TSTP Solution File: ITP124^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP124^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 13:24:15 EDT 2021
% Result : Timeout 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP124^1 : TPTP v7.5.0. Released v7.5.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 19 06:11:17 EDT 2021
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.42/0.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba5614424d0>, <kernel.Type object at 0xdc78c0>) of role type named ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring set_set_a:Type
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561442b48>, <kernel.Type object at 0xb2ffc8>) of role type named ty_n_t__Set__Oset_Itf__a_J
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring set_a:Type
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xb2fd40>, <kernel.Type object at 0xdc78c0>) of role type named ty_n_tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring a:Type
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xdc7bd8>, <kernel.DependentProduct object at 0x2ba5614408c0>) of role type named sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring condit1627435690bove_a:((a->(a->Prop))->(set_a->Prop))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xdc7cf8>, <kernel.DependentProduct object at 0x2ba561440998>) of role type named sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring condit1001553558elow_a:((a->(a->Prop))->(set_a->Prop))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xdc7bd8>, <kernel.DependentProduct object at 0x2ba561440cf8>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring finite40241356em_a_a:((a->(a->a))->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xdc7cf8>, <kernel.DependentProduct object at 0x2ba561440998>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__a_J
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring finite_finite_set_a:(set_set_a->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xdc7cf8>, <kernel.DependentProduct object at 0x2ba561425128>) of role type named sy_c_Finite__Set_Ofinite_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring finite_finite_a:(set_a->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0xdc7cf8>, <kernel.DependentProduct object at 0x2ba5614402d8>) of role type named sy_c_Groups_Oabel__semigroup_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring abel_semigroup_a:((a->(a->a))->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561425440>, <kernel.DependentProduct object at 0x2ba5614408c0>) of role type named sy_c_Groups_Osemigroup_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring semigroup_a:((a->(a->a))->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561425248>, <kernel.DependentProduct object at 0x2ba561440998>) of role type named sy_c_Lattices_Osemilattice_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring semilattice_a:((a->(a->a))->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561425128>, <kernel.DependentProduct object at 0x2ba561440710>) of role type named sy_c_Lattices__Big_Osemilattice__inf_OInf__fin_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring lattic247676691_fin_a:((a->(a->a))->(set_a->a))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561425248>, <kernel.DependentProduct object at 0x2ba5614403b0>) of role type named sy_c_Lattices__Big_Osemilattice__set_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring lattic1885654924_set_a:((a->(a->a))->Prop)
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561425248>, <kernel.DependentProduct object at 0x2ba5614402d8>) of role type named sy_c_Lattices__Big_Osemilattice__sup_OSup__fin_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring lattic1781219155_fin_a:((a->(a->a))->(set_a->a))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba561440368>, <kernel.DependentProduct object at 0x2ba561440cf8>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring modula1936294176_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba5614402d8>, <kernel.DependentProduct object at 0x2ba56143d7e8>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring modula1144073633_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2ba56143d830>, <kernel.Constant object at 0x2ba5614408c0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_Itf__a_J_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring bot_bot_set_set_a:set_set_a
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba56143d830>, <kernel.Constant object at 0x2ba5614408c0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring bot_bot_set_a:set_a
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba5614403b0>, <kernel.DependentProduct object at 0xb2acf8>) of role type named sy_c_Orderings_Oord_OLeast_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring least_a:((a->(a->Prop))->((a->Prop)->a))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba561440998>, <kernel.DependentProduct object at 0xb2abd8>) of role type named sy_c_Orderings_Oord_Omax_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring max_a:((a->(a->Prop))->(a->(a->a)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba5614403b0>, <kernel.DependentProduct object at 0xb2ac68>) of role type named sy_c_Orderings_Oord_Omin_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring min_a:((a->(a->Prop))->(a->(a->a)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba5614408c0>, <kernel.DependentProduct object at 0xb2aab8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__a_J_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring ord_le318720350_set_a:(set_set_a->(set_set_a->Prop))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba5614403b0>, <kernel.DependentProduct object at 0xb2a950>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring ord_less_eq_set_a:(set_a->(set_a->Prop))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2ba5614403b0>, <kernel.DependentProduct object at 0xb2aa70>) of role type named sy_c_Orderings_Oorder_OGreatest_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring greatest_a:((a->(a->Prop))->((a->Prop)->a))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2aab8>, <kernel.DependentProduct object at 0xb2a878>) of role type named sy_c_Orderings_Oorder_Oantimono_001tf__a_001t__Set__Oset_Itf__a_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring antimono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2ab90>, <kernel.DependentProduct object at 0xb2a5f0>) of role type named sy_c_Orderings_Oorder_Omono_001tf__a_001t__Set__Oset_Itf__a_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2a998>, <kernel.DependentProduct object at 0xb2a710>) of role type named sy_c_Relation_Otransp_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring transp_a:((a->(a->Prop))->Prop)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2a878>, <kernel.DependentProduct object at 0xb2a6c8>) of role type named sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring collect_set_a:((set_a->Prop)->set_set_a)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2a5f0>, <kernel.DependentProduct object at 0xb2acb0>) of role type named sy_c_Set_OCollect_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring collect_a:((a->Prop)->set_a)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2aab8>, <kernel.DependentProduct object at 0xb2a950>) of role type named sy_c_Set_Oinsert_001t__Set__Oset_Itf__a_J
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring insert_set_a:(set_a->(set_set_a->set_set_a))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2abd8>, <kernel.DependentProduct object at 0xb2a560>) of role type named sy_c_Set_Oinsert_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring insert_a:(a->(set_a->set_a))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2acb0>, <kernel.DependentProduct object at 0xb2ab90>) of role type named sy_c_Set__Interval_Oord_OatLeastAtMost_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring set_atLeastAtMost_a:((a->(a->Prop))->(a->(a->set_a)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2a950>, <kernel.DependentProduct object at 0xb2a290>) of role type named sy_c_Set__Interval_Oord_OatLeast_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring set_atLeast_a:((a->(a->Prop))->(a->set_a))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2a638>, <kernel.DependentProduct object at 0xb2ab90>) of role type named sy_c_Set__Interval_Oord_OatMost_001tf__a
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring set_atMost_a:((a->(a->Prop))->(a->set_a))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0xb2a878>, <kernel.DependentProduct object at 0xb2a5a8>) of role type named sy_c_member_001t__Set__Oset_Itf__a_J
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring member_set_a:(set_a->(set_set_a->Prop))
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2a200>, <kernel.DependentProduct object at 0xb2a290>) of role type named sy_c_member_001tf__a
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring member_a:(a->(set_a->Prop))
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2ab90>, <kernel.Constant object at 0xb2a290>) of role type named sy_v_a
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring a2:a
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2a878>, <kernel.Constant object at 0xb2a290>) of role type named sy_v_b
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring b:a
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2a200>, <kernel.Constant object at 0xb2a290>) of role type named sy_v_c
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring c:a
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2ab90>, <kernel.DependentProduct object at 0xb2a2d8>) of role type named sy_v_inf
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring inf:(a->(a->a))
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2a5f0>, <kernel.DependentProduct object at 0xb2a9e0>) of role type named sy_v_less__eq
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring less_eq:(a->(a->Prop))
% 0.42/0.63 FOF formula (<kernel.Constant object at 0xb2a290>, <kernel.DependentProduct object at 0xb2a7a0>) of role type named sy_v_sup
% 0.42/0.63 Using role type
% 0.42/0.63 Declaring sup:(a->(a->a))
% 0.42/0.63 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_0_local_Oinf_Oassoc
% 0.42/0.63 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C))))
% 0.42/0.63 FOF formula (forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A))) of role axiom named fact_1_local_Oinf_Ocommute
% 0.42/0.63 A new axiom: (forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A)))
% 0.42/0.63 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_2_local_Oinf_Oleft__commute
% 0.42/0.63 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C))))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a) (Z:a), (((eq a) ((inf ((inf X) Y)) Z)) ((inf X) ((inf Y) Z)))) of role axiom named fact_3_local_Oinf__assoc
% 0.42/0.63 A new axiom: (forall (X:a) (Y:a) (Z:a), (((eq a) ((inf ((inf X) Y)) Z)) ((inf X) ((inf Y) Z))))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X))) of role axiom named fact_4_local_Oinf__commute
% 0.42/0.63 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X)))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a) (Z:a), (((eq a) ((inf X) ((inf Y) Z))) ((inf Y) ((inf X) Z)))) of role axiom named fact_5_local_Oinf__left__commute
% 0.42/0.63 A new axiom: (forall (X:a) (Y:a) (Z:a), (((eq a) ((inf X) ((inf Y) Z))) ((inf Y) ((inf X) Z))))
% 0.42/0.63 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_6_local_Osup_Oassoc
% 0.42/0.63 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C))))
% 0.42/0.63 FOF formula (forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A))) of role axiom named fact_7_local_Osup_Ocommute
% 0.42/0.63 A new axiom: (forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A)))
% 0.42/0.63 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_8_local_Osup_Oleft__commute
% 0.42/0.63 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C))))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a) (Z:a), (((eq a) ((sup ((sup X) Y)) Z)) ((sup X) ((sup Y) Z)))) of role axiom named fact_9_local_Osup__assoc
% 0.42/0.63 A new axiom: (forall (X:a) (Y:a) (Z:a), (((eq a) ((sup ((sup X) Y)) Z)) ((sup X) ((sup Y) Z))))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X))) of role axiom named fact_10_local_Osup__commute
% 0.42/0.63 A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X)))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a) (Z:a), (((eq a) ((sup X) ((sup Y) Z))) ((sup Y) ((sup X) Z)))) of role axiom named fact_11_local_Osup__left__commute
% 0.42/0.63 A new axiom: (forall (X:a) (Y:a) (Z:a), (((eq a) ((sup X) ((sup Y) Z))) ((sup Y) ((sup X) Z))))
% 0.42/0.63 FOF formula (forall (X:a) (Y:a) (Z:a), ((forall (X2:a) (Y2:a) (Z2:a), (((eq a) ((inf X2) ((sup Y2) Z2))) ((sup ((inf X2) Y2)) ((inf X2) Z2))))->(((eq a) ((sup X) ((inf Y) Z))) ((inf ((sup X) Y)) ((sup X) Z))))) of role axiom named fact_12_local_Odistrib__imp1
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a) (Z:a), ((forall (X2:a) (Y2:a) (Z2:a), (((eq a) ((inf X2) ((sup Y2) Z2))) ((sup ((inf X2) Y2)) ((inf X2) Z2))))->(((eq a) ((sup X) ((inf Y) Z))) ((inf ((sup X) Y)) ((sup X) Z)))))
% 0.48/0.65 FOF formula (forall (X:a) (Y:a) (Z:a), ((forall (X2:a) (Y2:a) (Z2:a), (((eq a) ((sup X2) ((inf Y2) Z2))) ((inf ((sup X2) Y2)) ((sup X2) Z2))))->(((eq a) ((inf X) ((sup Y) Z))) ((sup ((inf X) Y)) ((inf X) Z))))) of role axiom named fact_13_local_Odistrib__imp2
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a) (Z:a), ((forall (X2:a) (Y2:a) (Z2:a), (((eq a) ((sup X2) ((inf Y2) Z2))) ((inf ((sup X2) Y2)) ((sup X2) Z2))))->(((eq a) ((inf X) ((sup Y) Z))) ((sup ((inf X) Y)) ((inf X) Z)))))
% 0.48/0.65 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_14_e__aux__def
% 0.48/0.65 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))))
% 0.48/0.65 FOF formula (forall (A:a), (((eq a) ((inf A) A)) A)) of role axiom named fact_15_local_Oinf_Oidem
% 0.48/0.65 A new axiom: (forall (A:a), (((eq a) ((inf A) A)) A))
% 0.48/0.65 FOF formula (forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B))) of role axiom named fact_16_local_Oinf_Oleft__idem
% 0.48/0.65 A new axiom: (forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B)))
% 0.48/0.65 FOF formula (forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B))) of role axiom named fact_17_local_Oinf_Oright__idem
% 0.48/0.65 A new axiom: (forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B)))
% 0.48/0.65 FOF formula (forall (X:a), (((eq a) ((inf X) X)) X)) of role axiom named fact_18_local_Oinf__idem
% 0.48/0.65 A new axiom: (forall (X:a), (((eq a) ((inf X) X)) X))
% 0.48/0.65 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y))) of role axiom named fact_19_local_Oinf__left__idem
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y)))
% 0.48/0.65 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y))) of role axiom named fact_20_local_Oinf__right__idem
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y)))
% 0.48/0.65 FOF formula (forall (A:a), (((eq a) ((sup A) A)) A)) of role axiom named fact_21_local_Osup_Oidem
% 0.48/0.65 A new axiom: (forall (A:a), (((eq a) ((sup A) A)) A))
% 0.48/0.65 FOF formula (forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B))) of role axiom named fact_22_local_Osup_Oleft__idem
% 0.48/0.65 A new axiom: (forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B)))
% 0.48/0.65 FOF formula (forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B))) of role axiom named fact_23_local_Osup_Oright__idem
% 0.48/0.65 A new axiom: (forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B)))
% 0.48/0.65 FOF formula (forall (X:a), (((eq a) ((sup X) X)) X)) of role axiom named fact_24_local_Osup__idem
% 0.48/0.65 A new axiom: (forall (X:a), (((eq a) ((sup X) X)) X))
% 0.48/0.65 FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y))) of role axiom named fact_25_local_Osup__left__idem
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y)))
% 0.48/0.65 FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X)) of role axiom named fact_26_local_Oinf__sup__absorb
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X))
% 0.48/0.65 FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X)) of role axiom named fact_27_local_Osup__inf__absorb
% 0.48/0.65 A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X))
% 0.48/0.65 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_28_d__aux__def
% 0.48/0.65 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))))
% 0.48/0.65 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_29_d__b__c__a
% 0.48/0.65 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)))
% 0.48/0.66 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_30_d__c__a__b
% 0.48/0.66 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)))
% 0.48/0.66 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a) of role axiom named fact_31_lattice_Oe__aux_Ocong
% 0.48/0.66 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a)
% 0.48/0.66 FOF formula (finite40241356em_a_a sup) of role axiom named fact_32_local_Ocomp__fun__idem__sup
% 0.48/0.66 A new axiom: (finite40241356em_a_a sup)
% 0.48/0.66 FOF formula (finite40241356em_a_a inf) of role axiom named fact_33_local_Ocomp__fun__idem__inf
% 0.48/0.66 A new axiom: (finite40241356em_a_a inf)
% 0.48/0.66 FOF formula (semigroup_a sup) of role axiom named fact_34_local_Osup_Osemigroup__axioms
% 0.48/0.66 A new axiom: (semigroup_a sup)
% 0.48/0.66 FOF formula (semigroup_a inf) of role axiom named fact_35_local_Oinf_Osemigroup__axioms
% 0.48/0.66 A new axiom: (semigroup_a inf)
% 0.48/0.66 FOF formula (semilattice_a sup) of role axiom named fact_36_local_Osup_Osemilattice__axioms
% 0.48/0.66 A new axiom: (semilattice_a sup)
% 0.48/0.66 FOF formula (semilattice_a inf) of role axiom named fact_37_local_Oinf_Osemilattice__axioms
% 0.48/0.66 A new axiom: (semilattice_a inf)
% 0.48/0.66 FOF formula (abel_semigroup_a sup) of role axiom named fact_38_local_Osup_Oabel__semigroup__axioms
% 0.48/0.66 A new axiom: (abel_semigroup_a sup)
% 0.48/0.66 FOF formula (abel_semigroup_a inf) of role axiom named fact_39_local_Oinf_Oabel__semigroup__axioms
% 0.48/0.66 A new axiom: (abel_semigroup_a inf)
% 0.48/0.66 FOF formula (lattic1885654924_set_a sup) of role axiom named fact_40_local_OSup__fin_Osemilattice__set__axioms
% 0.48/0.66 A new axiom: (lattic1885654924_set_a sup)
% 0.48/0.66 FOF formula (lattic1885654924_set_a inf) of role axiom named fact_41_local_OInf__fin_Osemilattice__set__axioms
% 0.48/0.66 A new axiom: (lattic1885654924_set_a inf)
% 0.48/0.66 FOF formula (forall (X:a) (Y:a) (Z:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z))) ((inf X) ((sup Y) Z)))) of role axiom named fact_42_local_Odistrib__inf__le
% 0.48/0.66 A new axiom: (forall (X:a) (Y:a) (Z:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z))) ((inf X) ((sup Y) Z))))
% 0.48/0.66 FOF formula (forall (X:a) (Y:a) (Z:a), ((less_eq ((sup X) ((inf Y) Z))) ((inf ((sup X) Y)) ((sup X) Z)))) of role axiom named fact_43_local_Odistrib__sup__le
% 0.48/0.66 A new axiom: (forall (X:a) (Y:a) (Z:a), ((less_eq ((sup X) ((inf Y) Z))) ((inf ((sup X) Y)) ((sup X) Z))))
% 0.48/0.66 FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y)))) of role axiom named fact_44_local_Oantisym
% 0.48/0.66 A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y))))
% 0.48/0.66 FOF formula (forall (A:set_a) (P:(set_a->Prop)), (((eq Prop) ((member_set_a A) (collect_set_a P))) (P A))) of role axiom named fact_45_mem__Collect__eq
% 0.48/0.66 A new axiom: (forall (A:set_a) (P:(set_a->Prop)), (((eq Prop) ((member_set_a A) (collect_set_a P))) (P A)))
% 0.48/0.66 FOF formula (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))) of role axiom named fact_46_mem__Collect__eq
% 0.48/0.66 A new axiom: (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A)))
% 0.48/0.66 FOF formula (forall (A2:set_set_a), (((eq set_set_a) (collect_set_a (fun (X3:set_a)=> ((member_set_a X3) A2)))) A2)) of role axiom named fact_47_Collect__mem__eq
% 0.48/0.66 A new axiom: (forall (A2:set_set_a), (((eq set_set_a) (collect_set_a (fun (X3:set_a)=> ((member_set_a X3) A2)))) A2))
% 0.48/0.66 FOF formula (forall (A2:set_a), (((eq set_a) (collect_a (fun (X3:a)=> ((member_a X3) A2)))) A2)) of role axiom named fact_48_Collect__mem__eq
% 0.48/0.66 A new axiom: (forall (A2:set_a), (((eq set_a) (collect_a (fun (X3:a)=> ((member_a X3) A2)))) A2))
% 0.48/0.66 FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X2:a), (((eq Prop) (P X2)) (Q X2)))->(((eq set_a) (collect_a P)) (collect_a Q)))) of role axiom named fact_49_Collect__cong
% 0.48/0.66 A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X2:a), (((eq Prop) (P X2)) (Q X2)))->(((eq set_a) (collect_a P)) (collect_a Q))))
% 0.51/0.68 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_50_local_Oantisym__conv
% 0.51/0.68 A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y))))
% 0.51/0.68 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B)))) of role axiom named fact_51_local_Odual__order_Oantisym
% 0.51/0.68 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B))))
% 0.51/0.68 FOF formula (((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (A3:a) (B2:a)=> ((and ((less_eq B2) A3)) ((less_eq A3) B2)))) of role axiom named fact_52_local_Odual__order_Oeq__iff
% 0.51/0.68 A new axiom: (((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (A3:a) (B2:a)=> ((and ((less_eq B2) A3)) ((less_eq A3) B2))))
% 0.51/0.68 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_53_local_Odual__order_Otrans
% 0.51/0.68 A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A))))
% 0.51/0.68 FOF formula (((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (X3:a) (Y4:a)=> ((and ((less_eq X3) Y4)) ((less_eq Y4) X3)))) of role axiom named fact_54_local_Oeq__iff
% 0.51/0.68 A new axiom: (((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (X3:a) (Y4:a)=> ((and ((less_eq X3) Y4)) ((less_eq Y4) X3))))
% 0.51/0.68 FOF formula (forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y))) of role axiom named fact_55_local_Oeq__refl
% 0.51/0.68 A new axiom: (forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y)))
% 0.51/0.68 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_56_local_Oord__eq__le__trans
% 0.51/0.68 A new axiom: (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C))))
% 0.51/0.68 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_57_local_Oord__le__eq__trans
% 0.51/0.68 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C))))
% 0.51/0.68 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B)))) of role axiom named fact_58_local_Oorder_Oantisym
% 0.51/0.68 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B))))
% 0.51/0.68 FOF formula (((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (A3:a) (B2:a)=> ((and ((less_eq A3) B2)) ((less_eq B2) A3)))) of role axiom named fact_59_local_Oorder_Oeq__iff
% 0.51/0.68 A new axiom: (((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (A3:a) (B2:a)=> ((and ((less_eq A3) B2)) ((less_eq B2) A3))))
% 0.51/0.68 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_60_local_Oorder_Otrans
% 0.51/0.68 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C))))
% 0.51/0.68 FOF formula (forall (X:a) (Y:a) (Z:a), (((less_eq X) Y)->(((less_eq Y) Z)->((less_eq X) Z)))) of role axiom named fact_61_local_Oorder__trans
% 0.51/0.68 A new axiom: (forall (X:a) (Y:a) (Z:a), (((less_eq X) Y)->(((less_eq Y) Z)->((less_eq X) Z))))
% 0.51/0.68 FOF formula (forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X))) of role axiom named fact_62_local_Ole__infI2
% 0.51/0.68 A new axiom: (forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X)))
% 0.51/0.68 FOF formula (forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X))) of role axiom named fact_63_local_Ole__infI1
% 0.51/0.68 A new axiom: (forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X)))
% 0.51/0.68 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_64_local_Ole__infI
% 0.51/0.68 A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B)))))
% 0.51/0.68 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_65_local_Ole__infE
% 0.51/0.68 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)))
% 0.51/0.70 FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X))) of role axiom named fact_66_local_Ole__iff__inf
% 0.51/0.70 A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X)))
% 0.51/0.70 FOF formula (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X2:a) (Y2:a), ((less_eq ((F X2) Y2)) X2))->((forall (X2:a) (Y2:a), ((less_eq ((F X2) Y2)) Y2))->((forall (X2:a) (Y2:a) (Z2:a), (((less_eq X2) Y2)->(((less_eq X2) Z2)->((less_eq X2) ((F Y2) Z2)))))->(((eq a) ((inf X) Y)) ((F X) Y)))))) of role axiom named fact_67_local_Oinf__unique
% 0.51/0.70 A new axiom: (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X2:a) (Y2:a), ((less_eq ((F X2) Y2)) X2))->((forall (X2:a) (Y2:a), ((less_eq ((F X2) Y2)) Y2))->((forall (X2:a) (Y2:a) (Z2:a), (((less_eq X2) Y2)->(((less_eq X2) Z2)->((less_eq X2) ((F Y2) Z2)))))->(((eq a) ((inf X) Y)) ((F X) Y))))))
% 0.51/0.70 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_68_local_Oinf__mono
% 0.51/0.70 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)))))
% 0.51/0.70 FOF formula (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y)) of role axiom named fact_69_local_Oinf__le2
% 0.51/0.70 A new axiom: (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y))
% 0.51/0.70 FOF formula (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X)) of role axiom named fact_70_local_Oinf__le1
% 0.51/0.70 A new axiom: (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X))
% 0.51/0.70 FOF formula (forall (X:a) (Y:a) (Z:a), (((less_eq X) Y)->(((less_eq X) Z)->((less_eq X) ((inf Y) Z))))) of role axiom named fact_71_local_Oinf__greatest
% 0.51/0.70 A new axiom: (forall (X:a) (Y:a) (Z:a), (((less_eq X) Y)->(((less_eq X) Z)->((less_eq X) ((inf Y) Z)))))
% 0.51/0.70 FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y))) of role axiom named fact_72_local_Oinf__absorb2
% 0.51/0.70 A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y)))
% 0.51/0.70 FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X))) of role axiom named fact_73_local_Oinf__absorb1
% 0.51/0.70 A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X)))
% 0.51/0.70 FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B)))) of role axiom named fact_74_local_Oinf_Oorder__iff
% 0.51/0.70 A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B))))
% 0.51/0.70 FOF formula (forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B))) of role axiom named fact_75_local_Oinf_OorderI
% 0.51/0.70 A new axiom: (forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B)))
% 0.51/0.70 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B)))) of role axiom named fact_76_local_Oinf_OorderE
% 0.51/0.70 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B))))
% 0.51/0.70 FOF formula (forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C))) of role axiom named fact_77_local_Oinf_OcoboundedI2
% 0.51/0.70 A new axiom: (forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C)))
% 0.51/0.70 FOF formula (forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C))) of role axiom named fact_78_local_Oinf_OcoboundedI1
% 0.51/0.70 A new axiom: (forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C)))
% 0.51/0.70 FOF formula (forall (A:a) (B:a), ((less_eq ((inf A) B)) B)) of role axiom named fact_79_local_Oinf_Ocobounded2
% 0.51/0.70 A new axiom: (forall (A:a) (B:a), ((less_eq ((inf A) B)) B))
% 0.51/0.70 FOF formula (forall (A:a) (B:a), ((less_eq ((inf A) B)) A)) of role axiom named fact_80_local_Oinf_Ocobounded1
% 0.51/0.70 A new axiom: (forall (A:a) (B:a), ((less_eq ((inf A) B)) A))
% 0.51/0.70 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_81_local_Oinf_OboundedI
% 0.51/0.70 A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C)))))
% 0.51/0.70 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_82_local_Oinf_OboundedE
% 0.51/0.70 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)))
% 0.51/0.72 FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B))) of role axiom named fact_83_local_Oinf_Oabsorb__iff2
% 0.51/0.72 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B)))
% 0.51/0.72 FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A))) of role axiom named fact_84_local_Oinf_Oabsorb__iff1
% 0.51/0.72 A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A)))
% 0.51/0.72 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B))) of role axiom named fact_85_local_Oinf_Oabsorb2
% 0.51/0.72 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B)))
% 0.51/0.72 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A))) of role axiom named fact_86_local_Oinf_Oabsorb1
% 0.51/0.72 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A)))
% 0.51/0.72 FOF formula (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X2:a) (Y2:a), ((less_eq X2) ((F X2) Y2)))->((forall (X2:a) (Y2:a), ((less_eq Y2) ((F X2) Y2)))->((forall (X2:a) (Y2:a) (Z2:a), (((less_eq Y2) X2)->(((less_eq Z2) X2)->((less_eq ((F Y2) Z2)) X2))))->(((eq a) ((sup X) Y)) ((F X) Y)))))) of role axiom named fact_87_local_Osup__unique
% 0.51/0.72 A new axiom: (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X2:a) (Y2:a), ((less_eq X2) ((F X2) Y2)))->((forall (X2:a) (Y2:a), ((less_eq Y2) ((F X2) Y2)))->((forall (X2:a) (Y2:a) (Z2:a), (((less_eq Y2) X2)->(((less_eq Z2) X2)->((less_eq ((F Y2) Z2)) X2))))->(((eq a) ((sup X) Y)) ((F X) Y))))))
% 0.51/0.72 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_88_local_Osup__mono
% 0.51/0.72 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)))))
% 0.51/0.72 FOF formula (forall (Y:a) (X:a) (Z:a), (((less_eq Y) X)->(((less_eq Z) X)->((less_eq ((sup Y) Z)) X)))) of role axiom named fact_89_local_Osup__least
% 0.51/0.72 A new axiom: (forall (Y:a) (X:a) (Z:a), (((less_eq Y) X)->(((less_eq Z) X)->((less_eq ((sup Y) Z)) X))))
% 0.51/0.72 FOF formula (forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y))) of role axiom named fact_90_local_Osup__ge2
% 0.51/0.72 A new axiom: (forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y)))
% 0.51/0.72 FOF formula (forall (X:a) (Y:a), ((less_eq X) ((sup X) Y))) of role axiom named fact_91_local_Osup__ge1
% 0.51/0.72 A new axiom: (forall (X:a) (Y:a), ((less_eq X) ((sup X) Y)))
% 0.51/0.72 FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y))) of role axiom named fact_92_local_Osup__absorb2
% 0.51/0.72 A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y)))
% 0.51/0.72 FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X))) of role axiom named fact_93_local_Osup__absorb1
% 0.51/0.72 A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X)))
% 0.51/0.72 FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B)))) of role axiom named fact_94_local_Osup_Oorder__iff
% 0.51/0.72 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B))))
% 0.51/0.72 FOF formula (forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A))) of role axiom named fact_95_local_Osup_OorderI
% 0.51/0.72 A new axiom: (forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A)))
% 0.51/0.72 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B)))) of role axiom named fact_96_local_Osup_OorderE
% 0.51/0.72 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B))))
% 0.51/0.72 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_97_local_Osup_Omono
% 0.51/0.72 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)))))
% 0.51/0.72 FOF formula (forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B)))) of role axiom named fact_98_local_Osup_OcoboundedI2
% 0.51/0.72 A new axiom: (forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B))))
% 0.51/0.72 FOF formula (forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B)))) of role axiom named fact_99_local_Osup_OcoboundedI1
% 0.58/0.74 A new axiom: (forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B))))
% 0.58/0.74 FOF formula (forall (B:a) (A:a), ((less_eq B) ((sup A) B))) of role axiom named fact_100_local_Osup_Ocobounded2
% 0.58/0.74 A new axiom: (forall (B:a) (A:a), ((less_eq B) ((sup A) B)))
% 0.58/0.74 FOF formula (forall (A:a) (B:a), ((less_eq A) ((sup A) B))) of role axiom named fact_101_local_Osup_Ocobounded1
% 0.58/0.74 A new axiom: (forall (A:a) (B:a), ((less_eq A) ((sup A) B)))
% 0.58/0.74 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_102_local_Osup_OboundedI
% 0.58/0.74 A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A))))
% 0.58/0.74 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_103_local_Osup_OboundedE
% 0.58/0.74 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)))
% 0.58/0.74 FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B))) of role axiom named fact_104_local_Osup_Oabsorb__iff2
% 0.58/0.74 A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B)))
% 0.58/0.74 FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A))) of role axiom named fact_105_local_Osup_Oabsorb__iff1
% 0.58/0.74 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A)))
% 0.58/0.74 FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B))) of role axiom named fact_106_local_Osup_Oabsorb2
% 0.58/0.74 A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B)))
% 0.58/0.74 FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A))) of role axiom named fact_107_local_Osup_Oabsorb1
% 0.58/0.74 A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A)))
% 0.58/0.74 FOF formula (forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B)))) of role axiom named fact_108_local_Ole__supI2
% 0.58/0.74 A new axiom: (forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B))))
% 0.58/0.74 FOF formula (forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B)))) of role axiom named fact_109_local_Ole__supI1
% 0.58/0.74 A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B))))
% 0.58/0.74 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_110_local_Ole__supI
% 0.58/0.74 A new axiom: (forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X))))
% 0.58/0.74 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_111_local_Ole__supE
% 0.58/0.74 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)))
% 0.58/0.74 FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y))) of role axiom named fact_112_local_Ole__iff__sup
% 0.58/0.74 A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y)))
% 0.58/0.74 FOF formula (forall (A:a), ((less_eq A) A)) of role axiom named fact_113_local_Oorder_Orefl
% 0.58/0.74 A new axiom: (forall (A:a), ((less_eq A) A))
% 0.58/0.74 FOF formula (forall (X:a), ((less_eq X) X)) of role axiom named fact_114_local_Oorder__refl
% 0.58/0.74 A new axiom: (forall (X:a), ((less_eq X) X))
% 0.58/0.74 FOF formula (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq Y2) X)))->((forall (X2:a), ((P X2)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X2)))->(Q X2))))->(Q ((greatest_a less_eq) P)))))) of role axiom named fact_115_local_OGreatestI2__order
% 0.58/0.74 A new axiom: (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq Y2) X)))->((forall (X2:a), ((P X2)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X2)))->(Q X2))))->(Q ((greatest_a less_eq) P))))))
% 0.58/0.74 FOF formula (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq Y2) X)))->(((eq a) ((greatest_a less_eq) P)) X)))) of role axiom named fact_116_local_OGreatest__equality
% 0.58/0.74 A new axiom: (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq Y2) X)))->(((eq a) ((greatest_a less_eq) P)) X))))
% 0.58/0.76 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_117_local_Omax__def
% 0.58/0.76 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))))
% 0.58/0.76 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_118_local_Omin__def
% 0.58/0.76 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))))
% 0.58/0.76 FOF formula (forall (X:a) (Y:a) (Z:a), (((eq Prop) ((less_eq X) ((inf Y) Z))) ((and ((less_eq X) Y)) ((less_eq X) Z)))) of role axiom named fact_119_local_Ole__inf__iff
% 0.58/0.76 A new axiom: (forall (X:a) (Y:a) (Z:a), (((eq Prop) ((less_eq X) ((inf Y) Z))) ((and ((less_eq X) Y)) ((less_eq X) Z))))
% 0.58/0.76 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_120_local_Oinf_Obounded__iff
% 0.58/0.76 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))))
% 0.58/0.76 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_121_local_Osup_Obounded__iff
% 0.58/0.76 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))))
% 0.58/0.76 FOF formula (forall (X:a) (Y:a) (Z:a), (((eq Prop) ((less_eq ((sup X) Y)) Z)) ((and ((less_eq X) Z)) ((less_eq Y) Z)))) of role axiom named fact_122_local_Ole__sup__iff
% 0.58/0.76 A new axiom: (forall (X:a) (Y:a) (Z:a), (((eq Prop) ((less_eq ((sup X) Y)) Z)) ((and ((less_eq X) Z)) ((less_eq Y) Z))))
% 0.58/0.76 FOF formula (forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y2:a), ((P Y2)->((less_eq X4) Y2))))) (forall (Y2:a), (((and (P Y2)) (forall (Ya:a), ((P Ya)->((less_eq Y2) Ya))))->(((eq a) Y2) X4))))))->(P ((least_a less_eq) P)))) of role axiom named fact_123_local_OLeast1I
% 0.58/0.76 A new axiom: (forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y2:a), ((P Y2)->((less_eq X4) Y2))))) (forall (Y2:a), (((and (P Y2)) (forall (Ya:a), ((P Ya)->((less_eq Y2) Ya))))->(((eq a) Y2) X4))))))->(P ((least_a less_eq) P))))
% 0.58/0.76 FOF formula (forall (P:(a->Prop)) (Z:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y2:a), ((P Y2)->((less_eq X4) Y2))))) (forall (Y2:a), (((and (P Y2)) (forall (Ya:a), ((P Ya)->((less_eq Y2) Ya))))->(((eq a) Y2) X4))))))->((P Z)->((less_eq ((least_a less_eq) P)) Z)))) of role axiom named fact_124_local_OLeast1__le
% 0.58/0.76 A new axiom: (forall (P:(a->Prop)) (Z:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y2:a), ((P Y2)->((less_eq X4) Y2))))) (forall (Y2:a), (((and (P Y2)) (forall (Ya:a), ((P Ya)->((less_eq Y2) Ya))))->(((eq a) Y2) X4))))))->((P Z)->((less_eq ((least_a less_eq) P)) Z))))
% 0.58/0.76 FOF formula (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq X) Y2)))->((forall (X2:a), ((P X2)->((forall (Y5:a), ((P Y5)->((less_eq X2) Y5)))->(Q X2))))->(Q ((least_a less_eq) P)))))) of role axiom named fact_125_local_OLeastI2__order
% 0.58/0.76 A new axiom: (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq X) Y2)))->((forall (X2:a), ((P X2)->((forall (Y5:a), ((P Y5)->((less_eq X2) Y5)))->(Q X2))))->(Q ((least_a less_eq) P))))))
% 0.58/0.76 FOF formula (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq X) Y2)))->(((eq a) ((least_a less_eq) P)) X)))) of role axiom named fact_126_local_OLeast__equality
% 0.58/0.76 A new axiom: (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq X) Y2)))->(((eq a) ((least_a less_eq) P)) X))))
% 0.58/0.76 FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a) of role axiom named fact_127_lattice_Od__aux_Ocong
% 0.61/0.77 A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a)
% 0.61/0.77 FOF formula (forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F))) of role axiom named fact_128_abel__semigroup_Oaxioms_I1_J
% 0.61/0.77 A new axiom: (forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F)))
% 0.61/0.77 FOF formula (((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a) of role axiom named fact_129_semilattice__set__def
% 0.61/0.77 A new axiom: (((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a)
% 0.61/0.77 FOF formula (forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F))) of role axiom named fact_130_semilattice__set_Ointro
% 0.61/0.77 A new axiom: (forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F)))
% 0.61/0.77 FOF formula (forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F))) of role axiom named fact_131_semilattice__set_Oaxioms
% 0.61/0.77 A new axiom: (forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F)))
% 0.61/0.77 FOF formula (forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F))) of role axiom named fact_132_semilattice_Oaxioms_I1_J
% 0.61/0.77 A new axiom: (forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F)))
% 0.61/0.77 FOF formula (forall (A2:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A2)) ((ex a) (fun (M:a)=> (forall (X3:a), (((member_a X3) A2)->((less_eq X3) M))))))) of role axiom named fact_133_local_Obdd__above__def
% 0.61/0.77 A new axiom: (forall (A2:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A2)) ((ex a) (fun (M:a)=> (forall (X3:a), (((member_a X3) A2)->((less_eq X3) M)))))))
% 0.61/0.77 FOF formula (forall (A2:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A2)) ((ex a) (fun (M2:a)=> (forall (X3:a), (((member_a X3) A2)->((less_eq M2) X3))))))) of role axiom named fact_134_local_Obdd__below__def
% 0.61/0.77 A new axiom: (forall (A2:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A2)) ((ex a) (fun (M2:a)=> (forall (X3:a), (((member_a X3) A2)->((less_eq M2) X3)))))))
% 0.61/0.77 FOF formula (transp_a less_eq) of role axiom named fact_135_local_Otransp__le
% 0.61/0.77 A new axiom: (transp_a less_eq)
% 0.61/0.77 FOF formula (forall (A2:set_a) (M3:a), ((forall (X2:a), (((member_a X2) A2)->((less_eq M3) X2)))->((condit1001553558elow_a less_eq) A2))) of role axiom named fact_136_local_Obdd__belowI
% 0.61/0.77 A new axiom: (forall (A2:set_a) (M3:a), ((forall (X2:a), (((member_a X2) A2)->((less_eq M3) X2)))->((condit1001553558elow_a less_eq) A2)))
% 0.61/0.77 FOF formula (forall (A2:set_a) (M4:a), ((forall (X2:a), (((member_a X2) A2)->((less_eq X2) M4)))->((condit1627435690bove_a less_eq) A2))) of role axiom named fact_137_local_Obdd__aboveI
% 0.61/0.77 A new axiom: (forall (A2:set_a) (M4:a), ((forall (X2:a), (((member_a X2) A2)->((less_eq X2) M4)))->((condit1627435690bove_a less_eq) A2)))
% 0.61/0.77 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_138_abel__semigroup_Oleft__commute
% 0.61/0.77 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)))))
% 0.61/0.77 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_139_semilattice_Oright__idem
% 0.61/0.77 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))))
% 0.61/0.77 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_140_semilattice_Oleft__idem
% 0.61/0.77 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))))
% 0.61/0.77 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_141_abel__semigroup_Ocommute
% 0.61/0.77 A new axiom: (forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A))))
% 0.61/0.77 FOF formula (forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A))) of role axiom named fact_142_semilattice_Oidem
% 0.61/0.77 A new axiom: (forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A)))
% 0.61/0.79 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_143_semigroup_Ointro
% 0.61/0.79 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)))
% 0.61/0.79 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_144_semigroup_Oassoc
% 0.61/0.79 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)))))
% 0.61/0.79 FOF formula (((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A3:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A3) B2)) C3)) ((F2 A3) ((F2 B2) C3)))))) of role axiom named fact_145_semigroup__def
% 0.61/0.79 A new axiom: (((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A3:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A3) B2)) C3)) ((F2 A3) ((F2 B2) C3))))))
% 0.61/0.79 FOF formula (forall (B4:set_a) (A2:set_a), (((condit1001553558elow_a less_eq) B4)->(((ord_less_eq_set_a A2) B4)->((condit1001553558elow_a less_eq) A2)))) of role axiom named fact_146_local_Obdd__below__mono
% 0.61/0.79 A new axiom: (forall (B4:set_a) (A2:set_a), (((condit1001553558elow_a less_eq) B4)->(((ord_less_eq_set_a A2) B4)->((condit1001553558elow_a less_eq) A2))))
% 0.61/0.79 FOF formula (forall (B4:set_a) (A2:set_a), (((condit1627435690bove_a less_eq) B4)->(((ord_less_eq_set_a A2) B4)->((condit1627435690bove_a less_eq) A2)))) of role axiom named fact_147_local_Obdd__above__mono
% 0.61/0.79 A new axiom: (forall (B4:set_a) (A2:set_a), (((condit1627435690bove_a less_eq) B4)->(((ord_less_eq_set_a A2) B4)->((condit1627435690bove_a less_eq) A2))))
% 0.61/0.79 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((condit1001553558elow_a less_eq) A2))) of role axiom named fact_148_local_Obdd__below__finite
% 0.61/0.79 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((condit1001553558elow_a less_eq) A2)))
% 0.61/0.79 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((condit1627435690bove_a less_eq) A2))) of role axiom named fact_149_local_Obdd__above__finite
% 0.61/0.79 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((condit1627435690bove_a less_eq) A2)))
% 0.61/0.79 FOF formula (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((ex a) (fun (X2:a)=> ((and ((and ((member_a X2) A2)) ((less_eq A) X2))) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq X2) Xa)->(((eq a) X2) Xa)))))))))) of role axiom named fact_150_local_Ofinite__has__maximal2
% 0.61/0.79 A new axiom: (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((ex a) (fun (X2:a)=> ((and ((and ((member_a X2) A2)) ((less_eq A) X2))) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq X2) Xa)->(((eq a) X2) Xa))))))))))
% 0.61/0.79 FOF formula (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((ex a) (fun (X2:a)=> ((and ((and ((member_a X2) A2)) ((less_eq X2) A))) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq Xa) X2)->(((eq a) X2) Xa)))))))))) of role axiom named fact_151_local_Ofinite__has__minimal2
% 0.61/0.79 A new axiom: (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((ex a) (fun (X2:a)=> ((and ((and ((member_a X2) A2)) ((less_eq X2) A))) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq Xa) X2)->(((eq a) X2) Xa))))))))))
% 0.61/0.79 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_152_local_OantimonoD
% 0.61/0.79 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)))))
% 0.61/0.79 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_153_local_OantimonoE
% 0.61/0.79 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)))))
% 0.61/0.79 FOF formula (forall (F:(a->set_a)), ((forall (X2:a) (Y2:a), (((less_eq X2) Y2)->((ord_less_eq_set_a (F Y2)) (F X2))))->((antimono_a_set_a less_eq) F))) of role axiom named fact_154_local_OantimonoI
% 0.61/0.80 A new axiom: (forall (F:(a->set_a)), ((forall (X2:a) (Y2:a), (((less_eq X2) Y2)->((ord_less_eq_set_a (F Y2)) (F X2))))->((antimono_a_set_a less_eq) F)))
% 0.61/0.80 FOF formula (forall (F:(a->set_a)), (((eq Prop) ((antimono_a_set_a less_eq) F)) (forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F Y4)) (F X3)))))) of role axiom named fact_155_local_Oantimono__def
% 0.61/0.80 A new axiom: (forall (F:(a->set_a)), (((eq Prop) ((antimono_a_set_a less_eq) F)) (forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F Y4)) (F X3))))))
% 0.61/0.80 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_156_local_OmonoD
% 0.61/0.80 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)))))
% 0.61/0.80 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_157_local_OmonoE
% 0.61/0.80 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)))))
% 0.61/0.80 FOF formula (forall (F:(a->set_a)), ((forall (X2:a) (Y2:a), (((less_eq X2) Y2)->((ord_less_eq_set_a (F X2)) (F Y2))))->((mono_a_set_a less_eq) F))) of role axiom named fact_158_local_OmonoI
% 0.61/0.80 A new axiom: (forall (F:(a->set_a)), ((forall (X2:a) (Y2:a), (((less_eq X2) Y2)->((ord_less_eq_set_a (F X2)) (F Y2))))->((mono_a_set_a less_eq) F)))
% 0.61/0.80 FOF formula (forall (F:(a->set_a)), (((eq Prop) ((mono_a_set_a less_eq) F)) (forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4)))))) of role axiom named fact_159_local_Omono__def
% 0.61/0.80 A new axiom: (forall (F:(a->set_a)), (((eq Prop) ((mono_a_set_a less_eq) F)) (forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4))))))
% 0.61/0.80 FOF formula (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((less_eq A) ((lattic1781219155_fin_a sup) A2))))) of role axiom named fact_160_local_OSup__fin_OcoboundedI
% 0.61/0.80 A new axiom: (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((less_eq A) ((lattic1781219155_fin_a sup) A2)))))
% 0.61/0.80 FOF formula (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((less_eq ((lattic247676691_fin_a inf) A2)) A)))) of role axiom named fact_161_local_OInf__fin_OcoboundedI
% 0.61/0.80 A new axiom: (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((less_eq ((lattic247676691_fin_a inf) A2)) A))))
% 0.61/0.80 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->(((member_a X) A2)->(((eq a) ((sup X) ((lattic1781219155_fin_a sup) A2))) ((lattic1781219155_fin_a sup) A2))))) of role axiom named fact_162_local_OSup__fin_Oin__idem
% 0.61/0.80 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->(((member_a X) A2)->(((eq a) ((sup X) ((lattic1781219155_fin_a sup) A2))) ((lattic1781219155_fin_a sup) A2)))))
% 0.61/0.80 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->(((member_a X) A2)->(((eq a) ((inf X) ((lattic247676691_fin_a inf) A2))) ((lattic247676691_fin_a inf) A2))))) of role axiom named fact_163_local_OInf__fin_Oin__idem
% 0.61/0.80 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->(((member_a X) A2)->(((eq a) ((inf X) ((lattic247676691_fin_a inf) A2))) ((lattic247676691_fin_a inf) A2)))))
% 0.61/0.80 FOF formula (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->(((eq a) ((inf A) ((lattic1781219155_fin_a sup) A2))) A)))) of role axiom named fact_164_local_Oinf__Sup__absorb
% 0.61/0.80 A new axiom: (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->(((eq a) ((inf A) ((lattic1781219155_fin_a sup) A2))) A))))
% 0.61/0.80 FOF formula (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->(((eq a) ((sup ((lattic247676691_fin_a inf) A2)) A)) A)))) of role axiom named fact_165_local_Osup__Inf__absorb
% 0.61/0.80 A new axiom: (forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->(((eq a) ((sup ((lattic247676691_fin_a inf) A2)) A)) A))))
% 0.61/0.80 FOF formula (((eq ((a->(a->a))->(set_a->a))) lattic247676691_fin_a) lattic247676691_fin_a) of role axiom named fact_166_semilattice__inf_OInf__fin_Ocong
% 0.61/0.81 A new axiom: (((eq ((a->(a->a))->(set_a->a))) lattic247676691_fin_a) lattic247676691_fin_a)
% 0.61/0.81 FOF formula (((eq ((a->(a->a))->(set_a->a))) lattic1781219155_fin_a) lattic1781219155_fin_a) of role axiom named fact_167_semilattice__sup_OSup__fin_Ocong
% 0.61/0.81 A new axiom: (((eq ((a->(a->a))->(set_a->a))) lattic1781219155_fin_a) lattic1781219155_fin_a)
% 0.61/0.81 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((less_eq ((lattic247676691_fin_a inf) A2)) ((lattic1781219155_fin_a sup) A2))))) of role axiom named fact_168_local_OInf__fin__le__Sup__fin
% 0.61/0.81 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((less_eq ((lattic247676691_fin_a inf) A2)) ((lattic1781219155_fin_a sup) A2)))))
% 0.61/0.81 FOF formula (forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->((not (((eq set_a) A2) bot_bot_set_a))->((finite_finite_a B4)->((less_eq ((lattic1781219155_fin_a sup) A2)) ((lattic1781219155_fin_a sup) B4)))))) of role axiom named fact_169_local_OSup__fin_Osubset__imp
% 0.61/0.81 A new axiom: (forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->((not (((eq set_a) A2) bot_bot_set_a))->((finite_finite_a B4)->((less_eq ((lattic1781219155_fin_a sup) A2)) ((lattic1781219155_fin_a sup) B4))))))
% 0.61/0.81 FOF formula (forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->((not (((eq set_a) A2) bot_bot_set_a))->((finite_finite_a B4)->((less_eq ((lattic247676691_fin_a inf) B4)) ((lattic247676691_fin_a inf) A2)))))) of role axiom named fact_170_local_OInf__fin_Osubset__imp
% 0.61/0.81 A new axiom: (forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->((not (((eq set_a) A2) bot_bot_set_a))->((finite_finite_a B4)->((less_eq ((lattic247676691_fin_a inf) B4)) ((lattic247676691_fin_a inf) A2))))))
% 0.61/0.81 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((ex a) (fun (X2:a)=> ((and ((member_a X2) A2)) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq Xa) X2)->(((eq a) X2) Xa)))))))))) of role axiom named fact_171_local_Ofinite__has__minimal
% 0.61/0.81 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((ex a) (fun (X2:a)=> ((and ((member_a X2) A2)) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq Xa) X2)->(((eq a) X2) Xa))))))))))
% 0.61/0.81 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((ex a) (fun (X2:a)=> ((and ((member_a X2) A2)) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq X2) Xa)->(((eq a) X2) Xa)))))))))) of role axiom named fact_172_local_Ofinite__has__maximal
% 0.61/0.81 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((ex a) (fun (X2:a)=> ((and ((member_a X2) A2)) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq X2) Xa)->(((eq a) X2) Xa))))))))))
% 0.61/0.81 FOF formula (forall (A2:set_a) (B4:set_a), ((finite_finite_a A2)->((not (((eq set_a) B4) bot_bot_set_a))->(((ord_less_eq_set_a B4) A2)->(((eq a) ((inf ((lattic247676691_fin_a inf) B4)) ((lattic247676691_fin_a inf) A2))) ((lattic247676691_fin_a inf) A2)))))) of role axiom named fact_173_local_OInf__fin_Osubset
% 0.61/0.81 A new axiom: (forall (A2:set_a) (B4:set_a), ((finite_finite_a A2)->((not (((eq set_a) B4) bot_bot_set_a))->(((ord_less_eq_set_a B4) A2)->(((eq a) ((inf ((lattic247676691_fin_a inf) B4)) ((lattic247676691_fin_a inf) A2))) ((lattic247676691_fin_a inf) A2))))))
% 0.61/0.81 FOF formula (forall (A2:set_a) (B4:set_a), ((finite_finite_a A2)->((not (((eq set_a) B4) bot_bot_set_a))->(((ord_less_eq_set_a B4) A2)->(((eq a) ((sup ((lattic1781219155_fin_a sup) B4)) ((lattic1781219155_fin_a sup) A2))) ((lattic1781219155_fin_a sup) A2)))))) of role axiom named fact_174_local_OSup__fin_Osubset
% 0.61/0.81 A new axiom: (forall (A2:set_a) (B4:set_a), ((finite_finite_a A2)->((not (((eq set_a) B4) bot_bot_set_a))->(((ord_less_eq_set_a B4) A2)->(((eq a) ((sup ((lattic1781219155_fin_a sup) B4)) ((lattic1781219155_fin_a sup) A2))) ((lattic1781219155_fin_a sup) A2))))))
% 0.61/0.81 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq Prop) ((less_eq X) ((lattic247676691_fin_a inf) A2))) (forall (X3:a), (((member_a X3) A2)->((less_eq X) X3))))))) of role axiom named fact_175_local_OInf__fin_Obounded__iff
% 0.61/0.82 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq Prop) ((less_eq X) ((lattic247676691_fin_a inf) A2))) (forall (X3:a), (((member_a X3) A2)->((less_eq X) X3)))))))
% 0.61/0.82 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (A4:a), (((member_a A4) A2)->((less_eq X) A4)))->((less_eq X) ((lattic247676691_fin_a inf) A2)))))) of role axiom named fact_176_local_OInf__fin_OboundedI
% 0.61/0.82 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (A4:a), (((member_a A4) A2)->((less_eq X) A4)))->((less_eq X) ((lattic247676691_fin_a inf) A2))))))
% 0.61/0.82 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((less_eq X) ((lattic247676691_fin_a inf) A2))->(forall (A5:a), (((member_a A5) A2)->((less_eq X) A5))))))) of role axiom named fact_177_local_OInf__fin_OboundedE
% 0.61/0.82 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((less_eq X) ((lattic247676691_fin_a inf) A2))->(forall (A5:a), (((member_a A5) A2)->((less_eq X) A5)))))))
% 0.61/0.82 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq Prop) ((less_eq ((lattic1781219155_fin_a sup) A2)) X)) (forall (X3:a), (((member_a X3) A2)->((less_eq X3) X))))))) of role axiom named fact_178_local_OSup__fin_Obounded__iff
% 0.61/0.82 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq Prop) ((less_eq ((lattic1781219155_fin_a sup) A2)) X)) (forall (X3:a), (((member_a X3) A2)->((less_eq X3) X)))))))
% 0.61/0.82 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (A4:a), (((member_a A4) A2)->((less_eq A4) X)))->((less_eq ((lattic1781219155_fin_a sup) A2)) X))))) of role axiom named fact_179_local_OSup__fin_OboundedI
% 0.61/0.82 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (A4:a), (((member_a A4) A2)->((less_eq A4) X)))->((less_eq ((lattic1781219155_fin_a sup) A2)) X)))))
% 0.61/0.82 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((less_eq ((lattic1781219155_fin_a sup) A2)) X)->(forall (A5:a), (((member_a A5) A2)->((less_eq A5) X))))))) of role axiom named fact_180_local_OSup__fin_OboundedE
% 0.61/0.82 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((less_eq ((lattic1781219155_fin_a sup) A2)) X)->(forall (A5:a), (((member_a A5) A2)->((less_eq A5) X)))))))
% 0.61/0.82 FOF formula ((condit1627435690bove_a less_eq) bot_bot_set_a) of role axiom named fact_181_local_Obdd__above__empty
% 0.61/0.82 A new axiom: ((condit1627435690bove_a less_eq) bot_bot_set_a)
% 0.61/0.82 FOF formula ((condit1001553558elow_a less_eq) bot_bot_set_a) of role axiom named fact_182_local_Obdd__below__empty
% 0.61/0.82 A new axiom: ((condit1001553558elow_a less_eq) bot_bot_set_a)
% 0.61/0.82 FOF formula (forall (H:a), (not (((eq set_a) bot_bot_set_a) ((set_atMost_a less_eq) H)))) of role axiom named fact_183_local_Onot__empty__eq__Iic__eq__empty
% 0.61/0.82 A new axiom: (forall (H:a), (not (((eq set_a) bot_bot_set_a) ((set_atMost_a less_eq) H))))
% 0.61/0.82 FOF formula (forall (L:a), (not (((eq set_a) bot_bot_set_a) ((set_atLeast_a less_eq) L)))) of role axiom named fact_184_local_Onot__empty__eq__Ici__eq__empty
% 0.61/0.82 A new axiom: (forall (L:a), (not (((eq set_a) bot_bot_set_a) ((set_atLeast_a less_eq) L))))
% 0.61/0.82 FOF formula (forall (A2:set_a), (((eq Prop) ((ord_less_eq_set_a A2) bot_bot_set_a)) (((eq set_a) A2) bot_bot_set_a))) of role axiom named fact_185_subset__empty
% 0.61/0.82 A new axiom: (forall (A2:set_a), (((eq Prop) ((ord_less_eq_set_a A2) bot_bot_set_a)) (((eq set_a) A2) bot_bot_set_a)))
% 0.61/0.82 FOF formula (forall (P:(a->Prop)), (((eq Prop) (((eq set_a) bot_bot_set_a) (collect_a P))) (forall (X3:a), ((P X3)->False)))) of role axiom named fact_186_empty__Collect__eq
% 0.61/0.83 A new axiom: (forall (P:(a->Prop)), (((eq Prop) (((eq set_a) bot_bot_set_a) (collect_a P))) (forall (X3:a), ((P X3)->False))))
% 0.61/0.83 FOF formula (forall (P:(a->Prop)), (((eq Prop) (((eq set_a) (collect_a P)) bot_bot_set_a)) (forall (X3:a), ((P X3)->False)))) of role axiom named fact_187_Collect__empty__eq
% 0.61/0.83 A new axiom: (forall (P:(a->Prop)), (((eq Prop) (((eq set_a) (collect_a P)) bot_bot_set_a)) (forall (X3:a), ((P X3)->False))))
% 0.61/0.83 FOF formula (forall (A2:set_set_a), (((eq Prop) (forall (X3:set_a), (((member_set_a X3) A2)->False))) (((eq set_set_a) A2) bot_bot_set_set_a))) of role axiom named fact_188_all__not__in__conv
% 0.61/0.83 A new axiom: (forall (A2:set_set_a), (((eq Prop) (forall (X3:set_a), (((member_set_a X3) A2)->False))) (((eq set_set_a) A2) bot_bot_set_set_a)))
% 0.61/0.83 FOF formula (forall (A2:set_a), (((eq Prop) (forall (X3:a), (((member_a X3) A2)->False))) (((eq set_a) A2) bot_bot_set_a))) of role axiom named fact_189_all__not__in__conv
% 0.61/0.83 A new axiom: (forall (A2:set_a), (((eq Prop) (forall (X3:a), (((member_a X3) A2)->False))) (((eq set_a) A2) bot_bot_set_a)))
% 0.61/0.83 FOF formula (forall (C:set_a), (((member_set_a C) bot_bot_set_set_a)->False)) of role axiom named fact_190_empty__iff
% 0.61/0.83 A new axiom: (forall (C:set_a), (((member_set_a C) bot_bot_set_set_a)->False))
% 0.61/0.83 FOF formula (forall (C:a), (((member_a C) bot_bot_set_a)->False)) of role axiom named fact_191_empty__iff
% 0.61/0.83 A new axiom: (forall (C:a), (((member_a C) bot_bot_set_a)->False))
% 0.61/0.83 FOF formula (forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) A2)->(((eq set_a) A2) B4)))) of role axiom named fact_192_subset__antisym
% 0.61/0.83 A new axiom: (forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) A2)->(((eq set_a) A2) B4))))
% 0.61/0.83 FOF formula (forall (A2:set_set_a) (B4:set_set_a), ((forall (X2:set_a), (((member_set_a X2) A2)->((member_set_a X2) B4)))->((ord_le318720350_set_a A2) B4))) of role axiom named fact_193_subsetI
% 0.61/0.83 A new axiom: (forall (A2:set_set_a) (B4:set_set_a), ((forall (X2:set_a), (((member_set_a X2) A2)->((member_set_a X2) B4)))->((ord_le318720350_set_a A2) B4)))
% 0.61/0.83 FOF formula (forall (A2:set_a) (B4:set_a), ((forall (X2:a), (((member_a X2) A2)->((member_a X2) B4)))->((ord_less_eq_set_a A2) B4))) of role axiom named fact_194_subsetI
% 0.61/0.83 A new axiom: (forall (A2:set_a) (B4:set_a), ((forall (X2:a), (((member_a X2) A2)->((member_a X2) B4)))->((ord_less_eq_set_a A2) B4)))
% 0.61/0.83 FOF formula (forall (A2:set_a), ((ord_less_eq_set_a bot_bot_set_a) A2)) of role axiom named fact_195_empty__subsetI
% 0.61/0.83 A new axiom: (forall (A2:set_a), ((ord_less_eq_set_a bot_bot_set_a) A2))
% 0.61/0.83 FOF formula (forall (_TPTP_I:a) (K:a), (((eq Prop) ((member_a _TPTP_I) ((set_atLeast_a less_eq) K))) ((less_eq K) _TPTP_I))) of role axiom named fact_196_local_OatLeast__iff
% 0.61/0.83 A new axiom: (forall (_TPTP_I:a) (K:a), (((eq Prop) ((member_a _TPTP_I) ((set_atLeast_a less_eq) K))) ((less_eq K) _TPTP_I)))
% 0.61/0.83 FOF formula (forall (_TPTP_I:a) (K:a), (((eq Prop) ((member_a _TPTP_I) ((set_atMost_a less_eq) K))) ((less_eq _TPTP_I) K))) of role axiom named fact_197_local_OatMost__iff
% 0.61/0.83 A new axiom: (forall (_TPTP_I:a) (K:a), (((eq Prop) ((member_a _TPTP_I) ((set_atMost_a less_eq) K))) ((less_eq _TPTP_I) K)))
% 0.61/0.83 FOF formula (forall (A:a), ((condit1001553558elow_a less_eq) ((set_atLeast_a less_eq) A))) of role axiom named fact_198_local_Obdd__below__Ici
% 0.61/0.83 A new axiom: (forall (A:a), ((condit1001553558elow_a less_eq) ((set_atLeast_a less_eq) A)))
% 0.61/0.83 FOF formula (forall (B:a), ((condit1627435690bove_a less_eq) ((set_atMost_a less_eq) B))) of role axiom named fact_199_local_Obdd__above__Iic
% 0.61/0.83 A new axiom: (forall (B:a), ((condit1627435690bove_a less_eq) ((set_atMost_a less_eq) B)))
% 0.61/0.83 FOF formula (forall (A2:set_set_a), (((eq Prop) ((ex set_a) (fun (X3:set_a)=> ((member_set_a X3) A2)))) (not (((eq set_set_a) A2) bot_bot_set_set_a)))) of role axiom named fact_200_ex__in__conv
% 0.61/0.83 A new axiom: (forall (A2:set_set_a), (((eq Prop) ((ex set_a) (fun (X3:set_a)=> ((member_set_a X3) A2)))) (not (((eq set_set_a) A2) bot_bot_set_set_a))))
% 0.61/0.83 FOF formula (forall (A2:set_a), (((eq Prop) ((ex a) (fun (X3:a)=> ((member_a X3) A2)))) (not (((eq set_a) A2) bot_bot_set_a)))) of role axiom named fact_201_ex__in__conv
% 0.68/0.84 A new axiom: (forall (A2:set_a), (((eq Prop) ((ex a) (fun (X3:a)=> ((member_a X3) A2)))) (not (((eq set_a) A2) bot_bot_set_a))))
% 0.68/0.84 FOF formula (forall (A2:set_set_a), ((forall (Y2:set_a), (((member_set_a Y2) A2)->False))->(((eq set_set_a) A2) bot_bot_set_set_a))) of role axiom named fact_202_equals0I
% 0.68/0.84 A new axiom: (forall (A2:set_set_a), ((forall (Y2:set_a), (((member_set_a Y2) A2)->False))->(((eq set_set_a) A2) bot_bot_set_set_a)))
% 0.68/0.84 FOF formula (forall (A2:set_a), ((forall (Y2:a), (((member_a Y2) A2)->False))->(((eq set_a) A2) bot_bot_set_a))) of role axiom named fact_203_equals0I
% 0.68/0.84 A new axiom: (forall (A2:set_a), ((forall (Y2:a), (((member_a Y2) A2)->False))->(((eq set_a) A2) bot_bot_set_a)))
% 0.68/0.84 FOF formula (forall (A2:set_set_a) (A:set_a), ((((eq set_set_a) A2) bot_bot_set_set_a)->(((member_set_a A) A2)->False))) of role axiom named fact_204_equals0D
% 0.68/0.84 A new axiom: (forall (A2:set_set_a) (A:set_a), ((((eq set_set_a) A2) bot_bot_set_set_a)->(((member_set_a A) A2)->False)))
% 0.68/0.84 FOF formula (forall (A2:set_a) (A:a), ((((eq set_a) A2) bot_bot_set_a)->(((member_a A) A2)->False))) of role axiom named fact_205_equals0D
% 0.68/0.84 A new axiom: (forall (A2:set_a) (A:a), ((((eq set_a) A2) bot_bot_set_a)->(((member_a A) A2)->False)))
% 0.68/0.84 FOF formula (forall (A:set_a), (((member_set_a A) bot_bot_set_set_a)->False)) of role axiom named fact_206_emptyE
% 0.68/0.84 A new axiom: (forall (A:set_a), (((member_set_a A) bot_bot_set_set_a)->False))
% 0.68/0.84 FOF formula (forall (A:a), (((member_a A) bot_bot_set_a)->False)) of role axiom named fact_207_emptyE
% 0.68/0.84 A new axiom: (forall (A:a), (((member_a A) bot_bot_set_a)->False))
% 0.68/0.84 FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X3:a), ((P X3)->(Q X3))))) of role axiom named fact_208_Collect__mono__iff
% 0.68/0.84 A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X3:a), ((P X3)->(Q X3)))))
% 0.68/0.84 FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y3:set_a) (Z3:set_a)=> (((eq set_a) Y3) Z3))) (fun (A6:set_a) (B5:set_a)=> ((and ((ord_less_eq_set_a A6) B5)) ((ord_less_eq_set_a B5) A6)))) of role axiom named fact_209_set__eq__subset
% 0.68/0.84 A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y3:set_a) (Z3:set_a)=> (((eq set_a) Y3) Z3))) (fun (A6:set_a) (B5:set_a)=> ((and ((ord_less_eq_set_a A6) B5)) ((ord_less_eq_set_a B5) A6))))
% 0.68/0.84 FOF formula (forall (A2:set_a) (B4:set_a) (C4:set_a), (((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) C4)->((ord_less_eq_set_a A2) C4)))) of role axiom named fact_210_subset__trans
% 0.68/0.84 A new axiom: (forall (A2:set_a) (B4:set_a) (C4:set_a), (((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) C4)->((ord_less_eq_set_a A2) C4))))
% 0.68/0.84 FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X2:a), ((P X2)->(Q X2)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q)))) of role axiom named fact_211_Collect__mono
% 0.68/0.84 A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X2:a), ((P X2)->(Q X2)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q))))
% 0.68/0.84 FOF formula (forall (A2:set_a), ((ord_less_eq_set_a A2) A2)) of role axiom named fact_212_subset__refl
% 0.68/0.84 A new axiom: (forall (A2:set_a), ((ord_less_eq_set_a A2) A2))
% 0.68/0.84 FOF formula (((eq (set_set_a->(set_set_a->Prop))) ord_le318720350_set_a) (fun (A6:set_set_a) (B5:set_set_a)=> (forall (T:set_a), (((member_set_a T) A6)->((member_set_a T) B5))))) of role axiom named fact_213_subset__iff
% 0.68/0.84 A new axiom: (((eq (set_set_a->(set_set_a->Prop))) ord_le318720350_set_a) (fun (A6:set_set_a) (B5:set_set_a)=> (forall (T:set_a), (((member_set_a T) A6)->((member_set_a T) B5)))))
% 0.68/0.84 FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A6:set_a) (B5:set_a)=> (forall (T:a), (((member_a T) A6)->((member_a T) B5))))) of role axiom named fact_214_subset__iff
% 0.68/0.84 A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A6:set_a) (B5:set_a)=> (forall (T:a), (((member_a T) A6)->((member_a T) B5)))))
% 0.68/0.84 FOF formula (forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((ord_less_eq_set_a B4) A2))) of role axiom named fact_215_equalityD2
% 0.68/0.85 A new axiom: (forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((ord_less_eq_set_a B4) A2)))
% 0.68/0.85 FOF formula (forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((ord_less_eq_set_a A2) B4))) of role axiom named fact_216_equalityD1
% 0.68/0.85 A new axiom: (forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((ord_less_eq_set_a A2) B4)))
% 0.68/0.85 FOF formula (((eq (set_set_a->(set_set_a->Prop))) ord_le318720350_set_a) (fun (A6:set_set_a) (B5:set_set_a)=> (forall (X3:set_a), (((member_set_a X3) A6)->((member_set_a X3) B5))))) of role axiom named fact_217_subset__eq
% 0.68/0.85 A new axiom: (((eq (set_set_a->(set_set_a->Prop))) ord_le318720350_set_a) (fun (A6:set_set_a) (B5:set_set_a)=> (forall (X3:set_a), (((member_set_a X3) A6)->((member_set_a X3) B5)))))
% 0.68/0.85 FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A6:set_a) (B5:set_a)=> (forall (X3:a), (((member_a X3) A6)->((member_a X3) B5))))) of role axiom named fact_218_subset__eq
% 0.68/0.85 A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A6:set_a) (B5:set_a)=> (forall (X3:a), (((member_a X3) A6)->((member_a X3) B5)))))
% 0.68/0.85 FOF formula (forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) A2)->False))->False))) of role axiom named fact_219_equalityE
% 0.68/0.85 A new axiom: (forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) A2)->False))->False)))
% 0.68/0.85 FOF formula (forall (A2:set_set_a) (B4:set_set_a) (C:set_a), (((ord_le318720350_set_a A2) B4)->(((member_set_a C) A2)->((member_set_a C) B4)))) of role axiom named fact_220_subsetD
% 0.68/0.85 A new axiom: (forall (A2:set_set_a) (B4:set_set_a) (C:set_a), (((ord_le318720350_set_a A2) B4)->(((member_set_a C) A2)->((member_set_a C) B4))))
% 0.68/0.85 FOF formula (forall (A2:set_a) (B4:set_a) (C:a), (((ord_less_eq_set_a A2) B4)->(((member_a C) A2)->((member_a C) B4)))) of role axiom named fact_221_subsetD
% 0.68/0.85 A new axiom: (forall (A2:set_a) (B4:set_a) (C:a), (((ord_less_eq_set_a A2) B4)->(((member_a C) A2)->((member_a C) B4))))
% 0.68/0.85 FOF formula (forall (A2:set_set_a) (B4:set_set_a) (X:set_a), (((ord_le318720350_set_a A2) B4)->(((member_set_a X) A2)->((member_set_a X) B4)))) of role axiom named fact_222_in__mono
% 0.68/0.85 A new axiom: (forall (A2:set_set_a) (B4:set_set_a) (X:set_a), (((ord_le318720350_set_a A2) B4)->(((member_set_a X) A2)->((member_set_a X) B4))))
% 0.68/0.85 FOF formula (forall (A2:set_a) (B4:set_a) (X:a), (((ord_less_eq_set_a A2) B4)->(((member_a X) A2)->((member_a X) B4)))) of role axiom named fact_223_in__mono
% 0.68/0.85 A new axiom: (forall (A2:set_a) (B4:set_a) (X:a), (((ord_less_eq_set_a A2) B4)->(((member_a X) A2)->((member_a X) B4))))
% 0.68/0.85 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (X2:a) (Y2:a), ((member_a ((sup X2) Y2)) ((insert_a X2) ((insert_a Y2) bot_bot_set_a))))->((member_a ((lattic1781219155_fin_a sup) A2)) A2))))) of role axiom named fact_224_local_OSup__fin_Oclosed
% 0.68/0.85 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (X2:a) (Y2:a), ((member_a ((sup X2) Y2)) ((insert_a X2) ((insert_a Y2) bot_bot_set_a))))->((member_a ((lattic1781219155_fin_a sup) A2)) A2)))))
% 0.68/0.85 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((((member_a X) A2)->False)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) A2))) ((sup X) ((lattic1781219155_fin_a sup) A2))))))) of role axiom named fact_225_local_OSup__fin_Oinsert__not__elem
% 0.68/0.85 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((((member_a X) A2)->False)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) A2))) ((sup X) ((lattic1781219155_fin_a sup) A2)))))))
% 0.68/0.85 FOF formula (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (X2:a) (Y2:a), ((member_a ((inf X2) Y2)) ((insert_a X2) ((insert_a Y2) bot_bot_set_a))))->((member_a ((lattic247676691_fin_a inf) A2)) A2))))) of role axiom named fact_226_local_OInf__fin_Oclosed
% 0.68/0.85 A new axiom: (forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (X2:a) (Y2:a), ((member_a ((inf X2) Y2)) ((insert_a X2) ((insert_a Y2) bot_bot_set_a))))->((member_a ((lattic247676691_fin_a inf) A2)) A2)))))
% 0.68/0.86 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((((member_a X) A2)->False)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic247676691_fin_a inf) ((insert_a X) A2))) ((inf X) ((lattic247676691_fin_a inf) A2))))))) of role axiom named fact_227_local_OInf__fin_Oinsert__not__elem
% 0.68/0.86 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((((member_a X) A2)->False)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic247676691_fin_a inf) ((insert_a X) A2))) ((inf X) ((lattic247676691_fin_a inf) A2)))))))
% 0.68/0.86 FOF formula (forall (A:set_a), ((member_set_a A) ((insert_set_a A) bot_bot_set_set_a))) of role axiom named fact_228_singletonI
% 0.68/0.86 A new axiom: (forall (A:set_a), ((member_set_a A) ((insert_set_a A) bot_bot_set_set_a)))
% 0.68/0.86 FOF formula (forall (A:a), ((member_a A) ((insert_a A) bot_bot_set_a))) of role axiom named fact_229_singletonI
% 0.68/0.86 A new axiom: (forall (A:a), ((member_a A) ((insert_a A) bot_bot_set_a)))
% 0.68/0.86 FOF formula (forall (X:set_a) (A2:set_set_a) (B4:set_set_a), (((eq Prop) ((ord_le318720350_set_a ((insert_set_a X) A2)) B4)) ((and ((member_set_a X) B4)) ((ord_le318720350_set_a A2) B4)))) of role axiom named fact_230_insert__subset
% 0.68/0.86 A new axiom: (forall (X:set_a) (A2:set_set_a) (B4:set_set_a), (((eq Prop) ((ord_le318720350_set_a ((insert_set_a X) A2)) B4)) ((and ((member_set_a X) B4)) ((ord_le318720350_set_a A2) B4))))
% 0.68/0.86 FOF formula (forall (X:a) (A2:set_a) (B4:set_a), (((eq Prop) ((ord_less_eq_set_a ((insert_a X) A2)) B4)) ((and ((member_a X) B4)) ((ord_less_eq_set_a A2) B4)))) of role axiom named fact_231_insert__subset
% 0.68/0.86 A new axiom: (forall (X:a) (A2:set_a) (B4:set_a), (((eq Prop) ((ord_less_eq_set_a ((insert_a X) A2)) B4)) ((and ((member_a X) B4)) ((ord_less_eq_set_a A2) B4))))
% 0.68/0.86 FOF formula (forall (A:a) (A2:set_a) (B:a), (((eq Prop) (((eq set_a) ((insert_a A) A2)) ((insert_a B) bot_bot_set_a))) ((and (((eq a) A) B)) ((ord_less_eq_set_a A2) ((insert_a B) bot_bot_set_a))))) of role axiom named fact_232_singleton__insert__inj__eq_H
% 0.68/0.86 A new axiom: (forall (A:a) (A2:set_a) (B:a), (((eq Prop) (((eq set_a) ((insert_a A) A2)) ((insert_a B) bot_bot_set_a))) ((and (((eq a) A) B)) ((ord_less_eq_set_a A2) ((insert_a B) bot_bot_set_a)))))
% 0.68/0.86 FOF formula (forall (B:a) (A:a) (A2:set_a), (((eq Prop) (((eq set_a) ((insert_a B) bot_bot_set_a)) ((insert_a A) A2))) ((and (((eq a) A) B)) ((ord_less_eq_set_a A2) ((insert_a B) bot_bot_set_a))))) of role axiom named fact_233_singleton__insert__inj__eq
% 0.68/0.86 A new axiom: (forall (B:a) (A:a) (A2:set_a), (((eq Prop) (((eq set_a) ((insert_a B) bot_bot_set_a)) ((insert_a A) A2))) ((and (((eq a) A) B)) ((ord_less_eq_set_a A2) ((insert_a B) bot_bot_set_a)))))
% 0.68/0.86 FOF formula (forall (A:a) (A2:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) ((insert_a A) A2))) ((condit1627435690bove_a less_eq) A2))) of role axiom named fact_234_local_Obdd__above__insert
% 0.68/0.86 A new axiom: (forall (A:a) (A2:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) ((insert_a A) A2))) ((condit1627435690bove_a less_eq) A2)))
% 0.68/0.86 FOF formula (forall (A:a) (A2:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) ((insert_a A) A2))) ((condit1001553558elow_a less_eq) A2))) of role axiom named fact_235_local_Obdd__below__insert
% 0.68/0.86 A new axiom: (forall (A:a) (A2:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) ((insert_a A) A2))) ((condit1001553558elow_a less_eq) A2)))
% 0.68/0.86 FOF formula (forall (X:a), (((eq a) ((lattic247676691_fin_a inf) ((insert_a X) bot_bot_set_a))) X)) of role axiom named fact_236_local_OInf__fin_Osingleton
% 0.68/0.86 A new axiom: (forall (X:a), (((eq a) ((lattic247676691_fin_a inf) ((insert_a X) bot_bot_set_a))) X))
% 0.68/0.86 FOF formula (forall (X:a), (((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) bot_bot_set_a))) X)) of role axiom named fact_237_local_OSup__fin_Osingleton
% 0.68/0.86 A new axiom: (forall (X:a), (((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) bot_bot_set_a))) X))
% 0.68/0.86 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic247676691_fin_a inf) ((insert_a X) A2))) ((inf X) ((lattic247676691_fin_a inf) A2)))))) of role axiom named fact_238_local_OInf__fin_Oinsert
% 0.72/0.87 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic247676691_fin_a inf) ((insert_a X) A2))) ((inf X) ((lattic247676691_fin_a inf) A2))))))
% 0.72/0.87 FOF formula (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) A2))) ((sup X) ((lattic1781219155_fin_a sup) A2)))))) of role axiom named fact_239_local_OSup__fin_Oinsert
% 0.72/0.87 A new axiom: (forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) A2))) ((sup X) ((lattic1781219155_fin_a sup) A2))))))
% 0.72/0.87 FOF formula (forall (A2:set_a) (X:a), (((ord_less_eq_set_a A2) ((insert_a X) bot_bot_set_a))->((or (((eq set_a) A2) bot_bot_set_a)) (((eq set_a) A2) ((insert_a X) bot_bot_set_a))))) of role axiom named fact_240_subset__singletonD
% 0.72/0.87 A new axiom: (forall (A2:set_a) (X:a), (((ord_less_eq_set_a A2) ((insert_a X) bot_bot_set_a))->((or (((eq set_a) A2) bot_bot_set_a)) (((eq set_a) A2) ((insert_a X) bot_bot_set_a)))))
% 0.72/0.87 FOF formula (forall (X5:set_a) (A:a), (((eq Prop) ((ord_less_eq_set_a X5) ((insert_a A) bot_bot_set_a))) ((or (((eq set_a) X5) bot_bot_set_a)) (((eq set_a) X5) ((insert_a A) bot_bot_set_a))))) of role axiom named fact_241_subset__singleton__iff
% 0.72/0.87 A new axiom: (forall (X5:set_a) (A:a), (((eq Prop) ((ord_less_eq_set_a X5) ((insert_a A) bot_bot_set_a))) ((or (((eq set_a) X5) bot_bot_set_a)) (((eq set_a) X5) ((insert_a A) bot_bot_set_a)))))
% 0.72/0.87 FOF formula (forall (B:set_a) (A:set_a), (((member_set_a B) ((insert_set_a A) bot_bot_set_set_a))->(((eq set_a) B) A))) of role axiom named fact_242_singletonD
% 0.72/0.87 A new axiom: (forall (B:set_a) (A:set_a), (((member_set_a B) ((insert_set_a A) bot_bot_set_set_a))->(((eq set_a) B) A)))
% 0.72/0.87 FOF formula (forall (B:a) (A:a), (((member_a B) ((insert_a A) bot_bot_set_a))->(((eq a) B) A))) of role axiom named fact_243_singletonD
% 0.72/0.87 A new axiom: (forall (B:a) (A:a), (((member_a B) ((insert_a A) bot_bot_set_a))->(((eq a) B) A)))
% 0.72/0.87 FOF formula (forall (B:set_a) (A:set_a), (((eq Prop) ((member_set_a B) ((insert_set_a A) bot_bot_set_set_a))) (((eq set_a) B) A))) of role axiom named fact_244_singleton__iff
% 0.72/0.87 A new axiom: (forall (B:set_a) (A:set_a), (((eq Prop) ((member_set_a B) ((insert_set_a A) bot_bot_set_set_a))) (((eq set_a) B) A)))
% 0.72/0.87 FOF formula (forall (B:a) (A:a), (((eq Prop) ((member_a B) ((insert_a A) bot_bot_set_a))) (((eq a) B) A))) of role axiom named fact_245_singleton__iff
% 0.72/0.87 A new axiom: (forall (B:a) (A:a), (((eq Prop) ((member_a B) ((insert_a A) bot_bot_set_a))) (((eq a) B) A)))
% 0.72/0.87 FOF formula (forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) (((eq set_a) ((insert_a A) ((insert_a B) bot_bot_set_a))) ((insert_a C) ((insert_a D) bot_bot_set_a)))) ((or ((and (((eq a) A) C)) (((eq a) B) D))) ((and (((eq a) A) D)) (((eq a) B) C))))) of role axiom named fact_246_doubleton__eq__iff
% 0.72/0.87 A new axiom: (forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) (((eq set_a) ((insert_a A) ((insert_a B) bot_bot_set_a))) ((insert_a C) ((insert_a D) bot_bot_set_a)))) ((or ((and (((eq a) A) C)) (((eq a) B) D))) ((and (((eq a) A) D)) (((eq a) B) C)))))
% 0.72/0.87 FOF formula (forall (A:a) (A2:set_a), (not (((eq set_a) ((insert_a A) A2)) bot_bot_set_a))) of role axiom named fact_247_insert__not__empty
% 0.72/0.87 A new axiom: (forall (A:a) (A2:set_a), (not (((eq set_a) ((insert_a A) A2)) bot_bot_set_a)))
% 0.72/0.87 FOF formula (forall (A:a) (B:a), ((((eq set_a) ((insert_a A) bot_bot_set_a)) ((insert_a B) bot_bot_set_a))->(((eq a) A) B))) of role axiom named fact_248_singleton__inject
% 0.72/0.87 A new axiom: (forall (A:a) (B:a), ((((eq set_a) ((insert_a A) bot_bot_set_a)) ((insert_a B) bot_bot_set_a))->(((eq a) A) B)))
% 0.72/0.87 FOF formula (forall (A2:set_a) (B4:set_a) (B:a), (((ord_less_eq_set_a A2) B4)->((ord_less_eq_set_a A2) ((insert_a B) B4)))) of role axiom named fact_249_subset__insertI2
% 0.72/0.87 A new axiom: (forall (A2:set_a) (B4:set_a) (B:a), (((ord_less_eq_set_a A2) B4)->((ord_less_eq_set_a A2) ((insert_a B) B4))))
% 0.72/0.88 FOF formula (forall (B4:set_a) (A:a), ((ord_less_eq_set_a B4) ((insert_a A) B4))) of role axiom named fact_250_subset__insertI
% 0.72/0.88 A new axiom: (forall (B4:set_a) (A:a), ((ord_less_eq_set_a B4) ((insert_a A) B4)))
% 0.72/0.88 FOF formula (forall (X:set_a) (A2:set_set_a) (B4:set_set_a), ((((member_set_a X) A2)->False)->(((eq Prop) ((ord_le318720350_set_a A2) ((insert_set_a X) B4))) ((ord_le318720350_set_a A2) B4)))) of role axiom named fact_251_subset__insert
% 0.72/0.88 A new axiom: (forall (X:set_a) (A2:set_set_a) (B4:set_set_a), ((((member_set_a X) A2)->False)->(((eq Prop) ((ord_le318720350_set_a A2) ((insert_set_a X) B4))) ((ord_le318720350_set_a A2) B4))))
% 0.72/0.88 FOF formula (forall (X:a) (A2:set_a) (B4:set_a), ((((member_a X) A2)->False)->(((eq Prop) ((ord_less_eq_set_a A2) ((insert_a X) B4))) ((ord_less_eq_set_a A2) B4)))) of role axiom named fact_252_subset__insert
% 0.72/0.88 A new axiom: (forall (X:a) (A2:set_a) (B4:set_a), ((((member_a X) A2)->False)->(((eq Prop) ((ord_less_eq_set_a A2) ((insert_a X) B4))) ((ord_less_eq_set_a A2) B4))))
% 0.72/0.88 FOF formula (forall (C4:set_a) (D2:set_a) (A:a), (((ord_less_eq_set_a C4) D2)->((ord_less_eq_set_a ((insert_a A) C4)) ((insert_a A) D2)))) of role axiom named fact_253_insert__mono
% 0.72/0.88 A new axiom: (forall (C4:set_a) (D2:set_a) (A:a), (((ord_less_eq_set_a C4) D2)->((ord_less_eq_set_a ((insert_a A) C4)) ((insert_a A) D2))))
% 0.72/0.88 FOF formula (forall (A:a) (B:a), ((((eq a) A) B)->(((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) ((insert_a A) bot_bot_set_a)))) of role axiom named fact_254_local_OatLeastAtMost__singleton_H
% 0.72/0.88 A new axiom: (forall (A:a) (B:a), ((((eq a) A) B)->(((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) ((insert_a A) bot_bot_set_a))))
% 0.72/0.88 FOF formula (forall (A:set_a) (A2:set_set_a), (((eq Prop) (finite_finite_set_a ((insert_set_a A) A2))) (finite_finite_set_a A2))) of role axiom named fact_255_finite__insert
% 0.72/0.88 A new axiom: (forall (A:set_a) (A2:set_set_a), (((eq Prop) (finite_finite_set_a ((insert_set_a A) A2))) (finite_finite_set_a A2)))
% 0.72/0.88 FOF formula (forall (A:a) (A2:set_a), (((eq Prop) (finite_finite_a ((insert_a A) A2))) (finite_finite_a A2))) of role axiom named fact_256_finite__insert
% 0.72/0.88 A new axiom: (forall (A:a) (A2:set_a), (((eq Prop) (finite_finite_a ((insert_a A) A2))) (finite_finite_a A2)))
% 0.72/0.88 FOF formula (forall (L:a) (H:a) (L2:a) (H2:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) L) H)) (((set_atLeastAtMost_a less_eq) L2) H2))) ((or ((and (((eq a) L) L2)) (((eq a) H) H2))) ((and (((less_eq L) H)->False)) (((less_eq L2) H2)->False))))) of role axiom named fact_257_local_OIcc__eq__Icc
% 0.72/0.88 A new axiom: (forall (L:a) (H:a) (L2:a) (H2:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) L) H)) (((set_atLeastAtMost_a less_eq) L2) H2))) ((or ((and (((eq a) L) L2)) (((eq a) H) H2))) ((and (((less_eq L) H)->False)) (((less_eq L2) H2)->False)))))
% 0.72/0.88 FOF formula (forall (_TPTP_I:a) (L:a) (U:a), (((eq Prop) ((member_a _TPTP_I) (((set_atLeastAtMost_a less_eq) L) U))) ((and ((less_eq L) _TPTP_I)) ((less_eq _TPTP_I) U)))) of role axiom named fact_258_local_OatLeastAtMost__iff
% 0.72/0.88 A new axiom: (forall (_TPTP_I:a) (L:a) (U:a), (((eq Prop) ((member_a _TPTP_I) (((set_atLeastAtMost_a less_eq) L) U))) ((and ((less_eq L) _TPTP_I)) ((less_eq _TPTP_I) U))))
% 0.72/0.88 FOF formula (forall (A:a) (B:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) bot_bot_set_a)) (((less_eq A) B)->False))) of role axiom named fact_259_local_OatLeastatMost__empty__iff
% 0.72/0.88 A new axiom: (forall (A:a) (B:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) bot_bot_set_a)) (((less_eq A) B)->False)))
% 0.72/0.88 FOF formula (forall (A:a) (B:a), (((eq Prop) (((eq set_a) bot_bot_set_a) (((set_atLeastAtMost_a less_eq) A) B))) (((less_eq A) B)->False))) of role axiom named fact_260_local_OatLeastatMost__empty__iff2
% 0.72/0.88 A new axiom: (forall (A:a) (B:a), (((eq Prop) (((eq set_a) bot_bot_set_a) (((set_atLeastAtMost_a less_eq) A) B))) (((less_eq A) B)->False)))
% 0.72/0.88 FOF formula (forall (A:a) (B:a), ((condit1001553558elow_a less_eq) (((set_atLeastAtMost_a less_eq) A) B))) of role axiom named fact_261_local_Obdd__below__Icc
% 0.72/0.89 A new axiom: (forall (A:a) (B:a), ((condit1001553558elow_a less_eq) (((set_atLeastAtMost_a less_eq) A) B)))
% 0.72/0.89 FOF formula (forall (A:a) (B:a), ((condit1627435690bove_a less_eq) (((set_atLeastAtMost_a less_eq) A) B))) of role axiom named fact_262_local_Obdd__above__Icc
% 0.72/0.89 A new axiom: (forall (A:a) (B:a), ((condit1627435690bove_a less_eq) (((set_atLeastAtMost_a less_eq) A) B)))
% 0.72/0.89 FOF formula (forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) A) B)) (((set_atLeastAtMost_a less_eq) C) D))) ((or (((less_eq A) B)->False)) ((and ((less_eq C) A)) ((less_eq B) D))))) of role axiom named fact_263_local_OatLeastatMost__subset__iff
% 0.72/0.89 A new axiom: (forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) A) B)) (((set_atLeastAtMost_a less_eq) C) D))) ((or (((less_eq A) B)->False)) ((and ((less_eq C) A)) ((less_eq B) D)))))
% 0.72/0.89 FOF formula (forall (A:a), (((eq set_a) (((set_atLeastAtMost_a less_eq) A) A)) ((insert_a A) bot_bot_set_a))) of role axiom named fact_264_local_OatLeastAtMost__singleton
% 0.72/0.89 A new axiom: (forall (A:a), (((eq set_a) (((set_atLeastAtMost_a less_eq) A) A)) ((insert_a A) bot_bot_set_a)))
% 0.72/0.89 FOF formula (forall (A:a) (B:a) (C:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) ((insert_a C) bot_bot_set_a))) ((and (((eq a) A) B)) (((eq a) B) C)))) of role axiom named fact_265_local_OatLeastAtMost__singleton__iff
% 0.72/0.89 A new axiom: (forall (A:a) (B:a) (C:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) ((insert_a C) bot_bot_set_a))) ((and (((eq a) A) B)) (((eq a) B) C))))
% 0.72/0.89 FOF formula (forall (L:a) (H:a) (L2:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) L) H)) ((set_atLeast_a less_eq) L2))) ((or (((less_eq L) H)->False)) ((less_eq L2) L)))) of role axiom named fact_266_local_OIcc__subset__Ici__iff
% 0.72/0.89 A new axiom: (forall (L:a) (H:a) (L2:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) L) H)) ((set_atLeast_a less_eq) L2))) ((or (((less_eq L) H)->False)) ((less_eq L2) L))))
% 0.72/0.89 FOF formula (forall (L:a) (H:a) (H2:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) L) H)) ((set_atMost_a less_eq) H2))) ((or (((less_eq L) H)->False)) ((less_eq H) H2)))) of role axiom named fact_267_local_OIcc__subset__Iic__iff
% 0.72/0.89 A new axiom: (forall (L:a) (H:a) (H2:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) L) H)) ((set_atMost_a less_eq) H2))) ((or (((less_eq L) H)->False)) ((less_eq H) H2))))
% 0.72/0.89 FOF formula (forall (F:(a->(a->a))) (X:a) (Z:a), ((finite40241356em_a_a F)->(((eq a) ((F X) ((F X) Z))) ((F X) Z)))) of role axiom named fact_268_comp__fun__idem_Ofun__left__idem
% 0.72/0.89 A new axiom: (forall (F:(a->(a->a))) (X:a) (Z:a), ((finite40241356em_a_a F)->(((eq a) ((F X) ((F X) Z))) ((F X) Z))))
% 0.72/0.89 FOF formula (forall (A2:set_set_a) (A:set_a), ((finite_finite_set_a A2)->(((member_set_a A) A2)->((ex set_a) (fun (X2:set_a)=> ((and ((and ((member_set_a X2) A2)) ((ord_less_eq_set_a X2) A))) (forall (Xa:set_a), (((member_set_a Xa) A2)->(((ord_less_eq_set_a Xa) X2)->(((eq set_a) X2) Xa)))))))))) of role axiom named fact_269_order__class_Ofinite__has__minimal2
% 0.72/0.89 A new axiom: (forall (A2:set_set_a) (A:set_a), ((finite_finite_set_a A2)->(((member_set_a A) A2)->((ex set_a) (fun (X2:set_a)=> ((and ((and ((member_set_a X2) A2)) ((ord_less_eq_set_a X2) A))) (forall (Xa:set_a), (((member_set_a Xa) A2)->(((ord_less_eq_set_a Xa) X2)->(((eq set_a) X2) Xa))))))))))
% 0.72/0.89 FOF formula (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) (((((modula1144073633_aux_a inf) sup) a2) b) c)) of role conjecture named conj_0
% 0.72/0.89 Conjecture to prove = (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) (((((modula1144073633_aux_a inf) sup) a2) b) c)):Prop
% 0.72/0.89 We need to prove ['(((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) (((((modula1144073633_aux_a inf) sup) a2) b) c))']
% 0.72/0.89 Parameter set_set_a:Type.
% 0.72/0.89 Parameter set_a:Type.
% 0.72/0.89 Parameter a:Type.
% 0.72/0.89 Parameter condit1627435690bove_a:((a->(a->Prop))->(set_a->Prop)).
% 0.72/0.89 Parameter condit1001553558elow_a:((a->(a->Prop))->(set_a->Prop)).
% 0.72/0.89 Parameter finite40241356em_a_a:((a->(a->a))->Prop).
% 0.72/0.89 Parameter finite_finite_set_a:(set_set_a->Prop).
% 0.72/0.89 Parameter finite_finite_a:(set_a->Prop).
% 0.72/0.89 Parameter abel_semigroup_a:((a->(a->a))->Prop).
% 0.72/0.89 Parameter semigroup_a:((a->(a->a))->Prop).
% 0.72/0.89 Parameter semilattice_a:((a->(a->a))->Prop).
% 0.72/0.89 Parameter lattic247676691_fin_a:((a->(a->a))->(set_a->a)).
% 0.72/0.89 Parameter lattic1885654924_set_a:((a->(a->a))->Prop).
% 0.72/0.89 Parameter lattic1781219155_fin_a:((a->(a->a))->(set_a->a)).
% 0.72/0.89 Parameter modula1936294176_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.72/0.89 Parameter modula1144073633_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.72/0.89 Parameter bot_bot_set_set_a:set_set_a.
% 0.72/0.89 Parameter bot_bot_set_a:set_a.
% 0.72/0.89 Parameter least_a:((a->(a->Prop))->((a->Prop)->a)).
% 0.72/0.89 Parameter max_a:((a->(a->Prop))->(a->(a->a))).
% 0.72/0.89 Parameter min_a:((a->(a->Prop))->(a->(a->a))).
% 0.72/0.89 Parameter ord_le318720350_set_a:(set_set_a->(set_set_a->Prop)).
% 0.72/0.89 Parameter ord_less_eq_set_a:(set_a->(set_a->Prop)).
% 0.72/0.89 Parameter greatest_a:((a->(a->Prop))->((a->Prop)->a)).
% 0.72/0.89 Parameter antimono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop)).
% 0.72/0.89 Parameter mono_a_set_a:((a->(a->Prop))->((a->set_a)->Prop)).
% 0.72/0.89 Parameter transp_a:((a->(a->Prop))->Prop).
% 0.72/0.89 Parameter collect_set_a:((set_a->Prop)->set_set_a).
% 0.72/0.89 Parameter collect_a:((a->Prop)->set_a).
% 0.72/0.89 Parameter insert_set_a:(set_a->(set_set_a->set_set_a)).
% 0.72/0.89 Parameter insert_a:(a->(set_a->set_a)).
% 0.72/0.89 Parameter set_atLeastAtMost_a:((a->(a->Prop))->(a->(a->set_a))).
% 0.72/0.89 Parameter set_atLeast_a:((a->(a->Prop))->(a->set_a)).
% 0.72/0.89 Parameter set_atMost_a:((a->(a->Prop))->(a->set_a)).
% 0.72/0.89 Parameter member_set_a:(set_a->(set_set_a->Prop)).
% 0.72/0.89 Parameter member_a:(a->(set_a->Prop)).
% 0.72/0.89 Parameter a2:a.
% 0.72/0.89 Parameter b:a.
% 0.72/0.89 Parameter c:a.
% 0.72/0.89 Parameter inf:(a->(a->a)).
% 0.72/0.89 Parameter less_eq:(a->(a->Prop)).
% 0.72/0.89 Parameter sup:(a->(a->a)).
% 0.72/0.89 Axiom fact_0_local_Oinf_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C)))).
% 0.72/0.89 Axiom fact_1_local_Oinf_Ocommute:(forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A))).
% 0.72/0.89 Axiom fact_2_local_Oinf_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C)))).
% 0.72/0.89 Axiom fact_3_local_Oinf__assoc:(forall (X:a) (Y:a) (Z:a), (((eq a) ((inf ((inf X) Y)) Z)) ((inf X) ((inf Y) Z)))).
% 0.72/0.89 Axiom fact_4_local_Oinf__commute:(forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X))).
% 0.72/0.89 Axiom fact_5_local_Oinf__left__commute:(forall (X:a) (Y:a) (Z:a), (((eq a) ((inf X) ((inf Y) Z))) ((inf Y) ((inf X) Z)))).
% 0.72/0.89 Axiom fact_6_local_Osup_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C)))).
% 0.72/0.89 Axiom fact_7_local_Osup_Ocommute:(forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A))).
% 0.72/0.89 Axiom fact_8_local_Osup_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C)))).
% 0.72/0.89 Axiom fact_9_local_Osup__assoc:(forall (X:a) (Y:a) (Z:a), (((eq a) ((sup ((sup X) Y)) Z)) ((sup X) ((sup Y) Z)))).
% 0.72/0.89 Axiom fact_10_local_Osup__commute:(forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X))).
% 0.72/0.89 Axiom fact_11_local_Osup__left__commute:(forall (X:a) (Y:a) (Z:a), (((eq a) ((sup X) ((sup Y) Z))) ((sup Y) ((sup X) Z)))).
% 0.72/0.89 Axiom fact_12_local_Odistrib__imp1:(forall (X:a) (Y:a) (Z:a), ((forall (X2:a) (Y2:a) (Z2:a), (((eq a) ((inf X2) ((sup Y2) Z2))) ((sup ((inf X2) Y2)) ((inf X2) Z2))))->(((eq a) ((sup X) ((inf Y) Z))) ((inf ((sup X) Y)) ((sup X) Z))))).
% 0.72/0.89 Axiom fact_13_local_Odistrib__imp2:(forall (X:a) (Y:a) (Z:a), ((forall (X2:a) (Y2:a) (Z2:a), (((eq a) ((sup X2) ((inf Y2) Z2))) ((inf ((sup X2) Y2)) ((sup X2) Z2))))->(((eq a) ((inf X) ((sup Y) Z))) ((sup ((inf X) Y)) ((inf X) Z))))).
% 0.72/0.89 Axiom fact_14_e__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)))).
% 0.72/0.89 Axiom fact_15_local_Oinf_Oidem:(forall (A:a), (((eq a) ((inf A) A)) A)).
% 0.72/0.89 Axiom fact_16_local_Oinf_Oleft__idem:(forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B))).
% 0.72/0.89 Axiom fact_17_local_Oinf_Oright__idem:(forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B))).
% 0.72/0.89 Axiom fact_18_local_Oinf__idem:(forall (X:a), (((eq a) ((inf X) X)) X)).
% 0.72/0.89 Axiom fact_19_local_Oinf__left__idem:(forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y))).
% 0.72/0.90 Axiom fact_20_local_Oinf__right__idem:(forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y))).
% 0.72/0.90 Axiom fact_21_local_Osup_Oidem:(forall (A:a), (((eq a) ((sup A) A)) A)).
% 0.72/0.90 Axiom fact_22_local_Osup_Oleft__idem:(forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B))).
% 0.72/0.90 Axiom fact_23_local_Osup_Oright__idem:(forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B))).
% 0.72/0.90 Axiom fact_24_local_Osup__idem:(forall (X:a), (((eq a) ((sup X) X)) X)).
% 0.72/0.90 Axiom fact_25_local_Osup__left__idem:(forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y))).
% 0.72/0.90 Axiom fact_26_local_Oinf__sup__absorb:(forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X)).
% 0.72/0.90 Axiom fact_27_local_Osup__inf__absorb:(forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X)).
% 0.72/0.90 Axiom fact_28_d__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)))).
% 0.72/0.90 Axiom fact_29_d__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))).
% 0.72/0.90 Axiom fact_30_d__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))).
% 0.72/0.90 Axiom fact_31_lattice_Oe__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a).
% 0.72/0.90 Axiom fact_32_local_Ocomp__fun__idem__sup:(finite40241356em_a_a sup).
% 0.72/0.90 Axiom fact_33_local_Ocomp__fun__idem__inf:(finite40241356em_a_a inf).
% 0.72/0.90 Axiom fact_34_local_Osup_Osemigroup__axioms:(semigroup_a sup).
% 0.72/0.90 Axiom fact_35_local_Oinf_Osemigroup__axioms:(semigroup_a inf).
% 0.72/0.90 Axiom fact_36_local_Osup_Osemilattice__axioms:(semilattice_a sup).
% 0.72/0.90 Axiom fact_37_local_Oinf_Osemilattice__axioms:(semilattice_a inf).
% 0.72/0.90 Axiom fact_38_local_Osup_Oabel__semigroup__axioms:(abel_semigroup_a sup).
% 0.72/0.90 Axiom fact_39_local_Oinf_Oabel__semigroup__axioms:(abel_semigroup_a inf).
% 0.72/0.90 Axiom fact_40_local_OSup__fin_Osemilattice__set__axioms:(lattic1885654924_set_a sup).
% 0.72/0.90 Axiom fact_41_local_OInf__fin_Osemilattice__set__axioms:(lattic1885654924_set_a inf).
% 0.72/0.90 Axiom fact_42_local_Odistrib__inf__le:(forall (X:a) (Y:a) (Z:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z))) ((inf X) ((sup Y) Z)))).
% 0.72/0.90 Axiom fact_43_local_Odistrib__sup__le:(forall (X:a) (Y:a) (Z:a), ((less_eq ((sup X) ((inf Y) Z))) ((inf ((sup X) Y)) ((sup X) Z)))).
% 0.72/0.90 Axiom fact_44_local_Oantisym:(forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y)))).
% 0.72/0.90 Axiom fact_45_mem__Collect__eq:(forall (A:set_a) (P:(set_a->Prop)), (((eq Prop) ((member_set_a A) (collect_set_a P))) (P A))).
% 0.72/0.90 Axiom fact_46_mem__Collect__eq:(forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))).
% 0.72/0.90 Axiom fact_47_Collect__mem__eq:(forall (A2:set_set_a), (((eq set_set_a) (collect_set_a (fun (X3:set_a)=> ((member_set_a X3) A2)))) A2)).
% 0.72/0.90 Axiom fact_48_Collect__mem__eq:(forall (A2:set_a), (((eq set_a) (collect_a (fun (X3:a)=> ((member_a X3) A2)))) A2)).
% 0.72/0.90 Axiom fact_49_Collect__cong:(forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X2:a), (((eq Prop) (P X2)) (Q X2)))->(((eq set_a) (collect_a P)) (collect_a Q)))).
% 0.72/0.90 Axiom fact_50_local_Oantisym__conv:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))).
% 0.72/0.90 Axiom fact_51_local_Odual__order_Oantisym:(forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B)))).
% 0.72/0.90 Axiom fact_52_local_Odual__order_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (A3:a) (B2:a)=> ((and ((less_eq B2) A3)) ((less_eq A3) B2)))).
% 0.72/0.90 Axiom fact_53_local_Odual__order_Otrans:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A)))).
% 0.72/0.90 Axiom fact_54_local_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (X3:a) (Y4:a)=> ((and ((less_eq X3) Y4)) ((less_eq Y4) X3)))).
% 0.72/0.90 Axiom fact_55_local_Oeq__refl:(forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y))).
% 0.72/0.90 Axiom fact_56_local_Oord__eq__le__trans:(forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C)))).
% 0.72/0.90 Axiom fact_57_local_Oord__le__eq__trans:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C)))).
% 0.72/0.90 Axiom fact_58_local_Oorder_Oantisym:(forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B)))).
% 0.72/0.90 Axiom fact_59_local_Oorder_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y3:a) (Z3:a)=> (((eq a) Y3) Z3))) (fun (A3:a) (B2:a)=> ((and ((less_eq A3) B2)) ((less_eq B2) A3)))).
% 0.72/0.90 Axiom fact_60_local_Oorder_Otrans:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C)))).
% 0.72/0.90 Axiom fact_61_local_Oorder__trans:(forall (X:a) (Y:a) (Z:a), (((less_eq X) Y)->(((less_eq Y) Z)->((less_eq X) Z)))).
% 0.72/0.90 Axiom fact_62_local_Ole__infI2:(forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X))).
% 0.72/0.90 Axiom fact_63_local_Ole__infI1:(forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X))).
% 0.72/0.90 Axiom fact_64_local_Ole__infI:(forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B))))).
% 0.72/0.90 Axiom fact_65_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))).
% 0.72/0.90 Axiom fact_66_local_Ole__iff__inf:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X))).
% 0.72/0.90 Axiom fact_67_local_Oinf__unique:(forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X2:a) (Y2:a), ((less_eq ((F X2) Y2)) X2))->((forall (X2:a) (Y2:a), ((less_eq ((F X2) Y2)) Y2))->((forall (X2:a) (Y2:a) (Z2:a), (((less_eq X2) Y2)->(((less_eq X2) Z2)->((less_eq X2) ((F Y2) Z2)))))->(((eq a) ((inf X) Y)) ((F X) Y)))))).
% 0.72/0.90 Axiom fact_68_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))))).
% 0.72/0.90 Axiom fact_69_local_Oinf__le2:(forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y)).
% 0.72/0.90 Axiom fact_70_local_Oinf__le1:(forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X)).
% 0.72/0.90 Axiom fact_71_local_Oinf__greatest:(forall (X:a) (Y:a) (Z:a), (((less_eq X) Y)->(((less_eq X) Z)->((less_eq X) ((inf Y) Z))))).
% 0.72/0.90 Axiom fact_72_local_Oinf__absorb2:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y))).
% 0.72/0.90 Axiom fact_73_local_Oinf__absorb1:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X))).
% 0.72/0.90 Axiom fact_74_local_Oinf_Oorder__iff:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B)))).
% 0.72/0.90 Axiom fact_75_local_Oinf_OorderI:(forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B))).
% 0.72/0.90 Axiom fact_76_local_Oinf_OorderE:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B)))).
% 0.72/0.90 Axiom fact_77_local_Oinf_OcoboundedI2:(forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C))).
% 0.72/0.90 Axiom fact_78_local_Oinf_OcoboundedI1:(forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C))).
% 0.72/0.90 Axiom fact_79_local_Oinf_Ocobounded2:(forall (A:a) (B:a), ((less_eq ((inf A) B)) B)).
% 0.72/0.90 Axiom fact_80_local_Oinf_Ocobounded1:(forall (A:a) (B:a), ((less_eq ((inf A) B)) A)).
% 0.72/0.90 Axiom fact_81_local_Oinf_OboundedI:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C))))).
% 0.72/0.90 Axiom fact_82_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))).
% 0.72/0.90 Axiom fact_83_local_Oinf_Oabsorb__iff2:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B))).
% 0.72/0.90 Axiom fact_84_local_Oinf_Oabsorb__iff1:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A))).
% 0.72/0.90 Axiom fact_85_local_Oinf_Oabsorb2:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B))).
% 0.72/0.90 Axiom fact_86_local_Oinf_Oabsorb1:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A))).
% 0.72/0.90 Axiom fact_87_local_Osup__unique:(forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X2:a) (Y2:a), ((less_eq X2) ((F X2) Y2)))->((forall (X2:a) (Y2:a), ((less_eq Y2) ((F X2) Y2)))->((forall (X2:a) (Y2:a) (Z2:a), (((less_eq Y2) X2)->(((less_eq Z2) X2)->((less_eq ((F Y2) Z2)) X2))))->(((eq a) ((sup X) Y)) ((F X) Y)))))).
% 0.72/0.90 Axiom fact_88_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))))).
% 0.72/0.90 Axiom fact_89_local_Osup__least:(forall (Y:a) (X:a) (Z:a), (((less_eq Y) X)->(((less_eq Z) X)->((less_eq ((sup Y) Z)) X)))).
% 0.72/0.90 Axiom fact_90_local_Osup__ge2:(forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y))).
% 0.72/0.90 Axiom fact_91_local_Osup__ge1:(forall (X:a) (Y:a), ((less_eq X) ((sup X) Y))).
% 0.72/0.90 Axiom fact_92_local_Osup__absorb2:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y))).
% 0.72/0.90 Axiom fact_93_local_Osup__absorb1:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X))).
% 0.72/0.90 Axiom fact_94_local_Osup_Oorder__iff:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B)))).
% 0.72/0.90 Axiom fact_95_local_Osup_OorderI:(forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A))).
% 0.72/0.90 Axiom fact_96_local_Osup_OorderE:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B)))).
% 0.72/0.90 Axiom fact_97_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))))).
% 0.72/0.90 Axiom fact_98_local_Osup_OcoboundedI2:(forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B)))).
% 0.72/0.90 Axiom fact_99_local_Osup_OcoboundedI1:(forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B)))).
% 0.72/0.90 Axiom fact_100_local_Osup_Ocobounded2:(forall (B:a) (A:a), ((less_eq B) ((sup A) B))).
% 0.72/0.90 Axiom fact_101_local_Osup_Ocobounded1:(forall (A:a) (B:a), ((less_eq A) ((sup A) B))).
% 0.72/0.90 Axiom fact_102_local_Osup_OboundedI:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A)))).
% 0.72/0.90 Axiom fact_103_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))).
% 0.72/0.90 Axiom fact_104_local_Osup_Oabsorb__iff2:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B))).
% 0.72/0.90 Axiom fact_105_local_Osup_Oabsorb__iff1:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A))).
% 0.72/0.90 Axiom fact_106_local_Osup_Oabsorb2:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B))).
% 0.72/0.90 Axiom fact_107_local_Osup_Oabsorb1:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A))).
% 0.72/0.90 Axiom fact_108_local_Ole__supI2:(forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B)))).
% 0.72/0.90 Axiom fact_109_local_Ole__supI1:(forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B)))).
% 0.72/0.90 Axiom fact_110_local_Ole__supI:(forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X)))).
% 0.72/0.90 Axiom fact_111_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))).
% 0.72/0.90 Axiom fact_112_local_Ole__iff__sup:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y))).
% 0.72/0.90 Axiom fact_113_local_Oorder_Orefl:(forall (A:a), ((less_eq A) A)).
% 0.72/0.90 Axiom fact_114_local_Oorder__refl:(forall (X:a), ((less_eq X) X)).
% 0.72/0.90 Axiom fact_115_local_OGreatestI2__order:(forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq Y2) X)))->((forall (X2:a), ((P X2)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X2)))->(Q X2))))->(Q ((greatest_a less_eq) P)))))).
% 0.72/0.90 Axiom fact_116_local_OGreatest__equality:(forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq Y2) X)))->(((eq a) ((greatest_a less_eq) P)) X)))).
% 0.72/0.90 Axiom fact_117_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)))).
% 0.72/0.90 Axiom fact_118_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)))).
% 0.72/0.90 Axiom fact_119_local_Ole__inf__iff:(forall (X:a) (Y:a) (Z:a), (((eq Prop) ((less_eq X) ((inf Y) Z))) ((and ((less_eq X) Y)) ((less_eq X) Z)))).
% 0.72/0.90 Axiom fact_120_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)))).
% 0.72/0.90 Axiom fact_121_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)))).
% 0.72/0.90 Axiom fact_122_local_Ole__sup__iff:(forall (X:a) (Y:a) (Z:a), (((eq Prop) ((less_eq ((sup X) Y)) Z)) ((and ((less_eq X) Z)) ((less_eq Y) Z)))).
% 0.72/0.90 Axiom fact_123_local_OLeast1I:(forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y2:a), ((P Y2)->((less_eq X4) Y2))))) (forall (Y2:a), (((and (P Y2)) (forall (Ya:a), ((P Ya)->((less_eq Y2) Ya))))->(((eq a) Y2) X4))))))->(P ((least_a less_eq) P)))).
% 0.72/0.90 Axiom fact_124_local_OLeast1__le:(forall (P:(a->Prop)) (Z:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y2:a), ((P Y2)->((less_eq X4) Y2))))) (forall (Y2:a), (((and (P Y2)) (forall (Ya:a), ((P Ya)->((less_eq Y2) Ya))))->(((eq a) Y2) X4))))))->((P Z)->((less_eq ((least_a less_eq) P)) Z)))).
% 0.72/0.90 Axiom fact_125_local_OLeastI2__order:(forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq X) Y2)))->((forall (X2:a), ((P X2)->((forall (Y5:a), ((P Y5)->((less_eq X2) Y5)))->(Q X2))))->(Q ((least_a less_eq) P)))))).
% 0.72/0.90 Axiom fact_126_local_OLeast__equality:(forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y2:a), ((P Y2)->((less_eq X) Y2)))->(((eq a) ((least_a less_eq) P)) X)))).
% 0.72/0.90 Axiom fact_127_lattice_Od__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a).
% 0.72/0.90 Axiom fact_128_abel__semigroup_Oaxioms_I1_J:(forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F))).
% 0.72/0.90 Axiom fact_129_semilattice__set__def:(((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a).
% 0.72/0.90 Axiom fact_130_semilattice__set_Ointro:(forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F))).
% 0.72/0.90 Axiom fact_131_semilattice__set_Oaxioms:(forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F))).
% 0.72/0.90 Axiom fact_132_semilattice_Oaxioms_I1_J:(forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F))).
% 0.72/0.90 Axiom fact_133_local_Obdd__above__def:(forall (A2:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A2)) ((ex a) (fun (M:a)=> (forall (X3:a), (((member_a X3) A2)->((less_eq X3) M))))))).
% 0.72/0.90 Axiom fact_134_local_Obdd__below__def:(forall (A2:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A2)) ((ex a) (fun (M2:a)=> (forall (X3:a), (((member_a X3) A2)->((less_eq M2) X3))))))).
% 0.72/0.90 Axiom fact_135_local_Otransp__le:(transp_a less_eq).
% 0.72/0.90 Axiom fact_136_local_Obdd__belowI:(forall (A2:set_a) (M3:a), ((forall (X2:a), (((member_a X2) A2)->((less_eq M3) X2)))->((condit1001553558elow_a less_eq) A2))).
% 0.72/0.90 Axiom fact_137_local_Obdd__aboveI:(forall (A2:set_a) (M4:a), ((forall (X2:a), (((member_a X2) A2)->((less_eq X2) M4)))->((condit1627435690bove_a less_eq) A2))).
% 0.72/0.90 Axiom fact_138_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))))).
% 0.72/0.90 Axiom fact_139_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)))).
% 0.72/0.90 Axiom fact_140_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)))).
% 0.72/0.90 Axiom fact_141_abel__semigroup_Ocommute:(forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A)))).
% 0.72/0.90 Axiom fact_142_semilattice_Oidem:(forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A))).
% 0.72/0.90 Axiom fact_143_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))).
% 0.72/0.90 Axiom fact_144_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))))).
% 0.72/0.90 Axiom fact_145_semigroup__def:(((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A3:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A3) B2)) C3)) ((F2 A3) ((F2 B2) C3)))))).
% 0.72/0.90 Axiom fact_146_local_Obdd__below__mono:(forall (B4:set_a) (A2:set_a), (((condit1001553558elow_a less_eq) B4)->(((ord_less_eq_set_a A2) B4)->((condit1001553558elow_a less_eq) A2)))).
% 0.72/0.90 Axiom fact_147_local_Obdd__above__mono:(forall (B4:set_a) (A2:set_a), (((condit1627435690bove_a less_eq) B4)->(((ord_less_eq_set_a A2) B4)->((condit1627435690bove_a less_eq) A2)))).
% 0.72/0.90 Axiom fact_148_local_Obdd__below__finite:(forall (A2:set_a), ((finite_finite_a A2)->((condit1001553558elow_a less_eq) A2))).
% 0.72/0.90 Axiom fact_149_local_Obdd__above__finite:(forall (A2:set_a), ((finite_finite_a A2)->((condit1627435690bove_a less_eq) A2))).
% 0.72/0.90 Axiom fact_150_local_Ofinite__has__maximal2:(forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((ex a) (fun (X2:a)=> ((and ((and ((member_a X2) A2)) ((less_eq A) X2))) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq X2) Xa)->(((eq a) X2) Xa)))))))))).
% 0.72/0.90 Axiom fact_151_local_Ofinite__has__minimal2:(forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((ex a) (fun (X2:a)=> ((and ((and ((member_a X2) A2)) ((less_eq X2) A))) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq Xa) X2)->(((eq a) X2) Xa)))))))))).
% 0.72/0.90 Axiom fact_152_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))))).
% 0.72/0.90 Axiom fact_153_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))))).
% 0.72/0.90 Axiom fact_154_local_OantimonoI:(forall (F:(a->set_a)), ((forall (X2:a) (Y2:a), (((less_eq X2) Y2)->((ord_less_eq_set_a (F Y2)) (F X2))))->((antimono_a_set_a less_eq) F))).
% 0.72/0.90 Axiom fact_155_local_Oantimono__def:(forall (F:(a->set_a)), (((eq Prop) ((antimono_a_set_a less_eq) F)) (forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F Y4)) (F X3)))))).
% 0.72/0.90 Axiom fact_156_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))))).
% 0.72/0.90 Axiom fact_157_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))))).
% 0.72/0.90 Axiom fact_158_local_OmonoI:(forall (F:(a->set_a)), ((forall (X2:a) (Y2:a), (((less_eq X2) Y2)->((ord_less_eq_set_a (F X2)) (F Y2))))->((mono_a_set_a less_eq) F))).
% 0.72/0.90 Axiom fact_159_local_Omono__def:(forall (F:(a->set_a)), (((eq Prop) ((mono_a_set_a less_eq) F)) (forall (X3:a) (Y4:a), (((less_eq X3) Y4)->((ord_less_eq_set_a (F X3)) (F Y4)))))).
% 0.72/0.90 Axiom fact_160_local_OSup__fin_OcoboundedI:(forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((less_eq A) ((lattic1781219155_fin_a sup) A2))))).
% 0.72/0.90 Axiom fact_161_local_OInf__fin_OcoboundedI:(forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->((less_eq ((lattic247676691_fin_a inf) A2)) A)))).
% 0.72/0.90 Axiom fact_162_local_OSup__fin_Oin__idem:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->(((member_a X) A2)->(((eq a) ((sup X) ((lattic1781219155_fin_a sup) A2))) ((lattic1781219155_fin_a sup) A2))))).
% 0.72/0.90 Axiom fact_163_local_OInf__fin_Oin__idem:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->(((member_a X) A2)->(((eq a) ((inf X) ((lattic247676691_fin_a inf) A2))) ((lattic247676691_fin_a inf) A2))))).
% 0.72/0.90 Axiom fact_164_local_Oinf__Sup__absorb:(forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->(((eq a) ((inf A) ((lattic1781219155_fin_a sup) A2))) A)))).
% 0.72/0.90 Axiom fact_165_local_Osup__Inf__absorb:(forall (A2:set_a) (A:a), ((finite_finite_a A2)->(((member_a A) A2)->(((eq a) ((sup ((lattic247676691_fin_a inf) A2)) A)) A)))).
% 0.72/0.90 Axiom fact_166_semilattice__inf_OInf__fin_Ocong:(((eq ((a->(a->a))->(set_a->a))) lattic247676691_fin_a) lattic247676691_fin_a).
% 0.72/0.90 Axiom fact_167_semilattice__sup_OSup__fin_Ocong:(((eq ((a->(a->a))->(set_a->a))) lattic1781219155_fin_a) lattic1781219155_fin_a).
% 0.72/0.90 Axiom fact_168_local_OInf__fin__le__Sup__fin:(forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((less_eq ((lattic247676691_fin_a inf) A2)) ((lattic1781219155_fin_a sup) A2))))).
% 0.72/0.90 Axiom fact_169_local_OSup__fin_Osubset__imp:(forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->((not (((eq set_a) A2) bot_bot_set_a))->((finite_finite_a B4)->((less_eq ((lattic1781219155_fin_a sup) A2)) ((lattic1781219155_fin_a sup) B4)))))).
% 0.72/0.90 Axiom fact_170_local_OInf__fin_Osubset__imp:(forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->((not (((eq set_a) A2) bot_bot_set_a))->((finite_finite_a B4)->((less_eq ((lattic247676691_fin_a inf) B4)) ((lattic247676691_fin_a inf) A2)))))).
% 0.72/0.90 Axiom fact_171_local_Ofinite__has__minimal:(forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((ex a) (fun (X2:a)=> ((and ((member_a X2) A2)) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq Xa) X2)->(((eq a) X2) Xa)))))))))).
% 0.72/0.90 Axiom fact_172_local_Ofinite__has__maximal:(forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((ex a) (fun (X2:a)=> ((and ((member_a X2) A2)) (forall (Xa:a), (((member_a Xa) A2)->(((less_eq X2) Xa)->(((eq a) X2) Xa)))))))))).
% 0.72/0.90 Axiom fact_173_local_OInf__fin_Osubset:(forall (A2:set_a) (B4:set_a), ((finite_finite_a A2)->((not (((eq set_a) B4) bot_bot_set_a))->(((ord_less_eq_set_a B4) A2)->(((eq a) ((inf ((lattic247676691_fin_a inf) B4)) ((lattic247676691_fin_a inf) A2))) ((lattic247676691_fin_a inf) A2)))))).
% 0.72/0.90 Axiom fact_174_local_OSup__fin_Osubset:(forall (A2:set_a) (B4:set_a), ((finite_finite_a A2)->((not (((eq set_a) B4) bot_bot_set_a))->(((ord_less_eq_set_a B4) A2)->(((eq a) ((sup ((lattic1781219155_fin_a sup) B4)) ((lattic1781219155_fin_a sup) A2))) ((lattic1781219155_fin_a sup) A2)))))).
% 0.72/0.90 Axiom fact_175_local_OInf__fin_Obounded__iff:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq Prop) ((less_eq X) ((lattic247676691_fin_a inf) A2))) (forall (X3:a), (((member_a X3) A2)->((less_eq X) X3))))))).
% 0.72/0.90 Axiom fact_176_local_OInf__fin_OboundedI:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (A4:a), (((member_a A4) A2)->((less_eq X) A4)))->((less_eq X) ((lattic247676691_fin_a inf) A2)))))).
% 0.72/0.90 Axiom fact_177_local_OInf__fin_OboundedE:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((less_eq X) ((lattic247676691_fin_a inf) A2))->(forall (A5:a), (((member_a A5) A2)->((less_eq X) A5))))))).
% 0.72/0.90 Axiom fact_178_local_OSup__fin_Obounded__iff:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq Prop) ((less_eq ((lattic1781219155_fin_a sup) A2)) X)) (forall (X3:a), (((member_a X3) A2)->((less_eq X3) X))))))).
% 0.72/0.90 Axiom fact_179_local_OSup__fin_OboundedI:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (A4:a), (((member_a A4) A2)->((less_eq A4) X)))->((less_eq ((lattic1781219155_fin_a sup) A2)) X))))).
% 0.72/0.90 Axiom fact_180_local_OSup__fin_OboundedE:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((less_eq ((lattic1781219155_fin_a sup) A2)) X)->(forall (A5:a), (((member_a A5) A2)->((less_eq A5) X))))))).
% 0.72/0.90 Axiom fact_181_local_Obdd__above__empty:((condit1627435690bove_a less_eq) bot_bot_set_a).
% 0.72/0.90 Axiom fact_182_local_Obdd__below__empty:((condit1001553558elow_a less_eq) bot_bot_set_a).
% 0.72/0.90 Axiom fact_183_local_Onot__empty__eq__Iic__eq__empty:(forall (H:a), (not (((eq set_a) bot_bot_set_a) ((set_atMost_a less_eq) H)))).
% 0.72/0.90 Axiom fact_184_local_Onot__empty__eq__Ici__eq__empty:(forall (L:a), (not (((eq set_a) bot_bot_set_a) ((set_atLeast_a less_eq) L)))).
% 0.72/0.90 Axiom fact_185_subset__empty:(forall (A2:set_a), (((eq Prop) ((ord_less_eq_set_a A2) bot_bot_set_a)) (((eq set_a) A2) bot_bot_set_a))).
% 0.72/0.90 Axiom fact_186_empty__Collect__eq:(forall (P:(a->Prop)), (((eq Prop) (((eq set_a) bot_bot_set_a) (collect_a P))) (forall (X3:a), ((P X3)->False)))).
% 0.72/0.90 Axiom fact_187_Collect__empty__eq:(forall (P:(a->Prop)), (((eq Prop) (((eq set_a) (collect_a P)) bot_bot_set_a)) (forall (X3:a), ((P X3)->False)))).
% 0.72/0.90 Axiom fact_188_all__not__in__conv:(forall (A2:set_set_a), (((eq Prop) (forall (X3:set_a), (((member_set_a X3) A2)->False))) (((eq set_set_a) A2) bot_bot_set_set_a))).
% 0.72/0.90 Axiom fact_189_all__not__in__conv:(forall (A2:set_a), (((eq Prop) (forall (X3:a), (((member_a X3) A2)->False))) (((eq set_a) A2) bot_bot_set_a))).
% 0.72/0.90 Axiom fact_190_empty__iff:(forall (C:set_a), (((member_set_a C) bot_bot_set_set_a)->False)).
% 0.72/0.90 Axiom fact_191_empty__iff:(forall (C:a), (((member_a C) bot_bot_set_a)->False)).
% 0.72/0.90 Axiom fact_192_subset__antisym:(forall (A2:set_a) (B4:set_a), (((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) A2)->(((eq set_a) A2) B4)))).
% 0.72/0.90 Axiom fact_193_subsetI:(forall (A2:set_set_a) (B4:set_set_a), ((forall (X2:set_a), (((member_set_a X2) A2)->((member_set_a X2) B4)))->((ord_le318720350_set_a A2) B4))).
% 0.72/0.91 Axiom fact_194_subsetI:(forall (A2:set_a) (B4:set_a), ((forall (X2:a), (((member_a X2) A2)->((member_a X2) B4)))->((ord_less_eq_set_a A2) B4))).
% 0.72/0.91 Axiom fact_195_empty__subsetI:(forall (A2:set_a), ((ord_less_eq_set_a bot_bot_set_a) A2)).
% 0.72/0.91 Axiom fact_196_local_OatLeast__iff:(forall (_TPTP_I:a) (K:a), (((eq Prop) ((member_a _TPTP_I) ((set_atLeast_a less_eq) K))) ((less_eq K) _TPTP_I))).
% 0.72/0.91 Axiom fact_197_local_OatMost__iff:(forall (_TPTP_I:a) (K:a), (((eq Prop) ((member_a _TPTP_I) ((set_atMost_a less_eq) K))) ((less_eq _TPTP_I) K))).
% 0.72/0.91 Axiom fact_198_local_Obdd__below__Ici:(forall (A:a), ((condit1001553558elow_a less_eq) ((set_atLeast_a less_eq) A))).
% 0.72/0.91 Axiom fact_199_local_Obdd__above__Iic:(forall (B:a), ((condit1627435690bove_a less_eq) ((set_atMost_a less_eq) B))).
% 0.72/0.91 Axiom fact_200_ex__in__conv:(forall (A2:set_set_a), (((eq Prop) ((ex set_a) (fun (X3:set_a)=> ((member_set_a X3) A2)))) (not (((eq set_set_a) A2) bot_bot_set_set_a)))).
% 0.72/0.91 Axiom fact_201_ex__in__conv:(forall (A2:set_a), (((eq Prop) ((ex a) (fun (X3:a)=> ((member_a X3) A2)))) (not (((eq set_a) A2) bot_bot_set_a)))).
% 0.72/0.91 Axiom fact_202_equals0I:(forall (A2:set_set_a), ((forall (Y2:set_a), (((member_set_a Y2) A2)->False))->(((eq set_set_a) A2) bot_bot_set_set_a))).
% 0.72/0.91 Axiom fact_203_equals0I:(forall (A2:set_a), ((forall (Y2:a), (((member_a Y2) A2)->False))->(((eq set_a) A2) bot_bot_set_a))).
% 0.72/0.91 Axiom fact_204_equals0D:(forall (A2:set_set_a) (A:set_a), ((((eq set_set_a) A2) bot_bot_set_set_a)->(((member_set_a A) A2)->False))).
% 0.72/0.91 Axiom fact_205_equals0D:(forall (A2:set_a) (A:a), ((((eq set_a) A2) bot_bot_set_a)->(((member_a A) A2)->False))).
% 0.72/0.91 Axiom fact_206_emptyE:(forall (A:set_a), (((member_set_a A) bot_bot_set_set_a)->False)).
% 0.72/0.91 Axiom fact_207_emptyE:(forall (A:a), (((member_a A) bot_bot_set_a)->False)).
% 0.72/0.91 Axiom fact_208_Collect__mono__iff:(forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X3:a), ((P X3)->(Q X3))))).
% 0.72/0.91 Axiom fact_209_set__eq__subset:(((eq (set_a->(set_a->Prop))) (fun (Y3:set_a) (Z3:set_a)=> (((eq set_a) Y3) Z3))) (fun (A6:set_a) (B5:set_a)=> ((and ((ord_less_eq_set_a A6) B5)) ((ord_less_eq_set_a B5) A6)))).
% 0.72/0.91 Axiom fact_210_subset__trans:(forall (A2:set_a) (B4:set_a) (C4:set_a), (((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) C4)->((ord_less_eq_set_a A2) C4)))).
% 0.72/0.91 Axiom fact_211_Collect__mono:(forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X2:a), ((P X2)->(Q X2)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q)))).
% 0.72/0.91 Axiom fact_212_subset__refl:(forall (A2:set_a), ((ord_less_eq_set_a A2) A2)).
% 0.72/0.91 Axiom fact_213_subset__iff:(((eq (set_set_a->(set_set_a->Prop))) ord_le318720350_set_a) (fun (A6:set_set_a) (B5:set_set_a)=> (forall (T:set_a), (((member_set_a T) A6)->((member_set_a T) B5))))).
% 0.72/0.91 Axiom fact_214_subset__iff:(((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A6:set_a) (B5:set_a)=> (forall (T:a), (((member_a T) A6)->((member_a T) B5))))).
% 0.72/0.91 Axiom fact_215_equalityD2:(forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((ord_less_eq_set_a B4) A2))).
% 0.72/0.91 Axiom fact_216_equalityD1:(forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((ord_less_eq_set_a A2) B4))).
% 0.72/0.91 Axiom fact_217_subset__eq:(((eq (set_set_a->(set_set_a->Prop))) ord_le318720350_set_a) (fun (A6:set_set_a) (B5:set_set_a)=> (forall (X3:set_a), (((member_set_a X3) A6)->((member_set_a X3) B5))))).
% 0.72/0.91 Axiom fact_218_subset__eq:(((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A6:set_a) (B5:set_a)=> (forall (X3:a), (((member_a X3) A6)->((member_a X3) B5))))).
% 0.72/0.91 Axiom fact_219_equalityE:(forall (A2:set_a) (B4:set_a), ((((eq set_a) A2) B4)->((((ord_less_eq_set_a A2) B4)->(((ord_less_eq_set_a B4) A2)->False))->False))).
% 0.72/0.91 Axiom fact_220_subsetD:(forall (A2:set_set_a) (B4:set_set_a) (C:set_a), (((ord_le318720350_set_a A2) B4)->(((member_set_a C) A2)->((member_set_a C) B4)))).
% 0.72/0.91 Axiom fact_221_subsetD:(forall (A2:set_a) (B4:set_a) (C:a), (((ord_less_eq_set_a A2) B4)->(((member_a C) A2)->((member_a C) B4)))).
% 0.72/0.91 Axiom fact_222_in__mono:(forall (A2:set_set_a) (B4:set_set_a) (X:set_a), (((ord_le318720350_set_a A2) B4)->(((member_set_a X) A2)->((member_set_a X) B4)))).
% 0.72/0.91 Axiom fact_223_in__mono:(forall (A2:set_a) (B4:set_a) (X:a), (((ord_less_eq_set_a A2) B4)->(((member_a X) A2)->((member_a X) B4)))).
% 0.72/0.91 Axiom fact_224_local_OSup__fin_Oclosed:(forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (X2:a) (Y2:a), ((member_a ((sup X2) Y2)) ((insert_a X2) ((insert_a Y2) bot_bot_set_a))))->((member_a ((lattic1781219155_fin_a sup) A2)) A2))))).
% 0.72/0.91 Axiom fact_225_local_OSup__fin_Oinsert__not__elem:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((((member_a X) A2)->False)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) A2))) ((sup X) ((lattic1781219155_fin_a sup) A2))))))).
% 0.72/0.91 Axiom fact_226_local_OInf__fin_Oclosed:(forall (A2:set_a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->((forall (X2:a) (Y2:a), ((member_a ((inf X2) Y2)) ((insert_a X2) ((insert_a Y2) bot_bot_set_a))))->((member_a ((lattic247676691_fin_a inf) A2)) A2))))).
% 0.72/0.91 Axiom fact_227_local_OInf__fin_Oinsert__not__elem:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((((member_a X) A2)->False)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic247676691_fin_a inf) ((insert_a X) A2))) ((inf X) ((lattic247676691_fin_a inf) A2))))))).
% 0.72/0.91 Axiom fact_228_singletonI:(forall (A:set_a), ((member_set_a A) ((insert_set_a A) bot_bot_set_set_a))).
% 0.72/0.91 Axiom fact_229_singletonI:(forall (A:a), ((member_a A) ((insert_a A) bot_bot_set_a))).
% 0.72/0.91 Axiom fact_230_insert__subset:(forall (X:set_a) (A2:set_set_a) (B4:set_set_a), (((eq Prop) ((ord_le318720350_set_a ((insert_set_a X) A2)) B4)) ((and ((member_set_a X) B4)) ((ord_le318720350_set_a A2) B4)))).
% 0.72/0.91 Axiom fact_231_insert__subset:(forall (X:a) (A2:set_a) (B4:set_a), (((eq Prop) ((ord_less_eq_set_a ((insert_a X) A2)) B4)) ((and ((member_a X) B4)) ((ord_less_eq_set_a A2) B4)))).
% 0.72/0.91 Axiom fact_232_singleton__insert__inj__eq_H:(forall (A:a) (A2:set_a) (B:a), (((eq Prop) (((eq set_a) ((insert_a A) A2)) ((insert_a B) bot_bot_set_a))) ((and (((eq a) A) B)) ((ord_less_eq_set_a A2) ((insert_a B) bot_bot_set_a))))).
% 0.72/0.91 Axiom fact_233_singleton__insert__inj__eq:(forall (B:a) (A:a) (A2:set_a), (((eq Prop) (((eq set_a) ((insert_a B) bot_bot_set_a)) ((insert_a A) A2))) ((and (((eq a) A) B)) ((ord_less_eq_set_a A2) ((insert_a B) bot_bot_set_a))))).
% 0.72/0.91 Axiom fact_234_local_Obdd__above__insert:(forall (A:a) (A2:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) ((insert_a A) A2))) ((condit1627435690bove_a less_eq) A2))).
% 0.72/0.91 Axiom fact_235_local_Obdd__below__insert:(forall (A:a) (A2:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) ((insert_a A) A2))) ((condit1001553558elow_a less_eq) A2))).
% 0.72/0.91 Axiom fact_236_local_OInf__fin_Osingleton:(forall (X:a), (((eq a) ((lattic247676691_fin_a inf) ((insert_a X) bot_bot_set_a))) X)).
% 0.72/0.91 Axiom fact_237_local_OSup__fin_Osingleton:(forall (X:a), (((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) bot_bot_set_a))) X)).
% 0.72/0.91 Axiom fact_238_local_OInf__fin_Oinsert:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic247676691_fin_a inf) ((insert_a X) A2))) ((inf X) ((lattic247676691_fin_a inf) A2)))))).
% 0.72/0.91 Axiom fact_239_local_OSup__fin_Oinsert:(forall (A2:set_a) (X:a), ((finite_finite_a A2)->((not (((eq set_a) A2) bot_bot_set_a))->(((eq a) ((lattic1781219155_fin_a sup) ((insert_a X) A2))) ((sup X) ((lattic1781219155_fin_a sup) A2)))))).
% 0.72/0.91 Axiom fact_240_subset__singletonD:(forall (A2:set_a) (X:a), (((ord_less_eq_set_a A2) ((insert_a X) bot_bot_set_a))->((or (((eq set_a) A2) bot_bot_set_a)) (((eq set_a) A2) ((insert_a X) bot_bot_set_a))))).
% 0.72/0.91 Axiom fact_241_subset__singleton__iff:(forall (X5:set_a) (A:a), (((eq Prop) ((ord_less_eq_set_a X5) ((insert_a A) bot_bot_set_a))) ((or (((eq set_a) X5) bot_bot_set_a)) (((eq set_a) X5) ((insert_a A) bot_bot_set_a))))).
% 0.72/0.91 Axiom fact_242_singletonD:(forall (B:set_a) (A:set_a), (((member_set_a B) ((insert_set_a A) bot_bot_set_set_a))->(((eq set_a) B) A))).
% 0.72/0.91 Axiom fact_243_singletonD:(forall (B:a) (A:a), (((member_a B) ((insert_a A) bot_bot_set_a))->(((eq a) B) A))).
% 0.72/0.91 Axiom fact_244_singleton__iff:(forall (B:set_a) (A:set_a), (((eq Prop) ((member_set_a B) ((insert_set_a A) bot_bot_set_set_a))) (((eq set_a) B) A))).
% 0.72/0.91 Axiom fact_245_singleton__iff:(forall (B:a) (A:a), (((eq Prop) ((member_a B) ((insert_a A) bot_bot_set_a))) (((eq a) B) A))).
% 0.72/0.91 Axiom fact_246_doubleton__eq__iff:(forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) (((eq set_a) ((insert_a A) ((insert_a B) bot_bot_set_a))) ((insert_a C) ((insert_a D) bot_bot_set_a)))) ((or ((and (((eq a) A) C)) (((eq a) B) D))) ((and (((eq a) A) D)) (((eq a) B) C))))).
% 0.72/0.91 Axiom fact_247_insert__not__empty:(forall (A:a) (A2:set_a), (not (((eq set_a) ((insert_a A) A2)) bot_bot_set_a))).
% 0.72/0.91 Axiom fact_248_singleton__inject:(forall (A:a) (B:a), ((((eq set_a) ((insert_a A) bot_bot_set_a)) ((insert_a B) bot_bot_set_a))->(((eq a) A) B))).
% 0.72/0.91 Axiom fact_249_subset__insertI2:(forall (A2:set_a) (B4:set_a) (B:a), (((ord_less_eq_set_a A2) B4)->((ord_less_eq_set_a A2) ((insert_a B) B4)))).
% 0.72/0.91 Axiom fact_250_subset__insertI:(forall (B4:set_a) (A:a), ((ord_less_eq_set_a B4) ((insert_a A) B4))).
% 0.72/0.91 Axiom fact_251_subset__insert:(forall (X:set_a) (A2:set_set_a) (B4:set_set_a), ((((member_set_a X) A2)->False)->(((eq Prop) ((ord_le318720350_set_a A2) ((insert_set_a X) B4))) ((ord_le318720350_set_a A2) B4)))).
% 0.72/0.91 Axiom fact_252_subset__insert:(forall (X:a) (A2:set_a) (B4:set_a), ((((member_a X) A2)->False)->(((eq Prop) ((ord_less_eq_set_a A2) ((insert_a X) B4))) ((ord_less_eq_set_a A2) B4)))).
% 0.72/0.91 Axiom fact_253_insert__mono:(forall (C4:set_a) (D2:set_a) (A:a), (((ord_less_eq_set_a C4) D2)->((ord_less_eq_set_a ((insert_a A) C4)) ((insert_a A) D2)))).
% 0.72/0.91 Axiom fact_254_local_OatLeastAtMost__singleton_H:(forall (A:a) (B:a), ((((eq a) A) B)->(((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) ((insert_a A) bot_bot_set_a)))).
% 0.72/0.91 Axiom fact_255_finite__insert:(forall (A:set_a) (A2:set_set_a), (((eq Prop) (finite_finite_set_a ((insert_set_a A) A2))) (finite_finite_set_a A2))).
% 0.72/0.91 Axiom fact_256_finite__insert:(forall (A:a) (A2:set_a), (((eq Prop) (finite_finite_a ((insert_a A) A2))) (finite_finite_a A2))).
% 0.72/0.91 Axiom fact_257_local_OIcc__eq__Icc:(forall (L:a) (H:a) (L2:a) (H2:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) L) H)) (((set_atLeastAtMost_a less_eq) L2) H2))) ((or ((and (((eq a) L) L2)) (((eq a) H) H2))) ((and (((less_eq L) H)->False)) (((less_eq L2) H2)->False))))).
% 0.72/0.91 Axiom fact_258_local_OatLeastAtMost__iff:(forall (_TPTP_I:a) (L:a) (U:a), (((eq Prop) ((member_a _TPTP_I) (((set_atLeastAtMost_a less_eq) L) U))) ((and ((less_eq L) _TPTP_I)) ((less_eq _TPTP_I) U)))).
% 0.72/0.91 Axiom fact_259_local_OatLeastatMost__empty__iff:(forall (A:a) (B:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) bot_bot_set_a)) (((less_eq A) B)->False))).
% 0.72/0.91 Axiom fact_260_local_OatLeastatMost__empty__iff2:(forall (A:a) (B:a), (((eq Prop) (((eq set_a) bot_bot_set_a) (((set_atLeastAtMost_a less_eq) A) B))) (((less_eq A) B)->False))).
% 0.72/0.91 Axiom fact_261_local_Obdd__below__Icc:(forall (A:a) (B:a), ((condit1001553558elow_a less_eq) (((set_atLeastAtMost_a less_eq) A) B))).
% 0.72/0.91 Axiom fact_262_local_Obdd__above__Icc:(forall (A:a) (B:a), ((condit1627435690bove_a less_eq) (((set_atLeastAtMost_a less_eq) A) B))).
% 0.72/0.91 Axiom fact_263_local_OatLeastatMost__subset__iff:(forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) A) B)) (((set_atLeastAtMost_a less_eq) C) D))) ((or (((less_eq A) B)->False)) ((and ((less_eq C) A)) ((less_eq B) D))))).
% 0.72/0.91 Axiom fact_264_local_OatLeastAtMost__singleton:(forall (A:a), (((eq set_a) (((set_atLeastAtMost_a less_eq) A) A)) ((insert_a A) bot_bot_set_a))).
% 0.72/0.91 Axiom fact_265_local_OatLeastAtMost__singleton__iff:(forall (A:a) (B:a) (C:a), (((eq Prop) (((eq set_a) (((set_atLeastAtMost_a less_eq) A) B)) ((insert_a C) bot_bot_set_a))) ((and (((eq a) A) B)) (((eq a) B) C)))).
% 0.72/0.91 Axiom fact_266_local_OIcc__subset__Ici__iff:(forall (L:a) (H:a) (L2:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) L) H)) ((set_atLeast_a less_eq) L2))) ((or (((less_eq L) H)->False)) ((less_eq L2) L)))).
% 0.72/0.91 Axiom fact_267_local_OIcc__subset__Iic__iff:(forall (L:a) (H:a) (H2:a), (((eq Prop) ((ord_less_eq_set_a (((set_atLeastAtMost_a less_eq) L) H)) ((set_atMost_a less_eq) H2))) ((or (((less_eq L) H)->False)) ((less_eq H) H2)))).
% 46.67/46.88 Axiom fact_268_comp__fun__idem_Ofun__left__idem:(forall (F:(a->(a->a))) (X:a) (Z:a), ((finite40241356em_a_a F)->(((eq a) ((F X) ((F X) Z))) ((F X) Z)))).
% 46.67/46.88 Axiom fact_269_order__class_Ofinite__has__minimal2:(forall (A2:set_set_a) (A:set_a), ((finite_finite_set_a A2)->(((member_set_a A) A2)->((ex set_a) (fun (X2:set_a)=> ((and ((and ((member_set_a X2) A2)) ((ord_less_eq_set_a X2) A))) (forall (Xa:set_a), (((member_set_a Xa) A2)->(((ord_less_eq_set_a Xa) X2)->(((eq set_a) X2) Xa)))))))))).
% 46.67/46.88 Trying to prove (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 46.67/46.88 Found fact_31_lattice_Oe__aux_Ocong0:=(fact_31_lattice_Oe__aux_Ocong (fun (x:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))))=> (P (((((x inf) sup) b) c) a2)))):((P (((((modula1144073633_aux_a inf) sup) b) c) a2))->(P (((((modula1144073633_aux_a inf) sup) b) c) a2)))
% 46.67/46.88 Found (fact_31_lattice_Oe__aux_Ocong (fun (x:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))))=> (P (((((x inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found (fact_31_lattice_Oe__aux_Ocong (fun (x:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))))=> (P (((((x inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 46.67/46.88 Found (eq_ref0 b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 46.67/46.88 Found ((eq_ref a) b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 46.67/46.88 Found ((eq_ref a) b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 46.67/46.88 Found ((eq_ref a) b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 46.67/46.88 Found eq_ref00:=(eq_ref0 (((((modula1144073633_aux_a inf) sup) b) c) a2)):(((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found (eq_ref0 (((((modula1144073633_aux_a inf) sup) b) c) a2)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) b0)
% 46.67/46.88 Found ((eq_ref a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) b0)
% 46.67/46.88 Found ((eq_ref a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) b0)
% 46.67/46.88 Found ((eq_ref a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) b) c) a2)) b0)
% 46.67/46.88 Found fact_129_semilattice__set__def0:=(fact_129_semilattice__set__def (fun (x:((a->(a->a))->Prop))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))):((P (((((modula1144073633_aux_a inf) sup) b) c) a2))->(P (((((modula1144073633_aux_a inf) sup) b) c) a2)))
% 46.67/46.88 Found (fact_129_semilattice__set__def (fun (x:((a->(a->a))->Prop))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found (fact_129_semilattice__set__def (fun (x:((a->(a->a))->Prop))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found fact_59_local_Oorder_Oeq__iff0:=(fact_59_local_Oorder_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))):((P (((((modula1144073633_aux_a inf) sup) b) c) a2))->(P (((((modula1144073633_aux_a inf) sup) b) c) a2)))
% 46.67/46.88 Found (fact_59_local_Oorder_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found (fact_59_local_Oorder_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 46.67/46.88 Found fact_218_subset__eq0:=(fact_218_subset__eq (fun (x:(set_a->(set_a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))):((P (((((modula1144073633_aux_a inf) sup) b) c) a2))->(P (((((modula1144073633_aux_a inf) sup) b) c) a2)))
% 122.44/122.71 Found (fact_218_subset__eq (fun (x:(set_a->(set_a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found (fact_218_subset__eq (fun (x:(set_a->(set_a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found fact_54_local_Oeq__iff0:=(fact_54_local_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))):((P (((((modula1144073633_aux_a inf) sup) b) c) a2))->(P (((((modula1144073633_aux_a inf) sup) b) c) a2)))
% 122.44/122.71 Found (fact_54_local_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found (fact_54_local_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found fact_167_semilattice__sup_OSup__fin_Ocong0:=(fact_167_semilattice__sup_OSup__fin_Ocong (fun (x:((a->(a->a))->(set_a->a)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))):((P (((((modula1144073633_aux_a inf) sup) b) c) a2))->(P (((((modula1144073633_aux_a inf) sup) b) c) a2)))
% 122.44/122.71 Found (fact_167_semilattice__sup_OSup__fin_Ocong (fun (x:((a->(a->a))->(set_a->a)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found (fact_167_semilattice__sup_OSup__fin_Ocong (fun (x:((a->(a->a))->(set_a->a)))=> (P (((((modula1144073633_aux_a inf) sup) b) c) a2)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% 122.44/122.71 Found (eq_ref0 b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found ((eq_ref a) b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found ((eq_ref a) b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found ((eq_ref a) b0) as proof of (((eq a) b0) (((((modula1144073633_aux_a inf) sup) b) c) a2))
% 122.44/122.71 Found eq_ref00:=(eq_ref0 (((((modula1144073633_aux_a inf) sup) a2) b) c)):(((eq a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 122.44/122.71 Found (eq_ref0 (((((modula1144073633_aux_a inf) sup) a2) b) c)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) b0)
% 122.44/122.71 Found ((eq_ref a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) b0)
% 122.44/122.71 Found ((eq_ref a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) b0)
% 122.44/122.71 Found ((eq_ref a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) as proof of (((eq a) (((((modula1144073633_aux_a inf) sup) a2) b) c)) b0)
% 122.44/122.71 Found fact_218_subset__eq0:=(fact_218_subset__eq (fun (x:(set_a->(set_a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) a2) b) c)))):((P (((((modula1144073633_aux_a inf) sup) a2) b) c))->(P (((((modula1144073633_aux_a inf) sup) a2) b) c)))
% 122.44/122.71 Found (fact_218_subset__eq (fun (x:(set_a->(set_a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) a2) b) c)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 122.44/122.71 Found (fact_218_subset__eq (fun (x:(set_a->(set_a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) a2) b) c)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 122.44/122.71 Found fact_59_local_Oorder_Oeq__iff0:=(fact_59_local_Oorder_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) a2) b) c)))):((P (((((modula1144073633_aux_a inf) sup) a2) b) c))->(P (((((modula1144073633_aux_a inf) sup) a2) b) c)))
% 122.44/122.71 Found (fact_59_local_Oorder_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) a2) b) c)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 122.44/122.71 Found (fact_59_local_Oorder_Oeq__iff (fun (x:(a->(a->Prop)))=> (P (((((modula1144073633_aux_a inf) sup) a2) b) c)))) as proof of (P0 (((((modula1144073633_aux_a inf) sup) a2) b) c))
% 122.44/122.71 Found fact_31_lattice_Oe__aux_Ocong0:=(fac
%------------------------------------------------------------------------------