%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ITP123^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n004.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   : Theorem 28.17s
% Output   : Proof 28.17s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : ITP123^1 : TPTP v7.5.0. Released v7.5.0.
% 0.08/0.13  % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % DateTime : Fri Mar 19 06:11:58 EDT 2021
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.14/0.36  Python 2.7.5
% 0.54/0.69  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x2b9b52261170>, <kernel.Type object at 0x224a3b0>) of role type named ty_n_t__Set__Oset_Itf__a_J
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring set_a:Type
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x2b9b52261ea8>, <kernel.Type object at 0x224a3b0>) of role type named ty_n_tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring a:Type
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x2b9b52261050>, <kernel.DependentProduct object at 0x224a3f8>) of role type named sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__above_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring condit1627435690bove_a:((a->(a->Prop))->(set_a->Prop))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x2b9b52261ea8>, <kernel.DependentProduct object at 0x224a6c8>) of role type named sy_c_Conditionally__Complete__Lattices_Opreorder_Obdd__below_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring condit1001553558elow_a:((a->(a->Prop))->(set_a->Prop))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x2b9b52261248>, <kernel.DependentProduct object at 0x224ac68>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring finite40241356em_a_a:((a->(a->a))->Prop)
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x2b9b52261ea8>, <kernel.DependentProduct object at 0x224a6c8>) of role type named sy_c_Groups_Oabel__semigroup_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring abel_semigroup_a:((a->(a->a))->Prop)
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a3f8>, <kernel.DependentProduct object at 0x224a2d8>) of role type named sy_c_Groups_Osemigroup_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring semigroup_a:((a->(a->a))->Prop)
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224ac68>, <kernel.DependentProduct object at 0x224a680>) of role type named sy_c_Lattices_Oclass_Olattice_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring lattice_a:((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->((a->(a->a))->Prop))))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a9e0>, <kernel.DependentProduct object at 0x224a290>) of role type named sy_c_Lattices_Osemilattice_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring semilattice_a:((a->(a->a))->Prop)
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a908>, <kernel.DependentProduct object at 0x224a998>) of role type named sy_c_Lattices_Osemilattice__order_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring semilattice_order_a:((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop)))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a680>, <kernel.DependentProduct object at 0x224ab48>) of role type named sy_c_Lattices__Big_Osemilattice__order__set_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring lattic655834328_set_a:((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop)))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a3f8>, <kernel.DependentProduct object at 0x224a2d8>) of role type named sy_c_Lattices__Big_Osemilattice__set_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring lattic1885654924_set_a:((a->(a->a))->Prop)
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a9e0>, <kernel.DependentProduct object at 0x224a878>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_OM5__lattice_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring modula1376131916tice_a:((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a998>, <kernel.DependentProduct object at 0x224a908>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_ON5__lattice_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring modula397570059tice_a:((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a098>, <kernel.DependentProduct object at 0x224a050>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oa__aux_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring modula17988509_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.54/0.69  FOF formula (<kernel.Constant object at 0x224a680>, <kernel.DependentProduct object at 0x224a9e0>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ob__aux_001tf__a
% 0.54/0.69  Using role type
% 0.54/0.69  Declaring modula1373251614_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a2d8>, <kernel.DependentProduct object at 0x224a998>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oc__aux_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring modula581031071_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a3f8>, <kernel.DependentProduct object at 0x224a098>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Od__aux_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring modula1936294176_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a950>, <kernel.DependentProduct object at 0x224a680>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oe__aux_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring modula1144073633_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224af38>, <kernel.DependentProduct object at 0x224a758>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Oincomp_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring modula1727524044comp_a:((a->(a->Prop))->(a->(a->Prop)))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224aef0>, <kernel.DependentProduct object at 0x224a2d8>) of role type named sy_c_Modular__Distrib__Lattice__Mirabelle__ybbibajlty_Olattice_Ono__distrib_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring modula1962211574trib_a:((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a6c8>, <kernel.DependentProduct object at 0x224a200>) of role type named sy_c_Orderings_Oord_OLeast_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring least_a:((a->(a->Prop))->((a->Prop)->a))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a908>, <kernel.DependentProduct object at 0x224af38>) of role type named sy_c_Orderings_Oord_Omax_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring max_a:((a->(a->Prop))->(a->(a->a)))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a248>, <kernel.DependentProduct object at 0x224a680>) of role type named sy_c_Orderings_Oord_Omin_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring min_a:((a->(a->Prop))->(a->(a->a)))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a710>, <kernel.DependentProduct object at 0x224a950>) of role type named sy_c_Orderings_Oorder_OGreatest_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring greatest_a:((a->(a->Prop))->((a->Prop)->a))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224aef0>, <kernel.DependentProduct object at 0x224a998>) of role type named sy_c_Orderings_Oordering_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring ordering_a:((a->(a->Prop))->((a->(a->Prop))->Prop))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a248>, <kernel.DependentProduct object at 0x224a9e0>) of role type named sy_c_Set_OCollect_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring collect_a:((a->Prop)->set_a)
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a950>, <kernel.DependentProduct object at 0x224a710>) of role type named sy_c_Set__Interval_Oord_OgreaterThanLessThan_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring set_gr1491433118Than_a:((a->(a->Prop))->(a->(a->set_a)))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a200>, <kernel.DependentProduct object at 0x224acf8>) of role type named sy_c_member_001tf__a
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring member_a:(a->(set_a->Prop))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a998>, <kernel.DependentProduct object at 0x224af38>) of role type named sy_v_inf
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring inf:(a->(a->a))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224a710>, <kernel.DependentProduct object at 0x224a0e0>) of role type named sy_v_less
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring less:(a->(a->Prop))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224acf8>, <kernel.DependentProduct object at 0x224a248>) of role type named sy_v_less__eq
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring less_eq:(a->(a->Prop))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x224af38>, <kernel.DependentProduct object at 0x224a200>) of role type named sy_v_sup
% 0.54/0.70  Using role type
% 0.54/0.70  Declaring sup:(a->(a->a))
% 0.54/0.70  FOF formula (<kernel.Constant object at 0x2b9b4a7825f0>, <kernel.Constant object at 0x224a200>) of role type named sy_v_x
% 0.54/0.72  Using role type
% 0.54/0.72  Declaring x:a
% 0.54/0.72  FOF formula (<kernel.Constant object at 0x224acf8>, <kernel.Constant object at 0x224a200>) of role type named sy_v_y
% 0.54/0.72  Using role type
% 0.54/0.72  Declaring y:a
% 0.54/0.72  FOF formula (<kernel.Constant object at 0x224af38>, <kernel.Constant object at 0x224a200>) of role type named sy_v_z
% 0.54/0.72  Using role type
% 0.54/0.72  Declaring z:a
% 0.54/0.72  FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y)))) of role axiom named fact_0_local_Oantisym
% 0.54/0.72  A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y))))
% 0.54/0.72  FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))) of role axiom named fact_1_local_Oantisym__conv
% 0.54/0.72  A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y))))
% 0.54/0.72  FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B)))) of role axiom named fact_2_local_Odual__order_Oantisym
% 0.54/0.72  A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B))))
% 0.54/0.72  FOF formula (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq B2) A2)) ((less_eq A2) B2)))) of role axiom named fact_3_local_Odual__order_Oeq__iff
% 0.54/0.72  A new axiom: (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq B2) A2)) ((less_eq A2) B2))))
% 0.54/0.72  FOF formula (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A)))) of role axiom named fact_4_local_Odual__order_Otrans
% 0.54/0.72  A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A))))
% 0.54/0.72  FOF formula (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (X2:a) (Y3:a)=> ((and ((less_eq X2) Y3)) ((less_eq Y3) X2)))) of role axiom named fact_5_local_Oeq__iff
% 0.54/0.72  A new axiom: (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (X2:a) (Y3:a)=> ((and ((less_eq X2) Y3)) ((less_eq Y3) X2))))
% 0.54/0.72  FOF formula (forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y))) of role axiom named fact_6_local_Oeq__refl
% 0.54/0.72  A new axiom: (forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y)))
% 0.54/0.72  FOF formula (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C)))) of role axiom named fact_7_local_Oord__eq__le__trans
% 0.54/0.72  A new axiom: (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C))))
% 0.54/0.72  FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C)))) of role axiom named fact_8_local_Oord__le__eq__trans
% 0.54/0.72  A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C))))
% 0.54/0.72  FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B)))) of role axiom named fact_9_local_Oorder_Oantisym
% 0.54/0.72  A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B))))
% 0.54/0.72  FOF formula (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq A2) B2)) ((less_eq B2) A2)))) of role axiom named fact_10_local_Oorder_Oeq__iff
% 0.54/0.72  A new axiom: (((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq A2) B2)) ((less_eq B2) A2))))
% 0.54/0.72  FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C)))) of role axiom named fact_11_local_Oorder_Otrans
% 0.54/0.72  A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C))))
% 0.54/0.72  FOF formula (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq Y) Z2)->((less_eq X) Z2)))) of role axiom named fact_12_local_Oorder__trans
% 0.54/0.72  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq Y) Z2)->((less_eq X) Z2))))
% 0.54/0.72  FOF formula (forall (B:a) (A:a), (((less B) A)->(((less A) B)->False))) of role axiom named fact_13_local_Odual__order_Oasym
% 0.54/0.72  A new axiom: (forall (B:a) (A:a), (((less B) A)->(((less A) B)->False)))
% 0.54/0.72  FOF formula (forall (B:a) (A:a), (((less B) A)->(not (((eq a) A) B)))) of role axiom named fact_14_local_Odual__order_Ostrict__implies__not__eq
% 0.54/0.72  A new axiom: (forall (B:a) (A:a), (((less B) A)->(not (((eq a) A) B))))
% 0.54/0.72  FOF formula (forall (B:a) (A:a) (C:a), (((less B) A)->(((less C) B)->((less C) A)))) of role axiom named fact_15_local_Odual__order_Ostrict__trans
% 0.54/0.74  A new axiom: (forall (B:a) (A:a) (C:a), (((less B) A)->(((less C) B)->((less C) A))))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False))) of role axiom named fact_16_local_Oless__asym
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False)))
% 0.54/0.74  FOF formula (forall (A:a) (B:a), (((less A) B)->(((less B) A)->False))) of role axiom named fact_17_local_Oless__asym_H
% 0.54/0.74  A new axiom: (forall (A:a) (B:a), (((less A) B)->(((less B) A)->False)))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) X) Y)))) of role axiom named fact_18_local_Oless__imp__neq
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) X) Y))))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) X) Y)))) of role axiom named fact_19_local_Oless__imp__not__eq
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) X) Y))))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) Y) X)))) of role axiom named fact_20_local_Oless__imp__not__eq2
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) Y) X))))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False))) of role axiom named fact_21_local_Oless__imp__not__less
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False)))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a) (P:Prop), (((less X) Y)->(((less Y) X)->P))) of role axiom named fact_22_local_Oless__imp__triv
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a) (P:Prop), (((less X) Y)->(((less Y) X)->P)))
% 0.54/0.74  FOF formula (forall (X:a), (((less X) X)->False)) of role axiom named fact_23_local_Oless__irrefl
% 0.54/0.74  A new axiom: (forall (X:a), (((less X) X)->False))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False))) of role axiom named fact_24_local_Oless__not__sym
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False)))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a) (Z2:a), (((less X) Y)->(((less Y) Z2)->((less X) Z2)))) of role axiom named fact_25_local_Oless__trans
% 0.54/0.74  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less X) Y)->(((less Y) Z2)->((less X) Z2))))
% 0.54/0.74  FOF formula (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less B) C)->((less A) C)))) of role axiom named fact_26_local_Oord__eq__less__trans
% 0.54/0.74  A new axiom: (forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less B) C)->((less A) C))))
% 0.54/0.74  FOF formula (forall (A:a) (B:a) (C:a), (((less A) B)->((((eq a) B) C)->((less A) C)))) of role axiom named fact_27_local_Oord__less__eq__trans
% 0.54/0.74  A new axiom: (forall (A:a) (B:a) (C:a), (((less A) B)->((((eq a) B) C)->((less A) C))))
% 0.54/0.74  FOF formula (forall (A:a) (B:a), (((less A) B)->(((less B) A)->False))) of role axiom named fact_28_local_Oorder_Oasym
% 0.54/0.74  A new axiom: (forall (A:a) (B:a), (((less A) B)->(((less B) A)->False)))
% 0.54/0.74  FOF formula (forall (A:a), (((less A) A)->False)) of role axiom named fact_29_local_Oorder_Oirrefl
% 0.54/0.74  A new axiom: (forall (A:a), (((less A) A)->False))
% 0.54/0.74  FOF formula (forall (A:a) (B:a), (((less A) B)->(not (((eq a) A) B)))) of role axiom named fact_30_local_Oorder_Ostrict__implies__not__eq
% 0.54/0.74  A new axiom: (forall (A:a) (B:a), (((less A) B)->(not (((eq a) A) B))))
% 0.54/0.74  FOF formula (forall (A:a) (B:a) (C:a), (((less A) B)->(((less B) C)->((less A) C)))) of role axiom named fact_31_local_Oorder_Ostrict__trans
% 0.54/0.74  A new axiom: (forall (A:a) (B:a) (C:a), (((less A) B)->(((less B) C)->((less A) C))))
% 0.54/0.74  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_32_local_Oinf_Oassoc
% 0.54/0.74  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C))))
% 0.54/0.74  FOF formula (forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A))) of role axiom named fact_33_local_Oinf_Ocommute
% 0.54/0.74  A new axiom: (forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A)))
% 0.54/0.74  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_34_local_Oinf_Oleft__commute
% 0.54/0.74  A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C))))
% 0.54/0.74  FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf ((inf X) Y)) Z2)) ((inf X) ((inf Y) Z2)))) of role axiom named fact_35_local_Oinf__assoc
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf ((inf X) Y)) Z2)) ((inf X) ((inf Y) Z2))))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X))) of role axiom named fact_36_local_Oinf__commute
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X)))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf X) ((inf Y) Z2))) ((inf Y) ((inf X) Z2)))) of role axiom named fact_37_local_Oinf__left__commute
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf X) ((inf Y) Z2))) ((inf Y) ((inf X) Z2))))
% 0.61/0.76  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_38_local_Osup_Oassoc
% 0.61/0.76  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C))))
% 0.61/0.76  FOF formula (forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A))) of role axiom named fact_39_local_Osup_Ocommute
% 0.61/0.76  A new axiom: (forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A)))
% 0.61/0.76  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_40_local_Osup_Oleft__commute
% 0.61/0.76  A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C))))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup ((sup X) Y)) Z2)) ((sup X) ((sup Y) Z2)))) of role axiom named fact_41_local_Osup__assoc
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup ((sup X) Y)) Z2)) ((sup X) ((sup Y) Z2))))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X))) of role axiom named fact_42_local_Osup__commute
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X)))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup X) ((sup Y) Z2))) ((sup Y) ((sup X) Z2)))) of role axiom named fact_43_local_Osup__left__commute
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup X) ((sup Y) Z2))) ((sup Y) ((sup X) Z2))))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a), ((((less X) Y)->False)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))) of role axiom named fact_44_local_Oantisym__conv1
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a), ((((less X) Y)->False)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y))))
% 0.61/0.76  FOF formula (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))) of role axiom named fact_45_mem__Collect__eq
% 0.61/0.76  A new axiom: (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A)))
% 0.61/0.76  FOF formula (forall (A3:set_a), (((eq set_a) (collect_a (fun (X2:a)=> ((member_a X2) A3)))) A3)) of role axiom named fact_46_Collect__mem__eq
% 0.61/0.76  A new axiom: (forall (A3:set_a), (((eq set_a) (collect_a (fun (X2:a)=> ((member_a X2) A3)))) A3))
% 0.61/0.76  FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), (((eq Prop) (P X3)) (Q X3)))->(((eq set_a) (collect_a P)) (collect_a Q)))) of role axiom named fact_47_Collect__cong
% 0.61/0.76  A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), (((eq Prop) (P X3)) (Q X3)))->(((eq set_a) (collect_a P)) (collect_a Q))))
% 0.61/0.76  FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq Prop) (((less X) Y)->False)) (((eq a) X) Y)))) of role axiom named fact_48_local_Oantisym__conv2
% 0.61/0.76  A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq Prop) (((less X) Y)->False)) (((eq a) X) Y))))
% 0.61/0.76  FOF formula (forall (A:a) (B:a), ((not (((eq a) A) B))->(((less_eq B) A)->((less B) A)))) of role axiom named fact_49_local_Odual__order_Onot__eq__order__implies__strict
% 0.61/0.76  A new axiom: (forall (A:a) (B:a), ((not (((eq a) A) B))->(((less_eq B) A)->((less B) A))))
% 0.61/0.76  FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) ((or ((less B) A)) (((eq a) A) B)))) of role axiom named fact_50_local_Odual__order_Oorder__iff__strict
% 0.61/0.76  A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) ((or ((less B) A)) (((eq a) A) B))))
% 0.61/0.76  FOF formula (forall (B:a) (A:a), (((eq Prop) ((less B) A)) ((and ((less_eq B) A)) (not (((eq a) A) B))))) of role axiom named fact_51_local_Odual__order_Ostrict__iff__order
% 0.61/0.76  A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less B) A)) ((and ((less_eq B) A)) (not (((eq a) A) B)))))
% 0.61/0.76  FOF formula (forall (B:a) (A:a), (((less B) A)->((less_eq B) A))) of role axiom named fact_52_local_Odual__order_Ostrict__implies__order
% 0.62/0.78  A new axiom: (forall (B:a) (A:a), (((less B) A)->((less_eq B) A)))
% 0.62/0.78  FOF formula (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less C) B)->((less C) A)))) of role axiom named fact_53_local_Odual__order_Ostrict__trans1
% 0.62/0.78  A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less C) B)->((less C) A))))
% 0.62/0.78  FOF formula (forall (B:a) (A:a) (C:a), (((less B) A)->(((less_eq C) B)->((less C) A)))) of role axiom named fact_54_local_Odual__order_Ostrict__trans2
% 0.62/0.78  A new axiom: (forall (B:a) (A:a) (C:a), (((less B) A)->(((less_eq C) B)->((less C) A))))
% 0.62/0.78  FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((less X) Y)->False))) of role axiom named fact_55_local_OleD
% 0.62/0.78  A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((less X) Y)->False)))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->((or ((less X) Y)) (((eq a) X) Y)))) of role axiom named fact_56_local_Ole__imp__less__or__eq
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->((or ((less X) Y)) (((eq a) X) Y))))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) ((or ((less X) Y)) (((eq a) X) Y)))) of role axiom named fact_57_local_Ole__less
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) ((or ((less X) Y)) (((eq a) X) Y))))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less Y) Z2)->((less X) Z2)))) of role axiom named fact_58_local_Ole__less__trans
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less Y) Z2)->((less X) Z2))))
% 0.62/0.78  FOF formula (forall (A:a) (B:a), (((less_eq A) B)->((not (((eq a) A) B))->((less A) B)))) of role axiom named fact_59_local_Ole__neq__trans
% 0.62/0.78  A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->((not (((eq a) A) B))->((less A) B))))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a), (((less X) Y)->((less_eq X) Y))) of role axiom named fact_60_local_Oless__imp__le
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a), (((less X) Y)->((less_eq X) Y)))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less X) Y)) ((and ((less_eq X) Y)) (not (((eq a) X) Y))))) of role axiom named fact_61_local_Oless__le
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less X) Y)) ((and ((less_eq X) Y)) (not (((eq a) X) Y)))))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less X) Y)) ((and ((less_eq X) Y)) (((less_eq Y) X)->False)))) of role axiom named fact_62_local_Oless__le__not__le
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less X) Y)) ((and ((less_eq X) Y)) (((less_eq Y) X)->False))))
% 0.62/0.78  FOF formula (forall (X:a) (Y:a) (Z2:a), (((less X) Y)->(((less_eq Y) Z2)->((less X) Z2)))) of role axiom named fact_63_local_Oless__le__trans
% 0.62/0.78  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less X) Y)->(((less_eq Y) Z2)->((less X) Z2))))
% 0.62/0.78  FOF formula (forall (A:a) (B:a), ((not (((eq a) A) B))->(((less_eq A) B)->((less A) B)))) of role axiom named fact_64_local_Oorder_Onot__eq__order__implies__strict
% 0.62/0.78  A new axiom: (forall (A:a) (B:a), ((not (((eq a) A) B))->(((less_eq A) B)->((less A) B))))
% 0.62/0.78  FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) ((or ((less A) B)) (((eq a) A) B)))) of role axiom named fact_65_local_Oorder_Oorder__iff__strict
% 0.62/0.78  A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) ((or ((less A) B)) (((eq a) A) B))))
% 0.62/0.78  FOF formula (forall (A:a) (B:a), (((eq Prop) ((less A) B)) ((and ((less_eq A) B)) (not (((eq a) A) B))))) of role axiom named fact_66_local_Oorder_Ostrict__iff__order
% 0.62/0.78  A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less A) B)) ((and ((less_eq A) B)) (not (((eq a) A) B)))))
% 0.62/0.78  FOF formula (forall (A:a) (B:a), (((less A) B)->((less_eq A) B))) of role axiom named fact_67_local_Oorder_Ostrict__implies__order
% 0.62/0.78  A new axiom: (forall (A:a) (B:a), (((less A) B)->((less_eq A) B)))
% 0.62/0.78  FOF formula (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less B) C)->((less A) C)))) of role axiom named fact_68_local_Oorder_Ostrict__trans1
% 0.62/0.78  A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less B) C)->((less A) C))))
% 0.62/0.78  FOF formula (forall (A:a) (B:a) (C:a), (((less A) B)->(((less_eq B) C)->((less A) C)))) of role axiom named fact_69_local_Oorder_Ostrict__trans2
% 0.62/0.80  A new axiom: (forall (A:a) (B:a) (C:a), (((less A) B)->(((less_eq B) C)->((less A) C))))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A))) of role axiom named fact_70_local_Oinf_Oabsorb1
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A)))
% 0.62/0.80  FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B))) of role axiom named fact_71_local_Oinf_Oabsorb2
% 0.62/0.80  A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B)))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A))) of role axiom named fact_72_local_Oinf_Oabsorb__iff1
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A)))
% 0.62/0.80  FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B))) of role axiom named fact_73_local_Oinf_Oabsorb__iff2
% 0.62/0.80  A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B)))
% 0.62/0.80  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_74_local_Oinf_OboundedE
% 0.62/0.80  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)))
% 0.62/0.80  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_75_local_Oinf_OboundedI
% 0.62/0.80  A new axiom: (forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C)))))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), ((less_eq ((inf A) B)) A)) of role axiom named fact_76_local_Oinf_Ocobounded1
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), ((less_eq ((inf A) B)) A))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), ((less_eq ((inf A) B)) B)) of role axiom named fact_77_local_Oinf_Ocobounded2
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), ((less_eq ((inf A) B)) B))
% 0.62/0.80  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
% 0.62/0.80  A new axiom: (forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C)))
% 0.62/0.80  FOF formula (forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C))) of role axiom named fact_79_local_Oinf_OcoboundedI2
% 0.62/0.80  A new axiom: (forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C)))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B)))) of role axiom named fact_80_local_Oinf_OorderE
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B))))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B))) of role axiom named fact_81_local_Oinf_OorderI
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B)))
% 0.62/0.80  FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B)))) of role axiom named fact_82_local_Oinf_Oorder__iff
% 0.62/0.80  A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B))))
% 0.62/0.80  FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X))) of role axiom named fact_83_local_Oinf__absorb1
% 0.62/0.80  A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X)))
% 0.62/0.80  FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y))) of role axiom named fact_84_local_Oinf__absorb2
% 0.62/0.80  A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y)))
% 0.62/0.80  FOF formula (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq X) Z2)->((less_eq X) ((inf Y) Z2))))) of role axiom named fact_85_local_Oinf__greatest
% 0.62/0.80  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq X) Z2)->((less_eq X) ((inf Y) Z2)))))
% 0.62/0.80  FOF formula (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X)) of role axiom named fact_86_local_Oinf__le1
% 0.62/0.80  A new axiom: (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X))
% 0.62/0.80  FOF formula (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y)) of role axiom named fact_87_local_Oinf__le2
% 0.62/0.80  A new axiom: (forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y))
% 0.62/0.80  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_88_local_Oinf__mono
% 0.66/0.82  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)))))
% 0.66/0.82  FOF formula (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) X3))->((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) Y4))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq X3) Y4)->(((less_eq X3) Z3)->((less_eq X3) ((F Y4) Z3)))))->(((eq a) ((inf X) Y)) ((F X) Y)))))) of role axiom named fact_89_local_Oinf__unique
% 0.66/0.82  A new axiom: (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) X3))->((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) Y4))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq X3) Y4)->(((less_eq X3) Z3)->((less_eq X3) ((F Y4) Z3)))))->(((eq a) ((inf X) Y)) ((F X) Y))))))
% 0.66/0.82  FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X))) of role axiom named fact_90_local_Ole__iff__inf
% 0.66/0.82  A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X)))
% 0.66/0.82  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_91_local_Ole__infE
% 0.66/0.82  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)))
% 0.66/0.82  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_92_local_Ole__infI
% 0.66/0.82  A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B)))))
% 0.66/0.82  FOF formula (forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X))) of role axiom named fact_93_local_Ole__infI1
% 0.66/0.82  A new axiom: (forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X)))
% 0.66/0.82  FOF formula (forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X))) of role axiom named fact_94_local_Ole__infI2
% 0.66/0.82  A new axiom: (forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X)))
% 0.66/0.82  FOF formula (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y))) of role axiom named fact_95_local_Ole__iff__sup
% 0.66/0.82  A new axiom: (forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y)))
% 0.66/0.82  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_96_local_Ole__supE
% 0.66/0.82  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)))
% 0.66/0.82  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_97_local_Ole__supI
% 0.66/0.82  A new axiom: (forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X))))
% 0.66/0.82  FOF formula (forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B)))) of role axiom named fact_98_local_Ole__supI1
% 0.66/0.82  A new axiom: (forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B))))
% 0.66/0.82  FOF formula (forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B)))) of role axiom named fact_99_local_Ole__supI2
% 0.66/0.82  A new axiom: (forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B))))
% 0.66/0.82  FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A))) of role axiom named fact_100_local_Osup_Oabsorb1
% 0.66/0.82  A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A)))
% 0.66/0.82  FOF formula (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B))) of role axiom named fact_101_local_Osup_Oabsorb2
% 0.66/0.82  A new axiom: (forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B)))
% 0.66/0.82  FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A))) of role axiom named fact_102_local_Osup_Oabsorb__iff1
% 0.66/0.82  A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A)))
% 0.66/0.82  FOF formula (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B))) of role axiom named fact_103_local_Osup_Oabsorb__iff2
% 0.66/0.82  A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B)))
% 0.66/0.82  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_104_local_Osup_OboundedE
% 0.69/0.84  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)))
% 0.69/0.84  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_105_local_Osup_OboundedI
% 0.69/0.84  A new axiom: (forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A))))
% 0.69/0.84  FOF formula (forall (A:a) (B:a), ((less_eq A) ((sup A) B))) of role axiom named fact_106_local_Osup_Ocobounded1
% 0.69/0.84  A new axiom: (forall (A:a) (B:a), ((less_eq A) ((sup A) B)))
% 0.69/0.84  FOF formula (forall (B:a) (A:a), ((less_eq B) ((sup A) B))) of role axiom named fact_107_local_Osup_Ocobounded2
% 0.69/0.84  A new axiom: (forall (B:a) (A:a), ((less_eq B) ((sup A) B)))
% 0.69/0.84  FOF formula (forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B)))) of role axiom named fact_108_local_Osup_OcoboundedI1
% 0.69/0.84  A new axiom: (forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B))))
% 0.69/0.84  FOF formula (forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B)))) of role axiom named fact_109_local_Osup_OcoboundedI2
% 0.69/0.84  A new axiom: (forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B))))
% 0.69/0.84  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_110_local_Osup_Omono
% 0.69/0.84  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)))))
% 0.69/0.84  FOF formula (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B)))) of role axiom named fact_111_local_Osup_OorderE
% 0.69/0.84  A new axiom: (forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B))))
% 0.69/0.84  FOF formula (forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A))) of role axiom named fact_112_local_Osup_OorderI
% 0.69/0.84  A new axiom: (forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A)))
% 0.69/0.84  FOF formula (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B)))) of role axiom named fact_113_local_Osup_Oorder__iff
% 0.69/0.84  A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B))))
% 0.69/0.84  FOF formula (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X))) of role axiom named fact_114_local_Osup__absorb1
% 0.69/0.84  A new axiom: (forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X)))
% 0.69/0.84  FOF formula (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y))) of role axiom named fact_115_local_Osup__absorb2
% 0.69/0.84  A new axiom: (forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y)))
% 0.69/0.84  FOF formula (forall (X:a) (Y:a), ((less_eq X) ((sup X) Y))) of role axiom named fact_116_local_Osup__ge1
% 0.69/0.84  A new axiom: (forall (X:a) (Y:a), ((less_eq X) ((sup X) Y)))
% 0.69/0.84  FOF formula (forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y))) of role axiom named fact_117_local_Osup__ge2
% 0.69/0.84  A new axiom: (forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y)))
% 0.69/0.84  FOF formula (forall (Y:a) (X:a) (Z2:a), (((less_eq Y) X)->(((less_eq Z2) X)->((less_eq ((sup Y) Z2)) X)))) of role axiom named fact_118_local_Osup__least
% 0.69/0.84  A new axiom: (forall (Y:a) (X:a) (Z2:a), (((less_eq Y) X)->(((less_eq Z2) X)->((less_eq ((sup Y) Z2)) X))))
% 0.69/0.84  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_119_local_Osup__mono
% 0.69/0.84  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)))))
% 0.69/0.84  FOF formula (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq X3) ((F X3) Y4)))->((forall (X3:a) (Y4:a), ((less_eq Y4) ((F X3) Y4)))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq Y4) X3)->(((less_eq Z3) X3)->((less_eq ((F Y4) Z3)) X3))))->(((eq a) ((sup X) Y)) ((F X) Y)))))) of role axiom named fact_120_local_Osup__unique
% 0.69/0.84  A new axiom: (forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq X3) ((F X3) Y4)))->((forall (X3:a) (Y4:a), ((less_eq Y4) ((F X3) Y4)))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq Y4) X3)->(((less_eq Z3) X3)->((less_eq ((F Y4) Z3)) X3))))->(((eq a) ((sup X) Y)) ((F X) Y))))))
% 0.69/0.86  FOF formula (forall (A:a) (B:a) (C:a), (((less A) ((inf B) C))->((((less A) B)->(((less A) C)->False))->False))) of role axiom named fact_121_local_Oinf_Ostrict__boundedE
% 0.69/0.86  A new axiom: (forall (A:a) (B:a) (C:a), (((less A) ((inf B) C))->((((less A) B)->(((less A) C)->False))->False)))
% 0.69/0.86  FOF formula (forall (A:a) (C:a) (B:a), (((less A) C)->((less ((inf A) B)) C))) of role axiom named fact_122_local_Oinf_Ostrict__coboundedI1
% 0.69/0.86  A new axiom: (forall (A:a) (C:a) (B:a), (((less A) C)->((less ((inf A) B)) C)))
% 0.69/0.86  FOF formula (forall (B:a) (C:a) (A:a), (((less B) C)->((less ((inf A) B)) C))) of role axiom named fact_123_local_Oinf_Ostrict__coboundedI2
% 0.69/0.86  A new axiom: (forall (B:a) (C:a) (A:a), (((less B) C)->((less ((inf A) B)) C)))
% 0.69/0.86  FOF formula (forall (A:a) (B:a), (((eq Prop) ((less A) B)) ((and (((eq a) A) ((inf A) B))) (not (((eq a) A) B))))) of role axiom named fact_124_local_Oinf_Ostrict__order__iff
% 0.69/0.86  A new axiom: (forall (A:a) (B:a), (((eq Prop) ((less A) B)) ((and (((eq a) A) ((inf A) B))) (not (((eq a) A) B)))))
% 0.69/0.86  FOF formula (forall (A:a) (X:a) (B:a), (((less A) X)->((less ((inf A) B)) X))) of role axiom named fact_125_local_Oless__infI1
% 0.69/0.86  A new axiom: (forall (A:a) (X:a) (B:a), (((less A) X)->((less ((inf A) B)) X)))
% 0.69/0.86  FOF formula (forall (B:a) (X:a) (A:a), (((less B) X)->((less ((inf A) B)) X))) of role axiom named fact_126_local_Oless__infI2
% 0.69/0.86  A new axiom: (forall (B:a) (X:a) (A:a), (((less B) X)->((less ((inf A) B)) X)))
% 0.69/0.86  FOF formula (forall (X:a) (A:a) (B:a), (((less X) A)->((less X) ((sup A) B)))) of role axiom named fact_127_local_Oless__supI1
% 0.69/0.86  A new axiom: (forall (X:a) (A:a) (B:a), (((less X) A)->((less X) ((sup A) B))))
% 0.69/0.86  FOF formula (forall (X:a) (B:a) (A:a), (((less X) B)->((less X) ((sup A) B)))) of role axiom named fact_128_local_Oless__supI2
% 0.69/0.86  A new axiom: (forall (X:a) (B:a) (A:a), (((less X) B)->((less X) ((sup A) B))))
% 0.69/0.86  FOF formula (forall (B:a) (C:a) (A:a), (((less ((sup B) C)) A)->((((less B) A)->(((less C) A)->False))->False))) of role axiom named fact_129_local_Osup_Ostrict__boundedE
% 0.69/0.86  A new axiom: (forall (B:a) (C:a) (A:a), (((less ((sup B) C)) A)->((((less B) A)->(((less C) A)->False))->False)))
% 0.69/0.86  FOF formula (forall (C:a) (A:a) (B:a), (((less C) A)->((less C) ((sup A) B)))) of role axiom named fact_130_local_Osup_Ostrict__coboundedI1
% 0.69/0.86  A new axiom: (forall (C:a) (A:a) (B:a), (((less C) A)->((less C) ((sup A) B))))
% 0.69/0.86  FOF formula (forall (C:a) (B:a) (A:a), (((less C) B)->((less C) ((sup A) B)))) of role axiom named fact_131_local_Osup_Ostrict__coboundedI2
% 0.69/0.86  A new axiom: (forall (C:a) (B:a) (A:a), (((less C) B)->((less C) ((sup A) B))))
% 0.69/0.86  FOF formula (forall (B:a) (A:a), (((eq Prop) ((less B) A)) ((and (((eq a) A) ((sup A) B))) (not (((eq a) A) B))))) of role axiom named fact_132_local_Osup_Ostrict__order__iff
% 0.69/0.86  A new axiom: (forall (B:a) (A:a), (((eq Prop) ((less B) A)) ((and (((eq a) A) ((sup A) B))) (not (((eq a) A) B)))))
% 0.69/0.86  FOF formula (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((inf X3) ((sup Y4) Z3))) ((sup ((inf X3) Y4)) ((inf X3) Z3))))->(((eq a) ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2))))) of role axiom named fact_133_local_Odistrib__imp1
% 0.69/0.86  A new axiom: (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((inf X3) ((sup Y4) Z3))) ((sup ((inf X3) Y4)) ((inf X3) Z3))))->(((eq a) ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2)))))
% 0.69/0.86  FOF formula (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((sup X3) ((inf Y4) Z3))) ((inf ((sup X3) Y4)) ((sup X3) Z3))))->(((eq a) ((inf X) ((sup Y) Z2))) ((sup ((inf X) Y)) ((inf X) Z2))))) of role axiom named fact_134_local_Odistrib__imp2
% 0.69/0.86  A new axiom: (forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((sup X3) ((inf Y4) Z3))) ((inf ((sup X3) Y4)) ((sup X3) Z3))))->(((eq a) ((inf X) ((sup Y) Z2))) ((sup ((inf X) Y)) ((inf X) Z2)))))
% 0.69/0.86  FOF formula (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z2))) ((inf X) ((sup Y) Z2)))) of role axiom named fact_135_local_Odistrib__inf__le
% 0.69/0.86  A new axiom: (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z2))) ((inf X) ((sup Y) Z2))))
% 0.69/0.88  FOF formula (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2)))) of role axiom named fact_136_local_Odistrib__sup__le
% 0.69/0.88  A new axiom: (forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2))))
% 0.69/0.88  FOF formula (forall (X:a) (Y:a), (((eq Prop) (((modula1727524044comp_a less_eq) X) Y)) ((and (((less_eq X) Y)->False)) (((less_eq Y) X)->False)))) of role axiom named fact_137_local_Oincomp__def
% 0.69/0.88  A new axiom: (forall (X:a) (Y:a), (((eq Prop) (((modula1727524044comp_a less_eq) X) Y)) ((and (((less_eq X) Y)->False)) (((less_eq Y) X)->False))))
% 0.69/0.88  FOF formula (forall (A:a), ((less_eq A) A)) of role axiom named fact_138_local_Oorder_Orefl
% 0.69/0.88  A new axiom: (forall (A:a), ((less_eq A) A))
% 0.69/0.88  FOF formula (forall (X:a), ((less_eq X) X)) of role axiom named fact_139_local_Oorder__refl
% 0.69/0.88  A new axiom: (forall (X:a), ((less_eq X) X))
% 0.69/0.88  FOF formula (forall (A:a), (((eq a) ((inf A) A)) A)) of role axiom named fact_140_local_Oinf_Oidem
% 0.69/0.88  A new axiom: (forall (A:a), (((eq a) ((inf A) A)) A))
% 0.69/0.88  FOF formula (forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B))) of role axiom named fact_141_local_Oinf_Oleft__idem
% 0.69/0.88  A new axiom: (forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B)))
% 0.69/0.88  FOF formula (forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B))) of role axiom named fact_142_local_Oinf_Oright__idem
% 0.69/0.88  A new axiom: (forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B)))
% 0.69/0.88  FOF formula (forall (X:a), (((eq a) ((inf X) X)) X)) of role axiom named fact_143_local_Oinf__idem
% 0.69/0.88  A new axiom: (forall (X:a), (((eq a) ((inf X) X)) X))
% 0.69/0.88  FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y))) of role axiom named fact_144_local_Oinf__left__idem
% 0.69/0.88  A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y)))
% 0.69/0.88  FOF formula (forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y))) of role axiom named fact_145_local_Oinf__right__idem
% 0.69/0.88  A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y)))
% 0.69/0.88  FOF formula (forall (A:a), (((eq a) ((sup A) A)) A)) of role axiom named fact_146_local_Osup_Oidem
% 0.69/0.88  A new axiom: (forall (A:a), (((eq a) ((sup A) A)) A))
% 0.69/0.88  FOF formula (forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B))) of role axiom named fact_147_local_Osup_Oleft__idem
% 0.69/0.88  A new axiom: (forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B)))
% 0.69/0.88  FOF formula (forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B))) of role axiom named fact_148_local_Osup_Oright__idem
% 0.69/0.88  A new axiom: (forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B)))
% 0.69/0.88  FOF formula (forall (X:a), (((eq a) ((sup X) X)) X)) of role axiom named fact_149_local_Osup__idem
% 0.69/0.88  A new axiom: (forall (X:a), (((eq a) ((sup X) X)) X))
% 0.69/0.88  FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y))) of role axiom named fact_150_local_Osup__left__idem
% 0.69/0.88  A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y)))
% 0.69/0.88  FOF formula (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X3)))->(Q X3))))->(Q ((greatest_a less_eq) P)))))) of role axiom named fact_151_local_OGreatestI2__order
% 0.69/0.88  A new axiom: (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X3)))->(Q X3))))->(Q ((greatest_a less_eq) P))))))
% 0.69/0.88  FOF formula (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->(((eq a) ((greatest_a less_eq) P)) X)))) of role axiom named fact_152_local_OGreatest__equality
% 0.69/0.88  A new axiom: (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->(((eq a) ((greatest_a less_eq) P)) X))))
% 0.69/0.88  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_153_local_Omax__def
% 0.69/0.90  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))))
% 0.69/0.90  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_154_local_Omin__def
% 0.69/0.90  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))))
% 0.69/0.90  FOF formula (forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula397570059tice_a inf) less) sup) A) B) C)) ((and ((and (((eq a) ((inf A) C)) ((inf B) C))) ((less A) B))) (((eq a) ((sup A) C)) ((sup B) C))))) of role axiom named fact_155_local_ON5__lattice__def
% 0.69/0.90  A new axiom: (forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula397570059tice_a inf) less) sup) A) B) C)) ((and ((and (((eq a) ((inf A) C)) ((inf B) C))) ((less A) B))) (((eq a) ((sup A) C)) ((sup B) C)))))
% 0.69/0.90  FOF formula (forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula1962211574trib_a inf) less) sup) A) B) C)) ((less ((sup ((inf A) B)) ((inf C) A))) ((inf A) ((sup B) C))))) of role axiom named fact_156_local_Ono__distrib__def
% 0.69/0.90  A new axiom: (forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula1962211574trib_a inf) less) sup) A) B) C)) ((less ((sup ((inf A) B)) ((inf C) A))) ((inf A) ((sup B) C)))))
% 0.69/0.90  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_157_local_Oinf_Obounded__iff
% 0.69/0.90  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))))
% 0.69/0.90  FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq X) ((inf Y) Z2))) ((and ((less_eq X) Y)) ((less_eq X) Z2)))) of role axiom named fact_158_local_Ole__inf__iff
% 0.69/0.90  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq X) ((inf Y) Z2))) ((and ((less_eq X) Y)) ((less_eq X) Z2))))
% 0.69/0.90  FOF formula (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq ((sup X) Y)) Z2)) ((and ((less_eq X) Z2)) ((less_eq Y) Z2)))) of role axiom named fact_159_local_Ole__sup__iff
% 0.69/0.90  A new axiom: (forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq ((sup X) Y)) Z2)) ((and ((less_eq X) Z2)) ((less_eq Y) Z2))))
% 0.69/0.90  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_160_local_Osup_Obounded__iff
% 0.69/0.90  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))))
% 0.69/0.90  FOF formula (forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X)) of role axiom named fact_161_local_Oinf__sup__absorb
% 0.69/0.90  A new axiom: (forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X))
% 0.69/0.90  FOF formula (forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X)) of role axiom named fact_162_local_Osup__inf__absorb
% 0.69/0.90  A new axiom: (forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X))
% 0.69/0.90  FOF formula (forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula1376131916tice_a inf) less) sup) A) B) C)) ((and ((and ((and ((and (((eq a) ((inf A) B)) ((inf B) C))) (((eq a) ((inf C) A)) ((inf B) C)))) (((eq a) ((sup A) B)) ((sup B) C)))) (((eq a) ((sup C) A)) ((sup B) C)))) ((less ((inf A) B)) ((sup A) B))))) of role axiom named fact_163_local_OM5__lattice__def
% 0.69/0.90  A new axiom: (forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula1376131916tice_a inf) less) sup) A) B) C)) ((and ((and ((and ((and (((eq a) ((inf A) B)) ((inf B) C))) (((eq a) ((inf C) A)) ((inf B) C)))) (((eq a) ((sup A) B)) ((sup B) C)))) (((eq a) ((sup C) A)) ((sup B) C)))) ((less ((inf A) B)) ((sup A) B)))))
% 0.69/0.90  FOF formula (forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->(P ((least_a less_eq) P)))) of role axiom named fact_164_local_OLeast1I
% 0.69/0.90  A new axiom: (forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->(P ((least_a less_eq) P))))
% 0.69/0.91  FOF formula (forall (P:(a->Prop)) (Z2:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->((P Z2)->((less_eq ((least_a less_eq) P)) Z2)))) of role axiom named fact_165_local_OLeast1__le
% 0.69/0.91  A new axiom: (forall (P:(a->Prop)) (Z2:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->((P Z2)->((less_eq ((least_a less_eq) P)) Z2))))
% 0.69/0.91  FOF formula (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq X3) Y5)))->(Q X3))))->(Q ((least_a less_eq) P)))))) of role axiom named fact_166_local_OLeastI2__order
% 0.69/0.91  A new axiom: (forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq X3) Y5)))->(Q X3))))->(Q ((least_a less_eq) P))))))
% 0.69/0.91  FOF formula (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->(((eq a) ((least_a less_eq) P)) X)))) of role axiom named fact_167_local_OLeast__equality
% 0.69/0.91  A new axiom: (forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->(((eq a) ((least_a less_eq) P)) X))))
% 0.69/0.91  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((sup A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup A) ((inf B) C)))) of role axiom named fact_168_local_Oa__join__d
% 0.69/0.91  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((sup A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup A) ((inf B) C))))
% 0.69/0.91  FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup B) ((inf C) A)))) of role axiom named fact_169_local_Ob__join__d
% 0.69/0.91  A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((sup B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup B) ((inf C) A))))
% 0.69/0.92  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_170_local_Od__aux__def
% 0.69/0.92  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))))
% 0.69/0.92  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_171_local_Od__b__c__a
% 0.69/0.92  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)))
% 0.69/0.92  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_172_local_Od__c__a__b
% 0.69/0.92  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)))
% 0.69/0.92  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf A) ((sup B) C)))) of role axiom named fact_173_local_Oa__meet__e
% 0.69/0.92  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf A) ((sup B) C))))
% 0.69/0.92  FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf B) ((sup C) A)))) of role axiom named fact_174_local_Ob__meet__e
% 0.69/0.92  A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf B) ((sup C) A))))
% 0.69/0.92  FOF formula (forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf C) ((sup A) B)))) of role axiom named fact_175_local_Oc__meet__e
% 0.69/0.92  A new axiom: (forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf C) ((sup A) B))))
% 0.78/0.93  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_176_local_Oe__aux__def
% 0.78/0.93  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))))
% 0.78/0.93  FOF formula (forall (B:a) (C:a) (A:a), (((eq a) (((((modula1144073633_aux_a inf) sup) B) C) A)) (((((modula1144073633_aux_a inf) sup) A) B) C))) of role axiom named fact_177_local_Oe__b__c__a
% 0.78/0.93  A new axiom: (forall (B:a) (C:a) (A:a), (((eq a) (((((modula1144073633_aux_a inf) sup) B) C) A)) (((((modula1144073633_aux_a inf) sup) A) B) C)))
% 0.78/0.93  FOF formula (forall (C:a) (A:a) (B:a), (((eq a) (((((modula1144073633_aux_a inf) sup) C) A) B)) (((((modula1144073633_aux_a inf) sup) A) B) C))) of role axiom named fact_178_local_Oe__c__a__b
% 0.78/0.93  A new axiom: (forall (C:a) (A:a) (B:a), (((eq a) (((((modula1144073633_aux_a inf) sup) C) A) B)) (((((modula1144073633_aux_a inf) sup) A) B) C)))
% 0.78/0.93  FOF formula (((lattic655834328_set_a inf) less_eq) less) of role axiom named fact_179_local_OInf__fin_Osemilattice__order__set__axioms
% 0.78/0.93  A new axiom: (((lattic655834328_set_a inf) less_eq) less)
% 0.78/0.93  FOF formula (forall (A:a) (B:a) (C:a), (((((((modula1376131916tice_a inf) less) sup) A) B) C)->(((modula1727524044comp_a less_eq) A) B))) of role axiom named fact_180_local_OM5__lattice__incomp
% 0.78/0.93  A new axiom: (forall (A:a) (B:a) (C:a), (((((((modula1376131916tice_a inf) less) sup) A) B) C)->(((modula1727524044comp_a less_eq) A) B)))
% 0.78/0.93  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) ((sup ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_181_local_Oc__aux__def
% 0.78/0.93  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) ((sup ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.78/0.93  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) ((sup ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_182_local_Ob__aux__def
% 0.78/0.93  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) ((sup ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.78/0.93  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula17988509_aux_a inf) sup) A) B) C)) ((sup ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))) of role axiom named fact_183_local_Oa__aux__def
% 0.78/0.93  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula17988509_aux_a inf) sup) A) B) C)) ((sup ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C))))
% 0.78/0.93  FOF formula (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula1962211574trib_a) modula1962211574trib_a) of role axiom named fact_184_lattice_Ono__distrib_Ocong
% 0.78/0.93  A new axiom: (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula1962211574trib_a) modula1962211574trib_a)
% 0.78/0.93  FOF formula (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula397570059tice_a) modula397570059tice_a) of role axiom named fact_185_lattice_ON5__lattice_Ocong
% 0.78/0.93  A new axiom: (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula397570059tice_a) modula397570059tice_a)
% 0.78/0.93  FOF formula (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula1376131916tice_a) modula1376131916tice_a) of role axiom named fact_186_lattice_OM5__lattice_Ocong
% 0.78/0.93  A new axiom: (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula1376131916tice_a) modula1376131916tice_a)
% 0.78/0.93  FOF formula (((eq ((a->(a->Prop))->(a->(a->Prop)))) modula1727524044comp_a) modula1727524044comp_a) of role axiom named fact_187_lattice_Oincomp_Ocong
% 0.78/0.93  A new axiom: (((eq ((a->(a->Prop))->(a->(a->Prop)))) modula1727524044comp_a) modula1727524044comp_a)
% 0.78/0.94  FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a) of role axiom named fact_188_lattice_Oe__aux_Ocong
% 0.78/0.94  A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a)
% 0.78/0.94  FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a) of role axiom named fact_189_lattice_Od__aux_Ocong
% 0.78/0.94  A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a)
% 0.78/0.94  FOF formula (((semilattice_order_a inf) less_eq) less) of role axiom named fact_190_local_Oinf_Osemilattice__order__axioms
% 0.78/0.94  A new axiom: (((semilattice_order_a inf) less_eq) less)
% 0.78/0.94  FOF formula ((ordering_a less_eq) less) of role axiom named fact_191_local_Oorder_Oordering__axioms
% 0.78/0.94  A new axiom: ((ordering_a less_eq) less)
% 0.78/0.94  FOF formula (finite40241356em_a_a sup) of role axiom named fact_192_local_Ocomp__fun__idem__sup
% 0.78/0.94  A new axiom: (finite40241356em_a_a sup)
% 0.78/0.94  FOF formula (finite40241356em_a_a inf) of role axiom named fact_193_local_Ocomp__fun__idem__inf
% 0.78/0.94  A new axiom: (finite40241356em_a_a inf)
% 0.78/0.94  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) B) C) A))) of role axiom named fact_194_local_Ob__a
% 0.78/0.94  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) B) C) A)))
% 0.78/0.94  FOF formula (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) C) A) B))) of role axiom named fact_195_local_Oc__a
% 0.78/0.94  A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) C) A) B)))
% 0.78/0.94  FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula581031071_aux_a) modula581031071_aux_a) of role axiom named fact_196_lattice_Oc__aux_Ocong
% 0.78/0.94  A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula581031071_aux_a) modula581031071_aux_a)
% 0.78/0.94  FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1373251614_aux_a) modula1373251614_aux_a) of role axiom named fact_197_lattice_Ob__aux_Ocong
% 0.78/0.94  A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1373251614_aux_a) modula1373251614_aux_a)
% 0.78/0.94  FOF formula (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula17988509_aux_a) modula17988509_aux_a) of role axiom named fact_198_lattice_Oa__aux_Ocong
% 0.78/0.94  A new axiom: (((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula17988509_aux_a) modula17988509_aux_a)
% 0.78/0.94  FOF formula (semigroup_a sup) of role axiom named fact_199_local_Osup_Osemigroup__axioms
% 0.78/0.94  A new axiom: (semigroup_a sup)
% 0.78/0.94  FOF formula (semigroup_a inf) of role axiom named fact_200_local_Oinf_Osemigroup__axioms
% 0.78/0.94  A new axiom: (semigroup_a inf)
% 0.78/0.94  FOF formula (semilattice_a sup) of role axiom named fact_201_local_Osup_Osemilattice__axioms
% 0.78/0.94  A new axiom: (semilattice_a sup)
% 0.78/0.94  FOF formula (semilattice_a inf) of role axiom named fact_202_local_Oinf_Osemilattice__axioms
% 0.78/0.94  A new axiom: (semilattice_a inf)
% 0.78/0.94  FOF formula (abel_semigroup_a sup) of role axiom named fact_203_local_Osup_Oabel__semigroup__axioms
% 0.78/0.94  A new axiom: (abel_semigroup_a sup)
% 0.78/0.94  FOF formula (abel_semigroup_a inf) of role axiom named fact_204_local_Oinf_Oabel__semigroup__axioms
% 0.78/0.94  A new axiom: (abel_semigroup_a inf)
% 0.78/0.94  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((lattic655834328_set_a F) Less_eq) Less)->(((semilattice_order_a F) Less_eq) Less))) of role axiom named fact_205_semilattice__order__set_Oaxioms_I1_J
% 0.78/0.94  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((lattic655834328_set_a F) Less_eq) Less)->(((semilattice_order_a F) Less_eq) Less)))
% 0.78/0.94  FOF formula (forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F))) of role axiom named fact_206_abel__semigroup_Oaxioms_I1_J
% 0.78/0.94  A new axiom: (forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F)))
% 0.78/0.95  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_207_abel__semigroup_Oleft__commute
% 0.78/0.95  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)))))
% 0.78/0.95  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_208_abel__semigroup_Ocommute
% 0.78/0.95  A new axiom: (forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A))))
% 0.78/0.95  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_209_semigroup_Ointro
% 0.78/0.95  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)))
% 0.78/0.95  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_210_semigroup_Oassoc
% 0.78/0.95  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)))))
% 0.78/0.95  FOF formula (((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A2:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A2) B2)) C3)) ((F2 A2) ((F2 B2) C3)))))) of role axiom named fact_211_semigroup__def
% 0.78/0.95  A new axiom: (((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A2:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A2) B2)) C3)) ((F2 A2) ((F2 B2) C3))))))
% 0.78/0.95  FOF formula (forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F))) of role axiom named fact_212_semilattice_Oaxioms_I1_J
% 0.78/0.95  A new axiom: (forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F)))
% 0.78/0.95  FOF formula (lattic1885654924_set_a sup) of role axiom named fact_213_local_OSup__fin_Osemilattice__set__axioms
% 0.78/0.95  A new axiom: (lattic1885654924_set_a sup)
% 0.78/0.95  FOF formula (lattic1885654924_set_a inf) of role axiom named fact_214_local_OInf__fin_Osemilattice__set__axioms
% 0.78/0.95  A new axiom: (lattic1885654924_set_a inf)
% 0.78/0.95  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((lattic655834328_set_a F) Less_eq) Less)->(lattic1885654924_set_a F))) of role axiom named fact_215_semilattice__order__set_Oaxioms_I2_J
% 0.78/0.95  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((lattic655834328_set_a F) Less_eq) Less)->(lattic1885654924_set_a F)))
% 0.78/0.95  FOF formula (((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a) of role axiom named fact_216_semilattice__set__def
% 0.78/0.95  A new axiom: (((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a)
% 0.78/0.95  FOF formula (forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F))) of role axiom named fact_217_semilattice__set_Ointro
% 0.78/0.95  A new axiom: (forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F)))
% 0.78/0.95  FOF formula (forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F))) of role axiom named fact_218_semilattice__set_Oaxioms
% 0.78/0.95  A new axiom: (forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F)))
% 0.78/0.95  FOF formula (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop)))) lattic655834328_set_a) (fun (F2:(a->(a->a))) (Less_eq2:(a->(a->Prop))) (Less2:(a->(a->Prop)))=> ((and (((semilattice_order_a F2) Less_eq2) Less2)) (lattic1885654924_set_a F2)))) of role axiom named fact_219_semilattice__order__set__def
% 0.78/0.95  A new axiom: (((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop)))) lattic655834328_set_a) (fun (F2:(a->(a->a))) (Less_eq2:(a->(a->Prop))) (Less2:(a->(a->Prop)))=> ((and (((semilattice_order_a F2) Less_eq2) Less2)) (lattic1885654924_set_a F2))))
% 0.78/0.95  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((semilattice_order_a F) Less_eq) Less)->((lattic1885654924_set_a F)->(((lattic655834328_set_a F) Less_eq) Less)))) of role axiom named fact_220_semilattice__order__set_Ointro
% 0.78/0.95  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((semilattice_order_a F) Less_eq) Less)->((lattic1885654924_set_a F)->(((lattic655834328_set_a F) Less_eq) Less))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a) (D:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) C)->(((Less_eq B) D)->((Less_eq ((F A) B)) ((F C) D)))))) of role axiom named fact_221_semilattice__order_Omono
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a) (D:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) C)->(((Less_eq B) D)->((Less_eq ((F A) B)) ((F C) D))))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((eq a) A) ((F A) B))))) of role axiom named fact_222_semilattice__order_OorderE
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((eq a) A) ((F A) B)))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((((eq a) A) ((F A) B))->((Less_eq A) B)))) of role axiom named fact_223_semilattice__order_OorderI
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((((eq a) A) ((F A) B))->((Less_eq A) B))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((eq a) ((F A) B)) A)))) of role axiom named fact_224_semilattice__order_Oabsorb1
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((eq a) ((F A) B)) A))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq B) A)->(((eq a) ((F A) B)) B)))) of role axiom named fact_225_semilattice__order_Oabsorb2
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq B) A)->(((eq a) ((F A) B)) B))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) ((F B) C))->((((Less_eq A) B)->(((Less_eq A) C)->False))->False)))) of role axiom named fact_226_semilattice__order_OboundedE
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) ((F B) C))->((((Less_eq A) B)->(((Less_eq A) C)->False))->False))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((Less_eq A) C)->((Less_eq A) ((F B) C)))))) of role axiom named fact_227_semilattice__order_OboundedI
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((Less_eq A) C)->((Less_eq A) ((F B) C))))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) B)) (((eq a) A) ((F A) B))))) of role axiom named fact_228_semilattice__order_Oorder__iff
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) B)) (((eq a) A) ((F A) B)))))
% 0.78/0.97  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((Less_eq ((F A) B)) A))) of role axiom named fact_229_semilattice__order_Ocobounded1
% 0.78/0.97  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((Less_eq ((F A) B)) A)))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((Less_eq ((F A) B)) B))) of role axiom named fact_230_semilattice__order_Ocobounded2
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((Less_eq ((F A) B)) B)))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) B)) (((eq a) ((F A) B)) A)))) of role axiom named fact_231_semilattice__order_Oabsorb__iff1
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) B)) (((eq a) ((F A) B)) A))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq B) A)) (((eq a) ((F A) B)) B)))) of role axiom named fact_232_semilattice__order_Oabsorb__iff2
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq B) A)) (((eq a) ((F A) B)) B))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) ((F B) C))) ((and ((Less_eq A) B)) ((Less_eq A) C))))) of role axiom named fact_233_semilattice__order_Obounded__iff
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) ((F B) C))) ((and ((Less_eq A) B)) ((Less_eq A) C)))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) C)->((Less_eq ((F A) B)) C)))) of role axiom named fact_234_semilattice__order_OcoboundedI1
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) C)->((Less_eq ((F A) B)) C))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (C:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq B) C)->((Less_eq ((F A) B)) C)))) of role axiom named fact_235_semilattice__order_OcoboundedI2
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (C:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq B) C)->((Less_eq ((F A) B)) C))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less A) ((F B) C))->((((Less A) B)->(((Less A) C)->False))->False)))) of role axiom named fact_236_semilattice__order_Ostrict__boundedE
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less A) ((F B) C))->((((Less A) B)->(((Less A) C)->False))->False))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less A) B)) ((and (((eq a) A) ((F A) B))) (not (((eq a) A) B)))))) of role axiom named fact_237_semilattice__order_Ostrict__order__iff
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less A) B)) ((and (((eq a) A) ((F A) B))) (not (((eq a) A) B))))))
% 0.78/0.99  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less A) C)->((Less ((F A) B)) C)))) of role axiom named fact_238_semilattice__order_Ostrict__coboundedI1
% 0.78/0.99  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less A) C)->((Less ((F A) B)) C))))
% 0.84/1.00  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (C:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less B) C)->((Less ((F A) B)) C)))) of role axiom named fact_239_semilattice__order_Ostrict__coboundedI2
% 0.84/1.00  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (C:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less B) C)->((Less ((F A) B)) C))))
% 0.84/1.00  FOF formula (forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A))) of role axiom named fact_240_semilattice_Oidem
% 0.84/1.00  A new axiom: (forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A)))
% 0.84/1.00  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_241_semilattice_Oleft__idem
% 0.84/1.00  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))))
% 0.84/1.00  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_242_semilattice_Oright__idem
% 0.84/1.00  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))))
% 0.84/1.00  FOF formula (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((semilattice_order_a F) Less_eq) Less)->(semilattice_a F))) of role axiom named fact_243_semilattice__order_Oaxioms_I1_J
% 0.84/1.00  A new axiom: (forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((semilattice_order_a F) Less_eq) Less)->(semilattice_a F)))
% 0.84/1.00  FOF formula (forall (A3:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A3)) ((ex a) (fun (M:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq M) X2))))))) of role axiom named fact_244_local_Obdd__below__def
% 0.84/1.00  A new axiom: (forall (A3:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A3)) ((ex a) (fun (M:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq M) X2)))))))
% 0.84/1.00  FOF formula (forall (A3:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A3)) ((ex a) (fun (M2:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq X2) M2))))))) of role axiom named fact_245_local_Obdd__above__def
% 0.84/1.00  A new axiom: (forall (A3:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A3)) ((ex a) (fun (M2:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq X2) M2)))))))
% 0.84/1.00  FOF formula (forall (A3:set_a) (M3:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq M3) X3)))->((condit1001553558elow_a less_eq) A3))) of role axiom named fact_246_local_Obdd__belowI
% 0.84/1.00  A new axiom: (forall (A3:set_a) (M3:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq M3) X3)))->((condit1001553558elow_a less_eq) A3)))
% 0.84/1.00  FOF formula (forall (A3:set_a) (M4:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq X3) M4)))->((condit1627435690bove_a less_eq) A3))) of role axiom named fact_247_local_Obdd__aboveI
% 0.84/1.00  A new axiom: (forall (A3:set_a) (M4:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq X3) M4)))->((condit1627435690bove_a less_eq) A3)))
% 0.84/1.00  FOF formula (forall (A:a) (B:a), ((condit1001553558elow_a less_eq) (((set_gr1491433118Than_a less) A) B))) of role axiom named fact_248_local_Obdd__below__Ioo
% 0.84/1.00  A new axiom: (forall (A:a) (B:a), ((condit1001553558elow_a less_eq) (((set_gr1491433118Than_a less) A) B)))
% 0.84/1.00  FOF formula ((((lattice_a inf) less_eq) less) sup) of role hypothesis named conj_0
% 0.84/1.00  A new axiom: ((((lattice_a inf) less_eq) less) sup)
% 0.84/1.00  FOF formula ((less_eq x) y) of role hypothesis named conj_1
% 0.84/1.00  A new axiom: ((less_eq x) y)
% 0.84/1.00  FOF formula (not (((eq a) ((sup x) ((inf y) z))) ((inf y) ((sup x) z)))) of role hypothesis named conj_2
% 0.84/1.00  A new axiom: (not (((eq a) ((sup x) ((inf y) z))) ((inf y) ((sup x) z))))
% 0.84/1.00  FOF formula ((less ((sup x) ((inf y) z))) ((inf y) ((sup x) z))) of role hypothesis named conj_3
% 0.84/1.00  A new axiom: ((less ((sup x) ((inf y) z))) ((inf y) ((sup x) z)))
% 0.84/1.00  FOF formula ((less_eq x) ((sup ((inf y) ((sup x) z))) z)) of role conjecture named conj_4
% 0.84/1.00  Conjecture to prove = ((less_eq x) ((sup ((inf y) ((sup x) z))) z)):Prop
% 0.84/1.00  Parameter set_a_DUMMY:set_a.
% 0.84/1.00  We need to prove ['((less_eq x) ((sup ((inf y) ((sup x) z))) z))']
% 0.84/1.01  Parameter set_a:Type.
% 0.84/1.01  Parameter a:Type.
% 0.84/1.01  Parameter condit1627435690bove_a:((a->(a->Prop))->(set_a->Prop)).
% 0.84/1.01  Parameter condit1001553558elow_a:((a->(a->Prop))->(set_a->Prop)).
% 0.84/1.01  Parameter finite40241356em_a_a:((a->(a->a))->Prop).
% 0.84/1.01  Parameter abel_semigroup_a:((a->(a->a))->Prop).
% 0.84/1.01  Parameter semigroup_a:((a->(a->a))->Prop).
% 0.84/1.01  Parameter lattice_a:((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->((a->(a->a))->Prop)))).
% 0.84/1.01  Parameter semilattice_a:((a->(a->a))->Prop).
% 0.84/1.01  Parameter semilattice_order_a:((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop))).
% 0.84/1.01  Parameter lattic655834328_set_a:((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop))).
% 0.84/1.01  Parameter lattic1885654924_set_a:((a->(a->a))->Prop).
% 0.84/1.01  Parameter modula1376131916tice_a:((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop)))))).
% 0.84/1.01  Parameter modula397570059tice_a:((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop)))))).
% 0.84/1.01  Parameter modula17988509_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.84/1.01  Parameter modula1373251614_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.84/1.01  Parameter modula581031071_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.84/1.01  Parameter modula1936294176_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.84/1.01  Parameter modula1144073633_aux_a:((a->(a->a))->((a->(a->a))->(a->(a->(a->a))))).
% 0.84/1.01  Parameter modula1727524044comp_a:((a->(a->Prop))->(a->(a->Prop))).
% 0.84/1.01  Parameter modula1962211574trib_a:((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop)))))).
% 0.84/1.01  Parameter least_a:((a->(a->Prop))->((a->Prop)->a)).
% 0.84/1.01  Parameter max_a:((a->(a->Prop))->(a->(a->a))).
% 0.84/1.01  Parameter min_a:((a->(a->Prop))->(a->(a->a))).
% 0.84/1.01  Parameter greatest_a:((a->(a->Prop))->((a->Prop)->a)).
% 0.84/1.01  Parameter ordering_a:((a->(a->Prop))->((a->(a->Prop))->Prop)).
% 0.84/1.01  Parameter collect_a:((a->Prop)->set_a).
% 0.84/1.01  Parameter set_gr1491433118Than_a:((a->(a->Prop))->(a->(a->set_a))).
% 0.84/1.01  Parameter member_a:(a->(set_a->Prop)).
% 0.84/1.01  Parameter inf:(a->(a->a)).
% 0.84/1.01  Parameter less:(a->(a->Prop)).
% 0.84/1.01  Parameter less_eq:(a->(a->Prop)).
% 0.84/1.01  Parameter sup:(a->(a->a)).
% 0.84/1.01  Parameter x:a.
% 0.84/1.01  Parameter y:a.
% 0.84/1.01  Parameter z:a.
% 0.84/1.01  Axiom fact_0_local_Oantisym:(forall (X:a) (Y:a), (((less_eq X) Y)->(((less_eq Y) X)->(((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_1_local_Oantisym__conv:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_2_local_Odual__order_Oantisym:(forall (B:a) (A:a), (((less_eq B) A)->(((less_eq A) B)->(((eq a) A) B)))).
% 0.84/1.01  Axiom fact_3_local_Odual__order_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq B2) A2)) ((less_eq A2) B2)))).
% 0.84/1.01  Axiom fact_4_local_Odual__order_Otrans:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) B)->((less_eq C) A)))).
% 0.84/1.01  Axiom fact_5_local_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (X2:a) (Y3:a)=> ((and ((less_eq X2) Y3)) ((less_eq Y3) X2)))).
% 0.84/1.01  Axiom fact_6_local_Oeq__refl:(forall (X:a) (Y:a), ((((eq a) X) Y)->((less_eq X) Y))).
% 0.84/1.01  Axiom fact_7_local_Oord__eq__le__trans:(forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less_eq B) C)->((less_eq A) C)))).
% 0.84/1.01  Axiom fact_8_local_Oord__le__eq__trans:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->((((eq a) B) C)->((less_eq A) C)))).
% 0.84/1.01  Axiom fact_9_local_Oorder_Oantisym:(forall (A:a) (B:a), (((less_eq A) B)->(((less_eq B) A)->(((eq a) A) B)))).
% 0.84/1.01  Axiom fact_10_local_Oorder_Oeq__iff:(((eq (a->(a->Prop))) (fun (Y2:a) (Z:a)=> (((eq a) Y2) Z))) (fun (A2:a) (B2:a)=> ((and ((less_eq A2) B2)) ((less_eq B2) A2)))).
% 0.84/1.01  Axiom fact_11_local_Oorder_Otrans:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq B) C)->((less_eq A) C)))).
% 0.84/1.01  Axiom fact_12_local_Oorder__trans:(forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq Y) Z2)->((less_eq X) Z2)))).
% 0.84/1.01  Axiom fact_13_local_Odual__order_Oasym:(forall (B:a) (A:a), (((less B) A)->(((less A) B)->False))).
% 0.84/1.01  Axiom fact_14_local_Odual__order_Ostrict__implies__not__eq:(forall (B:a) (A:a), (((less B) A)->(not (((eq a) A) B)))).
% 0.84/1.01  Axiom fact_15_local_Odual__order_Ostrict__trans:(forall (B:a) (A:a) (C:a), (((less B) A)->(((less C) B)->((less C) A)))).
% 0.84/1.01  Axiom fact_16_local_Oless__asym:(forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False))).
% 0.84/1.01  Axiom fact_17_local_Oless__asym_H:(forall (A:a) (B:a), (((less A) B)->(((less B) A)->False))).
% 0.84/1.01  Axiom fact_18_local_Oless__imp__neq:(forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_19_local_Oless__imp__not__eq:(forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_20_local_Oless__imp__not__eq2:(forall (X:a) (Y:a), (((less X) Y)->(not (((eq a) Y) X)))).
% 0.84/1.01  Axiom fact_21_local_Oless__imp__not__less:(forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False))).
% 0.84/1.01  Axiom fact_22_local_Oless__imp__triv:(forall (X:a) (Y:a) (P:Prop), (((less X) Y)->(((less Y) X)->P))).
% 0.84/1.01  Axiom fact_23_local_Oless__irrefl:(forall (X:a), (((less X) X)->False)).
% 0.84/1.01  Axiom fact_24_local_Oless__not__sym:(forall (X:a) (Y:a), (((less X) Y)->(((less Y) X)->False))).
% 0.84/1.01  Axiom fact_25_local_Oless__trans:(forall (X:a) (Y:a) (Z2:a), (((less X) Y)->(((less Y) Z2)->((less X) Z2)))).
% 0.84/1.01  Axiom fact_26_local_Oord__eq__less__trans:(forall (A:a) (B:a) (C:a), ((((eq a) A) B)->(((less B) C)->((less A) C)))).
% 0.84/1.01  Axiom fact_27_local_Oord__less__eq__trans:(forall (A:a) (B:a) (C:a), (((less A) B)->((((eq a) B) C)->((less A) C)))).
% 0.84/1.01  Axiom fact_28_local_Oorder_Oasym:(forall (A:a) (B:a), (((less A) B)->(((less B) A)->False))).
% 0.84/1.01  Axiom fact_29_local_Oorder_Oirrefl:(forall (A:a), (((less A) A)->False)).
% 0.84/1.01  Axiom fact_30_local_Oorder_Ostrict__implies__not__eq:(forall (A:a) (B:a), (((less A) B)->(not (((eq a) A) B)))).
% 0.84/1.01  Axiom fact_31_local_Oorder_Ostrict__trans:(forall (A:a) (B:a) (C:a), (((less A) B)->(((less B) C)->((less A) C)))).
% 0.84/1.01  Axiom fact_32_local_Oinf_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((inf ((inf A) B)) C)) ((inf A) ((inf B) C)))).
% 0.84/1.01  Axiom fact_33_local_Oinf_Ocommute:(forall (A:a) (B:a), (((eq a) ((inf A) B)) ((inf B) A))).
% 0.84/1.01  Axiom fact_34_local_Oinf_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((inf B) ((inf A) C))) ((inf A) ((inf B) C)))).
% 0.84/1.01  Axiom fact_35_local_Oinf__assoc:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf ((inf X) Y)) Z2)) ((inf X) ((inf Y) Z2)))).
% 0.84/1.01  Axiom fact_36_local_Oinf__commute:(forall (X:a) (Y:a), (((eq a) ((inf X) Y)) ((inf Y) X))).
% 0.84/1.01  Axiom fact_37_local_Oinf__left__commute:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((inf X) ((inf Y) Z2))) ((inf Y) ((inf X) Z2)))).
% 0.84/1.01  Axiom fact_38_local_Osup_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((sup ((sup A) B)) C)) ((sup A) ((sup B) C)))).
% 0.84/1.01  Axiom fact_39_local_Osup_Ocommute:(forall (A:a) (B:a), (((eq a) ((sup A) B)) ((sup B) A))).
% 0.84/1.01  Axiom fact_40_local_Osup_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((sup B) ((sup A) C))) ((sup A) ((sup B) C)))).
% 0.84/1.01  Axiom fact_41_local_Osup__assoc:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup ((sup X) Y)) Z2)) ((sup X) ((sup Y) Z2)))).
% 0.84/1.01  Axiom fact_42_local_Osup__commute:(forall (X:a) (Y:a), (((eq a) ((sup X) Y)) ((sup Y) X))).
% 0.84/1.01  Axiom fact_43_local_Osup__left__commute:(forall (X:a) (Y:a) (Z2:a), (((eq a) ((sup X) ((sup Y) Z2))) ((sup Y) ((sup X) Z2)))).
% 0.84/1.01  Axiom fact_44_local_Oantisym__conv1:(forall (X:a) (Y:a), ((((less X) Y)->False)->(((eq Prop) ((less_eq X) Y)) (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_45_mem__Collect__eq:(forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))).
% 0.84/1.01  Axiom fact_46_Collect__mem__eq:(forall (A3:set_a), (((eq set_a) (collect_a (fun (X2:a)=> ((member_a X2) A3)))) A3)).
% 0.84/1.01  Axiom fact_47_Collect__cong:(forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X3:a), (((eq Prop) (P X3)) (Q X3)))->(((eq set_a) (collect_a P)) (collect_a Q)))).
% 0.84/1.01  Axiom fact_48_local_Oantisym__conv2:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq Prop) (((less X) Y)->False)) (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_49_local_Odual__order_Onot__eq__order__implies__strict:(forall (A:a) (B:a), ((not (((eq a) A) B))->(((less_eq B) A)->((less B) A)))).
% 0.84/1.01  Axiom fact_50_local_Odual__order_Oorder__iff__strict:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) ((or ((less B) A)) (((eq a) A) B)))).
% 0.84/1.01  Axiom fact_51_local_Odual__order_Ostrict__iff__order:(forall (B:a) (A:a), (((eq Prop) ((less B) A)) ((and ((less_eq B) A)) (not (((eq a) A) B))))).
% 0.84/1.01  Axiom fact_52_local_Odual__order_Ostrict__implies__order:(forall (B:a) (A:a), (((less B) A)->((less_eq B) A))).
% 0.84/1.01  Axiom fact_53_local_Odual__order_Ostrict__trans1:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less C) B)->((less C) A)))).
% 0.84/1.01  Axiom fact_54_local_Odual__order_Ostrict__trans2:(forall (B:a) (A:a) (C:a), (((less B) A)->(((less_eq C) B)->((less C) A)))).
% 0.84/1.01  Axiom fact_55_local_OleD:(forall (Y:a) (X:a), (((less_eq Y) X)->(((less X) Y)->False))).
% 0.84/1.01  Axiom fact_56_local_Ole__imp__less__or__eq:(forall (X:a) (Y:a), (((less_eq X) Y)->((or ((less X) Y)) (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_57_local_Ole__less:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) ((or ((less X) Y)) (((eq a) X) Y)))).
% 0.84/1.01  Axiom fact_58_local_Ole__less__trans:(forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less Y) Z2)->((less X) Z2)))).
% 0.84/1.01  Axiom fact_59_local_Ole__neq__trans:(forall (A:a) (B:a), (((less_eq A) B)->((not (((eq a) A) B))->((less A) B)))).
% 0.84/1.01  Axiom fact_60_local_Oless__imp__le:(forall (X:a) (Y:a), (((less X) Y)->((less_eq X) Y))).
% 0.84/1.01  Axiom fact_61_local_Oless__le:(forall (X:a) (Y:a), (((eq Prop) ((less X) Y)) ((and ((less_eq X) Y)) (not (((eq a) X) Y))))).
% 0.84/1.01  Axiom fact_62_local_Oless__le__not__le:(forall (X:a) (Y:a), (((eq Prop) ((less X) Y)) ((and ((less_eq X) Y)) (((less_eq Y) X)->False)))).
% 0.84/1.01  Axiom fact_63_local_Oless__le__trans:(forall (X:a) (Y:a) (Z2:a), (((less X) Y)->(((less_eq Y) Z2)->((less X) Z2)))).
% 0.84/1.01  Axiom fact_64_local_Oorder_Onot__eq__order__implies__strict:(forall (A:a) (B:a), ((not (((eq a) A) B))->(((less_eq A) B)->((less A) B)))).
% 0.84/1.01  Axiom fact_65_local_Oorder_Oorder__iff__strict:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) ((or ((less A) B)) (((eq a) A) B)))).
% 0.84/1.01  Axiom fact_66_local_Oorder_Ostrict__iff__order:(forall (A:a) (B:a), (((eq Prop) ((less A) B)) ((and ((less_eq A) B)) (not (((eq a) A) B))))).
% 0.84/1.01  Axiom fact_67_local_Oorder_Ostrict__implies__order:(forall (A:a) (B:a), (((less A) B)->((less_eq A) B))).
% 0.84/1.01  Axiom fact_68_local_Oorder_Ostrict__trans1:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less B) C)->((less A) C)))).
% 0.84/1.01  Axiom fact_69_local_Oorder_Ostrict__trans2:(forall (A:a) (B:a) (C:a), (((less A) B)->(((less_eq B) C)->((less A) C)))).
% 0.84/1.01  Axiom fact_70_local_Oinf_Oabsorb1:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((inf A) B)) A))).
% 0.84/1.01  Axiom fact_71_local_Oinf_Oabsorb2:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((inf A) B)) B))).
% 0.84/1.01  Axiom fact_72_local_Oinf_Oabsorb__iff1:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((inf A) B)) A))).
% 0.84/1.01  Axiom fact_73_local_Oinf_Oabsorb__iff2:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((inf A) B)) B))).
% 0.84/1.01  Axiom fact_74_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))).
% 0.84/1.01  Axiom fact_75_local_Oinf_OboundedI:(forall (A:a) (B:a) (C:a), (((less_eq A) B)->(((less_eq A) C)->((less_eq A) ((inf B) C))))).
% 0.84/1.01  Axiom fact_76_local_Oinf_Ocobounded1:(forall (A:a) (B:a), ((less_eq ((inf A) B)) A)).
% 0.84/1.01  Axiom fact_77_local_Oinf_Ocobounded2:(forall (A:a) (B:a), ((less_eq ((inf A) B)) B)).
% 0.84/1.01  Axiom fact_78_local_Oinf_OcoboundedI1:(forall (A:a) (C:a) (B:a), (((less_eq A) C)->((less_eq ((inf A) B)) C))).
% 0.84/1.01  Axiom fact_79_local_Oinf_OcoboundedI2:(forall (B:a) (C:a) (A:a), (((less_eq B) C)->((less_eq ((inf A) B)) C))).
% 0.84/1.01  Axiom fact_80_local_Oinf_OorderE:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) A) ((inf A) B)))).
% 0.84/1.01  Axiom fact_81_local_Oinf_OorderI:(forall (A:a) (B:a), ((((eq a) A) ((inf A) B))->((less_eq A) B))).
% 0.84/1.01  Axiom fact_82_local_Oinf_Oorder__iff:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) A) ((inf A) B)))).
% 0.84/1.01  Axiom fact_83_local_Oinf__absorb1:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((inf X) Y)) X))).
% 0.84/1.01  Axiom fact_84_local_Oinf__absorb2:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((inf X) Y)) Y))).
% 0.84/1.01  Axiom fact_85_local_Oinf__greatest:(forall (X:a) (Y:a) (Z2:a), (((less_eq X) Y)->(((less_eq X) Z2)->((less_eq X) ((inf Y) Z2))))).
% 0.84/1.01  Axiom fact_86_local_Oinf__le1:(forall (X:a) (Y:a), ((less_eq ((inf X) Y)) X)).
% 0.84/1.01  Axiom fact_87_local_Oinf__le2:(forall (X:a) (Y:a), ((less_eq ((inf X) Y)) Y)).
% 0.84/1.01  Axiom fact_88_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))))).
% 0.84/1.01  Axiom fact_89_local_Oinf__unique:(forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) X3))->((forall (X3:a) (Y4:a), ((less_eq ((F X3) Y4)) Y4))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq X3) Y4)->(((less_eq X3) Z3)->((less_eq X3) ((F Y4) Z3)))))->(((eq a) ((inf X) Y)) ((F X) Y)))))).
% 0.84/1.01  Axiom fact_90_local_Ole__iff__inf:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((inf X) Y)) X))).
% 0.84/1.01  Axiom fact_91_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))).
% 0.84/1.01  Axiom fact_92_local_Ole__infI:(forall (X:a) (A:a) (B:a), (((less_eq X) A)->(((less_eq X) B)->((less_eq X) ((inf A) B))))).
% 0.84/1.01  Axiom fact_93_local_Ole__infI1:(forall (A:a) (X:a) (B:a), (((less_eq A) X)->((less_eq ((inf A) B)) X))).
% 0.84/1.01  Axiom fact_94_local_Ole__infI2:(forall (B:a) (X:a) (A:a), (((less_eq B) X)->((less_eq ((inf A) B)) X))).
% 0.84/1.01  Axiom fact_95_local_Ole__iff__sup:(forall (X:a) (Y:a), (((eq Prop) ((less_eq X) Y)) (((eq a) ((sup X) Y)) Y))).
% 0.84/1.01  Axiom fact_96_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))).
% 0.84/1.01  Axiom fact_97_local_Ole__supI:(forall (A:a) (X:a) (B:a), (((less_eq A) X)->(((less_eq B) X)->((less_eq ((sup A) B)) X)))).
% 0.84/1.01  Axiom fact_98_local_Ole__supI1:(forall (X:a) (A:a) (B:a), (((less_eq X) A)->((less_eq X) ((sup A) B)))).
% 0.84/1.01  Axiom fact_99_local_Ole__supI2:(forall (X:a) (B:a) (A:a), (((less_eq X) B)->((less_eq X) ((sup A) B)))).
% 0.84/1.01  Axiom fact_100_local_Osup_Oabsorb1:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) ((sup A) B)) A))).
% 0.84/1.01  Axiom fact_101_local_Osup_Oabsorb2:(forall (A:a) (B:a), (((less_eq A) B)->(((eq a) ((sup A) B)) B))).
% 0.84/1.01  Axiom fact_102_local_Osup_Oabsorb__iff1:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) ((sup A) B)) A))).
% 0.84/1.01  Axiom fact_103_local_Osup_Oabsorb__iff2:(forall (A:a) (B:a), (((eq Prop) ((less_eq A) B)) (((eq a) ((sup A) B)) B))).
% 0.84/1.01  Axiom fact_104_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))).
% 0.84/1.01  Axiom fact_105_local_Osup_OboundedI:(forall (B:a) (A:a) (C:a), (((less_eq B) A)->(((less_eq C) A)->((less_eq ((sup B) C)) A)))).
% 0.84/1.01  Axiom fact_106_local_Osup_Ocobounded1:(forall (A:a) (B:a), ((less_eq A) ((sup A) B))).
% 0.84/1.01  Axiom fact_107_local_Osup_Ocobounded2:(forall (B:a) (A:a), ((less_eq B) ((sup A) B))).
% 0.84/1.01  Axiom fact_108_local_Osup_OcoboundedI1:(forall (C:a) (A:a) (B:a), (((less_eq C) A)->((less_eq C) ((sup A) B)))).
% 0.84/1.01  Axiom fact_109_local_Osup_OcoboundedI2:(forall (C:a) (B:a) (A:a), (((less_eq C) B)->((less_eq C) ((sup A) B)))).
% 0.84/1.01  Axiom fact_110_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))))).
% 0.84/1.01  Axiom fact_111_local_Osup_OorderE:(forall (B:a) (A:a), (((less_eq B) A)->(((eq a) A) ((sup A) B)))).
% 0.84/1.01  Axiom fact_112_local_Osup_OorderI:(forall (A:a) (B:a), ((((eq a) A) ((sup A) B))->((less_eq B) A))).
% 0.84/1.01  Axiom fact_113_local_Osup_Oorder__iff:(forall (B:a) (A:a), (((eq Prop) ((less_eq B) A)) (((eq a) A) ((sup A) B)))).
% 0.84/1.01  Axiom fact_114_local_Osup__absorb1:(forall (Y:a) (X:a), (((less_eq Y) X)->(((eq a) ((sup X) Y)) X))).
% 0.84/1.01  Axiom fact_115_local_Osup__absorb2:(forall (X:a) (Y:a), (((less_eq X) Y)->(((eq a) ((sup X) Y)) Y))).
% 0.84/1.01  Axiom fact_116_local_Osup__ge1:(forall (X:a) (Y:a), ((less_eq X) ((sup X) Y))).
% 0.84/1.01  Axiom fact_117_local_Osup__ge2:(forall (Y:a) (X:a), ((less_eq Y) ((sup X) Y))).
% 0.84/1.01  Axiom fact_118_local_Osup__least:(forall (Y:a) (X:a) (Z2:a), (((less_eq Y) X)->(((less_eq Z2) X)->((less_eq ((sup Y) Z2)) X)))).
% 0.84/1.01  Axiom fact_119_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))))).
% 0.84/1.01  Axiom fact_120_local_Osup__unique:(forall (F:(a->(a->a))) (X:a) (Y:a), ((forall (X3:a) (Y4:a), ((less_eq X3) ((F X3) Y4)))->((forall (X3:a) (Y4:a), ((less_eq Y4) ((F X3) Y4)))->((forall (X3:a) (Y4:a) (Z3:a), (((less_eq Y4) X3)->(((less_eq Z3) X3)->((less_eq ((F Y4) Z3)) X3))))->(((eq a) ((sup X) Y)) ((F X) Y)))))).
% 0.84/1.01  Axiom fact_121_local_Oinf_Ostrict__boundedE:(forall (A:a) (B:a) (C:a), (((less A) ((inf B) C))->((((less A) B)->(((less A) C)->False))->False))).
% 0.84/1.01  Axiom fact_122_local_Oinf_Ostrict__coboundedI1:(forall (A:a) (C:a) (B:a), (((less A) C)->((less ((inf A) B)) C))).
% 0.84/1.01  Axiom fact_123_local_Oinf_Ostrict__coboundedI2:(forall (B:a) (C:a) (A:a), (((less B) C)->((less ((inf A) B)) C))).
% 0.84/1.01  Axiom fact_124_local_Oinf_Ostrict__order__iff:(forall (A:a) (B:a), (((eq Prop) ((less A) B)) ((and (((eq a) A) ((inf A) B))) (not (((eq a) A) B))))).
% 0.84/1.01  Axiom fact_125_local_Oless__infI1:(forall (A:a) (X:a) (B:a), (((less A) X)->((less ((inf A) B)) X))).
% 0.84/1.01  Axiom fact_126_local_Oless__infI2:(forall (B:a) (X:a) (A:a), (((less B) X)->((less ((inf A) B)) X))).
% 0.84/1.01  Axiom fact_127_local_Oless__supI1:(forall (X:a) (A:a) (B:a), (((less X) A)->((less X) ((sup A) B)))).
% 0.84/1.01  Axiom fact_128_local_Oless__supI2:(forall (X:a) (B:a) (A:a), (((less X) B)->((less X) ((sup A) B)))).
% 0.84/1.01  Axiom fact_129_local_Osup_Ostrict__boundedE:(forall (B:a) (C:a) (A:a), (((less ((sup B) C)) A)->((((less B) A)->(((less C) A)->False))->False))).
% 0.84/1.01  Axiom fact_130_local_Osup_Ostrict__coboundedI1:(forall (C:a) (A:a) (B:a), (((less C) A)->((less C) ((sup A) B)))).
% 0.84/1.01  Axiom fact_131_local_Osup_Ostrict__coboundedI2:(forall (C:a) (B:a) (A:a), (((less C) B)->((less C) ((sup A) B)))).
% 0.84/1.01  Axiom fact_132_local_Osup_Ostrict__order__iff:(forall (B:a) (A:a), (((eq Prop) ((less B) A)) ((and (((eq a) A) ((sup A) B))) (not (((eq a) A) B))))).
% 0.84/1.01  Axiom fact_133_local_Odistrib__imp1:(forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((inf X3) ((sup Y4) Z3))) ((sup ((inf X3) Y4)) ((inf X3) Z3))))->(((eq a) ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2))))).
% 0.84/1.01  Axiom fact_134_local_Odistrib__imp2:(forall (X:a) (Y:a) (Z2:a), ((forall (X3:a) (Y4:a) (Z3:a), (((eq a) ((sup X3) ((inf Y4) Z3))) ((inf ((sup X3) Y4)) ((sup X3) Z3))))->(((eq a) ((inf X) ((sup Y) Z2))) ((sup ((inf X) Y)) ((inf X) Z2))))).
% 0.84/1.01  Axiom fact_135_local_Odistrib__inf__le:(forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup ((inf X) Y)) ((inf X) Z2))) ((inf X) ((sup Y) Z2)))).
% 0.84/1.01  Axiom fact_136_local_Odistrib__sup__le:(forall (X:a) (Y:a) (Z2:a), ((less_eq ((sup X) ((inf Y) Z2))) ((inf ((sup X) Y)) ((sup X) Z2)))).
% 0.84/1.01  Axiom fact_137_local_Oincomp__def:(forall (X:a) (Y:a), (((eq Prop) (((modula1727524044comp_a less_eq) X) Y)) ((and (((less_eq X) Y)->False)) (((less_eq Y) X)->False)))).
% 0.84/1.01  Axiom fact_138_local_Oorder_Orefl:(forall (A:a), ((less_eq A) A)).
% 0.84/1.01  Axiom fact_139_local_Oorder__refl:(forall (X:a), ((less_eq X) X)).
% 0.84/1.01  Axiom fact_140_local_Oinf_Oidem:(forall (A:a), (((eq a) ((inf A) A)) A)).
% 0.84/1.01  Axiom fact_141_local_Oinf_Oleft__idem:(forall (A:a) (B:a), (((eq a) ((inf A) ((inf A) B))) ((inf A) B))).
% 0.84/1.01  Axiom fact_142_local_Oinf_Oright__idem:(forall (A:a) (B:a), (((eq a) ((inf ((inf A) B)) B)) ((inf A) B))).
% 0.84/1.01  Axiom fact_143_local_Oinf__idem:(forall (X:a), (((eq a) ((inf X) X)) X)).
% 0.84/1.01  Axiom fact_144_local_Oinf__left__idem:(forall (X:a) (Y:a), (((eq a) ((inf X) ((inf X) Y))) ((inf X) Y))).
% 0.84/1.01  Axiom fact_145_local_Oinf__right__idem:(forall (X:a) (Y:a), (((eq a) ((inf ((inf X) Y)) Y)) ((inf X) Y))).
% 0.84/1.01  Axiom fact_146_local_Osup_Oidem:(forall (A:a), (((eq a) ((sup A) A)) A)).
% 0.84/1.01  Axiom fact_147_local_Osup_Oleft__idem:(forall (A:a) (B:a), (((eq a) ((sup A) ((sup A) B))) ((sup A) B))).
% 0.84/1.01  Axiom fact_148_local_Osup_Oright__idem:(forall (A:a) (B:a), (((eq a) ((sup ((sup A) B)) B)) ((sup A) B))).
% 0.84/1.01  Axiom fact_149_local_Osup__idem:(forall (X:a), (((eq a) ((sup X) X)) X)).
% 0.84/1.01  Axiom fact_150_local_Osup__left__idem:(forall (X:a) (Y:a), (((eq a) ((sup X) ((sup X) Y))) ((sup X) Y))).
% 0.84/1.01  Axiom fact_151_local_OGreatestI2__order:(forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq Y5) X3)))->(Q X3))))->(Q ((greatest_a less_eq) P)))))).
% 0.84/1.01  Axiom fact_152_local_OGreatest__equality:(forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq Y4) X)))->(((eq a) ((greatest_a less_eq) P)) X)))).
% 0.84/1.01  Axiom fact_153_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)))).
% 0.84/1.01  Axiom fact_154_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)))).
% 0.84/1.01  Axiom fact_155_local_ON5__lattice__def:(forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula397570059tice_a inf) less) sup) A) B) C)) ((and ((and (((eq a) ((inf A) C)) ((inf B) C))) ((less A) B))) (((eq a) ((sup A) C)) ((sup B) C))))).
% 0.84/1.01  Axiom fact_156_local_Ono__distrib__def:(forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula1962211574trib_a inf) less) sup) A) B) C)) ((less ((sup ((inf A) B)) ((inf C) A))) ((inf A) ((sup B) C))))).
% 0.84/1.01  Axiom fact_157_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)))).
% 0.84/1.01  Axiom fact_158_local_Ole__inf__iff:(forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq X) ((inf Y) Z2))) ((and ((less_eq X) Y)) ((less_eq X) Z2)))).
% 0.84/1.01  Axiom fact_159_local_Ole__sup__iff:(forall (X:a) (Y:a) (Z2:a), (((eq Prop) ((less_eq ((sup X) Y)) Z2)) ((and ((less_eq X) Z2)) ((less_eq Y) Z2)))).
% 0.84/1.01  Axiom fact_160_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)))).
% 0.84/1.01  Axiom fact_161_local_Oinf__sup__absorb:(forall (X:a) (Y:a), (((eq a) ((inf X) ((sup X) Y))) X)).
% 0.84/1.01  Axiom fact_162_local_Osup__inf__absorb:(forall (X:a) (Y:a), (((eq a) ((sup X) ((inf X) Y))) X)).
% 0.84/1.01  Axiom fact_163_local_OM5__lattice__def:(forall (A:a) (B:a) (C:a), (((eq Prop) ((((((modula1376131916tice_a inf) less) sup) A) B) C)) ((and ((and ((and ((and (((eq a) ((inf A) B)) ((inf B) C))) (((eq a) ((inf C) A)) ((inf B) C)))) (((eq a) ((sup A) B)) ((sup B) C)))) (((eq a) ((sup C) A)) ((sup B) C)))) ((less ((inf A) B)) ((sup A) B))))).
% 0.84/1.01  Axiom fact_164_local_OLeast1I:(forall (P:(a->Prop)), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->(P ((least_a less_eq) P)))).
% 0.84/1.01  Axiom fact_165_local_OLeast1__le:(forall (P:(a->Prop)) (Z2:a), (((ex a) (fun (X4:a)=> ((and ((and (P X4)) (forall (Y4:a), ((P Y4)->((less_eq X4) Y4))))) (forall (Y4:a), (((and (P Y4)) (forall (Ya:a), ((P Ya)->((less_eq Y4) Ya))))->(((eq a) Y4) X4))))))->((P Z2)->((less_eq ((least_a less_eq) P)) Z2)))).
% 0.84/1.01  Axiom fact_166_local_OLeastI2__order:(forall (P:(a->Prop)) (X:a) (Q:(a->Prop)), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->((forall (X3:a), ((P X3)->((forall (Y5:a), ((P Y5)->((less_eq X3) Y5)))->(Q X3))))->(Q ((least_a less_eq) P)))))).
% 0.84/1.01  Axiom fact_167_local_OLeast__equality:(forall (P:(a->Prop)) (X:a), ((P X)->((forall (Y4:a), ((P Y4)->((less_eq X) Y4)))->(((eq a) ((least_a less_eq) P)) X)))).
% 0.84/1.01  Axiom fact_168_local_Oa__join__d:(forall (A:a) (B:a) (C:a), (((eq a) ((sup A) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup A) ((inf B) C)))).
% 0.84/1.01  Axiom fact_169_local_Ob__join__d:(forall (B:a) (A:a) (C:a), (((eq a) ((sup B) (((((modula1936294176_aux_a inf) sup) A) B) C))) ((sup B) ((inf C) A)))).
% 0.84/1.01  Axiom fact_170_local_Od__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1936294176_aux_a inf) sup) A) B) C)) ((sup ((sup ((inf A) B)) ((inf B) C))) ((inf C) A)))).
% 0.84/1.01  Axiom fact_171_local_Od__b__c__a:(forall (B:a) (C:a) (A:a), (((eq a) (((((modula1936294176_aux_a inf) sup) B) C) A)) (((((modula1936294176_aux_a inf) sup) A) B) C))).
% 0.84/1.01  Axiom fact_172_local_Od__c__a__b:(forall (C:a) (A:a) (B:a), (((eq a) (((((modula1936294176_aux_a inf) sup) C) A) B)) (((((modula1936294176_aux_a inf) sup) A) B) C))).
% 0.84/1.01  Axiom fact_173_local_Oa__meet__e:(forall (A:a) (B:a) (C:a), (((eq a) ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf A) ((sup B) C)))).
% 0.84/1.01  Axiom fact_174_local_Ob__meet__e:(forall (B:a) (A:a) (C:a), (((eq a) ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf B) ((sup C) A)))).
% 0.84/1.01  Axiom fact_175_local_Oc__meet__e:(forall (C:a) (A:a) (B:a), (((eq a) ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) ((inf C) ((sup A) B)))).
% 0.84/1.01  Axiom fact_176_local_Oe__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1144073633_aux_a inf) sup) A) B) C)) ((inf ((inf ((sup A) B)) ((sup B) C))) ((sup C) A)))).
% 0.84/1.02  Axiom fact_177_local_Oe__b__c__a:(forall (B:a) (C:a) (A:a), (((eq a) (((((modula1144073633_aux_a inf) sup) B) C) A)) (((((modula1144073633_aux_a inf) sup) A) B) C))).
% 0.84/1.02  Axiom fact_178_local_Oe__c__a__b:(forall (C:a) (A:a) (B:a), (((eq a) (((((modula1144073633_aux_a inf) sup) C) A) B)) (((((modula1144073633_aux_a inf) sup) A) B) C))).
% 0.84/1.02  Axiom fact_179_local_OInf__fin_Osemilattice__order__set__axioms:(((lattic655834328_set_a inf) less_eq) less).
% 0.84/1.02  Axiom fact_180_local_OM5__lattice__incomp:(forall (A:a) (B:a) (C:a), (((((((modula1376131916tice_a inf) less) sup) A) B) C)->(((modula1727524044comp_a less_eq) A) B))).
% 0.84/1.02  Axiom fact_181_local_Oc__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) ((sup ((inf C) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.84/1.02  Axiom fact_182_local_Ob__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) ((sup ((inf B) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.84/1.02  Axiom fact_183_local_Oa__aux__def:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula17988509_aux_a inf) sup) A) B) C)) ((sup ((inf A) (((((modula1144073633_aux_a inf) sup) A) B) C))) (((((modula1936294176_aux_a inf) sup) A) B) C)))).
% 0.84/1.02  Axiom fact_184_lattice_Ono__distrib_Ocong:(((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula1962211574trib_a) modula1962211574trib_a).
% 0.84/1.02  Axiom fact_185_lattice_ON5__lattice_Ocong:(((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula397570059tice_a) modula397570059tice_a).
% 0.84/1.02  Axiom fact_186_lattice_OM5__lattice_Ocong:(((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->a))->(a->(a->(a->Prop))))))) modula1376131916tice_a) modula1376131916tice_a).
% 0.84/1.02  Axiom fact_187_lattice_Oincomp_Ocong:(((eq ((a->(a->Prop))->(a->(a->Prop)))) modula1727524044comp_a) modula1727524044comp_a).
% 0.84/1.02  Axiom fact_188_lattice_Oe__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1144073633_aux_a) modula1144073633_aux_a).
% 0.84/1.02  Axiom fact_189_lattice_Od__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1936294176_aux_a) modula1936294176_aux_a).
% 0.84/1.02  Axiom fact_190_local_Oinf_Osemilattice__order__axioms:(((semilattice_order_a inf) less_eq) less).
% 0.84/1.02  Axiom fact_191_local_Oorder_Oordering__axioms:((ordering_a less_eq) less).
% 0.84/1.02  Axiom fact_192_local_Ocomp__fun__idem__sup:(finite40241356em_a_a sup).
% 0.84/1.02  Axiom fact_193_local_Ocomp__fun__idem__inf:(finite40241356em_a_a inf).
% 0.84/1.02  Axiom fact_194_local_Ob__a:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula1373251614_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) B) C) A))).
% 0.84/1.02  Axiom fact_195_local_Oc__a:(forall (A:a) (B:a) (C:a), (((eq a) (((((modula581031071_aux_a inf) sup) A) B) C)) (((((modula17988509_aux_a inf) sup) C) A) B))).
% 0.84/1.02  Axiom fact_196_lattice_Oc__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula581031071_aux_a) modula581031071_aux_a).
% 0.84/1.02  Axiom fact_197_lattice_Ob__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula1373251614_aux_a) modula1373251614_aux_a).
% 0.84/1.02  Axiom fact_198_lattice_Oa__aux_Ocong:(((eq ((a->(a->a))->((a->(a->a))->(a->(a->(a->a)))))) modula17988509_aux_a) modula17988509_aux_a).
% 0.84/1.02  Axiom fact_199_local_Osup_Osemigroup__axioms:(semigroup_a sup).
% 0.84/1.02  Axiom fact_200_local_Oinf_Osemigroup__axioms:(semigroup_a inf).
% 0.84/1.02  Axiom fact_201_local_Osup_Osemilattice__axioms:(semilattice_a sup).
% 0.84/1.02  Axiom fact_202_local_Oinf_Osemilattice__axioms:(semilattice_a inf).
% 0.84/1.02  Axiom fact_203_local_Osup_Oabel__semigroup__axioms:(abel_semigroup_a sup).
% 0.84/1.02  Axiom fact_204_local_Oinf_Oabel__semigroup__axioms:(abel_semigroup_a inf).
% 0.84/1.02  Axiom fact_205_semilattice__order__set_Oaxioms_I1_J:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((lattic655834328_set_a F) Less_eq) Less)->(((semilattice_order_a F) Less_eq) Less))).
% 0.84/1.02  Axiom fact_206_abel__semigroup_Oaxioms_I1_J:(forall (F:(a->(a->a))), ((abel_semigroup_a F)->(semigroup_a F))).
% 0.84/1.02  Axiom fact_207_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))))).
% 0.84/1.02  Axiom fact_208_abel__semigroup_Ocommute:(forall (F:(a->(a->a))) (A:a) (B:a), ((abel_semigroup_a F)->(((eq a) ((F A) B)) ((F B) A)))).
% 0.84/1.02  Axiom fact_209_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))).
% 0.84/1.02  Axiom fact_210_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))))).
% 0.84/1.02  Axiom fact_211_semigroup__def:(((eq ((a->(a->a))->Prop)) semigroup_a) (fun (F2:(a->(a->a)))=> (forall (A2:a) (B2:a) (C3:a), (((eq a) ((F2 ((F2 A2) B2)) C3)) ((F2 A2) ((F2 B2) C3)))))).
% 0.84/1.02  Axiom fact_212_semilattice_Oaxioms_I1_J:(forall (F:(a->(a->a))), ((semilattice_a F)->(abel_semigroup_a F))).
% 0.84/1.02  Axiom fact_213_local_OSup__fin_Osemilattice__set__axioms:(lattic1885654924_set_a sup).
% 0.84/1.02  Axiom fact_214_local_OInf__fin_Osemilattice__set__axioms:(lattic1885654924_set_a inf).
% 0.84/1.02  Axiom fact_215_semilattice__order__set_Oaxioms_I2_J:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((lattic655834328_set_a F) Less_eq) Less)->(lattic1885654924_set_a F))).
% 0.84/1.02  Axiom fact_216_semilattice__set__def:(((eq ((a->(a->a))->Prop)) lattic1885654924_set_a) semilattice_a).
% 0.84/1.02  Axiom fact_217_semilattice__set_Ointro:(forall (F:(a->(a->a))), ((semilattice_a F)->(lattic1885654924_set_a F))).
% 0.84/1.02  Axiom fact_218_semilattice__set_Oaxioms:(forall (F:(a->(a->a))), ((lattic1885654924_set_a F)->(semilattice_a F))).
% 0.84/1.02  Axiom fact_219_semilattice__order__set__def:(((eq ((a->(a->a))->((a->(a->Prop))->((a->(a->Prop))->Prop)))) lattic655834328_set_a) (fun (F2:(a->(a->a))) (Less_eq2:(a->(a->Prop))) (Less2:(a->(a->Prop)))=> ((and (((semilattice_order_a F2) Less_eq2) Less2)) (lattic1885654924_set_a F2)))).
% 0.84/1.02  Axiom fact_220_semilattice__order__set_Ointro:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((semilattice_order_a F) Less_eq) Less)->((lattic1885654924_set_a F)->(((lattic655834328_set_a F) Less_eq) Less)))).
% 0.84/1.02  Axiom fact_221_semilattice__order_Omono:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a) (D:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) C)->(((Less_eq B) D)->((Less_eq ((F A) B)) ((F C) D)))))).
% 0.84/1.02  Axiom fact_222_semilattice__order_OorderE:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((eq a) A) ((F A) B))))).
% 0.84/1.02  Axiom fact_223_semilattice__order_OorderI:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((((eq a) A) ((F A) B))->((Less_eq A) B)))).
% 0.84/1.02  Axiom fact_224_semilattice__order_Oabsorb1:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((eq a) ((F A) B)) A)))).
% 0.84/1.02  Axiom fact_225_semilattice__order_Oabsorb2:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq B) A)->(((eq a) ((F A) B)) B)))).
% 0.84/1.02  Axiom fact_226_semilattice__order_OboundedE:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) ((F B) C))->((((Less_eq A) B)->(((Less_eq A) C)->False))->False)))).
% 0.84/1.02  Axiom fact_227_semilattice__order_OboundedI:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) B)->(((Less_eq A) C)->((Less_eq A) ((F B) C)))))).
% 0.84/1.02  Axiom fact_228_semilattice__order_Oorder__iff:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) B)) (((eq a) A) ((F A) B))))).
% 0.84/1.02  Axiom fact_229_semilattice__order_Ocobounded1:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((Less_eq ((F A) B)) A))).
% 27.65/27.81  Axiom fact_230_semilattice__order_Ocobounded2:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->((Less_eq ((F A) B)) B))).
% 27.65/27.81  Axiom fact_231_semilattice__order_Oabsorb__iff1:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) B)) (((eq a) ((F A) B)) A)))).
% 27.65/27.81  Axiom fact_232_semilattice__order_Oabsorb__iff2:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq B) A)) (((eq a) ((F A) B)) B)))).
% 27.65/27.81  Axiom fact_233_semilattice__order_Obounded__iff:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less_eq A) ((F B) C))) ((and ((Less_eq A) B)) ((Less_eq A) C))))).
% 27.65/27.81  Axiom fact_234_semilattice__order_OcoboundedI1:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq A) C)->((Less_eq ((F A) B)) C)))).
% 27.65/27.81  Axiom fact_235_semilattice__order_OcoboundedI2:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (C:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less_eq B) C)->((Less_eq ((F A) B)) C)))).
% 27.65/27.81  Axiom fact_236_semilattice__order_Ostrict__boundedE:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a) (C:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less A) ((F B) C))->((((Less A) B)->(((Less A) C)->False))->False)))).
% 27.65/27.81  Axiom fact_237_semilattice__order_Ostrict__order__iff:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((eq Prop) ((Less A) B)) ((and (((eq a) A) ((F A) B))) (not (((eq a) A) B)))))).
% 27.65/27.81  Axiom fact_238_semilattice__order_Ostrict__coboundedI1:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (A:a) (C:a) (B:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less A) C)->((Less ((F A) B)) C)))).
% 27.65/27.81  Axiom fact_239_semilattice__order_Ostrict__coboundedI2:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))) (B:a) (C:a) (A:a), ((((semilattice_order_a F) Less_eq) Less)->(((Less B) C)->((Less ((F A) B)) C)))).
% 27.65/27.81  Axiom fact_240_semilattice_Oidem:(forall (F:(a->(a->a))) (A:a), ((semilattice_a F)->(((eq a) ((F A) A)) A))).
% 27.65/27.81  Axiom fact_241_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)))).
% 27.65/27.81  Axiom fact_242_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)))).
% 27.65/27.81  Axiom fact_243_semilattice__order_Oaxioms_I1_J:(forall (F:(a->(a->a))) (Less_eq:(a->(a->Prop))) (Less:(a->(a->Prop))), ((((semilattice_order_a F) Less_eq) Less)->(semilattice_a F))).
% 27.65/27.81  Axiom fact_244_local_Obdd__below__def:(forall (A3:set_a), (((eq Prop) ((condit1001553558elow_a less_eq) A3)) ((ex a) (fun (M:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq M) X2))))))).
% 27.65/27.81  Axiom fact_245_local_Obdd__above__def:(forall (A3:set_a), (((eq Prop) ((condit1627435690bove_a less_eq) A3)) ((ex a) (fun (M2:a)=> (forall (X2:a), (((member_a X2) A3)->((less_eq X2) M2))))))).
% 27.65/27.81  Axiom fact_246_local_Obdd__belowI:(forall (A3:set_a) (M3:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq M3) X3)))->((condit1001553558elow_a less_eq) A3))).
% 27.65/27.81  Axiom fact_247_local_Obdd__aboveI:(forall (A3:set_a) (M4:a), ((forall (X3:a), (((member_a X3) A3)->((less_eq X3) M4)))->((condit1627435690bove_a less_eq) A3))).
% 27.65/27.81  Axiom fact_248_local_Obdd__below__Ioo:(forall (A:a) (B:a), ((condit1001553558elow_a less_eq) (((set_gr1491433118Than_a less) A) B))).
% 27.65/27.81  Axiom conj_0:((((lattice_a inf) less_eq) less) sup).
% 27.65/27.81  Axiom conj_1:((less_eq x) y).
% 27.65/27.81  Axiom conj_2:(not (((eq a) ((sup x) ((inf y) z))) ((inf y) ((sup x) z)))).
% 27.65/27.81  Axiom conj_3:((less ((sup x) ((inf y) z))) ((inf y) ((sup x) z))).
% 27.65/27.81  Trying to prove ((less_eq x) ((sup ((inf y) ((sup x) z))) z))
% 27.65/27.81  Found fact_116_local_Osup__ge100:=(fact_116_local_Osup__ge10 z):((less_eq x) ((sup x) z))
% 28.17/28.32  Found (fact_116_local_Osup__ge10 z) as proof of ((less_eq x) ((sup x) z))
% 28.17/28.32  Found ((fact_116_local_Osup__ge1 x) z) as proof of ((less_eq x) ((sup x) z))
% 28.17/28.32  Found ((fact_116_local_Osup__ge1 x) z) as proof of ((less_eq x) ((sup x) z))
% 28.17/28.32  Found (fact_85_local_Oinf__greatest0000 ((fact_116_local_Osup__ge1 x) z)) as proof of ((less_eq x) ((inf y) ((sup x) z)))
% 28.17/28.32  Found ((fact_85_local_Oinf__greatest000 ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)) as proof of ((less_eq x) ((inf y) ((sup x) z)))
% 28.17/28.32  Found (((fun (Z2:a)=> ((fact_85_local_Oinf__greatest00 Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)) as proof of ((less_eq x) ((inf y) ((sup x) z)))
% 28.17/28.32  Found (((fun (Z2:a)=> (((fact_85_local_Oinf__greatest0 y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)) as proof of ((less_eq x) ((inf y) ((sup x) z)))
% 28.17/28.32  Found (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)) as proof of ((less_eq x) ((inf y) ((sup x) z)))
% 28.17/28.32  Found (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)) as proof of ((less_eq x) ((inf y) ((sup x) z)))
% 28.17/28.32  Found (fact_98_local_Ole__supI1000 (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z))) as proof of ((less_eq x) ((sup ((inf y) ((sup x) z))) z))
% 28.17/28.32  Found ((fact_98_local_Ole__supI100 z) (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z))) as proof of ((less_eq x) ((sup ((inf y) ((sup x) z))) z))
% 28.17/28.32  Found (((fact_98_local_Ole__supI10 ((inf y) ((sup x) z))) z) (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z))) as proof of ((less_eq x) ((sup ((inf y) ((sup x) z))) z))
% 28.17/28.32  Found ((((fact_98_local_Ole__supI1 x) ((inf y) ((sup x) z))) z) (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z))) as proof of ((less_eq x) ((sup ((inf y) ((sup x) z))) z))
% 28.17/28.32  Found ((((fact_98_local_Ole__supI1 x) ((inf y) ((sup x) z))) z) (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z))) as proof of ((less_eq x) ((sup ((inf y) ((sup x) z))) z))
% 28.17/28.32  Got proof ((((fact_98_local_Ole__supI1 x) ((inf y) ((sup x) z))) z) (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)))
% 28.17/28.32  Time elapsed = 26.810837s
% 28.17/28.32  node=5033 cost=637.000000 depth=13
% 28.17/28.32::::::::::::::::::::::
% 28.17/28.32  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.17/28.32  % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.17/28.32  ((((fact_98_local_Ole__supI1 x) ((inf y) ((sup x) z))) z) (((fun (Z2:a)=> ((((fact_85_local_Oinf__greatest x) y) Z2) conj_1)) ((sup x) z)) ((fact_116_local_Osup__ge1 x) z)))
% 28.17/28.32  % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------