92_local_Oe__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1144073633_aux_a inf) sup) A) B) C)) ((inf ((inf ((sup A) B)) ((sup B) C))) ((sup C) A)))).
% 0.70/0.89 Axiom fact_93_local_Oe__b__c__a:(forall (B:a) (C:a) (A:a), (((eq a) (((((modula1144073633_aux_a inf) sup) B) C) A)) (((((modula1144073633_aux_a inf) sup) A) B) C))).
% 0.70/0.89 Axiom fact_94_local_Oe__c__a__b:(forall (C:a) (A:a) (B:a), (((eq a) (((((modula1144073633_aux_a inf) sup) C) A) B)) (((((modula1144073633_aux_a inf) sup) A) B) C))).
% 0.70/0.89 Axiom fact_95_local_Odistrib__inf__le:(forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z2))) ((inf X) ((sup Y) Z2)))).
% 0.70/0.89 Axiom fact_96_local_Odistrib__sup__le:(forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2)))).
% 0.70/0.89 Axiom fact_97_local_Omodular:(forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((eq a) ((sup X) ((inf Y) Z2))) ((inf Y) ((sup X) Z2))))).
% 0.70/0.89 Axiom fact_98_local_Oincomp__def:(forall (X:a) (Y:a), (((eq Prop) (((modula1727524044comp_a less_eq) X) Y)) ((and (((less_eq X) Y)->False)) (((less_eq Y) X)->False)))).
% 0.70/0.89 Axiom fact_99_local_Oorder_Orefl:(forall (A:a), ((less_eq A) A)).
% 0.70/0.89 Axiom fact_100_local_Oorder__refl:(forall (X:a), ((less_eq X) X)).
% 0.70/0.89 Axiom fact_101_local_Oinf_Oidem:(forall (A:a), (((eq a) ((inf A) A)) A)).
% 0.70/0.89 Axiom fact_102_local_Oinf_Oleft__idem:(forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B))).
% 0.70/0.89 Axiom fact_103_local_Oinf_Oright__idem:(forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B))).
% 0.70/0.89 Axiom fact_104_local_Oinf__idem:(forall (X:a), (((eq a) ((inf X) X)) X)).
% 0.70/0.89 Axiom fact_105_local_Oinf__left__idem:(forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y))).
% 0.70/0.89 Axiom fact_106_local_Oinf__right__idem:(forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y))).
% 0.70/0.89 Axiom fact_107_local_Osup_Oidem:(forall (A:a), (((eq a) ((sup A) A)) A)).
% 0.70/0.89 Axiom fact_108_local_Osup_Oleft__idem:(forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B))).
% 0.70/0.89 Axiom fact_109_local_Osup_Oright__idem:(forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B))).
% 0.70/0.89 Axiom fact_110_local_Osup__idem:(forall (X:a), (((eq a) ((sup X) X)) X)).
% 0.70/0.89 Axiom fact_111_local_Osup__left__idem:(forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y))).
% 0.70/0.89 Axiom fact_112_local_Oc__a:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) C) A) B))).
% 0.70/0.89 Axiom fact_113_local_OGreatestI2__order:(forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X3)))->(Q X3))))->(Q ((greatest_a less_eq) P)))))).
% 0.70/0.89 Axiom fact_114_local_OGreatest__equality:(forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->(((eq a) ((greatest_a less_eq) P)) X)))).
% 0.70/0.89 Axiom fact_115_local_Omax__def:(forall (A:a) (B:a), ((and (((less_eq A) B)->(((eq a) (((max_a less_eq) A) B)) B))) ((((less_eq A) B)->False)->(((eq a) (((max_a less_eq) A) B)) A)))).
% 0.70/0.89 Axiom fact_116_local_Omin__def:(forall (A:a) (B:a), ((and (((less_eq A) B)->(((eq a) (((min_a less_eq) A) B)) A))) ((((less_eq A) B)->False)->(((eq a) (((min_a less_eq) A) B)) B)))).
% 0.70/0.89 Axiom fact_117_local_Oa__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula17988509_aux_a inf) sup) A) B) C)) ((sup ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.70/0.89 Axiom fact_118_local_Oc__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) ((sup ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.70/0.89 Axiom fact_119_local_Oinf_Obounded__iff:(forall (A:a) (B:a) (C:a), (((eq Prop) ((less_eq A) ((inf B) C))) ((and ((less_eq A) B)) ((less_eq A) C)))).
% 0.70/0.89 Axiom fact_120_local_Ole__inf__iff:(forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq X) ((inf Y) Z2))) ((and ((less_eq X) Y)) ((less_eq X) Z2)))).
% 0.70/0.89 Axiom fact_121_local_Ole__sup__iff:(forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq ((sup X) Y)) Z2)) ((and ((less_eq X) Z2)) ((less_eq Y) Z2)))).
% 0.70/0.89 Axiom fact_122_local_Osup_Obounded__iff:(forall (B:a) (C:a) (A:a), (((eq Prop) ((less_eq ((sup B) C)) A)) ((and ((less_eq B) A)) ((less_eq C) A)))).
% 0.70/0.89 Axiom fact_123_local_Oinf__sup__absorb:(forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X)).
% 0.70/0.89 Axiom fact_124_local_Osup__inf__absorb:(forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X)).
% 0.70/0.89 Axiom fact_125_local_Ob__a:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) B) C) A))).
% 0.70/0.89 Axiom fact_126_local_OLeast1I:(forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->(P ((least_a less_eq) P)))).
% 0.70/0.89 Axiom fact_127_local_OLeast1__le:(forall (P:(a->Prop)) (Z2:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->((P Z2)->((less_eq ((least_a less_eq) P)) Z2)))).
% 0.70/0.89 Axiom fact_128_local_OLeastI2__order:(forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq X3) Y5)))->(Q X3))))->(Q ((least_a less_eq) P)))))).
% 0.70/0.89 Axiom fact_129_local_OLeast__equality:(forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->(((eq a) ((least_a less_eq) P)) X)))).
% 0.70/0.89 Axiom fact_130_local_Ob__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) ((sup ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.70/0.89 Axiom fact_131_a__meet__b__eq__d:(forall (A:a) (B:a) (C:a), (((less_eq (((((modula1936294176_aux_a inf) sup) A) B) C)) (((((modula1144073633_aux_a inf) sup) A) B) C))->(((eq a) ((inf (((((modula17988509_aux_a inf) sup) A) B) C)) (((((modula1373251614_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.70/0.89 Axiom fact_132_lattice_Oa__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula17988509_aux_a) modula17988509_aux_a).
% 0.70/0.89 Axiom fact_133_lattice_Oc__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula581031071_aux_a) modula581031071_aux_a).
% 0.70/0.89 Axiom fact_134_lattice_Od__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a).
% 0.70/0.89 Axiom fact_135_lattice_Oe__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a).
% 0.70/0.89 Axiom fact_136_local_Ocomp__fun__idem__sup:(finite40241356em_a_a sup).
% 0.70/0.89 Axiom fact_137_local_Ocomp__fun__idem__inf:(finite40241356em_a_a inf).
% 0.70/0.89 Axiom fact_138_local_Osup_Osemigroup__axioms:(semigroup_a sup).
% 0.70/0.89 Axiom fact_139_local_Oinf_Osemigroup__axioms:(semigroup_a inf).
% 0.70/0.89 Axiom fact_140_local_Osup_Osemilattice__axioms:(semilattice_a sup).
% 0.70/0.89 Axiom fact_141_local_Oinf_Osemilattice__axioms:(semilattice_a inf).
% 0.70/0.89 Axiom fact_142_local_Osup_Oabel__semigroup__axioms:(abel_semigroup_a sup).
% 0.70/0.89 Axiom fact_143_local_Oinf_Oabel__semigroup__axioms:(abel_semigroup_a inf).
% 0.70/0.89 Axiom fact_144_local_OSup__fin_Osemilattice__set__axioms:(lattic1885654924_set_a sup).
% 0.70/0.89 Axiom fact_145_local_OInf__fin_Osemilattice__set__axioms:(lattic1885654924_set_a inf).
% 0.70/0.89 Axiom fact_146_local_Obdd__above__def:(forall (A3:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A3)) ((ex a) (fun (M:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq X2) M))))))).
% 0.70/0.89 Axiom fact_147_local_Obdd__below__def:(forall (A3:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A3)) ((ex a) (fun (M2:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq M2) X2))))))).
% 0.70/0.89 Axiom fact_148_local_Obdd__belowI:(forall (A3:set_a) (M3:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq M3) X3)))->((condit1001553558elow_a less_eq) A3))).
% 0.70/0.89 Axiom fact_149_local_Obdd__aboveI:(forall (A3:set_a) (M4:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq X3) M4)))->((condit1627435690bove_a less_eq) A3))).
% 0.70/0.89 Axiom fact_150_lattice_Oincomp_Ocong:(((eq ((a->(a->Prop))->(a->(a->Prop)))) modula1727524044comp_a) modula1727524044comp_a).
% 0.70/0.89 Axiom fact_151_lattice_Ob__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1373251614_aux_a) modula1373251614_aux_a).
% 0.70/0.89 Axiom fact_152_abel__semigroup_Oaxioms_I1_J:(forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F))).
% 0.70/0.89 Axiom fact_153_semilattice__set__def:(((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a).
% 0.70/0.89 Axiom fact_154_semilattice__set_Ointro:(forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F))).
% 0.70/0.89 Axiom fact_155_abel__semigroup_Oleft__commute:(forall (F:(a->(a->a))) (B:a) (A:a) (C:a), ((abel_semigroup_a F)->(((eq a) ((F B) ((F A) C))) ((F A) ((F B) C))))).
% 0.70/0.89 Axiom fact_156_abel__semigroup_Ocommute:(forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A)))).
% 0.70/0.89 Axiom fact_157_semigroup_Ointro:(forall (F:(a->(a->a))), ((forall (A4:a) (B3:a) (C2:a), (((eq a) ((F ((F A4) B3)) C2)) ((F A4) ((F B3) C2))))->(semigroup_a F))).
% 0.70/0.89 Axiom fact_158_semigroup_Oassoc:(forall (F:(a->(a->a))) (A:a) (B:a) (C:a), ((semigroup_a F)->(((eq a) ((F ((F A) B)) C)) ((F A) ((F B) C))))).
% 0.70/0.89 Axiom fact_159_semigroup__def:(((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A2:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A2) B2)) C3)) ((F2 A2) ((F2 B2) C3)))))).
% 0.70/0.89 Axiom fact_160_semilattice__set_Oaxioms:(forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F))).
% 0.70/0.89 Axiom fact_161_semilattice_Oaxioms_I1_J:(forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F))).
% 0.70/0.89 Axiom fact_162_local_Obdd__above__mono:(forall (B4:set_a) (A3:set_a), (((condit1627435690bove_a less_eq) B4)->(((ord_less_eq_set_a A3) B4)->((condit1627435690bove_a less_eq) A3)))).
% 0.70/0.89 Axiom fact_163_local_Obdd__below__mono:(forall (B4:set_a) (A3:set_a), (((condit1001553558elow_a less_eq) B4)->(((ord_less_eq_set_a A3) B4)->((condit1001553558elow_a less_eq) A3)))).
% 0.70/0.89 Axiom fact_164_local_Oantimono__def:(forall (F:(a->set_a)), (((eq Prop) ((antimono_a_set_a less_eq) F)) (forall (X2:a) (Y3:a), (((less_eq X2) Y3)->((ord_less_eq_set_a (F Y3)) (F X2)))))).
% 0.70/0.89 Axiom fact_165_local_OantimonoI:(forall (F:(a->set_a)), ((forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F Y4)) (F X3))))->((antimono_a_set_a less_eq) F))).
% 0.70/0.89 Axiom fact_166_local_OantimonoE:(forall (F:(a->set_a)) (X:a) (Y:a), (((antimono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F Y)) (F X))))).
% 0.70/0.89 Axiom fact_167_local_OantimonoD:(forall (F:(a->set_a)) (X:a) (Y:a), (((antimono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F Y)) (F X))))).
% 0.70/0.89 Axiom fact_168_local_OmonoD:(forall (F:(a->set_a)) (X:a) (Y:a), (((mono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F X)) (F Y))))).
% 0.70/0.89 Axiom fact_169_local_OmonoE:(forall (F:(a->set_a)) (X:a) (Y:a), (((mono_a_set_a less_eq) F)->(((less_eq X) Y)->((ord_less_eq_set_a (F X)) (F Y))))).
% 0.70/0.89 Axiom fact_170_local_OmonoI:(forall (F:(a->set_a)), ((forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((mono_a_set_a less_eq) F))).
% 0.70/0.89 Axiom fact_171_local_Omono__def:(forall (F:(a->set_a)), (((eq Prop) ((mono_a_set_a less_eq) F)) (forall (X2:a) (Y3:a), (((less_eq X2) Y3)->((ord_less_eq_set_a (F X2)) (F Y3)))))).
% 0.70/0.89 Axiom fact_172_semilattice_Oidem:(forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A))).
% 0.70/0.89 Axiom fact_173_semilattice_Oleft__idem:(forall (F:(a->(a->a))) (A:a) (B:a), ((semilattice_a F)->(((eq a) ((F A) ((F A) B))) ((F A) B)))).
% 0.70/0.89 Axiom fact_174_semilattice_Oright__idem:(forall (F:(a->(a->a))) (A:a) (B:a), ((semilattice_a F)->(((eq a) ((F ((F A) B)) B)) ((F A) B)))).
% 0.70/0.89 Axiom fact_175_subsetI:(forall (A3:set_a) (B4:set_a), ((forall (X3:a), (((member_a X3) A3)->((member_a X3) B4)))->((ord_less_eq_set_a A3) B4))).
% 0.70/0.89 Axiom fact_176_subset__antisym:(forall (A3:set_a) (B4:set_a), (((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) A3)->(((eq set_a) A3) B4)))).
% 0.70/0.89 Axiom fact_177_preorder__class_Oorder__refl:(forall (X:set_a), ((ord_less_eq_set_a X) X)).
% 0.70/0.89 Axiom fact_178_order_Oantimono_Ocong:(((eq ((a->(a->Prop))->((a->set_a)->Prop))) antimono_a_set_a) antimono_a_set_a).
% 0.70/0.89 Axiom fact_179_order_Omono_Ocong:(((eq ((a->(a->Prop))->((a->set_a)->Prop))) mono_a_set_a) mono_a_set_a).
% 0.70/0.89 Axiom fact_180_order__class_Odual__order_Oantisym:(forall (B:set_a) (A:set_a), (((ord_less_eq_set_a B) A)->(((ord_less_eq_set_a A) B)->(((eq set_a) A) B)))).
% 0.70/0.89 Axiom fact_181_order__class_Odual__order_Oeq__iff:(((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A2:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a B2) A2)) ((ord_less_eq_set_a A2) B2)))).
% 0.70/0.89 Axiom fact_182_order__class_Odual__order_Otrans:(forall (B:set_a) (A:set_a) (C:set_a), (((ord_less_eq_set_a B) A)->(((ord_less_eq_set_a C) B)->((ord_less_eq_set_a C) A)))).
% 0.70/0.89 Axiom fact_183_order__class_Odual__order_Orefl:(forall (A:set_a), ((ord_less_eq_set_a A) A)).
% 0.70/0.89 Axiom fact_184_preorder__class_Oorder__trans:(forall (X:set_a) (Y:set_a) (Z2:set_a), (((ord_less_eq_set_a X) Y)->(((ord_less_eq_set_a Y) Z2)->((ord_less_eq_set_a X) Z2)))).
% 0.70/0.89 Axiom fact_185_order__class_Oorder_Oantisym:(forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->(((eq set_a) A) B)))).
% 0.70/0.89 Axiom fact_186_ord__class_Oord__le__eq__trans:(forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->((((eq set_a) B) C)->((ord_less_eq_set_a A) C)))).
% 0.70/0.89 Axiom fact_187_ord__class_Oord__eq__le__trans:(forall (A:set_a) (B:set_a) (C:set_a), ((((eq set_a) A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C)))).
% 0.70/0.89 Axiom fact_188_order__class_Oorder_Oeq__iff:(((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A2:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a A2) B2)) ((ord_less_eq_set_a B2) A2)))).
% 0.70/0.89 Axiom fact_189_order__class_Oantisym__conv:(forall (Y:set_a) (X:set_a), (((ord_less_eq_set_a Y) X)->(((eq Prop) ((ord_less_eq_set_a X) Y)) (((eq set_a) X) Y)))).
% 0.70/0.89 Axiom fact_190_order__class_Oorder_Otrans:(forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C)))).
% 0.70/0.89 Axiom fact_191_preorder__class_Oeq__refl:(forall (X:set_a) (Y:set_a), ((((eq set_a) X) Y)->((ord_less_eq_set_a X) Y))).
% 0.70/0.89 Axiom fact_192_order__class_Oantisym:(forall (X:set_a) (Y:set_a), (((ord_less_eq_set_a X) Y)->(((ord_less_eq_set_a Y) X)->(((eq set_a) X) Y)))).
% 0.70/0.89 Axiom fact_193_order__class_Oeq__iff:(((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (X2:set_a) (Y3:set_a)=> ((and ((ord_less_eq_set_a X2) Y3)) ((ord_less_eq_set_a Y3) X2)))).
% 0.70/0.89 Axiom fact_194_ord__le__eq__subst:(forall (A:set_a) (B:set_a) (F:(set_a->set_a)) (C:set_a), (((ord_less_eq_set_a A) B)->((((eq set_a) (F B)) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a (F A)) C))))).
% 0.70/0.89 Axiom fact_195_ord__eq__le__subst:(forall (A:set_a) (F:(set_a->set_a)) (B:set_a) (C:set_a), ((((eq set_a) A) (F B))->(((ord_less_eq_set_a B) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a A) (F C)))))).
% 0.70/0.89 Axiom fact_196_order__subst2:(forall (A:set_a) (B:set_a) (F:(set_a->set_a)) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a (F B)) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a (F A)) C))))).
% 0.70/0.89 Axiom fact_197_order__subst1:(forall (A:set_a) (F:(set_a->set_a)) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) (F B))->(((ord_less_eq_set_a B) C)->((forall (X3:set_a) (Y4:set_a), (((ord_less_eq_set_a X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))->((ord_less_eq_set_a A) (F C)))))).
% 0.70/0.89 Axiom fact_198_Collect__mono__iff:(forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X2:a), ((P X2)->(Q X2))))).
% 0.70/0.89 Axiom fact_199_set__eq__subset:(((eq (set_a->(set_a->Prop))) (fun (Y2:set_a) (Z:set_a)=> (((eq set_a) Y2) Z))) (fun (A5:set_a) (B5:set_a)=> ((and ((ord_less_eq_set_a A5) B5)) ((ord_less_eq_set_a B5) A5)))).
% 0.70/0.89 Axiom fact_200_subset__trans:(forall (A3:set_a) (B4:set_a) (C4:set_a), (((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) C4)->((ord_less_eq_set_a A3) C4)))).
% 0.70/0.89 Axiom fact_201_Collect__mono:(forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), ((P X3)->(Q X3)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q)))).
% 0.70/0.89 Axiom fact_202_subset__refl:(forall (A3:set_a), ((ord_less_eq_set_a A3) A3)).
% 0.70/0.89 Axiom fact_203_subset__iff:(((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B5:set_a)=> (forall (T:a), (((member_a T) A5)->((member_a T) B5))))).
% 0.70/0.89 Axiom fact_204_equalityD2:(forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((ord_less_eq_set_a B4) A3))).
% 0.70/0.89 Axiom fact_205_equalityD1:(forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((ord_less_eq_set_a A3) B4))).
% 0.70/0.89 Axiom fact_206_subset__eq:(((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B5:set_a)=> (forall (X2:a), (((member_a X2) A5)->((member_a X2) B5))))).
% 0.70/0.89 Axiom fact_207_equalityE:(forall (A3:set_a) (B4:set_a), ((((eq set_a) A3) B4)->((((ord_less_eq_set_a A3) B4)->(((ord_less_eq_set_a B4) A3)->False))->False))).
% 0.70/0.89 Axiom fact_208_subsetD:(forall (A3:set_a) (B4:set_a) (C:a), (((ord_less_eq_set_a A3) B4)->(((member_a C) A3)->((member_a C) B4)))).
% 0.70/0.89 Axiom fact_209_in__mono:(forall (A3:set_a) (B4:set_a) (X:a), (((ord_less_eq_set_a A3) B4)->(((member_a X) A3)->((member_a X) B4)))).
% 0.70/0.89 Axiom fact_210_ord_OLeast_Ocong:(((eq ((a->(a->Prop))->((a->Prop)->a))) least_a) least_a).
% 0.70/0.89 Axiom fact_211_order_OGreatest_Ocong:(((eq ((a->(a->Prop))->((a->Prop)->a))) greatest_a) greatest_a).
% 0.70/0.89 Axiom fact_212_ord_Omin_Ocong:(((eq ((a->(a->Prop))->(a->(a->a)))) min_a) min_a).
% 0.70/0.89 Axiom fact_213_ord_Omax_Ocong:(((eq ((a->(a->Prop))->(a->(a->a)))) max_a) max_a).
% 0.70/0.89 Axiom fact_214_ord_Omin__def:(((eq ((a->(a->Prop))->(a->(a->a)))) min_a) (fun (Less_eq:(a->(a->Prop))) (A2:a) (B2:a)=> (((if_a ((Less_eq A2) B2)) A2) B2))).
% 0.70/0.89 Axiom fact_215_ord_Omax__def:(((eq ((a->(a->Prop))->(a->(a->a)))) max_a) (fun (Less_eq:(a->(a->Prop))) (A2:a) (B2:a)=> (((if_a ((Less_eq A2) B2)) B2) A2))).
% 0.70/0.90 Axiom fact_216_local_Omono__inf:(forall (F:(a->set_a)) (A3:a) (B4:a), (((mono_a_set_a less_eq) F)->((ord_less_eq_set_a (F ((inf A3) B4))) ((inf_inf_set_a (F A3)) (F B4))))).
% 0.70/0.90 Axiom fact_217_local_Omono__sup:(forall (F:(a->set_a)) (A3:a) (B4:a), (((mono_a_set_a less_eq) F)->((ord_less_eq_set_a ((sup_sup_set_a (F A3)) (F B4))) (F ((sup A3) B4))))).
% 0.70/0.90 Axiom fact_218_local_Obdd__above__finite:(forall (A3:set_a), ((finite_finite_a A3)->((condit1627435690bove_a less_eq) A3))).
% 0.70/0.90 Axiom fact_219_local_Ofinite__has__minimal2:(forall (A3:set_a) (A:a), ((finite_finite_a A3)->(((member_a A) A3)->((ex a) (fun (X3:a)=> ((and ((and ((member_a X3) A3)) ((less_eq X3) A))) (forall (Xa:a), (((member_a Xa) A3)->(((less_eq Xa) X3)->(((eq a) X3) Xa)))))))))).
% 0.70/0.90 Axiom fact_220_local_Ofinite__has__maximal2:(forall (A3:set_a) (A:a), ((finite_finite_a A3)->(((member_a A) A3)->((ex a) (fun (X3:a)=> ((and ((and ((member_a X3) A3)) ((less_eq A) X3))) (forall (Xa:a), (((member_a Xa) A3)->(((less_eq X3) Xa)->(((eq a) X3) Xa)))))))))).
% 0.70/0.90 Axiom fact_221_local_Obdd__below__Int2:(forall (B4:set_a) (A3:set_a), (((condit1001553558elow_a less_eq) B4)->((condit1001553558elow_a less_eq) ((inf_inf_set_a A3) B4)))).
% 0.70/0.90 Axiom fact_222_local_Obdd__below__Int1:(forall (A3:set_a) (B4:set_a), (((condit1001553558elow_a less_eq) A3)->((condit1001553558elow_a less_eq) ((inf_inf_set_a A3) B4)))).
% 0.70/0.90 Axiom fact_223_local_Obdd__above__Int2:(forall (B4:set_a) (A3:set_a), (((condit1627435690bove_a less_eq) B4)->((condit1627435690bove_a less_eq) ((inf_inf_set_a A3) B4)))).
% 0.70/0.90 Axiom fact_224_local_Obdd__above__Int1:(forall (A3:set_a) (B4:set_a), (((condit1627435690bove_a less_eq) A3)->((condit1627435690bove_a less_eq) ((inf_inf_set_a A3) B4)))).
% 0.70/0.90 Axiom fact_225_local_Obdd__below__finite:(forall (A3:set_a), ((finite_finite_a A3)->((condit1001553558elow_a less_eq) A3))).
% 0.70/0.90 Axiom fact_226_Un__subset__iff:(forall (A3:set_a) (B4:set_a) (C4:set_a), (((eq Prop) ((ord_less_eq_set_a ((sup_sup_set_a A3) B4)) C4)) ((and ((ord_less_eq_set_a A3) C4)) ((ord_less_eq_set_a B4) C4)))).
% 0.70/0.90 Axiom fact_227_Int__subset__iff:(forall (C4:set_a) (A3:set_a) (B4:set_a), (((eq Prop) ((ord_less_eq_set_a C4) ((inf_inf_set_a A3) B4))) ((and ((ord_less_eq_set_a C4) A3)) ((ord_less_eq_set_a C4) B4)))).
% 0.70/0.90 Axiom fact_228_semilattice__inf__class_Oinf__right__idem:(forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a ((inf_inf_set_a X) Y)) Y)) ((inf_inf_set_a X) Y))).
% 0.70/0.90 Axiom fact_229_semilattice__inf__class_Oinf_Oright__idem:(forall (A:set_a) (B:set_a), (((eq set_a) ((inf_inf_set_a ((inf_inf_set_a A) B)) B)) ((inf_inf_set_a A) B))).
% 0.70/0.90 Axiom fact_230_semilattice__inf__class_Oinf__left__idem:(forall (X:set_a) (Y:set_a), (((eq set_a) ((inf_inf_set_a X) ((inf_inf_set_a X) Y))) ((inf_inf_set_a X) Y))).
% 0.70/0.90 Axiom fact_231_semilattice__inf__class_Oinf_Oleft__idem:(forall (A:set_a) (B:set_a), (((eq set_a) ((inf_inf_set_a A) ((inf_inf_set_a A) B))) ((inf_inf_set_a A) B))).
% 0.70/0.90 Axiom fact_232_semilattice__inf__class_Oinf__idem:(forall (X:set_a), (((eq set_a) ((inf_inf_set_a X) X)) X)).
% 0.70/0.90 Axiom fact_233_semilattice__inf__class_Oinf_Oidem:(forall (A:set_a), (((eq set_a) ((inf_inf_set_a A) A)) A)).
% 0.70/0.90 Axiom fact_234_semilattice__sup__class_Osup_Oright__idem:(forall (A:set_a) (B:set_a), (((eq set_a) ((sup_sup_set_a ((sup_sup_set_a A) B)) B)) ((sup_sup_set_a A) B))).
% 0.70/0.90 Axiom fact_235_semilattice__sup__class_Osup__left__idem:(forall (X:set_a) (Y:set_a), (((eq set_a) ((sup_sup_set_a X) ((sup_sup_set_a X) Y))) ((sup_sup_set_a X) Y))).
% 0.70/0.90 Axiom fact_236_semilattice__sup__class_Osup_Oleft__idem:(forall (A:set_a) (B:set_a), (((eq set_a) ((sup_sup_set_a A) ((sup_sup_set_a A) B))) ((sup_sup_set_a A) B))).
% 0.70/0.90 Axiom fact_237_semilattice__sup__class_Osup__idem:(forall (X:set_a), (((eq set_a) ((sup_sup_set_a X) X)) X)).
% 0.70/0.90 Axiom fact_238_semilattice__sup__class_Osup_Oidem:(forall (A:set_a), (((eq set_a) ((sup_sup_set_a A) A)) A)).
% 0.70/0.90 Axiom fact_239_semilattice__inf__class_Ole__inf__iff:(forall (X:set_a) (Y:set_a) (Z2:set_a), (((eq Prop) ((ord_less_eq_set_a X) ((inf_inf_set
%------------------------------------------------------------------------------