TSTP Solution File: ITP050^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP050^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:24:02 EDT 2021
% Result : Unknown 0.85s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP050^1 : TPTP v7.5.0. Released v7.5.0.
% 0.12/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Fri Mar 19 04:53:41 EDT 2021
% 0.12/0.34 % CPUTime :
% 0.12/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 0.45/0.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e3680>, <kernel.Type object at 0x2ab6f35e3830>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring set_se1612935105at_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1b92fc8>, <kernel.Type object at 0x2ab6f35e3e18>) of role type named ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring list_P559422087at_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e3518>, <kernel.Type object at 0x2ab6f35e36c8>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring set_Pr1986765409at_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e3830>, <kernel.Type object at 0x2ab6f35e3e18>) of role type named ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring product_prod_nat_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e3998>, <kernel.Type object at 0x1e2a7e8>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring set_set_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e3878>, <kernel.Type object at 0x1e2a878>) of role type named ty_n_t__List__Olist_It__Nat__Onat_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring list_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e36c8>, <kernel.Type object at 0x1e2a950>) of role type named ty_n_t__Set__Oset_It__Nat__Onat_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring set_nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e3878>, <kernel.Type object at 0x1e2a7e8>) of role type named ty_n_t__Nat__Onat
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring nat:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e36c8>, <kernel.Type object at 0x1e2a758>) of role type named ty_n_tf__a
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring a:Type
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e36c8>, <kernel.DependentProduct object at 0x1e2a878>) of role type named sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis_001tf__a
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring edmond1517640972ysis_a:((product_prod_nat_nat->a)->Prop)
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x2ab6f35e36c8>, <kernel.DependentProduct object at 0x1e2a950>) of role type named sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis__defs_OspEdges_001tf__a
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring edmond475474835dges_a:((product_prod_nat_nat->a)->(nat->(nat->set_Pr1986765409at_nat)))
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1b8e908>, <kernel.DependentProduct object at 0x1e2a368>) of role type named sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis__defs_OuE_001tf__a
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring edmond771116670s_uE_a:((product_prod_nat_nat->a)->set_Pr1986765409at_nat)
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1b8e368>, <kernel.DependentProduct object at 0x1e2a7e8>) of role type named sy_c_Finite__Set_Ocard_001t__Nat__Onat
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring finite_card_nat:(set_nat->nat)
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1b8e7e8>, <kernel.DependentProduct object at 0x1e2ab48>) of role type named sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring finite447719721at_nat:(set_Pr1986765409at_nat->nat)
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1b8e7e8>, <kernel.DependentProduct object at 0x1b6b998>) of role type named sy_c_Finite__Set_Ofinite_001t__Nat__Onat
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring finite_finite_nat:(set_nat->Prop)
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1e2a368>, <kernel.DependentProduct object at 0x1b8d638>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.60 Using role type
% 0.45/0.60 Declaring finite772653738at_nat:(set_Pr1986765409at_nat->Prop)
% 0.45/0.60 FOF formula (<kernel.Constant object at 0x1e2a878>, <kernel.DependentProduct object at 0x1b8db90>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring finite2012248349et_nat:(set_set_nat->Prop)
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1e2a368>, <kernel.DependentProduct object at 0x1b8d320>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring finite1457549322at_nat:(set_se1612935105at_nat->Prop)
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1e2a368>, <kernel.DependentProduct object at 0x1b8d320>) of role type named sy_c_Graph_OFinite__Graph_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring finite_Graph_a:((product_prod_nat_nat->a)->Prop)
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b6bdd0>, <kernel.DependentProduct object at 0x1b8def0>) of role type named sy_c_Graph_OGraph_OE_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring e_a:((product_prod_nat_nat->a)->set_Pr1986765409at_nat)
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b6ba70>, <kernel.DependentProduct object at 0x1b8d368>) of role type named sy_c_Graph_OGraph_OV_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring v_a:((product_prod_nat_nat->a)->set_nat)
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b6be18>, <kernel.DependentProduct object at 0x1b8d368>) of role type named sy_c_Graph_OGraph_Oadjacent__nodes_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring adjacent_nodes_a:((product_prod_nat_nat->a)->(nat->set_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b6ba70>, <kernel.DependentProduct object at 0x1b8d7a0>) of role type named sy_c_Graph_OGraph_Oincoming_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring incoming_a:((product_prod_nat_nat->a)->(nat->set_Pr1986765409at_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b6ba70>, <kernel.DependentProduct object at 0x1b8def0>) of role type named sy_c_Graph_OGraph_Oincoming_H_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring incoming_a2:((product_prod_nat_nat->a)->(set_nat->set_Pr1986765409at_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8d368>, <kernel.DependentProduct object at 0x1b8d200>) of role type named sy_c_Graph_OGraph_OisPath_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring isPath_a:((product_prod_nat_nat->a)->(nat->(list_P559422087at_nat->(nat->Prop))))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8df38>, <kernel.DependentProduct object at 0x1b8d200>) of role type named sy_c_Graph_OGraph_OisShortestPath_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring isShortestPath_a:((product_prod_nat_nat->a)->(nat->(list_P559422087at_nat->(nat->Prop))))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8def0>, <kernel.DependentProduct object at 0x1b8d9e0>) of role type named sy_c_Graph_OGraph_Ooutgoing_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring outgoing_a:((product_prod_nat_nat->a)->(nat->set_Pr1986765409at_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8d1b8>, <kernel.DependentProduct object at 0x1b8df38>) of role type named sy_c_Graph_OGraph_Ooutgoing_H_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring outgoing_a2:((product_prod_nat_nat->a)->(set_nat->set_Pr1986765409at_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8d7e8>, <kernel.DependentProduct object at 0x1b8d1b8>) of role type named sy_c_Graph_OGraph_OpathVertices
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring pathVertices:(nat->(list_P559422087at_nat->list_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8d368>, <kernel.DependentProduct object at 0x1b8d1b8>) of role type named sy_c_Graph_OGraph_OreachableNodes_001tf__a
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring reachableNodes_a:((product_prod_nat_nat->a)->(nat->set_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8df38>, <kernel.DependentProduct object at 0x1b8d248>) of role type named sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring inf_inf_nat:(nat->(nat->nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8dd88>, <kernel.DependentProduct object at 0x1b8d3b0>) of role type named sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring inf_inf_set_nat:(set_nat->(set_nat->set_nat))
% 0.45/0.61 FOF formula (<kernel.Constant object at 0x1b8d1b8>, <kernel.DependentProduct object at 0x1b8d320>) of role type named sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.61 Using role type
% 0.45/0.61 Declaring inf_in586391887at_nat:(set_Pr1986765409at_nat->(set_Pr1986765409at_nat->set_Pr1986765409at_nat))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d248>, <kernel.DependentProduct object at 0x1b8d638>) of role type named sy_c_List_Olist_OCons_001t__Nat__Onat
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring cons_nat:(nat->(list_nat->list_nat))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d3b0>, <kernel.DependentProduct object at 0x1b8d368>) of role type named sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring cons_P66992567at_nat:(product_prod_nat_nat->(list_P559422087at_nat->list_P559422087at_nat))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d320>, <kernel.Constant object at 0x1b8d368>) of role type named sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring nil_Pr1308055047at_nat:list_P559422087at_nat
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d248>, <kernel.DependentProduct object at 0x1b8d1b8>) of role type named sy_c_List_Olist_Oset_001t__Nat__Onat
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring set_nat2:(list_nat->set_nat)
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d7e8>, <kernel.DependentProduct object at 0x1b8de18>) of role type named sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring set_Pr2131844118at_nat:(list_P559422087at_nat->set_Pr1986765409at_nat)
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d368>, <kernel.DependentProduct object at 0x1b8de60>) of role type named sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring size_s1990949619at_nat:(list_P559422087at_nat->nat)
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d1b8>, <kernel.DependentProduct object at 0x1b8d248>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8de18>, <kernel.DependentProduct object at 0x1b8d3b0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring ord_less_eq_set_nat:(set_nat->(set_nat->Prop))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8de60>, <kernel.DependentProduct object at 0x1b8d7e8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring ord_le841296385at_nat:(set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d248>, <kernel.DependentProduct object at 0x1b8d368>) of role type named sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring product_Pair_nat_nat:(nat->(nat->product_prod_nat_nat))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d170>, <kernel.DependentProduct object at 0x1b8de18>) of role type named sy_c_Set_OCollect_001t__Nat__Onat
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring collect_nat:((nat->Prop)->set_nat)
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d1b8>, <kernel.DependentProduct object at 0x1b8d248>) of role type named sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring collec7649004at_nat:((product_prod_nat_nat->Prop)->set_Pr1986765409at_nat)
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d368>, <kernel.DependentProduct object at 0x1b8de18>) of role type named sy_c_member_001t__Nat__Onat
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring member_nat:(nat->(set_nat->Prop))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d128>, <kernel.DependentProduct object at 0x1b8d440>) of role type named sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring member701585322at_nat:(product_prod_nat_nat->(set_Pr1986765409at_nat->Prop))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d248>, <kernel.DependentProduct object at 0x1b8d7e8>) of role type named sy_c_member_001t__Set__Oset_It__Nat__Onat_J
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring member_set_nat:(set_nat->(set_set_nat->Prop))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x1b8d950>, <kernel.DependentProduct object at 0x1b8d1b8>) of role type named sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring member298845450at_nat:(set_Pr1986765409at_nat->(set_se1612935105at_nat->Prop))
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x1b8d440>, <kernel.DependentProduct object at 0x2ab6f35e0320>) of role type named sy_v_c
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring c:(product_prod_nat_nat->a)
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x1b8dbd8>, <kernel.Constant object at 0x1b8d950>) of role type named sy_v_edges
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring edges:set_Pr1986765409at_nat
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x1b8d1b8>, <kernel.Constant object at 0x1b8d950>) of role type named sy_v_p
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring p:list_P559422087at_nat
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x1b8d440>, <kernel.Constant object at 0x1b8d950>) of role type named sy_v_s
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring s:nat
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x1b8dbd8>, <kernel.Constant object at 0x1b8d1b8>) of role type named sy_v_t
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring t:nat
% 0.45/0.63 FOF formula ((((isShortestPath_a c) s) p) t) of role axiom named fact_0_SP
% 0.45/0.63 A new axiom: ((((isShortestPath_a c) s) p) t)
% 0.45/0.63 FOF formula ((ord_le841296385at_nat edges) (set_Pr2131844118at_nat p)) of role axiom named fact_1_SP__EDGES
% 0.45/0.63 A new axiom: ((ord_le841296385at_nat edges) (set_Pr2131844118at_nat p))
% 0.45/0.63 FOF formula (edmond1517640972ysis_a c) of role axiom named fact_2_ek__analysis__axioms
% 0.45/0.63 A new axiom: (edmond1517640972ysis_a c)
% 0.45/0.63 FOF formula (forall (U:set_nat), ((ord_le841296385at_nat ((incoming_a2 c) U)) (e_a c))) of role axiom named fact_3_incoming_H__edges
% 0.45/0.63 A new axiom: (forall (U:set_nat), ((ord_le841296385at_nat ((incoming_a2 c) U)) (e_a c)))
% 0.45/0.63 FOF formula (forall (U:set_nat), ((ord_le841296385at_nat ((outgoing_a2 c) U)) (e_a c))) of role axiom named fact_4_outgoing_H__edges
% 0.45/0.63 A new axiom: (forall (U:set_nat), ((ord_le841296385at_nat ((outgoing_a2 c) U)) (e_a c)))
% 0.45/0.63 FOF formula ((ord_le841296385at_nat (e_a c)) (edmond771116670s_uE_a c)) of role axiom named fact_5_E__ss__uE
% 0.45/0.63 A new axiom: ((ord_le841296385at_nat (e_a c)) (edmond771116670s_uE_a c))
% 0.45/0.63 FOF formula (forall (U2:nat), ((ord_le841296385at_nat ((incoming_a c) U2)) (e_a c))) of role axiom named fact_6_incoming__edges
% 0.45/0.63 A new axiom: (forall (U2:nat), ((ord_le841296385at_nat ((incoming_a c) U2)) (e_a c)))
% 0.45/0.63 FOF formula (forall (U2:nat), ((ord_le841296385at_nat ((outgoing_a c) U2)) (e_a c))) of role axiom named fact_7_outgoing__edges
% 0.45/0.63 A new axiom: (forall (U2:nat), ((ord_le841296385at_nat ((outgoing_a c) U2)) (e_a c)))
% 0.45/0.63 FOF formula (finite_Graph_a c) of role axiom named fact_8_Finite__Graph__axioms
% 0.45/0.63 A new axiom: (finite_Graph_a c)
% 0.45/0.63 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((forall (X:product_prod_nat_nat), (((member701585322at_nat X) A)->((member701585322at_nat X) B)))->((ord_le841296385at_nat A) B))) of role axiom named fact_9_subsetI
% 0.45/0.63 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((forall (X:product_prod_nat_nat), (((member701585322at_nat X) A)->((member701585322at_nat X) B)))->((ord_le841296385at_nat A) B)))
% 0.45/0.63 FOF formula (forall (A:set_nat) (B:set_nat), ((forall (X:nat), (((member_nat X) A)->((member_nat X) B)))->((ord_less_eq_set_nat A) B))) of role axiom named fact_10_subsetI
% 0.45/0.63 A new axiom: (forall (A:set_nat) (B:set_nat), ((forall (X:nat), (((member_nat X) A)->((member_nat X) B)))->((ord_less_eq_set_nat A) B)))
% 0.45/0.63 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->(((ord_le841296385at_nat B) A)->(((eq set_Pr1986765409at_nat) A) B)))) of role axiom named fact_11_subset__antisym
% 0.45/0.63 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->(((ord_le841296385at_nat B) A)->(((eq set_Pr1986765409at_nat) A) B))))
% 0.45/0.63 FOF formula (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->(((eq set_nat) A) B)))) of role axiom named fact_12_subset__antisym
% 0.45/0.63 A new axiom: (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->(((eq set_nat) A) B))))
% 0.45/0.63 FOF formula (forall (X2:set_Pr1986765409at_nat), ((ord_le841296385at_nat X2) X2)) of role axiom named fact_13_order__refl
% 0.48/0.64 A new axiom: (forall (X2:set_Pr1986765409at_nat), ((ord_le841296385at_nat X2) X2))
% 0.48/0.64 FOF formula (forall (X2:set_nat), ((ord_less_eq_set_nat X2) X2)) of role axiom named fact_14_order__refl
% 0.48/0.64 A new axiom: (forall (X2:set_nat), ((ord_less_eq_set_nat X2) X2))
% 0.48/0.64 FOF formula (forall (X2:nat), ((ord_less_eq_nat X2) X2)) of role axiom named fact_15_order__refl
% 0.48/0.64 A new axiom: (forall (X2:nat), ((ord_less_eq_nat X2) X2))
% 0.48/0.64 FOF formula ((member_nat s) (v_a c)) of role axiom named fact_16_SV
% 0.48/0.64 A new axiom: ((member_nat s) (v_a c))
% 0.48/0.64 FOF formula ((ord_le841296385at_nat (((edmond475474835dges_a c) s) t)) (e_a c)) of role axiom named fact_17_spEdges__ss__E
% 0.48/0.64 A new axiom: ((ord_le841296385at_nat (((edmond475474835dges_a c) s) t)) (e_a c))
% 0.48/0.64 FOF formula (forall (U2:nat) (P:list_P559422087at_nat) (V:nat) (E:product_prod_nat_nat), (((((isPath_a c) U2) P) V)->(((member701585322at_nat E) (set_Pr2131844118at_nat P))->((member701585322at_nat E) (e_a c))))) of role axiom named fact_18_isPath__edgeset
% 0.48/0.64 A new axiom: (forall (U2:nat) (P:list_P559422087at_nat) (V:nat) (E:product_prod_nat_nat), (((((isPath_a c) U2) P) V)->(((member701585322at_nat E) (set_Pr2131844118at_nat P))->((member701585322at_nat E) (e_a c)))))
% 0.48/0.64 FOF formula (forall (U2:nat) (P:list_P559422087at_nat) (V:nat), (((((isShortestPath_a c) U2) P) V)->((((isPath_a c) U2) P) V))) of role axiom named fact_19_shortestPath__is__path
% 0.48/0.64 A new axiom: (forall (U2:nat) (P:list_P559422087at_nat) (V:nat), (((((isShortestPath_a c) U2) P) V)->((((isPath_a c) U2) P) V)))
% 0.48/0.64 FOF formula (forall (U2:nat), ((ord_less_eq_set_nat ((adjacent_nodes_a c) U2)) (v_a c))) of role axiom named fact_20_adjacent__nodes__ss__V
% 0.48/0.64 A new axiom: (forall (U2:nat), ((ord_less_eq_set_nat ((adjacent_nodes_a c) U2)) (v_a c)))
% 0.48/0.64 FOF formula (((eq ((product_prod_nat_nat->a)->Prop)) edmond1517640972ysis_a) finite_Graph_a) of role axiom named fact_21_ek__analysis__def
% 0.48/0.64 A new axiom: (((eq ((product_prod_nat_nat->a)->Prop)) edmond1517640972ysis_a) finite_Graph_a)
% 0.48/0.64 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite_Graph_a C)->(edmond1517640972ysis_a C))) of role axiom named fact_22_ek__analysis_Ointro
% 0.48/0.64 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite_Graph_a C)->(edmond1517640972ysis_a C)))
% 0.48/0.64 FOF formula (forall (C:(product_prod_nat_nat->a)), ((edmond1517640972ysis_a C)->(finite_Graph_a C))) of role axiom named fact_23_ek__analysis_Oaxioms
% 0.48/0.64 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((edmond1517640972ysis_a C)->(finite_Graph_a C)))
% 0.48/0.64 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->(nat->set_Pr1986765409at_nat)))) edmond475474835dges_a) edmond475474835dges_a) of role axiom named fact_24_ek__analysis__defs_OspEdges_Ocong
% 0.48/0.64 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->(nat->set_Pr1986765409at_nat)))) edmond475474835dges_a) edmond475474835dges_a)
% 0.48/0.64 FOF formula (((eq ((product_prod_nat_nat->a)->set_Pr1986765409at_nat)) edmond771116670s_uE_a) edmond771116670s_uE_a) of role axiom named fact_25_ek__analysis__defs_OuE_Ocong
% 0.48/0.64 A new axiom: (((eq ((product_prod_nat_nat->a)->set_Pr1986765409at_nat)) edmond771116670s_uE_a) edmond771116670s_uE_a)
% 0.48/0.64 FOF formula (forall (C:(product_prod_nat_nat->a)) (S:nat) (T:nat), ((edmond1517640972ysis_a C)->((ord_le841296385at_nat (((edmond475474835dges_a C) S) T)) (e_a C)))) of role axiom named fact_26_ek__analysis_OspEdges__ss__E
% 0.48/0.64 A new axiom: (forall (C:(product_prod_nat_nat->a)) (S:nat) (T:nat), ((edmond1517640972ysis_a C)->((ord_le841296385at_nat (((edmond475474835dges_a C) S) T)) (e_a C))))
% 0.48/0.64 FOF formula (forall (C:(product_prod_nat_nat->a)), ((edmond1517640972ysis_a C)->((ord_le841296385at_nat (e_a C)) (edmond771116670s_uE_a C)))) of role axiom named fact_27_ek__analysis_OE__ss__uE
% 0.48/0.64 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((edmond1517640972ysis_a C)->((ord_le841296385at_nat (e_a C)) (edmond771116670s_uE_a C))))
% 0.48/0.64 FOF formula (forall (B2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) A2)->(((ord_le841296385at_nat A2) B2)->(((eq set_Pr1986765409at_nat) A2) B2)))) of role axiom named fact_28_dual__order_Oantisym
% 0.48/0.65 A new axiom: (forall (B2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) A2)->(((ord_le841296385at_nat A2) B2)->(((eq set_Pr1986765409at_nat) A2) B2))))
% 0.48/0.65 FOF formula (forall (B2:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) A2)->(((ord_less_eq_set_nat A2) B2)->(((eq set_nat) A2) B2)))) of role axiom named fact_29_dual__order_Oantisym
% 0.48/0.65 A new axiom: (forall (B2:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) A2)->(((ord_less_eq_set_nat A2) B2)->(((eq set_nat) A2) B2))))
% 0.48/0.65 FOF formula (forall (B2:nat) (A2:nat), (((ord_less_eq_nat B2) A2)->(((ord_less_eq_nat A2) B2)->(((eq nat) A2) B2)))) of role axiom named fact_30_dual__order_Oantisym
% 0.48/0.65 A new axiom: (forall (B2:nat) (A2:nat), (((ord_less_eq_nat B2) A2)->(((ord_less_eq_nat A2) B2)->(((eq nat) A2) B2))))
% 0.48/0.65 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat B3) A3)) ((ord_le841296385at_nat A3) B3)))) of role axiom named fact_31_dual__order_Oeq__iff
% 0.48/0.65 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat B3) A3)) ((ord_le841296385at_nat A3) B3))))
% 0.48/0.65 FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A3:set_nat) (B3:set_nat)=> ((and ((ord_less_eq_set_nat B3) A3)) ((ord_less_eq_set_nat A3) B3)))) of role axiom named fact_32_dual__order_Oeq__iff
% 0.48/0.65 A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A3:set_nat) (B3:set_nat)=> ((and ((ord_less_eq_set_nat B3) A3)) ((ord_less_eq_set_nat A3) B3))))
% 0.48/0.65 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A3:nat) (B3:nat)=> ((and ((ord_less_eq_nat B3) A3)) ((ord_less_eq_nat A3) B3)))) of role axiom named fact_33_dual__order_Oeq__iff
% 0.48/0.65 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A3:nat) (B3:nat)=> ((and ((ord_less_eq_nat B3) A3)) ((ord_less_eq_nat A3) B3))))
% 0.48/0.65 FOF formula (forall (B2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) A2)->(((ord_le841296385at_nat C) B2)->((ord_le841296385at_nat C) A2)))) of role axiom named fact_34_dual__order_Otrans
% 0.48/0.65 A new axiom: (forall (B2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) A2)->(((ord_le841296385at_nat C) B2)->((ord_le841296385at_nat C) A2))))
% 0.48/0.65 FOF formula (forall (B2:set_nat) (A2:set_nat) (C:set_nat), (((ord_less_eq_set_nat B2) A2)->(((ord_less_eq_set_nat C) B2)->((ord_less_eq_set_nat C) A2)))) of role axiom named fact_35_dual__order_Otrans
% 0.48/0.65 A new axiom: (forall (B2:set_nat) (A2:set_nat) (C:set_nat), (((ord_less_eq_set_nat B2) A2)->(((ord_less_eq_set_nat C) B2)->((ord_less_eq_set_nat C) A2))))
% 0.48/0.65 FOF formula (forall (B2:nat) (A2:nat) (C:nat), (((ord_less_eq_nat B2) A2)->(((ord_less_eq_nat C) B2)->((ord_less_eq_nat C) A2)))) of role axiom named fact_36_dual__order_Otrans
% 0.48/0.65 A new axiom: (forall (B2:nat) (A2:nat) (C:nat), (((ord_less_eq_nat B2) A2)->(((ord_less_eq_nat C) B2)->((ord_less_eq_nat C) A2))))
% 0.48/0.65 FOF formula (forall (P2:(nat->(nat->Prop))) (A2:nat) (B2:nat), ((forall (A4:nat) (B4:nat), (((ord_less_eq_nat A4) B4)->((P2 A4) B4)))->((forall (A4:nat) (B4:nat), (((P2 B4) A4)->((P2 A4) B4)))->((P2 A2) B2)))) of role axiom named fact_37_linorder__wlog
% 0.48/0.65 A new axiom: (forall (P2:(nat->(nat->Prop))) (A2:nat) (B2:nat), ((forall (A4:nat) (B4:nat), (((ord_less_eq_nat A4) B4)->((P2 A4) B4)))->((forall (A4:nat) (B4:nat), (((P2 B4) A4)->((P2 A4) B4)))->((P2 A2) B2))))
% 0.48/0.65 FOF formula (forall (A2:set_Pr1986765409at_nat), ((ord_le841296385at_nat A2) A2)) of role axiom named fact_38_dual__order_Orefl
% 0.48/0.65 A new axiom: (forall (A2:set_Pr1986765409at_nat), ((ord_le841296385at_nat A2) A2))
% 0.48/0.66 FOF formula (forall (A2:set_nat), ((ord_less_eq_set_nat A2) A2)) of role axiom named fact_39_dual__order_Orefl
% 0.48/0.66 A new axiom: (forall (A2:set_nat), ((ord_less_eq_set_nat A2) A2))
% 0.48/0.66 FOF formula (forall (A2:nat), ((ord_less_eq_nat A2) A2)) of role axiom named fact_40_dual__order_Orefl
% 0.48/0.66 A new axiom: (forall (A2:nat), ((ord_less_eq_nat A2) A2))
% 0.48/0.66 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat) (Z2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((ord_le841296385at_nat Y2) Z2)->((ord_le841296385at_nat X2) Z2)))) of role axiom named fact_41_order__trans
% 0.48/0.66 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat) (Z2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((ord_le841296385at_nat Y2) Z2)->((ord_le841296385at_nat X2) Z2))))
% 0.48/0.66 FOF formula (forall (X2:set_nat) (Y2:set_nat) (Z2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((ord_less_eq_set_nat Y2) Z2)->((ord_less_eq_set_nat X2) Z2)))) of role axiom named fact_42_order__trans
% 0.48/0.66 A new axiom: (forall (X2:set_nat) (Y2:set_nat) (Z2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((ord_less_eq_set_nat Y2) Z2)->((ord_less_eq_set_nat X2) Z2))))
% 0.48/0.66 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_eq_nat X2) Z2)))) of role axiom named fact_43_order__trans
% 0.48/0.66 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_eq_nat X2) Z2))))
% 0.48/0.66 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat B2) A2)->(((eq set_Pr1986765409at_nat) A2) B2)))) of role axiom named fact_44_order__class_Oorder_Oantisym
% 0.48/0.66 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat B2) A2)->(((eq set_Pr1986765409at_nat) A2) B2))))
% 0.48/0.66 FOF formula (forall (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat B2) A2)->(((eq set_nat) A2) B2)))) of role axiom named fact_45_order__class_Oorder_Oantisym
% 0.48/0.66 A new axiom: (forall (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat B2) A2)->(((eq set_nat) A2) B2))))
% 0.48/0.66 FOF formula (forall (A2:nat) (B2:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat B2) A2)->(((eq nat) A2) B2)))) of role axiom named fact_46_order__class_Oorder_Oantisym
% 0.48/0.66 A new axiom: (forall (A2:nat) (B2:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat B2) A2)->(((eq nat) A2) B2))))
% 0.48/0.66 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->((((eq set_Pr1986765409at_nat) B2) C)->((ord_le841296385at_nat A2) C)))) of role axiom named fact_47_ord__le__eq__trans
% 0.48/0.66 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->((((eq set_Pr1986765409at_nat) B2) C)->((ord_le841296385at_nat A2) C))))
% 0.48/0.66 FOF formula (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->((((eq set_nat) B2) C)->((ord_less_eq_set_nat A2) C)))) of role axiom named fact_48_ord__le__eq__trans
% 0.48/0.66 A new axiom: (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->((((eq set_nat) B2) C)->((ord_less_eq_set_nat A2) C))))
% 0.48/0.66 FOF formula (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) B2)->((((eq nat) B2) C)->((ord_less_eq_nat A2) C)))) of role axiom named fact_49_ord__le__eq__trans
% 0.48/0.66 A new axiom: (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) B2)->((((eq nat) B2) C)->((ord_less_eq_nat A2) C))))
% 0.48/0.66 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A2) B2)->(((ord_le841296385at_nat B2) C)->((ord_le841296385at_nat A2) C)))) of role axiom named fact_50_ord__eq__le__trans
% 0.48/0.66 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A2) B2)->(((ord_le841296385at_nat B2) C)->((ord_le841296385at_nat A2) C))))
% 0.48/0.67 FOF formula (forall (A2:set_nat) (B2:set_nat) (C:set_nat), ((((eq set_nat) A2) B2)->(((ord_less_eq_set_nat B2) C)->((ord_less_eq_set_nat A2) C)))) of role axiom named fact_51_ord__eq__le__trans
% 0.48/0.67 A new axiom: (forall (A2:set_nat) (B2:set_nat) (C:set_nat), ((((eq set_nat) A2) B2)->(((ord_less_eq_set_nat B2) C)->((ord_less_eq_set_nat A2) C))))
% 0.48/0.67 FOF formula (forall (A2:nat) (B2:nat) (C:nat), ((((eq nat) A2) B2)->(((ord_less_eq_nat B2) C)->((ord_less_eq_nat A2) C)))) of role axiom named fact_52_ord__eq__le__trans
% 0.48/0.67 A new axiom: (forall (A2:nat) (B2:nat) (C:nat), ((((eq nat) A2) B2)->(((ord_less_eq_nat B2) C)->((ord_less_eq_nat A2) C))))
% 0.48/0.67 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat A3) B3)) ((ord_le841296385at_nat B3) A3)))) of role axiom named fact_53_order__class_Oorder_Oeq__iff
% 0.48/0.67 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat A3) B3)) ((ord_le841296385at_nat B3) A3))))
% 0.48/0.67 FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A3:set_nat) (B3:set_nat)=> ((and ((ord_less_eq_set_nat A3) B3)) ((ord_less_eq_set_nat B3) A3)))) of role axiom named fact_54_order__class_Oorder_Oeq__iff
% 0.48/0.67 A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A3:set_nat) (B3:set_nat)=> ((and ((ord_less_eq_set_nat A3) B3)) ((ord_less_eq_set_nat B3) A3))))
% 0.48/0.67 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A3:nat) (B3:nat)=> ((and ((ord_less_eq_nat A3) B3)) ((ord_less_eq_nat B3) A3)))) of role axiom named fact_55_order__class_Oorder_Oeq__iff
% 0.48/0.67 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A3:nat) (B3:nat)=> ((and ((ord_less_eq_nat A3) B3)) ((ord_less_eq_nat B3) A3))))
% 0.48/0.67 FOF formula (forall (Y2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat), (((ord_le841296385at_nat Y2) X2)->(((eq Prop) ((ord_le841296385at_nat X2) Y2)) (((eq set_Pr1986765409at_nat) X2) Y2)))) of role axiom named fact_56_antisym__conv
% 0.48/0.67 A new axiom: (forall (Y2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat), (((ord_le841296385at_nat Y2) X2)->(((eq Prop) ((ord_le841296385at_nat X2) Y2)) (((eq set_Pr1986765409at_nat) X2) Y2))))
% 0.48/0.67 FOF formula (forall (Y2:set_nat) (X2:set_nat), (((ord_less_eq_set_nat Y2) X2)->(((eq Prop) ((ord_less_eq_set_nat X2) Y2)) (((eq set_nat) X2) Y2)))) of role axiom named fact_57_antisym__conv
% 0.48/0.67 A new axiom: (forall (Y2:set_nat) (X2:set_nat), (((ord_less_eq_set_nat Y2) X2)->(((eq Prop) ((ord_less_eq_set_nat X2) Y2)) (((eq set_nat) X2) Y2))))
% 0.48/0.67 FOF formula (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((eq Prop) ((ord_less_eq_nat X2) Y2)) (((eq nat) X2) Y2)))) of role axiom named fact_58_antisym__conv
% 0.48/0.67 A new axiom: (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((eq Prop) ((ord_less_eq_nat X2) Y2)) (((eq nat) X2) Y2))))
% 0.48/0.67 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), ((((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->False))->((((ord_less_eq_nat Y2) X2)->(((ord_less_eq_nat X2) Z2)->False))->((((ord_less_eq_nat X2) Z2)->(((ord_less_eq_nat Z2) Y2)->False))->((((ord_less_eq_nat Z2) Y2)->(((ord_less_eq_nat Y2) X2)->False))->((((ord_less_eq_nat Y2) Z2)->(((ord_less_eq_nat Z2) X2)->False))->((((ord_less_eq_nat Z2) X2)->(((ord_less_eq_nat X2) Y2)->False))->False))))))) of role axiom named fact_59_le__cases3
% 0.48/0.67 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), ((((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->False))->((((ord_less_eq_nat Y2) X2)->(((ord_less_eq_nat X2) Z2)->False))->((((ord_less_eq_nat X2) Z2)->(((ord_less_eq_nat Z2) Y2)->False))->((((ord_less_eq_nat Z2) Y2)->(((ord_less_eq_nat Y2) X2)->False))->((((ord_less_eq_nat Y2) Z2)->(((ord_less_eq_nat Z2) X2)->False))->((((ord_less_eq_nat Z2) X2)->(((ord_less_eq_nat X2) Y2)->False))->False)))))))
% 0.48/0.68 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat B2) C)->((ord_le841296385at_nat A2) C)))) of role axiom named fact_60_order_Otrans
% 0.48/0.68 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat B2) C)->((ord_le841296385at_nat A2) C))))
% 0.48/0.68 FOF formula (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat B2) C)->((ord_less_eq_set_nat A2) C)))) of role axiom named fact_61_order_Otrans
% 0.48/0.68 A new axiom: (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat B2) C)->((ord_less_eq_set_nat A2) C))))
% 0.48/0.68 FOF formula (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat B2) C)->((ord_less_eq_nat A2) C)))) of role axiom named fact_62_order_Otrans
% 0.48/0.68 A new axiom: (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat B2) C)->((ord_less_eq_nat A2) C))))
% 0.48/0.68 FOF formula (forall (X2:nat) (Y2:nat), ((((ord_less_eq_nat X2) Y2)->False)->((ord_less_eq_nat Y2) X2))) of role axiom named fact_63_le__cases
% 0.48/0.68 A new axiom: (forall (X2:nat) (Y2:nat), ((((ord_less_eq_nat X2) Y2)->False)->((ord_less_eq_nat Y2) X2)))
% 0.48/0.68 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) X2) Y2)->((ord_le841296385at_nat X2) Y2))) of role axiom named fact_64_eq__refl
% 0.48/0.68 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) X2) Y2)->((ord_le841296385at_nat X2) Y2)))
% 0.48/0.68 FOF formula (forall (X2:set_nat) (Y2:set_nat), ((((eq set_nat) X2) Y2)->((ord_less_eq_set_nat X2) Y2))) of role axiom named fact_65_eq__refl
% 0.48/0.68 A new axiom: (forall (X2:set_nat) (Y2:set_nat), ((((eq set_nat) X2) Y2)->((ord_less_eq_set_nat X2) Y2)))
% 0.48/0.68 FOF formula (forall (X2:nat) (Y2:nat), ((((eq nat) X2) Y2)->((ord_less_eq_nat X2) Y2))) of role axiom named fact_66_eq__refl
% 0.48/0.68 A new axiom: (forall (X2:nat) (Y2:nat), ((((eq nat) X2) Y2)->((ord_less_eq_nat X2) Y2)))
% 0.48/0.68 FOF formula (forall (X2:nat) (Y2:nat), ((or ((ord_less_eq_nat X2) Y2)) ((ord_less_eq_nat Y2) X2))) of role axiom named fact_67_linear
% 0.48/0.68 A new axiom: (forall (X2:nat) (Y2:nat), ((or ((ord_less_eq_nat X2) Y2)) ((ord_less_eq_nat Y2) X2)))
% 0.48/0.68 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((ord_le841296385at_nat Y2) X2)->(((eq set_Pr1986765409at_nat) X2) Y2)))) of role axiom named fact_68_antisym
% 0.48/0.68 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((ord_le841296385at_nat Y2) X2)->(((eq set_Pr1986765409at_nat) X2) Y2))))
% 0.48/0.68 FOF formula (forall (X2:set_nat) (Y2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((ord_less_eq_set_nat Y2) X2)->(((eq set_nat) X2) Y2)))) of role axiom named fact_69_antisym
% 0.48/0.68 A new axiom: (forall (X2:set_nat) (Y2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((ord_less_eq_set_nat Y2) X2)->(((eq set_nat) X2) Y2))))
% 0.48/0.68 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) X2)->(((eq nat) X2) Y2)))) of role axiom named fact_70_antisym
% 0.48/0.68 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) X2)->(((eq nat) X2) Y2))))
% 0.48/0.68 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (X3:set_Pr1986765409at_nat) (Y3:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat X3) Y3)) ((ord_le841296385at_nat Y3) X3)))) of role axiom named fact_71_eq__iff
% 0.48/0.68 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (X3:set_Pr1986765409at_nat) (Y3:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat X3) Y3)) ((ord_le841296385at_nat Y3) X3))))
% 0.55/0.70 FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (X3:set_nat) (Y3:set_nat)=> ((and ((ord_less_eq_set_nat X3) Y3)) ((ord_less_eq_set_nat Y3) X3)))) of role axiom named fact_72_eq__iff
% 0.55/0.70 A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (X3:set_nat) (Y3:set_nat)=> ((and ((ord_less_eq_set_nat X3) Y3)) ((ord_less_eq_set_nat Y3) X3))))
% 0.55/0.70 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) ((ord_less_eq_nat Y3) X3)))) of role axiom named fact_73_eq__iff
% 0.55/0.70 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) ((ord_less_eq_nat Y3) X3))))
% 0.55/0.70 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->((((eq set_Pr1986765409at_nat) (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C))))) of role axiom named fact_74_ord__le__eq__subst
% 0.55/0.70 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->((((eq set_Pr1986765409at_nat) (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C)))))
% 0.55/0.70 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_nat)) (C:set_nat), (((ord_le841296385at_nat A2) B2)->((((eq set_nat) (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C))))) of role axiom named fact_75_ord__le__eq__subst
% 0.55/0.70 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_nat)) (C:set_nat), (((ord_le841296385at_nat A2) B2)->((((eq set_nat) (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C)))))
% 0.55/0.70 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->nat)) (C:nat), (((ord_le841296385at_nat A2) B2)->((((eq nat) (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C))))) of role axiom named fact_76_ord__le__eq__subst
% 0.55/0.70 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->nat)) (C:nat), (((ord_le841296385at_nat A2) B2)->((((eq nat) (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C)))))
% 0.55/0.70 FOF formula (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_set_nat A2) B2)->((((eq set_Pr1986765409at_nat) (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C))))) of role axiom named fact_77_ord__le__eq__subst
% 0.55/0.70 A new axiom: (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_set_nat A2) B2)->((((eq set_Pr1986765409at_nat) (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C)))))
% 0.55/0.70 FOF formula (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_nat)) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->((((eq set_nat) (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C))))) of role axiom named fact_78_ord__le__eq__subst
% 0.55/0.71 A new axiom: (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_nat)) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->((((eq set_nat) (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C)))))
% 0.55/0.71 FOF formula (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->nat)) (C:nat), (((ord_less_eq_set_nat A2) B2)->((((eq nat) (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C))))) of role axiom named fact_79_ord__le__eq__subst
% 0.55/0.71 A new axiom: (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->nat)) (C:nat), (((ord_less_eq_set_nat A2) B2)->((((eq nat) (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C)))))
% 0.55/0.71 FOF formula (forall (A2:nat) (B2:nat) (F:(nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_nat A2) B2)->((((eq set_Pr1986765409at_nat) (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C))))) of role axiom named fact_80_ord__le__eq__subst
% 0.55/0.71 A new axiom: (forall (A2:nat) (B2:nat) (F:(nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_nat A2) B2)->((((eq set_Pr1986765409at_nat) (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C)))))
% 0.55/0.71 FOF formula (forall (A2:nat) (B2:nat) (F:(nat->set_nat)) (C:set_nat), (((ord_less_eq_nat A2) B2)->((((eq set_nat) (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C))))) of role axiom named fact_81_ord__le__eq__subst
% 0.55/0.71 A new axiom: (forall (A2:nat) (B2:nat) (F:(nat->set_nat)) (C:set_nat), (((ord_less_eq_nat A2) B2)->((((eq set_nat) (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C)))))
% 0.55/0.71 FOF formula (forall (A2:nat) (B2:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A2) B2)->((((eq nat) (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C))))) of role axiom named fact_82_ord__le__eq__subst
% 0.55/0.71 A new axiom: (forall (A2:nat) (B2:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A2) B2)->((((eq nat) (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C)))))
% 0.55/0.71 FOF formula (forall (A2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C)))))) of role axiom named fact_83_ord__eq__le__subst
% 0.55/0.71 A new axiom: (forall (A2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C))))))
% 0.55/0.71 FOF formula (forall (A2:set_nat) (F:(set_Pr1986765409at_nat->set_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq set_nat) A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C)))))) of role axiom named fact_84_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:set_nat) (F:(set_Pr1986765409at_nat->set_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq set_nat) A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C))))))
% 0.55/0.73 FOF formula (forall (A2:nat) (F:(set_Pr1986765409at_nat->nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq nat) A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C)))))) of role axiom named fact_85_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:nat) (F:(set_Pr1986765409at_nat->nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), ((((eq nat) A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C))))))
% 0.55/0.73 FOF formula (forall (A2:set_Pr1986765409at_nat) (F:(set_nat->set_Pr1986765409at_nat)) (B2:set_nat) (C:set_nat), ((((eq set_Pr1986765409at_nat) A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C)))))) of role axiom named fact_86_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:set_Pr1986765409at_nat) (F:(set_nat->set_Pr1986765409at_nat)) (B2:set_nat) (C:set_nat), ((((eq set_Pr1986765409at_nat) A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C))))))
% 0.55/0.73 FOF formula (forall (A2:set_nat) (F:(set_nat->set_nat)) (B2:set_nat) (C:set_nat), ((((eq set_nat) A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C)))))) of role axiom named fact_87_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:set_nat) (F:(set_nat->set_nat)) (B2:set_nat) (C:set_nat), ((((eq set_nat) A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C))))))
% 0.55/0.73 FOF formula (forall (A2:nat) (F:(set_nat->nat)) (B2:set_nat) (C:set_nat), ((((eq nat) A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C)))))) of role axiom named fact_88_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:nat) (F:(set_nat->nat)) (B2:set_nat) (C:set_nat), ((((eq nat) A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C))))))
% 0.55/0.73 FOF formula (forall (A2:set_Pr1986765409at_nat) (F:(nat->set_Pr1986765409at_nat)) (B2:nat) (C:nat), ((((eq set_Pr1986765409at_nat) A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C)))))) of role axiom named fact_89_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:set_Pr1986765409at_nat) (F:(nat->set_Pr1986765409at_nat)) (B2:nat) (C:nat), ((((eq set_Pr1986765409at_nat) A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C))))))
% 0.55/0.73 FOF formula (forall (A2:set_nat) (F:(nat->set_nat)) (B2:nat) (C:nat), ((((eq set_nat) A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C)))))) of role axiom named fact_90_ord__eq__le__subst
% 0.55/0.73 A new axiom: (forall (A2:set_nat) (F:(nat->set_nat)) (B2:nat) (C:nat), ((((eq set_nat) A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C))))))
% 0.55/0.74 FOF formula (forall (A2:nat) (F:(nat->nat)) (B2:nat) (C:nat), ((((eq nat) A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C)))))) of role axiom named fact_91_ord__eq__le__subst
% 0.55/0.74 A new axiom: (forall (A2:nat) (F:(nat->nat)) (B2:nat) (C:nat), ((((eq nat) A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C))))))
% 0.55/0.74 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C))))) of role axiom named fact_92_order__subst2
% 0.55/0.74 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C)))))
% 0.55/0.74 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_nat)) (C:set_nat), (((ord_le841296385at_nat A2) B2)->(((ord_less_eq_set_nat (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C))))) of role axiom named fact_93_order__subst2
% 0.55/0.74 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_nat)) (C:set_nat), (((ord_le841296385at_nat A2) B2)->(((ord_less_eq_set_nat (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C)))))
% 0.55/0.74 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->nat)) (C:nat), (((ord_le841296385at_nat A2) B2)->(((ord_less_eq_nat (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C))))) of role axiom named fact_94_order__subst2
% 0.55/0.74 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->nat)) (C:nat), (((ord_le841296385at_nat A2) B2)->(((ord_less_eq_nat (F B2)) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C)))))
% 0.55/0.74 FOF formula (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_le841296385at_nat (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C))))) of role axiom named fact_95_order__subst2
% 0.55/0.74 A new axiom: (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_le841296385at_nat (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C)))))
% 0.55/0.74 FOF formula (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_nat)) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C))))) of role axiom named fact_96_order__subst2
% 0.61/0.76 A new axiom: (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->set_nat)) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C)))))
% 0.61/0.76 FOF formula (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->nat)) (C:nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_nat (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C))))) of role axiom named fact_97_order__subst2
% 0.61/0.76 A new axiom: (forall (A2:set_nat) (B2:set_nat) (F:(set_nat->nat)) (C:nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_nat (F B2)) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C)))))
% 0.61/0.76 FOF formula (forall (A2:nat) (B2:nat) (F:(nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_nat A2) B2)->(((ord_le841296385at_nat (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C))))) of role axiom named fact_98_order__subst2
% 0.61/0.76 A new axiom: (forall (A2:nat) (B2:nat) (F:(nat->set_Pr1986765409at_nat)) (C:set_Pr1986765409at_nat), (((ord_less_eq_nat A2) B2)->(((ord_le841296385at_nat (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat (F A2)) C)))))
% 0.61/0.76 FOF formula (forall (A2:nat) (B2:nat) (F:(nat->set_nat)) (C:set_nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_set_nat (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C))))) of role axiom named fact_99_order__subst2
% 0.61/0.76 A new axiom: (forall (A2:nat) (B2:nat) (F:(nat->set_nat)) (C:set_nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_set_nat (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C)))))
% 0.61/0.76 FOF formula (forall (A2:nat) (B2:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C))))) of role axiom named fact_100_order__subst2
% 0.61/0.76 A new axiom: (forall (A2:nat) (B2:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat (F B2)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C)))))
% 0.61/0.76 FOF formula (forall (A2:nat) (P2:(nat->Prop)), (((eq Prop) ((member_nat A2) (collect_nat P2))) (P2 A2))) of role axiom named fact_101_mem__Collect__eq
% 0.61/0.76 A new axiom: (forall (A2:nat) (P2:(nat->Prop)), (((eq Prop) ((member_nat A2) (collect_nat P2))) (P2 A2)))
% 0.61/0.76 FOF formula (forall (A2:product_prod_nat_nat) (P2:(product_prod_nat_nat->Prop)), (((eq Prop) ((member701585322at_nat A2) (collec7649004at_nat P2))) (P2 A2))) of role axiom named fact_102_mem__Collect__eq
% 0.61/0.76 A new axiom: (forall (A2:product_prod_nat_nat) (P2:(product_prod_nat_nat->Prop)), (((eq Prop) ((member701585322at_nat A2) (collec7649004at_nat P2))) (P2 A2)))
% 0.61/0.76 FOF formula (forall (A:set_nat), (((eq set_nat) (collect_nat (fun (X3:nat)=> ((member_nat X3) A)))) A)) of role axiom named fact_103_Collect__mem__eq
% 0.61/0.76 A new axiom: (forall (A:set_nat), (((eq set_nat) (collect_nat (fun (X3:nat)=> ((member_nat X3) A)))) A))
% 0.61/0.76 FOF formula (forall (A:set_Pr1986765409at_nat), (((eq set_Pr1986765409at_nat) (collec7649004at_nat (fun (X3:product_prod_nat_nat)=> ((member701585322at_nat X3) A)))) A)) of role axiom named fact_104_Collect__mem__eq
% 0.61/0.76 A new axiom: (forall (A:set_Pr1986765409at_nat), (((eq set_Pr1986765409at_nat) (collec7649004at_nat (fun (X3:product_prod_nat_nat)=> ((member701585322at_nat X3) A)))) A))
% 0.61/0.76 FOF formula (forall (A2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C)))))) of role axiom named fact_105_order__subst1
% 0.61/0.78 A new axiom: (forall (A2:set_Pr1986765409at_nat) (F:(set_Pr1986765409at_nat->set_Pr1986765409at_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C))))))
% 0.61/0.78 FOF formula (forall (A2:set_Pr1986765409at_nat) (F:(set_nat->set_Pr1986765409at_nat)) (B2:set_nat) (C:set_nat), (((ord_le841296385at_nat A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C)))))) of role axiom named fact_106_order__subst1
% 0.61/0.78 A new axiom: (forall (A2:set_Pr1986765409at_nat) (F:(set_nat->set_Pr1986765409at_nat)) (B2:set_nat) (C:set_nat), (((ord_le841296385at_nat A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C))))))
% 0.61/0.78 FOF formula (forall (A2:set_Pr1986765409at_nat) (F:(nat->set_Pr1986765409at_nat)) (B2:nat) (C:nat), (((ord_le841296385at_nat A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C)))))) of role axiom named fact_107_order__subst1
% 0.61/0.78 A new axiom: (forall (A2:set_Pr1986765409at_nat) (F:(nat->set_Pr1986765409at_nat)) (B2:nat) (C:nat), (((ord_le841296385at_nat A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le841296385at_nat (F X)) (F Y4))))->((ord_le841296385at_nat A2) (F C))))))
% 0.61/0.78 FOF formula (forall (A2:set_nat) (F:(set_Pr1986765409at_nat->set_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_less_eq_set_nat A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C)))))) of role axiom named fact_108_order__subst1
% 0.61/0.78 A new axiom: (forall (A2:set_nat) (F:(set_Pr1986765409at_nat->set_nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_less_eq_set_nat A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C))))))
% 0.61/0.78 FOF formula (forall (A2:set_nat) (F:(set_nat->set_nat)) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C)))))) of role axiom named fact_109_order__subst1
% 0.61/0.78 A new axiom: (forall (A2:set_nat) (F:(set_nat->set_nat)) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C))))))
% 0.61/0.78 FOF formula (forall (A2:set_nat) (F:(nat->set_nat)) (B2:nat) (C:nat), (((ord_less_eq_set_nat A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C)))))) of role axiom named fact_110_order__subst1
% 0.61/0.78 A new axiom: (forall (A2:set_nat) (F:(nat->set_nat)) (B2:nat) (C:nat), (((ord_less_eq_set_nat A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C))))))
% 0.61/0.78 FOF formula (forall (A2:nat) (F:(set_Pr1986765409at_nat->nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_less_eq_nat A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C)))))) of role axiom named fact_111_order__subst1
% 0.61/0.79 A new axiom: (forall (A2:nat) (F:(set_Pr1986765409at_nat->nat)) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_less_eq_nat A2) (F B2))->(((ord_le841296385at_nat B2) C)->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C))))))
% 0.61/0.79 FOF formula (forall (A2:nat) (F:(set_nat->nat)) (B2:set_nat) (C:set_nat), (((ord_less_eq_nat A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C)))))) of role axiom named fact_112_order__subst1
% 0.61/0.79 A new axiom: (forall (A2:nat) (F:(set_nat->nat)) (B2:set_nat) (C:set_nat), (((ord_less_eq_nat A2) (F B2))->(((ord_less_eq_set_nat B2) C)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C))))))
% 0.61/0.79 FOF formula (forall (A2:nat) (F:(nat->nat)) (B2:nat) (C:nat), (((ord_less_eq_nat A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C)))))) of role axiom named fact_113_order__subst1
% 0.61/0.79 A new axiom: (forall (A2:nat) (F:(nat->nat)) (B2:nat) (C:nat), (((ord_less_eq_nat A2) (F B2))->(((ord_less_eq_nat B2) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C))))))
% 0.61/0.79 FOF formula (forall (P2:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((eq Prop) ((ord_le841296385at_nat (collec7649004at_nat P2)) (collec7649004at_nat Q))) (forall (X3:product_prod_nat_nat), ((P2 X3)->(Q X3))))) of role axiom named fact_114_Collect__mono__iff
% 0.61/0.79 A new axiom: (forall (P2:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((eq Prop) ((ord_le841296385at_nat (collec7649004at_nat P2)) (collec7649004at_nat Q))) (forall (X3:product_prod_nat_nat), ((P2 X3)->(Q X3)))))
% 0.61/0.79 FOF formula (forall (P2:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) ((ord_less_eq_set_nat (collect_nat P2)) (collect_nat Q))) (forall (X3:nat), ((P2 X3)->(Q X3))))) of role axiom named fact_115_Collect__mono__iff
% 0.61/0.79 A new axiom: (forall (P2:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) ((ord_less_eq_set_nat (collect_nat P2)) (collect_nat Q))) (forall (X3:nat), ((P2 X3)->(Q X3)))))
% 0.61/0.79 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (A5:set_Pr1986765409at_nat) (B5:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat A5) B5)) ((ord_le841296385at_nat B5) A5)))) of role axiom named fact_116_set__eq__subset
% 0.61/0.79 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) (fun (Y:set_Pr1986765409at_nat) (Z:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) Y) Z))) (fun (A5:set_Pr1986765409at_nat) (B5:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat A5) B5)) ((ord_le841296385at_nat B5) A5))))
% 0.61/0.79 FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A5:set_nat) (B5:set_nat)=> ((and ((ord_less_eq_set_nat A5) B5)) ((ord_less_eq_set_nat B5) A5)))) of role axiom named fact_117_set__eq__subset
% 0.61/0.79 A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A5:set_nat) (B5:set_nat)=> ((and ((ord_less_eq_set_nat A5) B5)) ((ord_less_eq_set_nat B5) A5))))
% 0.61/0.79 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (C2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->(((ord_le841296385at_nat B) C2)->((ord_le841296385at_nat A) C2)))) of role axiom named fact_118_subset__trans
% 0.61/0.79 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (C2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->(((ord_le841296385at_nat B) C2)->((ord_le841296385at_nat A) C2))))
% 0.61/0.80 FOF formula (forall (A:set_nat) (B:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) C2)->((ord_less_eq_set_nat A) C2)))) of role axiom named fact_119_subset__trans
% 0.61/0.80 A new axiom: (forall (A:set_nat) (B:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) C2)->((ord_less_eq_set_nat A) C2))))
% 0.61/0.80 FOF formula (forall (P2:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), ((forall (X:product_prod_nat_nat), ((P2 X)->(Q X)))->((ord_le841296385at_nat (collec7649004at_nat P2)) (collec7649004at_nat Q)))) of role axiom named fact_120_Collect__mono
% 0.61/0.80 A new axiom: (forall (P2:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), ((forall (X:product_prod_nat_nat), ((P2 X)->(Q X)))->((ord_le841296385at_nat (collec7649004at_nat P2)) (collec7649004at_nat Q))))
% 0.61/0.80 FOF formula (forall (P2:(nat->Prop)) (Q:(nat->Prop)), ((forall (X:nat), ((P2 X)->(Q X)))->((ord_less_eq_set_nat (collect_nat P2)) (collect_nat Q)))) of role axiom named fact_121_Collect__mono
% 0.61/0.80 A new axiom: (forall (P2:(nat->Prop)) (Q:(nat->Prop)), ((forall (X:nat), ((P2 X)->(Q X)))->((ord_less_eq_set_nat (collect_nat P2)) (collect_nat Q))))
% 0.61/0.80 FOF formula (forall (A:set_Pr1986765409at_nat), ((ord_le841296385at_nat A) A)) of role axiom named fact_122_subset__refl
% 0.61/0.80 A new axiom: (forall (A:set_Pr1986765409at_nat), ((ord_le841296385at_nat A) A))
% 0.61/0.80 FOF formula (forall (A:set_nat), ((ord_less_eq_set_nat A) A)) of role axiom named fact_123_subset__refl
% 0.61/0.80 A new axiom: (forall (A:set_nat), ((ord_less_eq_set_nat A) A))
% 0.61/0.80 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A5:set_Pr1986765409at_nat) (B5:set_Pr1986765409at_nat)=> (forall (T2:product_prod_nat_nat), (((member701585322at_nat T2) A5)->((member701585322at_nat T2) B5))))) of role axiom named fact_124_subset__iff
% 0.61/0.80 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A5:set_Pr1986765409at_nat) (B5:set_Pr1986765409at_nat)=> (forall (T2:product_prod_nat_nat), (((member701585322at_nat T2) A5)->((member701585322at_nat T2) B5)))))
% 0.61/0.80 FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B5:set_nat)=> (forall (T2:nat), (((member_nat T2) A5)->((member_nat T2) B5))))) of role axiom named fact_125_subset__iff
% 0.61/0.80 A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B5:set_nat)=> (forall (T2:nat), (((member_nat T2) A5)->((member_nat T2) B5)))))
% 0.61/0.80 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A) B)->((ord_le841296385at_nat B) A))) of role axiom named fact_126_equalityD2
% 0.61/0.80 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A) B)->((ord_le841296385at_nat B) A)))
% 0.61/0.80 FOF formula (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat B) A))) of role axiom named fact_127_equalityD2
% 0.61/0.80 A new axiom: (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat B) A)))
% 0.61/0.80 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A) B)->((ord_le841296385at_nat A) B))) of role axiom named fact_128_equalityD1
% 0.61/0.80 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A) B)->((ord_le841296385at_nat A) B)))
% 0.61/0.80 FOF formula (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat A) B))) of role axiom named fact_129_equalityD1
% 0.61/0.80 A new axiom: (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat A) B)))
% 0.61/0.80 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A5:set_Pr1986765409at_nat) (B5:set_Pr1986765409at_nat)=> (forall (X3:product_prod_nat_nat), (((member701585322at_nat X3) A5)->((member701585322at_nat X3) B5))))) of role axiom named fact_130_subset__eq
% 0.61/0.80 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A5:set_Pr1986765409at_nat) (B5:set_Pr1986765409at_nat)=> (forall (X3:product_prod_nat_nat), (((member701585322at_nat X3) A5)->((member701585322at_nat X3) B5)))))
% 0.61/0.81 FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B5:set_nat)=> (forall (X3:nat), (((member_nat X3) A5)->((member_nat X3) B5))))) of role axiom named fact_131_subset__eq
% 0.61/0.81 A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B5:set_nat)=> (forall (X3:nat), (((member_nat X3) A5)->((member_nat X3) B5)))))
% 0.61/0.81 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A) B)->((((ord_le841296385at_nat A) B)->(((ord_le841296385at_nat B) A)->False))->False))) of role axiom named fact_132_equalityE
% 0.61/0.81 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A) B)->((((ord_le841296385at_nat A) B)->(((ord_le841296385at_nat B) A)->False))->False)))
% 0.61/0.81 FOF formula (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->False))->False))) of role axiom named fact_133_equalityE
% 0.61/0.81 A new axiom: (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->False))->False)))
% 0.61/0.81 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (C:product_prod_nat_nat), (((ord_le841296385at_nat A) B)->(((member701585322at_nat C) A)->((member701585322at_nat C) B)))) of role axiom named fact_134_subsetD
% 0.61/0.81 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (C:product_prod_nat_nat), (((ord_le841296385at_nat A) B)->(((member701585322at_nat C) A)->((member701585322at_nat C) B))))
% 0.61/0.81 FOF formula (forall (A:set_nat) (B:set_nat) (C:nat), (((ord_less_eq_set_nat A) B)->(((member_nat C) A)->((member_nat C) B)))) of role axiom named fact_135_subsetD
% 0.61/0.81 A new axiom: (forall (A:set_nat) (B:set_nat) (C:nat), (((ord_less_eq_set_nat A) B)->(((member_nat C) A)->((member_nat C) B))))
% 0.61/0.81 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (X2:product_prod_nat_nat), (((ord_le841296385at_nat A) B)->(((member701585322at_nat X2) A)->((member701585322at_nat X2) B)))) of role axiom named fact_136_in__mono
% 0.61/0.81 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (X2:product_prod_nat_nat), (((ord_le841296385at_nat A) B)->(((member701585322at_nat X2) A)->((member701585322at_nat X2) B))))
% 0.61/0.81 FOF formula (forall (A:set_nat) (B:set_nat) (X2:nat), (((ord_less_eq_set_nat A) B)->(((member_nat X2) A)->((member_nat X2) B)))) of role axiom named fact_137_in__mono
% 0.61/0.81 A new axiom: (forall (A:set_nat) (B:set_nat) (X2:nat), (((ord_less_eq_set_nat A) B)->(((member_nat X2) A)->((member_nat X2) B))))
% 0.61/0.81 FOF formula (forall (S:nat), (((member_nat S) (v_a c))->((ord_less_eq_set_nat ((reachableNodes_a c) S)) (v_a c)))) of role axiom named fact_138_reachable__ss__V
% 0.61/0.81 A new axiom: (forall (S:nat), (((member_nat S) (v_a c))->((ord_less_eq_set_nat ((reachableNodes_a c) S)) (v_a c))))
% 0.61/0.81 FOF formula (forall (P:list_P559422087at_nat) (C3:(product_prod_nat_nat->a)) (U2:nat) (V:nat), (((ord_le841296385at_nat ((inf_in586391887at_nat (set_Pr2131844118at_nat P)) (e_a c))) (e_a C3))->(((((isPath_a c) U2) P) V)->((((isPath_a C3) U2) P) V)))) of role axiom named fact_139_transfer__path
% 0.61/0.81 A new axiom: (forall (P:list_P559422087at_nat) (C3:(product_prod_nat_nat->a)) (U2:nat) (V:nat), (((ord_le841296385at_nat ((inf_in586391887at_nat (set_Pr2131844118at_nat P)) (e_a c))) (e_a C3))->(((((isPath_a c) U2) P) V)->((((isPath_a C3) U2) P) V))))
% 0.61/0.81 FOF formula ((ord_less_eq_nat (finite447719721at_nat (((edmond475474835dges_a c) s) t))) (finite447719721at_nat (edmond771116670s_uE_a c))) of role axiom named fact_140_card__spEdges__le
% 0.61/0.81 A new axiom: ((ord_less_eq_nat (finite447719721at_nat (((edmond475474835dges_a c) s) t))) (finite447719721at_nat (edmond771116670s_uE_a c)))
% 0.61/0.81 FOF formula ((finite772653738at_nat (e_a c))->(finite_Graph_a c)) of role axiom named fact_141_Finite__Graph__EI
% 0.61/0.82 A new axiom: ((finite772653738at_nat (e_a c))->(finite_Graph_a c))
% 0.61/0.82 FOF formula (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((ord_le841296385at_nat ((incoming_a2 C) U)) (e_a C))) of role axiom named fact_142_Graph_Oincoming_H__edges
% 0.61/0.82 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((ord_le841296385at_nat ((incoming_a2 C) U)) (e_a C)))
% 0.61/0.82 FOF formula (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((ord_le841296385at_nat ((outgoing_a2 C) U)) (e_a C))) of role axiom named fact_143_Graph_Ooutgoing_H__edges
% 0.61/0.82 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((ord_le841296385at_nat ((outgoing_a2 C) U)) (e_a C)))
% 0.61/0.82 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((ord_le841296385at_nat ((incoming_a C) U2)) (e_a C))) of role axiom named fact_144_Graph_Oincoming__edges
% 0.61/0.82 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((ord_le841296385at_nat ((incoming_a C) U2)) (e_a C)))
% 0.61/0.82 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((ord_le841296385at_nat ((outgoing_a C) U2)) (e_a C))) of role axiom named fact_145_Graph_Ooutgoing__edges
% 0.61/0.82 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((ord_le841296385at_nat ((outgoing_a C) U2)) (e_a C)))
% 0.61/0.82 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat) (E:product_prod_nat_nat), (((((isPath_a C) U2) P) V)->(((member701585322at_nat E) (set_Pr2131844118at_nat P))->((member701585322at_nat E) (e_a C))))) of role axiom named fact_146_Graph_OisPath__edgeset
% 0.61/0.82 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat) (E:product_prod_nat_nat), (((((isPath_a C) U2) P) V)->(((member701585322at_nat E) (set_Pr2131844118at_nat P))->((member701585322at_nat E) (e_a C)))))
% 0.61/0.82 FOF formula (forall (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a c) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) V1) V))->((ex nat) (fun (V2:nat)=> ((member701585322at_nat ((product_Pair_nat_nat V1) V2)) (set_Pr2131844118at_nat P)))))))) of role axiom named fact_147_isPath__ex__edge2
% 0.61/0.82 A new axiom: (forall (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a c) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) V1) V))->((ex nat) (fun (V2:nat)=> ((member701585322at_nat ((product_Pair_nat_nat V1) V2)) (set_Pr2131844118at_nat P))))))))
% 0.61/0.82 FOF formula (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) A)->(((member_nat C) B)->((member_nat C) ((inf_inf_set_nat A) B))))) of role axiom named fact_148_IntI
% 0.61/0.82 A new axiom: (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) A)->(((member_nat C) B)->((member_nat C) ((inf_inf_set_nat A) B)))))
% 0.61/0.82 FOF formula (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) A)->(((member701585322at_nat C) B)->((member701585322at_nat C) ((inf_in586391887at_nat A) B))))) of role axiom named fact_149_IntI
% 0.61/0.82 A new axiom: (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) A)->(((member701585322at_nat C) B)->((member701585322at_nat C) ((inf_in586391887at_nat A) B)))))
% 0.61/0.82 FOF formula (forall (C:nat) (A:set_nat) (B:set_nat), (((eq Prop) ((member_nat C) ((inf_inf_set_nat A) B))) ((and ((member_nat C) A)) ((member_nat C) B)))) of role axiom named fact_150_Int__iff
% 0.61/0.82 A new axiom: (forall (C:nat) (A:set_nat) (B:set_nat), (((eq Prop) ((member_nat C) ((inf_inf_set_nat A) B))) ((and ((member_nat C) A)) ((member_nat C) B))))
% 0.61/0.82 FOF formula (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((eq Prop) ((member701585322at_nat C) ((inf_in586391887at_nat A) B))) ((and ((member701585322at_nat C) A)) ((member701585322at_nat C) B)))) of role axiom named fact_151_Int__iff
% 0.61/0.82 A new axiom: (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((eq Prop) ((member701585322at_nat C) ((inf_in586391887at_nat A) B))) ((and ((member701585322at_nat C) A)) ((member701585322at_nat C) B))))
% 0.61/0.83 FOF formula (forall (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a c) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) U1) U2))->((ex nat) (fun (U22:nat)=> ((member701585322at_nat ((product_Pair_nat_nat U22) U1)) (set_Pr2131844118at_nat P)))))))) of role axiom named fact_152_isPath__ex__edge1
% 0.61/0.83 A new axiom: (forall (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a c) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) U1) U2))->((ex nat) (fun (U22:nat)=> ((member701585322at_nat ((product_Pair_nat_nat U22) U1)) (set_Pr2131844118at_nat P))))))))
% 0.61/0.83 FOF formula (forall (U2:nat) (S:nat) (V:nat), (((member_nat U2) ((reachableNodes_a c) S))->(((member701585322at_nat ((product_Pair_nat_nat U2) V)) (e_a c))->((member_nat V) ((reachableNodes_a c) S))))) of role axiom named fact_153_reachableNodes__append__edge
% 0.61/0.83 A new axiom: (forall (U2:nat) (S:nat) (V:nat), (((member_nat U2) ((reachableNodes_a c) S))->(((member701585322at_nat ((product_Pair_nat_nat U2) V)) (e_a c))->((member_nat V) ((reachableNodes_a c) S)))))
% 0.61/0.83 FOF formula (forall (C2:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat C2) ((inf_in586391887at_nat A) B))) ((and ((ord_le841296385at_nat C2) A)) ((ord_le841296385at_nat C2) B)))) of role axiom named fact_154_Int__subset__iff
% 0.61/0.83 A new axiom: (forall (C2:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat C2) ((inf_in586391887at_nat A) B))) ((and ((ord_le841296385at_nat C2) A)) ((ord_le841296385at_nat C2) B))))
% 0.61/0.83 FOF formula (forall (C2:set_nat) (A:set_nat) (B:set_nat), (((eq Prop) ((ord_less_eq_set_nat C2) ((inf_inf_set_nat A) B))) ((and ((ord_less_eq_set_nat C2) A)) ((ord_less_eq_set_nat C2) B)))) of role axiom named fact_155_Int__subset__iff
% 0.61/0.83 A new axiom: (forall (C2:set_nat) (A:set_nat) (B:set_nat), (((eq Prop) ((ord_less_eq_set_nat C2) ((inf_inf_set_nat A) B))) ((and ((ord_less_eq_set_nat C2) A)) ((ord_less_eq_set_nat C2) B))))
% 0.61/0.83 FOF formula (finite772653738at_nat (e_a c)) of role axiom named fact_156_finite__E
% 0.61/0.83 A new axiom: (finite772653738at_nat (e_a c))
% 0.61/0.83 FOF formula (finite772653738at_nat (edmond771116670s_uE_a c)) of role axiom named fact_157_finite__uE
% 0.61/0.83 A new axiom: (finite772653738at_nat (edmond771116670s_uE_a c))
% 0.61/0.83 FOF formula (finite772653738at_nat (((edmond475474835dges_a c) s) t)) of role axiom named fact_158_finite__spEdges
% 0.61/0.83 A new axiom: (finite772653738at_nat (((edmond475474835dges_a c) s) t))
% 0.61/0.83 FOF formula (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) ((inf_inf_set_nat A) B))->((((member_nat C) A)->(((member_nat C) B)->False))->False))) of role axiom named fact_159_IntE
% 0.61/0.83 A new axiom: (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) ((inf_inf_set_nat A) B))->((((member_nat C) A)->(((member_nat C) B)->False))->False)))
% 0.61/0.83 FOF formula (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) ((inf_in586391887at_nat A) B))->((((member701585322at_nat C) A)->(((member701585322at_nat C) B)->False))->False))) of role axiom named fact_160_IntE
% 0.61/0.83 A new axiom: (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) ((inf_in586391887at_nat A) B))->((((member701585322at_nat C) A)->(((member701585322at_nat C) B)->False))->False)))
% 0.61/0.83 FOF formula (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) ((inf_inf_set_nat A) B))->((member_nat C) A))) of role axiom named fact_161_IntD1
% 0.61/0.83 A new axiom: (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) ((inf_inf_set_nat A) B))->((member_nat C) A)))
% 0.61/0.83 FOF formula (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) ((inf_in586391887at_nat A) B))->((member701585322at_nat C) A))) of role axiom named fact_162_IntD1
% 0.61/0.83 A new axiom: (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) ((inf_in586391887at_nat A) B))->((member701585322at_nat C) A)))
% 0.61/0.84 FOF formula (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) ((inf_inf_set_nat A) B))->((member_nat C) B))) of role axiom named fact_163_IntD2
% 0.61/0.84 A new axiom: (forall (C:nat) (A:set_nat) (B:set_nat), (((member_nat C) ((inf_inf_set_nat A) B))->((member_nat C) B)))
% 0.61/0.84 FOF formula (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) ((inf_in586391887at_nat A) B))->((member701585322at_nat C) B))) of role axiom named fact_164_IntD2
% 0.61/0.84 A new axiom: (forall (C:product_prod_nat_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((member701585322at_nat C) ((inf_in586391887at_nat A) B))->((member701585322at_nat C) B)))
% 0.61/0.84 FOF formula (forall (U2:nat) (C:(product_prod_nat_nat->a)) (S:nat) (V:nat), (((member_nat U2) ((reachableNodes_a C) S))->(((member701585322at_nat ((product_Pair_nat_nat U2) V)) (e_a C))->((member_nat V) ((reachableNodes_a C) S))))) of role axiom named fact_165_Graph_OreachableNodes__append__edge
% 0.61/0.84 A new axiom: (forall (U2:nat) (C:(product_prod_nat_nat->a)) (S:nat) (V:nat), (((member_nat U2) ((reachableNodes_a C) S))->(((member701585322at_nat ((product_Pair_nat_nat U2) V)) (e_a C))->((member_nat V) ((reachableNodes_a C) S)))))
% 0.61/0.84 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->set_nat))) reachableNodes_a) reachableNodes_a) of role axiom named fact_166_Graph_OreachableNodes_Ocong
% 0.61/0.84 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->set_nat))) reachableNodes_a) reachableNodes_a)
% 0.61/0.84 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->set_nat))) adjacent_nodes_a) adjacent_nodes_a) of role axiom named fact_167_Graph_Oadjacent__nodes_Ocong
% 0.61/0.84 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->set_nat))) adjacent_nodes_a) adjacent_nodes_a)
% 0.61/0.84 FOF formula (forall (S:nat) (C:(product_prod_nat_nat->a)), (((member_nat S) (v_a C))->((ord_less_eq_set_nat ((reachableNodes_a C) S)) (v_a C)))) of role axiom named fact_168_Graph_Oreachable__ss__V
% 0.61/0.84 A new axiom: (forall (S:nat) (C:(product_prod_nat_nat->a)), (((member_nat S) (v_a C))->((ord_less_eq_set_nat ((reachableNodes_a C) S)) (v_a C))))
% 0.61/0.84 FOF formula (forall (A:set_Pr1986765409at_nat) (C2:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (D:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) C2)->(((ord_le841296385at_nat B) D)->((ord_le841296385at_nat ((inf_in586391887at_nat A) B)) ((inf_in586391887at_nat C2) D))))) of role axiom named fact_169_Int__mono
% 0.61/0.84 A new axiom: (forall (A:set_Pr1986765409at_nat) (C2:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (D:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) C2)->(((ord_le841296385at_nat B) D)->((ord_le841296385at_nat ((inf_in586391887at_nat A) B)) ((inf_in586391887at_nat C2) D)))))
% 0.61/0.84 FOF formula (forall (A:set_nat) (C2:set_nat) (B:set_nat) (D:set_nat), (((ord_less_eq_set_nat A) C2)->(((ord_less_eq_set_nat B) D)->((ord_less_eq_set_nat ((inf_inf_set_nat A) B)) ((inf_inf_set_nat C2) D))))) of role axiom named fact_170_Int__mono
% 0.61/0.84 A new axiom: (forall (A:set_nat) (C2:set_nat) (B:set_nat) (D:set_nat), (((ord_less_eq_set_nat A) C2)->(((ord_less_eq_set_nat B) D)->((ord_less_eq_set_nat ((inf_inf_set_nat A) B)) ((inf_inf_set_nat C2) D)))))
% 0.61/0.84 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A) B)) A)) of role axiom named fact_171_Int__lower1
% 0.61/0.84 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A) B)) A))
% 0.61/0.84 FOF formula (forall (A:set_nat) (B:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A) B)) A)) of role axiom named fact_172_Int__lower1
% 0.61/0.84 A new axiom: (forall (A:set_nat) (B:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A) B)) A))
% 0.61/0.84 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A) B)) B)) of role axiom named fact_173_Int__lower2
% 0.61/0.84 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A) B)) B))
% 0.61/0.85 FOF formula (forall (A:set_nat) (B:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A) B)) B)) of role axiom named fact_174_Int__lower2
% 0.61/0.85 A new axiom: (forall (A:set_nat) (B:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A) B)) B))
% 0.61/0.85 FOF formula (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), (((ord_le841296385at_nat B) A)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A) B)) B))) of role axiom named fact_175_Int__absorb1
% 0.61/0.85 A new axiom: (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), (((ord_le841296385at_nat B) A)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A) B)) B)))
% 0.61/0.85 FOF formula (forall (B:set_nat) (A:set_nat), (((ord_less_eq_set_nat B) A)->(((eq set_nat) ((inf_inf_set_nat A) B)) B))) of role axiom named fact_176_Int__absorb1
% 0.61/0.85 A new axiom: (forall (B:set_nat) (A:set_nat), (((ord_less_eq_set_nat B) A)->(((eq set_nat) ((inf_inf_set_nat A) B)) B)))
% 0.61/0.85 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A) B)) A))) of role axiom named fact_177_Int__absorb2
% 0.61/0.85 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A) B)) A)))
% 0.61/0.85 FOF formula (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->(((eq set_nat) ((inf_inf_set_nat A) B)) A))) of role axiom named fact_178_Int__absorb2
% 0.61/0.85 A new axiom: (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->(((eq set_nat) ((inf_inf_set_nat A) B)) A)))
% 0.61/0.85 FOF formula (forall (C2:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat C2) A)->(((ord_le841296385at_nat C2) B)->((ord_le841296385at_nat C2) ((inf_in586391887at_nat A) B))))) of role axiom named fact_179_Int__greatest
% 0.61/0.85 A new axiom: (forall (C2:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat C2) A)->(((ord_le841296385at_nat C2) B)->((ord_le841296385at_nat C2) ((inf_in586391887at_nat A) B)))))
% 0.61/0.85 FOF formula (forall (C2:set_nat) (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat C2) A)->(((ord_less_eq_set_nat C2) B)->((ord_less_eq_set_nat C2) ((inf_inf_set_nat A) B))))) of role axiom named fact_180_Int__greatest
% 0.61/0.85 A new axiom: (forall (C2:set_nat) (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat C2) A)->(((ord_less_eq_set_nat C2) B)->((ord_less_eq_set_nat C2) ((inf_inf_set_nat A) B)))))
% 0.61/0.85 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (P2:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((ord_le841296385at_nat A) B)->((forall (X:product_prod_nat_nat), (((member701585322at_nat X) A)->((P2 X)->(Q X))))->((ord_le841296385at_nat ((inf_in586391887at_nat A) (collec7649004at_nat P2))) ((inf_in586391887at_nat B) (collec7649004at_nat Q)))))) of role axiom named fact_181_Int__Collect__mono
% 0.61/0.85 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat) (P2:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((ord_le841296385at_nat A) B)->((forall (X:product_prod_nat_nat), (((member701585322at_nat X) A)->((P2 X)->(Q X))))->((ord_le841296385at_nat ((inf_in586391887at_nat A) (collec7649004at_nat P2))) ((inf_in586391887at_nat B) (collec7649004at_nat Q))))))
% 0.61/0.85 FOF formula (forall (A:set_nat) (B:set_nat) (P2:(nat->Prop)) (Q:(nat->Prop)), (((ord_less_eq_set_nat A) B)->((forall (X:nat), (((member_nat X) A)->((P2 X)->(Q X))))->((ord_less_eq_set_nat ((inf_inf_set_nat A) (collect_nat P2))) ((inf_inf_set_nat B) (collect_nat Q)))))) of role axiom named fact_182_Int__Collect__mono
% 0.61/0.85 A new axiom: (forall (A:set_nat) (B:set_nat) (P2:(nat->Prop)) (Q:(nat->Prop)), (((ord_less_eq_set_nat A) B)->((forall (X:nat), (((member_nat X) A)->((P2 X)->(Q X))))->((ord_less_eq_set_nat ((inf_inf_set_nat A) (collect_nat P2))) ((inf_inf_set_nat B) (collect_nat Q))))))
% 0.61/0.85 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((ord_less_eq_set_nat ((adjacent_nodes_a C) U2)) (v_a C))) of role axiom named fact_183_Graph_Oadjacent__nodes__ss__V
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((ord_less_eq_set_nat ((adjacent_nodes_a C) U2)) (v_a C)))
% 0.71/0.86 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a C) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) V1) V))->((ex nat) (fun (V2:nat)=> ((member701585322at_nat ((product_Pair_nat_nat V1) V2)) (set_Pr2131844118at_nat P)))))))) of role axiom named fact_184_Graph_OisPath__ex__edge2
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a C) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) V1) V))->((ex nat) (fun (V2:nat)=> ((member701585322at_nat ((product_Pair_nat_nat V1) V2)) (set_Pr2131844118at_nat P))))))))
% 0.71/0.86 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a C) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) U1) U2))->((ex nat) (fun (U22:nat)=> ((member701585322at_nat ((product_Pair_nat_nat U22) U1)) (set_Pr2131844118at_nat P)))))))) of role axiom named fact_185_Graph_OisPath__ex__edge1
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat) (U1:nat) (V1:nat), (((((isPath_a C) U2) P) V)->(((member701585322at_nat ((product_Pair_nat_nat U1) V1)) (set_Pr2131844118at_nat P))->((not (((eq nat) U1) U2))->((ex nat) (fun (U22:nat)=> ((member701585322at_nat ((product_Pair_nat_nat U22) U1)) (set_Pr2131844118at_nat P))))))))
% 0.71/0.86 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite772653738at_nat (e_a C))->(finite_Graph_a C))) of role axiom named fact_186_Graph_OFinite__Graph__EI
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite772653738at_nat (e_a C))->(finite_Graph_a C)))
% 0.71/0.86 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite_Graph_a C)->(finite772653738at_nat (e_a C)))) of role axiom named fact_187_Finite__Graph_Ofinite__E
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite_Graph_a C)->(finite772653738at_nat (e_a C))))
% 0.71/0.86 FOF formula (forall (C:(product_prod_nat_nat->a)) (S:nat) (T:nat), ((edmond1517640972ysis_a C)->(finite772653738at_nat (((edmond475474835dges_a C) S) T)))) of role axiom named fact_188_ek__analysis_Ofinite__spEdges
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)) (S:nat) (T:nat), ((edmond1517640972ysis_a C)->(finite772653738at_nat (((edmond475474835dges_a C) S) T))))
% 0.71/0.86 FOF formula (forall (C:(product_prod_nat_nat->a)), ((edmond1517640972ysis_a C)->(finite772653738at_nat (edmond771116670s_uE_a C)))) of role axiom named fact_189_ek__analysis_Ofinite__uE
% 0.71/0.86 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((edmond1517640972ysis_a C)->(finite772653738at_nat (edmond771116670s_uE_a C))))
% 0.71/0.86 FOF formula (forall (P:list_P559422087at_nat) (C:(product_prod_nat_nat->a)) (C3:(product_prod_nat_nat->a)) (U2:nat) (V:nat), (((ord_le841296385at_nat ((inf_in586391887at_nat (set_Pr2131844118at_nat P)) (e_a C))) (e_a C3))->(((((isPath_a C) U2) P) V)->((((isPath_a C3) U2) P) V)))) of role axiom named fact_190_Graph_Otransfer__path
% 0.71/0.86 A new axiom: (forall (P:list_P559422087at_nat) (C:(product_prod_nat_nat->a)) (C3:(product_prod_nat_nat->a)) (U2:nat) (V:nat), (((ord_le841296385at_nat ((inf_in586391887at_nat (set_Pr2131844118at_nat P)) (e_a C))) (e_a C3))->(((((isPath_a C) U2) P) V)->((((isPath_a C3) U2) P) V))))
% 0.71/0.86 FOF formula (((eq ((product_prod_nat_nat->a)->set_Pr1986765409at_nat)) e_a) e_a) of role axiom named fact_191_Graph_OE_Ocong
% 0.71/0.86 A new axiom: (((eq ((product_prod_nat_nat->a)->set_Pr1986765409at_nat)) e_a) e_a)
% 0.71/0.86 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->(list_P559422087at_nat->(nat->Prop))))) isPath_a) isPath_a) of role axiom named fact_192_Graph_OisPath_Ocong
% 0.71/0.86 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->(list_P559422087at_nat->(nat->Prop))))) isPath_a) isPath_a)
% 0.71/0.87 FOF formula (((eq ((product_prod_nat_nat->a)->set_nat)) v_a) v_a) of role axiom named fact_193_Graph_OV_Ocong
% 0.71/0.87 A new axiom: (((eq ((product_prod_nat_nat->a)->set_nat)) v_a) v_a)
% 0.71/0.87 FOF formula (forall (C:(product_prod_nat_nat->a)) (S:nat) (T:nat), ((edmond1517640972ysis_a C)->((ord_less_eq_nat (finite447719721at_nat (((edmond475474835dges_a C) S) T))) (finite447719721at_nat (edmond771116670s_uE_a C))))) of role axiom named fact_194_ek__analysis_Ocard__spEdges__le
% 0.71/0.87 A new axiom: (forall (C:(product_prod_nat_nat->a)) (S:nat) (T:nat), ((edmond1517640972ysis_a C)->((ord_less_eq_nat (finite447719721at_nat (((edmond475474835dges_a C) S) T))) (finite447719721at_nat (edmond771116670s_uE_a C)))))
% 0.71/0.87 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->(list_P559422087at_nat->(nat->Prop))))) isShortestPath_a) isShortestPath_a) of role axiom named fact_195_Graph_OisShortestPath_Ocong
% 0.71/0.87 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->(list_P559422087at_nat->(nat->Prop))))) isShortestPath_a) isShortestPath_a)
% 0.71/0.87 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->set_Pr1986765409at_nat))) outgoing_a) outgoing_a) of role axiom named fact_196_Graph_Ooutgoing_Ocong
% 0.71/0.87 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->set_Pr1986765409at_nat))) outgoing_a) outgoing_a)
% 0.71/0.87 FOF formula (((eq ((product_prod_nat_nat->a)->(nat->set_Pr1986765409at_nat))) incoming_a) incoming_a) of role axiom named fact_197_Graph_Oincoming_Ocong
% 0.71/0.87 A new axiom: (((eq ((product_prod_nat_nat->a)->(nat->set_Pr1986765409at_nat))) incoming_a) incoming_a)
% 0.71/0.87 FOF formula (((eq ((product_prod_nat_nat->a)->(set_nat->set_Pr1986765409at_nat))) outgoing_a2) outgoing_a2) of role axiom named fact_198_Graph_Ooutgoing_H_Ocong
% 0.71/0.87 A new axiom: (((eq ((product_prod_nat_nat->a)->(set_nat->set_Pr1986765409at_nat))) outgoing_a2) outgoing_a2)
% 0.71/0.87 FOF formula (((eq ((product_prod_nat_nat->a)->(set_nat->set_Pr1986765409at_nat))) incoming_a2) incoming_a2) of role axiom named fact_199_Graph_Oincoming_H_Ocong
% 0.71/0.87 A new axiom: (((eq ((product_prod_nat_nat->a)->(set_nat->set_Pr1986765409at_nat))) incoming_a2) incoming_a2)
% 0.71/0.87 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat), (((((isShortestPath_a C) U2) P) V)->((((isPath_a C) U2) P) V))) of role axiom named fact_200_Graph_OshortestPath__is__path
% 0.71/0.87 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat) (P:list_P559422087at_nat) (V:nat), (((((isShortestPath_a C) U2) P) V)->((((isPath_a C) U2) P) V)))
% 0.71/0.87 FOF formula (forall (F2:set_Pr1986765409at_nat) (G:set_Pr1986765409at_nat), (((or (finite772653738at_nat F2)) (finite772653738at_nat G))->(finite772653738at_nat ((inf_in586391887at_nat F2) G)))) of role axiom named fact_201_finite__Int
% 0.71/0.87 A new axiom: (forall (F2:set_Pr1986765409at_nat) (G:set_Pr1986765409at_nat), (((or (finite772653738at_nat F2)) (finite772653738at_nat G))->(finite772653738at_nat ((inf_in586391887at_nat F2) G))))
% 0.71/0.87 FOF formula (forall (F2:set_nat) (G:set_nat), (((or (finite_finite_nat F2)) (finite_finite_nat G))->(finite_finite_nat ((inf_inf_set_nat F2) G)))) of role axiom named fact_202_finite__Int
% 0.71/0.87 A new axiom: (forall (F2:set_nat) (G:set_nat), (((or (finite_finite_nat F2)) (finite_finite_nat G))->(finite_finite_nat ((inf_inf_set_nat F2) G))))
% 0.71/0.87 FOF formula (forall (Xs:list_P559422087at_nat), (finite772653738at_nat (set_Pr2131844118at_nat Xs))) of role axiom named fact_203_List_Ofinite__set
% 0.71/0.87 A new axiom: (forall (Xs:list_P559422087at_nat), (finite772653738at_nat (set_Pr2131844118at_nat Xs)))
% 0.71/0.87 FOF formula (forall (Xs:list_nat), (finite_finite_nat (set_nat2 Xs))) of role axiom named fact_204_List_Ofinite__set
% 0.71/0.87 A new axiom: (forall (Xs:list_nat), (finite_finite_nat (set_nat2 Xs)))
% 0.71/0.87 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat) (Z2:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat X2) ((inf_in586391887at_nat Y2) Z2))) ((and ((ord_le841296385at_nat X2) Y2)) ((ord_le841296385at_nat X2) Z2)))) of role axiom named fact_205_le__inf__iff
% 0.71/0.87 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat) (Z2:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat X2) ((inf_in586391887at_nat Y2) Z2))) ((and ((ord_le841296385at_nat X2) Y2)) ((ord_le841296385at_nat X2) Z2))))
% 0.71/0.87 FOF formula (forall (X2:set_nat) (Y2:set_nat) (Z2:set_nat), (((eq Prop) ((ord_less_eq_set_nat X2) ((inf_inf_set_nat Y2) Z2))) ((and ((ord_less_eq_set_nat X2) Y2)) ((ord_less_eq_set_nat X2) Z2)))) of role axiom named fact_206_le__inf__iff
% 0.71/0.87 A new axiom: (forall (X2:set_nat) (Y2:set_nat) (Z2:set_nat), (((eq Prop) ((ord_less_eq_set_nat X2) ((inf_inf_set_nat Y2) Z2))) ((and ((ord_less_eq_set_nat X2) Y2)) ((ord_less_eq_set_nat X2) Z2))))
% 0.71/0.87 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((eq Prop) ((ord_less_eq_nat X2) ((inf_inf_nat Y2) Z2))) ((and ((ord_less_eq_nat X2) Y2)) ((ord_less_eq_nat X2) Z2)))) of role axiom named fact_207_le__inf__iff
% 0.71/0.87 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((eq Prop) ((ord_less_eq_nat X2) ((inf_inf_nat Y2) Z2))) ((and ((ord_less_eq_nat X2) Y2)) ((ord_less_eq_nat X2) Z2))))
% 0.71/0.87 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat A2) ((inf_in586391887at_nat B2) C))) ((and ((ord_le841296385at_nat A2) B2)) ((ord_le841296385at_nat A2) C)))) of role axiom named fact_208_inf_Obounded__iff
% 0.71/0.87 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat A2) ((inf_in586391887at_nat B2) C))) ((and ((ord_le841296385at_nat A2) B2)) ((ord_le841296385at_nat A2) C))))
% 0.71/0.87 FOF formula (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((eq Prop) ((ord_less_eq_set_nat A2) ((inf_inf_set_nat B2) C))) ((and ((ord_less_eq_set_nat A2) B2)) ((ord_less_eq_set_nat A2) C)))) of role axiom named fact_209_inf_Obounded__iff
% 0.71/0.87 A new axiom: (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((eq Prop) ((ord_less_eq_set_nat A2) ((inf_inf_set_nat B2) C))) ((and ((ord_less_eq_set_nat A2) B2)) ((ord_less_eq_set_nat A2) C))))
% 0.71/0.87 FOF formula (forall (A2:nat) (B2:nat) (C:nat), (((eq Prop) ((ord_less_eq_nat A2) ((inf_inf_nat B2) C))) ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat A2) C)))) of role axiom named fact_210_inf_Obounded__iff
% 0.71/0.87 A new axiom: (forall (A2:nat) (B2:nat) (C:nat), (((eq Prop) ((ord_less_eq_nat A2) ((inf_inf_nat B2) C))) ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat A2) C))))
% 0.71/0.87 FOF formula (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->((ord_less_eq_nat (finite447719721at_nat A)) (finite447719721at_nat B))))) of role axiom named fact_211_card__mono
% 0.71/0.87 A new axiom: (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->((ord_less_eq_nat (finite447719721at_nat A)) (finite447719721at_nat B)))))
% 0.71/0.87 FOF formula (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->((ord_less_eq_nat (finite_card_nat A)) (finite_card_nat B))))) of role axiom named fact_212_card__mono
% 0.71/0.87 A new axiom: (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->((ord_less_eq_nat (finite_card_nat A)) (finite_card_nat B)))))
% 0.71/0.87 FOF formula (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->(((ord_less_eq_nat (finite447719721at_nat B)) (finite447719721at_nat A))->(((eq set_Pr1986765409at_nat) A) B))))) of role axiom named fact_213_card__seteq
% 0.71/0.87 A new axiom: (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->(((ord_less_eq_nat (finite447719721at_nat B)) (finite447719721at_nat A))->(((eq set_Pr1986765409at_nat) A) B)))))
% 0.71/0.87 FOF formula (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->(((ord_less_eq_nat (finite_card_nat B)) (finite_card_nat A))->(((eq set_nat) A) B))))) of role axiom named fact_214_card__seteq
% 0.71/0.87 A new axiom: (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->(((ord_less_eq_nat (finite_card_nat B)) (finite_card_nat A))->(((eq set_nat) A) B)))))
% 0.71/0.87 FOF formula ((finite772653738at_nat (e_a c))->(finite_finite_nat (v_a c))) of role axiom named fact_215_Efin__imp__Vfin
% 0.71/0.88 A new axiom: ((finite772653738at_nat (e_a c))->(finite_finite_nat (v_a c)))
% 0.71/0.88 FOF formula (finite_finite_nat (v_a c)) of role axiom named fact_216_finite__V
% 0.71/0.88 A new axiom: (finite_finite_nat (v_a c))
% 0.71/0.88 FOF formula (forall (U2:nat), (finite_finite_nat ((adjacent_nodes_a c) U2))) of role axiom named fact_217_adjacent__nodes__finite
% 0.71/0.88 A new axiom: (forall (U2:nat), (finite_finite_nat ((adjacent_nodes_a c) U2)))
% 0.71/0.88 FOF formula ((finite_finite_nat (v_a c))->(finite772653738at_nat (e_a c))) of role axiom named fact_218_Vfin__imp__Efin
% 0.71/0.88 A new axiom: ((finite_finite_nat (v_a c))->(finite772653738at_nat (e_a c)))
% 0.71/0.88 FOF formula (forall (U2:nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((incoming_a c) U2)))) of role axiom named fact_219_finite__incoming
% 0.71/0.88 A new axiom: (forall (U2:nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((incoming_a c) U2))))
% 0.71/0.88 FOF formula (forall (U2:nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((outgoing_a c) U2)))) of role axiom named fact_220_finite__outgoing
% 0.71/0.88 A new axiom: (forall (U2:nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((outgoing_a c) U2))))
% 0.71/0.88 FOF formula (forall (U:set_nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((incoming_a2 c) U)))) of role axiom named fact_221_finite__incoming_H
% 0.71/0.88 A new axiom: (forall (U:set_nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((incoming_a2 c) U))))
% 0.71/0.88 FOF formula (forall (U:set_nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((outgoing_a2 c) U)))) of role axiom named fact_222_finite__outgoing_H
% 0.71/0.88 A new axiom: (forall (U:set_nat), ((finite_finite_nat (v_a c))->(finite772653738at_nat ((outgoing_a2 c) U))))
% 0.71/0.88 FOF formula (((eq ((product_prod_nat_nat->a)->Prop)) finite_Graph_a) (fun (C4:(product_prod_nat_nat->a))=> (finite_finite_nat (v_a C4)))) of role axiom named fact_223_Finite__Graph__def
% 0.71/0.88 A new axiom: (((eq ((product_prod_nat_nat->a)->Prop)) finite_Graph_a) (fun (C4:(product_prod_nat_nat->a))=> (finite_finite_nat (v_a C4))))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite_finite_nat (v_a C))->(finite_Graph_a C))) of role axiom named fact_224_Finite__Graph_Ointro
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite_finite_nat (v_a C))->(finite_Graph_a C)))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite_Graph_a C)->(finite_finite_nat (v_a C)))) of role axiom named fact_225_Finite__Graph_Ofinite__V
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite_Graph_a C)->(finite_finite_nat (v_a C))))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((finite_Graph_a C)->(finite_finite_nat ((adjacent_nodes_a C) U2)))) of role axiom named fact_226_Finite__Graph_Oadjacent__nodes__finite
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((finite_Graph_a C)->(finite_finite_nat ((adjacent_nodes_a C) U2))))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite772653738at_nat (e_a C))->(finite_finite_nat (v_a C)))) of role axiom named fact_227_Graph_OEfin__imp__Vfin
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite772653738at_nat (e_a C))->(finite_finite_nat (v_a C))))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)), ((finite_finite_nat (v_a C))->(finite772653738at_nat (e_a C)))) of role axiom named fact_228_Graph_OVfin__imp__Efin
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)), ((finite_finite_nat (v_a C))->(finite772653738at_nat (e_a C))))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((outgoing_a C) U2)))) of role axiom named fact_229_Graph_Ofinite__outgoing
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((outgoing_a C) U2))))
% 0.71/0.88 FOF formula (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((incoming_a C) U2)))) of role axiom named fact_230_Graph_Ofinite__incoming
% 0.71/0.88 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U2:nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((incoming_a C) U2))))
% 0.71/0.89 FOF formula (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((outgoing_a2 C) U)))) of role axiom named fact_231_Graph_Ofinite__outgoing_H
% 0.71/0.89 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((outgoing_a2 C) U))))
% 0.71/0.89 FOF formula (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((incoming_a2 C) U)))) of role axiom named fact_232_Graph_Ofinite__incoming_H
% 0.71/0.89 A new axiom: (forall (C:(product_prod_nat_nat->a)) (U:set_nat), ((finite_finite_nat (v_a C))->(finite772653738at_nat ((incoming_a2 C) U))))
% 0.71/0.89 FOF formula (forall (A:set_se1612935105at_nat) (A2:set_Pr1986765409at_nat), ((finite1457549322at_nat A)->(((member298845450at_nat A2) A)->((ex set_Pr1986765409at_nat) (fun (X:set_Pr1986765409at_nat)=> ((and ((and ((member298845450at_nat X) A)) ((ord_le841296385at_nat X) A2))) (forall (Xa:set_Pr1986765409at_nat), (((member298845450at_nat Xa) A)->(((ord_le841296385at_nat Xa) X)->(((eq set_Pr1986765409at_nat) X) Xa)))))))))) of role axiom named fact_233_finite__has__minimal2
% 0.71/0.89 A new axiom: (forall (A:set_se1612935105at_nat) (A2:set_Pr1986765409at_nat), ((finite1457549322at_nat A)->(((member298845450at_nat A2) A)->((ex set_Pr1986765409at_nat) (fun (X:set_Pr1986765409at_nat)=> ((and ((and ((member298845450at_nat X) A)) ((ord_le841296385at_nat X) A2))) (forall (Xa:set_Pr1986765409at_nat), (((member298845450at_nat Xa) A)->(((ord_le841296385at_nat Xa) X)->(((eq set_Pr1986765409at_nat) X) Xa))))))))))
% 0.71/0.89 FOF formula (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat X) A2))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat Xa) X)->(((eq set_nat) X) Xa)))))))))) of role axiom named fact_234_finite__has__minimal2
% 0.71/0.89 A new axiom: (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat X) A2))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat Xa) X)->(((eq set_nat) X) Xa))))))))))
% 0.71/0.89 FOF formula (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat X) A2))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat Xa) X)->(((eq nat) X) Xa)))))))))) of role axiom named fact_235_finite__has__minimal2
% 0.71/0.89 A new axiom: (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat X) A2))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat Xa) X)->(((eq nat) X) Xa))))))))))
% 0.71/0.89 FOF formula (forall (A:set_se1612935105at_nat) (A2:set_Pr1986765409at_nat), ((finite1457549322at_nat A)->(((member298845450at_nat A2) A)->((ex set_Pr1986765409at_nat) (fun (X:set_Pr1986765409at_nat)=> ((and ((and ((member298845450at_nat X) A)) ((ord_le841296385at_nat A2) X))) (forall (Xa:set_Pr1986765409at_nat), (((member298845450at_nat Xa) A)->(((ord_le841296385at_nat X) Xa)->(((eq set_Pr1986765409at_nat) X) Xa)))))))))) of role axiom named fact_236_finite__has__maximal2
% 0.71/0.89 A new axiom: (forall (A:set_se1612935105at_nat) (A2:set_Pr1986765409at_nat), ((finite1457549322at_nat A)->(((member298845450at_nat A2) A)->((ex set_Pr1986765409at_nat) (fun (X:set_Pr1986765409at_nat)=> ((and ((and ((member298845450at_nat X) A)) ((ord_le841296385at_nat A2) X))) (forall (Xa:set_Pr1986765409at_nat), (((member298845450at_nat Xa) A)->(((ord_le841296385at_nat X) Xa)->(((eq set_Pr1986765409at_nat) X) Xa))))))))))
% 0.71/0.89 FOF formula (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat A2) X))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat X) Xa)->(((eq set_nat) X) Xa)))))))))) of role axiom named fact_237_finite__has__maximal2
% 0.75/0.90 A new axiom: (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat A2) X))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat X) Xa)->(((eq set_nat) X) Xa))))))))))
% 0.75/0.90 FOF formula (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat A2) X))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat X) Xa)->(((eq nat) X) Xa)))))))))) of role axiom named fact_238_finite__has__maximal2
% 0.75/0.90 A new axiom: (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat A2) X))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat X) Xa)->(((eq nat) X) Xa))))))))))
% 0.75/0.90 FOF formula (forall (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) C)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) C))) of role axiom named fact_239_inf_OcoboundedI2
% 0.75/0.90 A new axiom: (forall (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) C)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) C)))
% 0.75/0.90 FOF formula (forall (B2:set_nat) (C:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) C)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) C))) of role axiom named fact_240_inf_OcoboundedI2
% 0.75/0.90 A new axiom: (forall (B2:set_nat) (C:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) C)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) C)))
% 0.75/0.90 FOF formula (forall (B2:nat) (C:nat) (A2:nat), (((ord_less_eq_nat B2) C)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) C))) of role axiom named fact_241_inf_OcoboundedI2
% 0.75/0.90 A new axiom: (forall (B2:nat) (C:nat) (A2:nat), (((ord_less_eq_nat B2) C)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) C)))
% 0.75/0.90 FOF formula (forall (A2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) C)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) C))) of role axiom named fact_242_inf_OcoboundedI1
% 0.75/0.90 A new axiom: (forall (A2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) C)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) C)))
% 0.75/0.90 FOF formula (forall (A2:set_nat) (C:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) C)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) C))) of role axiom named fact_243_inf_OcoboundedI1
% 0.75/0.90 A new axiom: (forall (A2:set_nat) (C:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) C)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) C)))
% 0.75/0.90 FOF formula (forall (A2:nat) (C:nat) (B2:nat), (((ord_less_eq_nat A2) C)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) C))) of role axiom named fact_244_inf_OcoboundedI1
% 0.75/0.90 A new axiom: (forall (A2:nat) (C:nat) (B2:nat), (((ord_less_eq_nat A2) C)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) C)))
% 0.75/0.90 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (B3:set_Pr1986765409at_nat) (A3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A3) B3)) B3))) of role axiom named fact_245_inf_Oabsorb__iff2
% 0.75/0.90 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (B3:set_Pr1986765409at_nat) (A3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A3) B3)) B3)))
% 0.75/0.90 FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (B3:set_nat) (A3:set_nat)=> (((eq set_nat) ((inf_inf_set_nat A3) B3)) B3))) of role axiom named fact_246_inf_Oabsorb__iff2
% 0.75/0.90 A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (B3:set_nat) (A3:set_nat)=> (((eq set_nat) ((inf_inf_set_nat A3) B3)) B3)))
% 0.75/0.90 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (B3:nat) (A3:nat)=> (((eq nat) ((inf_inf_nat A3) B3)) B3))) of role axiom named fact_247_inf_Oabsorb__iff2
% 0.75/0.90 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (B3:nat) (A3:nat)=> (((eq nat) ((inf_inf_nat A3) B3)) B3)))
% 0.75/0.91 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A3) B3)) A3))) of role axiom named fact_248_inf_Oabsorb__iff1
% 0.75/0.91 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A3) B3)) A3)))
% 0.75/0.91 FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A3:set_nat) (B3:set_nat)=> (((eq set_nat) ((inf_inf_set_nat A3) B3)) A3))) of role axiom named fact_249_inf_Oabsorb__iff1
% 0.75/0.91 A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A3:set_nat) (B3:set_nat)=> (((eq set_nat) ((inf_inf_set_nat A3) B3)) A3)))
% 0.75/0.91 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A3:nat) (B3:nat)=> (((eq nat) ((inf_inf_nat A3) B3)) A3))) of role axiom named fact_250_inf_Oabsorb__iff1
% 0.75/0.91 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A3:nat) (B3:nat)=> (((eq nat) ((inf_inf_nat A3) B3)) A3)))
% 0.75/0.91 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) B2)) of role axiom named fact_251_inf_Ocobounded2
% 0.75/0.91 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) B2))
% 0.75/0.91 FOF formula (forall (A2:set_nat) (B2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) B2)) of role axiom named fact_252_inf_Ocobounded2
% 0.75/0.91 A new axiom: (forall (A2:set_nat) (B2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) B2))
% 0.75/0.91 FOF formula (forall (A2:nat) (B2:nat), ((ord_less_eq_nat ((inf_inf_nat A2) B2)) B2)) of role axiom named fact_253_inf_Ocobounded2
% 0.75/0.91 A new axiom: (forall (A2:nat) (B2:nat), ((ord_less_eq_nat ((inf_inf_nat A2) B2)) B2))
% 0.75/0.91 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) A2)) of role axiom named fact_254_inf_Ocobounded1
% 0.75/0.91 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) A2))
% 0.75/0.91 FOF formula (forall (A2:set_nat) (B2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) A2)) of role axiom named fact_255_inf_Ocobounded1
% 0.75/0.91 A new axiom: (forall (A2:set_nat) (B2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) A2))
% 0.75/0.91 FOF formula (forall (A2:nat) (B2:nat), ((ord_less_eq_nat ((inf_inf_nat A2) B2)) A2)) of role axiom named fact_256_inf_Ocobounded1
% 0.75/0.91 A new axiom: (forall (A2:nat) (B2:nat), ((ord_less_eq_nat ((inf_inf_nat A2) B2)) A2))
% 0.75/0.91 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) A3) ((inf_in586391887at_nat A3) B3)))) of role axiom named fact_257_inf_Oorder__iff
% 0.75/0.91 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (A3:set_Pr1986765409at_nat) (B3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) A3) ((inf_in586391887at_nat A3) B3))))
% 0.75/0.91 FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A3:set_nat) (B3:set_nat)=> (((eq set_nat) A3) ((inf_inf_set_nat A3) B3)))) of role axiom named fact_258_inf_Oorder__iff
% 0.75/0.91 A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A3:set_nat) (B3:set_nat)=> (((eq set_nat) A3) ((inf_inf_set_nat A3) B3))))
% 0.75/0.91 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A3:nat) (B3:nat)=> (((eq nat) A3) ((inf_inf_nat A3) B3)))) of role axiom named fact_259_inf_Oorder__iff
% 0.75/0.91 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A3:nat) (B3:nat)=> (((eq nat) A3) ((inf_inf_nat A3) B3))))
% 0.75/0.91 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat) (Z2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((ord_le841296385at_nat X2) Z2)->((ord_le841296385at_nat X2) ((inf_in586391887at_nat Y2) Z2))))) of role axiom named fact_260_inf__greatest
% 0.75/0.92 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat) (Z2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((ord_le841296385at_nat X2) Z2)->((ord_le841296385at_nat X2) ((inf_in586391887at_nat Y2) Z2)))))
% 0.75/0.92 FOF formula (forall (X2:set_nat) (Y2:set_nat) (Z2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((ord_less_eq_set_nat X2) Z2)->((ord_less_eq_set_nat X2) ((inf_inf_set_nat Y2) Z2))))) of role axiom named fact_261_inf__greatest
% 0.75/0.92 A new axiom: (forall (X2:set_nat) (Y2:set_nat) (Z2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((ord_less_eq_set_nat X2) Z2)->((ord_less_eq_set_nat X2) ((inf_inf_set_nat Y2) Z2)))))
% 0.75/0.92 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat X2) Z2)->((ord_less_eq_nat X2) ((inf_inf_nat Y2) Z2))))) of role axiom named fact_262_inf__greatest
% 0.75/0.92 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat X2) Z2)->((ord_less_eq_nat X2) ((inf_inf_nat Y2) Z2)))))
% 0.75/0.92 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat A2) C)->((ord_le841296385at_nat A2) ((inf_in586391887at_nat B2) C))))) of role axiom named fact_263_inf_OboundedI
% 0.75/0.92 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat A2) C)->((ord_le841296385at_nat A2) ((inf_in586391887at_nat B2) C)))))
% 0.75/0.92 FOF formula (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat A2) C)->((ord_less_eq_set_nat A2) ((inf_inf_set_nat B2) C))))) of role axiom named fact_264_inf_OboundedI
% 0.75/0.92 A new axiom: (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat A2) C)->((ord_less_eq_set_nat A2) ((inf_inf_set_nat B2) C)))))
% 0.75/0.92 FOF formula (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat A2) C)->((ord_less_eq_nat A2) ((inf_inf_nat B2) C))))) of role axiom named fact_265_inf_OboundedI
% 0.75/0.92 A new axiom: (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat A2) C)->((ord_less_eq_nat A2) ((inf_inf_nat B2) C)))))
% 0.75/0.92 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) ((inf_in586391887at_nat B2) C))->((((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat A2) C)->False))->False))) of role axiom named fact_266_inf_OboundedE
% 0.75/0.92 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) ((inf_in586391887at_nat B2) C))->((((ord_le841296385at_nat A2) B2)->(((ord_le841296385at_nat A2) C)->False))->False)))
% 0.75/0.92 FOF formula (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) ((inf_inf_set_nat B2) C))->((((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat A2) C)->False))->False))) of role axiom named fact_267_inf_OboundedE
% 0.75/0.92 A new axiom: (forall (A2:set_nat) (B2:set_nat) (C:set_nat), (((ord_less_eq_set_nat A2) ((inf_inf_set_nat B2) C))->((((ord_less_eq_set_nat A2) B2)->(((ord_less_eq_set_nat A2) C)->False))->False)))
% 0.75/0.92 FOF formula (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) ((inf_inf_nat B2) C))->((((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat A2) C)->False))->False))) of role axiom named fact_268_inf_OboundedE
% 0.75/0.92 A new axiom: (forall (A2:nat) (B2:nat) (C:nat), (((ord_less_eq_nat A2) ((inf_inf_nat B2) C))->((((ord_less_eq_nat A2) B2)->(((ord_less_eq_nat A2) C)->False))->False)))
% 0.75/0.92 FOF formula (forall (Y2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat), (((ord_le841296385at_nat Y2) X2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X2) Y2)) Y2))) of role axiom named fact_269_inf__absorb2
% 0.75/0.92 A new axiom: (forall (Y2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat), (((ord_le841296385at_nat Y2) X2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X2) Y2)) Y2)))
% 0.75/0.93 FOF formula (forall (Y2:set_nat) (X2:set_nat), (((ord_less_eq_set_nat Y2) X2)->(((eq set_nat) ((inf_inf_set_nat X2) Y2)) Y2))) of role axiom named fact_270_inf__absorb2
% 0.75/0.93 A new axiom: (forall (Y2:set_nat) (X2:set_nat), (((ord_less_eq_set_nat Y2) X2)->(((eq set_nat) ((inf_inf_set_nat X2) Y2)) Y2)))
% 0.75/0.93 FOF formula (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((eq nat) ((inf_inf_nat X2) Y2)) Y2))) of role axiom named fact_271_inf__absorb2
% 0.75/0.93 A new axiom: (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((eq nat) ((inf_inf_nat X2) Y2)) Y2)))
% 0.75/0.93 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X2) Y2)) X2))) of role axiom named fact_272_inf__absorb1
% 0.75/0.93 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) Y2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X2) Y2)) X2)))
% 0.75/0.93 FOF formula (forall (X2:set_nat) (Y2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((eq set_nat) ((inf_inf_set_nat X2) Y2)) X2))) of role axiom named fact_273_inf__absorb1
% 0.75/0.93 A new axiom: (forall (X2:set_nat) (Y2:set_nat), (((ord_less_eq_set_nat X2) Y2)->(((eq set_nat) ((inf_inf_set_nat X2) Y2)) X2)))
% 0.75/0.93 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((eq nat) ((inf_inf_nat X2) Y2)) X2))) of role axiom named fact_274_inf__absorb1
% 0.75/0.93 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((eq nat) ((inf_inf_nat X2) Y2)) X2)))
% 0.75/0.93 FOF formula (forall (B2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) A2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A2) B2)) B2))) of role axiom named fact_275_inf_Oabsorb2
% 0.75/0.93 A new axiom: (forall (B2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) A2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A2) B2)) B2)))
% 0.75/0.93 FOF formula (forall (B2:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) A2)->(((eq set_nat) ((inf_inf_set_nat A2) B2)) B2))) of role axiom named fact_276_inf_Oabsorb2
% 0.75/0.93 A new axiom: (forall (B2:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) A2)->(((eq set_nat) ((inf_inf_set_nat A2) B2)) B2)))
% 0.75/0.93 FOF formula (forall (B2:nat) (A2:nat), (((ord_less_eq_nat B2) A2)->(((eq nat) ((inf_inf_nat A2) B2)) B2))) of role axiom named fact_277_inf_Oabsorb2
% 0.75/0.93 A new axiom: (forall (B2:nat) (A2:nat), (((ord_less_eq_nat B2) A2)->(((eq nat) ((inf_inf_nat A2) B2)) B2)))
% 0.75/0.93 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A2) B2)) A2))) of role axiom named fact_278_inf_Oabsorb1
% 0.75/0.93 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat A2) B2)) A2)))
% 0.75/0.93 FOF formula (forall (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) B2)->(((eq set_nat) ((inf_inf_set_nat A2) B2)) A2))) of role axiom named fact_279_inf_Oabsorb1
% 0.75/0.93 A new axiom: (forall (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) B2)->(((eq set_nat) ((inf_inf_set_nat A2) B2)) A2)))
% 0.75/0.93 FOF formula (forall (A2:nat) (B2:nat), (((ord_less_eq_nat A2) B2)->(((eq nat) ((inf_inf_nat A2) B2)) A2))) of role axiom named fact_280_inf_Oabsorb1
% 0.75/0.93 A new axiom: (forall (A2:nat) (B2:nat), (((ord_less_eq_nat A2) B2)->(((eq nat) ((inf_inf_nat A2) B2)) A2)))
% 0.75/0.93 FOF formula (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (X3:set_Pr1986765409at_nat) (Y3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X3) Y3)) X3))) of role axiom named fact_281_le__iff__inf
% 0.75/0.93 A new axiom: (((eq (set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))) ord_le841296385at_nat) (fun (X3:set_Pr1986765409at_nat) (Y3:set_Pr1986765409at_nat)=> (((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X3) Y3)) X3)))
% 0.75/0.93 FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (X3:set_nat) (Y3:set_nat)=> (((eq set_nat) ((inf_inf_set_nat X3) Y3)) X3))) of role axiom named fact_282_le__iff__inf
% 0.78/0.95 A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (X3:set_nat) (Y3:set_nat)=> (((eq set_nat) ((inf_inf_set_nat X3) Y3)) X3)))
% 0.78/0.95 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X3:nat) (Y3:nat)=> (((eq nat) ((inf_inf_nat X3) Y3)) X3))) of role axiom named fact_283_le__iff__inf
% 0.78/0.95 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X3:nat) (Y3:nat)=> (((eq nat) ((inf_inf_nat X3) Y3)) X3)))
% 0.78/0.95 FOF formula (forall (F:(set_Pr1986765409at_nat->(set_Pr1986765409at_nat->set_Pr1986765409at_nat))) (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((F X) Y4)) X))->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((F X) Y4)) Y4))->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat) (Z3:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->(((ord_le841296385at_nat X) Z3)->((ord_le841296385at_nat X) ((F Y4) Z3)))))->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X2) Y2)) ((F X2) Y2)))))) of role axiom named fact_284_inf__unique
% 0.78/0.95 A new axiom: (forall (F:(set_Pr1986765409at_nat->(set_Pr1986765409at_nat->set_Pr1986765409at_nat))) (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((F X) Y4)) X))->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((F X) Y4)) Y4))->((forall (X:set_Pr1986765409at_nat) (Y4:set_Pr1986765409at_nat) (Z3:set_Pr1986765409at_nat), (((ord_le841296385at_nat X) Y4)->(((ord_le841296385at_nat X) Z3)->((ord_le841296385at_nat X) ((F Y4) Z3)))))->(((eq set_Pr1986765409at_nat) ((inf_in586391887at_nat X2) Y2)) ((F X2) Y2))))))
% 0.78/0.95 FOF formula (forall (F:(set_nat->(set_nat->set_nat))) (X2:set_nat) (Y2:set_nat), ((forall (X:set_nat) (Y4:set_nat), ((ord_less_eq_set_nat ((F X) Y4)) X))->((forall (X:set_nat) (Y4:set_nat), ((ord_less_eq_set_nat ((F X) Y4)) Y4))->((forall (X:set_nat) (Y4:set_nat) (Z3:set_nat), (((ord_less_eq_set_nat X) Y4)->(((ord_less_eq_set_nat X) Z3)->((ord_less_eq_set_nat X) ((F Y4) Z3)))))->(((eq set_nat) ((inf_inf_set_nat X2) Y2)) ((F X2) Y2)))))) of role axiom named fact_285_inf__unique
% 0.78/0.95 A new axiom: (forall (F:(set_nat->(set_nat->set_nat))) (X2:set_nat) (Y2:set_nat), ((forall (X:set_nat) (Y4:set_nat), ((ord_less_eq_set_nat ((F X) Y4)) X))->((forall (X:set_nat) (Y4:set_nat), ((ord_less_eq_set_nat ((F X) Y4)) Y4))->((forall (X:set_nat) (Y4:set_nat) (Z3:set_nat), (((ord_less_eq_set_nat X) Y4)->(((ord_less_eq_set_nat X) Z3)->((ord_less_eq_set_nat X) ((F Y4) Z3)))))->(((eq set_nat) ((inf_inf_set_nat X2) Y2)) ((F X2) Y2))))))
% 0.78/0.95 FOF formula (forall (F:(nat->(nat->nat))) (X2:nat) (Y2:nat), ((forall (X:nat) (Y4:nat), ((ord_less_eq_nat ((F X) Y4)) X))->((forall (X:nat) (Y4:nat), ((ord_less_eq_nat ((F X) Y4)) Y4))->((forall (X:nat) (Y4:nat) (Z3:nat), (((ord_less_eq_nat X) Y4)->(((ord_less_eq_nat X) Z3)->((ord_less_eq_nat X) ((F Y4) Z3)))))->(((eq nat) ((inf_inf_nat X2) Y2)) ((F X2) Y2)))))) of role axiom named fact_286_inf__unique
% 0.78/0.95 A new axiom: (forall (F:(nat->(nat->nat))) (X2:nat) (Y2:nat), ((forall (X:nat) (Y4:nat), ((ord_less_eq_nat ((F X) Y4)) X))->((forall (X:nat) (Y4:nat), ((ord_less_eq_nat ((F X) Y4)) Y4))->((forall (X:nat) (Y4:nat) (Z3:nat), (((ord_less_eq_nat X) Y4)->(((ord_less_eq_nat X) Z3)->((ord_less_eq_nat X) ((F Y4) Z3)))))->(((eq nat) ((inf_inf_nat X2) Y2)) ((F X2) Y2))))))
% 0.78/0.95 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A2) ((inf_in586391887at_nat A2) B2))->((ord_le841296385at_nat A2) B2))) of role axiom named fact_287_inf_OorderI
% 0.78/0.95 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), ((((eq set_Pr1986765409at_nat) A2) ((inf_in586391887at_nat A2) B2))->((ord_le841296385at_nat A2) B2)))
% 0.78/0.95 FOF formula (forall (A2:set_nat) (B2:set_nat), ((((eq set_nat) A2) ((inf_inf_set_nat A2) B2))->((ord_less_eq_set_nat A2) B2))) of role axiom named fact_288_inf_OorderI
% 0.78/0.96 A new axiom: (forall (A2:set_nat) (B2:set_nat), ((((eq set_nat) A2) ((inf_inf_set_nat A2) B2))->((ord_less_eq_set_nat A2) B2)))
% 0.78/0.96 FOF formula (forall (A2:nat) (B2:nat), ((((eq nat) A2) ((inf_inf_nat A2) B2))->((ord_less_eq_nat A2) B2))) of role axiom named fact_289_inf_OorderI
% 0.78/0.96 A new axiom: (forall (A2:nat) (B2:nat), ((((eq nat) A2) ((inf_inf_nat A2) B2))->((ord_less_eq_nat A2) B2)))
% 0.78/0.96 FOF formula (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((eq set_Pr1986765409at_nat) A2) ((inf_in586391887at_nat A2) B2)))) of role axiom named fact_290_inf_OorderE
% 0.78/0.96 A new axiom: (forall (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) B2)->(((eq set_Pr1986765409at_nat) A2) ((inf_in586391887at_nat A2) B2))))
% 0.78/0.96 FOF formula (forall (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) B2)->(((eq set_nat) A2) ((inf_inf_set_nat A2) B2)))) of role axiom named fact_291_inf_OorderE
% 0.78/0.96 A new axiom: (forall (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) B2)->(((eq set_nat) A2) ((inf_inf_set_nat A2) B2))))
% 0.78/0.96 FOF formula (forall (A2:nat) (B2:nat), (((ord_less_eq_nat A2) B2)->(((eq nat) A2) ((inf_inf_nat A2) B2)))) of role axiom named fact_292_inf_OorderE
% 0.78/0.96 A new axiom: (forall (A2:nat) (B2:nat), (((ord_less_eq_nat A2) B2)->(((eq nat) A2) ((inf_inf_nat A2) B2))))
% 0.78/0.96 FOF formula (forall (B2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) X2)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) X2))) of role axiom named fact_293_le__infI2
% 0.78/0.96 A new axiom: (forall (B2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat), (((ord_le841296385at_nat B2) X2)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) X2)))
% 0.78/0.96 FOF formula (forall (B2:set_nat) (X2:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) X2)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) X2))) of role axiom named fact_294_le__infI2
% 0.78/0.96 A new axiom: (forall (B2:set_nat) (X2:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B2) X2)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) X2)))
% 0.78/0.96 FOF formula (forall (B2:nat) (X2:nat) (A2:nat), (((ord_less_eq_nat B2) X2)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) X2))) of role axiom named fact_295_le__infI2
% 0.78/0.96 A new axiom: (forall (B2:nat) (X2:nat) (A2:nat), (((ord_less_eq_nat B2) X2)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) X2)))
% 0.78/0.96 FOF formula (forall (A2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) X2)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) X2))) of role axiom named fact_296_le__infI1
% 0.78/0.96 A new axiom: (forall (A2:set_Pr1986765409at_nat) (X2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) X2)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) X2)))
% 0.78/0.96 FOF formula (forall (A2:set_nat) (X2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) X2)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) X2))) of role axiom named fact_297_le__infI1
% 0.78/0.96 A new axiom: (forall (A2:set_nat) (X2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat A2) X2)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) X2)))
% 0.78/0.96 FOF formula (forall (A2:nat) (X2:nat) (B2:nat), (((ord_less_eq_nat A2) X2)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) X2))) of role axiom named fact_298_le__infI1
% 0.78/0.96 A new axiom: (forall (A2:nat) (X2:nat) (B2:nat), (((ord_less_eq_nat A2) X2)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) X2)))
% 0.78/0.96 FOF formula (forall (A2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (D2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) C)->(((ord_le841296385at_nat B2) D2)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) ((inf_in586391887at_nat C) D2))))) of role axiom named fact_299_inf__mono
% 0.78/0.96 A new axiom: (forall (A2:set_Pr1986765409at_nat) (C:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat) (D2:set_Pr1986765409at_nat), (((ord_le841296385at_nat A2) C)->(((ord_le841296385at_nat B2) D2)->((ord_le841296385at_nat ((inf_in586391887at_nat A2) B2)) ((inf_in586391887at_nat C) D2)))))
% 0.78/0.97 FOF formula (forall (A2:set_nat) (C:set_nat) (B2:set_nat) (D2:set_nat), (((ord_less_eq_set_nat A2) C)->(((ord_less_eq_set_nat B2) D2)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) ((inf_inf_set_nat C) D2))))) of role axiom named fact_300_inf__mono
% 0.78/0.97 A new axiom: (forall (A2:set_nat) (C:set_nat) (B2:set_nat) (D2:set_nat), (((ord_less_eq_set_nat A2) C)->(((ord_less_eq_set_nat B2) D2)->((ord_less_eq_set_nat ((inf_inf_set_nat A2) B2)) ((inf_inf_set_nat C) D2)))))
% 0.78/0.97 FOF formula (forall (A2:nat) (C:nat) (B2:nat) (D2:nat), (((ord_less_eq_nat A2) C)->(((ord_less_eq_nat B2) D2)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) ((inf_inf_nat C) D2))))) of role axiom named fact_301_inf__mono
% 0.78/0.97 A new axiom: (forall (A2:nat) (C:nat) (B2:nat) (D2:nat), (((ord_less_eq_nat A2) C)->(((ord_less_eq_nat B2) D2)->((ord_less_eq_nat ((inf_inf_nat A2) B2)) ((inf_inf_nat C) D2)))))
% 0.78/0.97 FOF formula (forall (X2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) A2)->(((ord_le841296385at_nat X2) B2)->((ord_le841296385at_nat X2) ((inf_in586391887at_nat A2) B2))))) of role axiom named fact_302_le__infI
% 0.78/0.97 A new axiom: (forall (X2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) A2)->(((ord_le841296385at_nat X2) B2)->((ord_le841296385at_nat X2) ((inf_in586391887at_nat A2) B2)))))
% 0.78/0.97 FOF formula (forall (X2:set_nat) (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat X2) A2)->(((ord_less_eq_set_nat X2) B2)->((ord_less_eq_set_nat X2) ((inf_inf_set_nat A2) B2))))) of role axiom named fact_303_le__infI
% 0.78/0.97 A new axiom: (forall (X2:set_nat) (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat X2) A2)->(((ord_less_eq_set_nat X2) B2)->((ord_less_eq_set_nat X2) ((inf_inf_set_nat A2) B2)))))
% 0.78/0.97 FOF formula (forall (X2:nat) (A2:nat) (B2:nat), (((ord_less_eq_nat X2) A2)->(((ord_less_eq_nat X2) B2)->((ord_less_eq_nat X2) ((inf_inf_nat A2) B2))))) of role axiom named fact_304_le__infI
% 0.78/0.97 A new axiom: (forall (X2:nat) (A2:nat) (B2:nat), (((ord_less_eq_nat X2) A2)->(((ord_less_eq_nat X2) B2)->((ord_less_eq_nat X2) ((inf_inf_nat A2) B2)))))
% 0.78/0.97 FOF formula (forall (X2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) ((inf_in586391887at_nat A2) B2))->((((ord_le841296385at_nat X2) A2)->(((ord_le841296385at_nat X2) B2)->False))->False))) of role axiom named fact_305_le__infE
% 0.78/0.97 A new axiom: (forall (X2:set_Pr1986765409at_nat) (A2:set_Pr1986765409at_nat) (B2:set_Pr1986765409at_nat), (((ord_le841296385at_nat X2) ((inf_in586391887at_nat A2) B2))->((((ord_le841296385at_nat X2) A2)->(((ord_le841296385at_nat X2) B2)->False))->False)))
% 0.78/0.97 FOF formula (forall (X2:set_nat) (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat X2) ((inf_inf_set_nat A2) B2))->((((ord_less_eq_set_nat X2) A2)->(((ord_less_eq_set_nat X2) B2)->False))->False))) of role axiom named fact_306_le__infE
% 0.78/0.97 A new axiom: (forall (X2:set_nat) (A2:set_nat) (B2:set_nat), (((ord_less_eq_set_nat X2) ((inf_inf_set_nat A2) B2))->((((ord_less_eq_set_nat X2) A2)->(((ord_less_eq_set_nat X2) B2)->False))->False)))
% 0.78/0.97 FOF formula (forall (X2:nat) (A2:nat) (B2:nat), (((ord_less_eq_nat X2) ((inf_inf_nat A2) B2))->((((ord_less_eq_nat X2) A2)->(((ord_less_eq_nat X2) B2)->False))->False))) of role axiom named fact_307_le__infE
% 0.78/0.97 A new axiom: (forall (X2:nat) (A2:nat) (B2:nat), (((ord_less_eq_nat X2) ((inf_inf_nat A2) B2))->((((ord_less_eq_nat X2) A2)->(((ord_less_eq_nat X2) B2)->False))->False)))
% 0.78/0.97 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) Y2)) of role axiom named fact_308_inf__le2
% 0.78/0.97 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) Y2))
% 0.78/0.97 FOF formula (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) Y2)) of role axiom named fact_309_inf__le2
% 0.78/0.97 A new axiom: (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) Y2))
% 0.78/0.97 FOF formula (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) Y2)) of role axiom named fact_310_inf__le2
% 0.78/0.98 A new axiom: (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) Y2))
% 0.78/0.98 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) X2)) of role axiom named fact_311_inf__le1
% 0.78/0.98 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) X2))
% 0.78/0.98 FOF formula (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) X2)) of role axiom named fact_312_inf__le1
% 0.78/0.98 A new axiom: (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) X2))
% 0.78/0.98 FOF formula (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) X2)) of role axiom named fact_313_inf__le1
% 0.78/0.98 A new axiom: (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) X2))
% 0.78/0.98 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) X2)) of role axiom named fact_314_inf__sup__ord_I1_J
% 0.78/0.98 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) X2))
% 0.78/0.98 FOF formula (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) X2)) of role axiom named fact_315_inf__sup__ord_I1_J
% 0.78/0.98 A new axiom: (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) X2))
% 0.78/0.98 FOF formula (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) X2)) of role axiom named fact_316_inf__sup__ord_I1_J
% 0.78/0.98 A new axiom: (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) X2))
% 0.78/0.98 FOF formula (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) Y2)) of role axiom named fact_317_inf__sup__ord_I2_J
% 0.78/0.98 A new axiom: (forall (X2:set_Pr1986765409at_nat) (Y2:set_Pr1986765409at_nat), ((ord_le841296385at_nat ((inf_in586391887at_nat X2) Y2)) Y2))
% 0.78/0.98 FOF formula (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) Y2)) of role axiom named fact_318_inf__sup__ord_I2_J
% 0.78/0.98 A new axiom: (forall (X2:set_nat) (Y2:set_nat), ((ord_less_eq_set_nat ((inf_inf_set_nat X2) Y2)) Y2))
% 0.78/0.98 FOF formula (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) Y2)) of role axiom named fact_319_inf__sup__ord_I2_J
% 0.78/0.98 A new axiom: (forall (X2:nat) (Y2:nat), ((ord_less_eq_nat ((inf_inf_nat X2) Y2)) Y2))
% 0.78/0.98 FOF formula (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->(finite772653738at_nat A)))) of role axiom named fact_320_rev__finite__subset
% 0.78/0.98 A new axiom: (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->(finite772653738at_nat A))))
% 0.78/0.98 FOF formula (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->(finite_finite_nat A)))) of role axiom named fact_321_rev__finite__subset
% 0.78/0.98 A new axiom: (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->(finite_finite_nat A))))
% 0.78/0.98 FOF formula (forall (S2:set_Pr1986765409at_nat) (T3:set_Pr1986765409at_nat), (((ord_le841296385at_nat S2) T3)->(((finite772653738at_nat S2)->False)->((finite772653738at_nat T3)->False)))) of role axiom named fact_322_infinite__super
% 0.78/0.98 A new axiom: (forall (S2:set_Pr1986765409at_nat) (T3:set_Pr1986765409at_nat), (((ord_le841296385at_nat S2) T3)->(((finite772653738at_nat S2)->False)->((finite772653738at_nat T3)->False))))
% 0.78/0.98 FOF formula (forall (S2:set_nat) (T3:set_nat), (((ord_less_eq_set_nat S2) T3)->(((finite_finite_nat S2)->False)->((finite_finite_nat T3)->False)))) of role axiom named fact_323_infinite__super
% 0.78/0.98 A new axiom: (forall (S2:set_nat) (T3:set_nat), (((ord_less_eq_set_nat S2) T3)->(((finite_finite_nat S2)->False)->((finite_finite_nat T3)->False))))
% 0.78/0.98 FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->((finite772653738at_nat B)->(finite772653738at_nat A)))) of role axiom named fact_324_finite__subset
% 0.78/0.99 A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->((finite772653738at_nat B)->(finite772653738at_nat A))))
% 0.78/0.99 FOF formula (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->((finite_finite_nat B)->(finite_finite_nat A)))) of role axiom named fact_325_finite__subset
% 0.78/0.99 A new axiom: (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->((finite_finite_nat B)->(finite_finite_nat A))))
% 0.78/0.99 FOF formula (forall (A:set_Pr1986765409at_nat), ((finite772653738at_nat A)->((ex list_P559422087at_nat) (fun (Xs2:list_P559422087at_nat)=> (((eq set_Pr1986765409at_nat) (set_Pr2131844118at_nat Xs2)) A))))) of role axiom named fact_326_finite__list
% 0.78/0.99 A new axiom: (forall (A:set_Pr1986765409at_nat), ((finite772653738at_nat A)->((ex list_P559422087at_nat) (fun (Xs2:list_P559422087at_nat)=> (((eq set_Pr1986765409at_nat) (set_Pr2131844118at_nat Xs2)) A)))))
% 0.78/0.99 FOF formula (forall (A:set_nat), ((finite_finite_nat A)->((ex list_nat) (fun (Xs2:list_nat)=> (((eq set_nat) (set_nat2 Xs2)) A))))) of role axiom named fact_327_finite__list
% 0.78/0.99 A new axiom: (forall (A:set_nat), ((finite_finite_nat A)->((ex list_nat) (fun (Xs2:list_nat)=> (((eq set_nat) (set_nat2 Xs2)) A)))))
% 0.78/0.99 FOF formula (forall (Xs:list_P559422087at_nat) (B:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat (set_Pr2131844118at_nat Xs)) B)) (forall (X3:product_prod_nat_nat), (((member701585322at_nat X3) (set_Pr2131844118at_nat Xs))->((member701585322at_nat X3) B))))) of role axiom named fact_328_subset__code_I1_J
% 0.78/0.99 A new axiom: (forall (Xs:list_P559422087at_nat) (B:set_Pr1986765409at_nat), (((eq Prop) ((ord_le841296385at_nat (set_Pr2131844118at_nat Xs)) B)) (forall (X3:product_prod_nat_nat), (((member701585322at_nat X3) (set_Pr2131844118at_nat Xs))->((member701585322at_nat X3) B)))))
% 0.78/0.99 FOF formula (forall (Xs:list_nat) (B:set_nat), (((eq Prop) ((ord_less_eq_set_nat (set_nat2 Xs)) B)) (forall (X3:nat), (((member_nat X3) (set_nat2 Xs))->((member_nat X3) B))))) of role axiom named fact_329_subset__code_I1_J
% 0.78/0.99 A new axiom: (forall (Xs:list_nat) (B:set_nat), (((eq Prop) ((ord_less_eq_set_nat (set_nat2 Xs)) B)) (forall (X3:nat), (((member_nat X3) (set_nat2 Xs))->((member_nat X3) B)))))
% 0.78/0.99 FOF formula (forall (A:set_Pr1986765409at_nat) (N:nat), (((finite772653738at_nat A)->False)->((ex set_Pr1986765409at_nat) (fun (B6:set_Pr1986765409at_nat)=> ((and ((and (finite772653738at_nat B6)) (((eq nat) (finite447719721at_nat B6)) N))) ((ord_le841296385at_nat B6) A)))))) of role axiom named fact_330_infinite__arbitrarily__large
% 0.78/0.99 A new axiom: (forall (A:set_Pr1986765409at_nat) (N:nat), (((finite772653738at_nat A)->False)->((ex set_Pr1986765409at_nat) (fun (B6:set_Pr1986765409at_nat)=> ((and ((and (finite772653738at_nat B6)) (((eq nat) (finite447719721at_nat B6)) N))) ((ord_le841296385at_nat B6) A))))))
% 0.78/0.99 FOF formula (forall (A:set_nat) (N:nat), (((finite_finite_nat A)->False)->((ex set_nat) (fun (B6:set_nat)=> ((and ((and (finite_finite_nat B6)) (((eq nat) (finite_card_nat B6)) N))) ((ord_less_eq_set_nat B6) A)))))) of role axiom named fact_331_infinite__arbitrarily__large
% 0.78/0.99 A new axiom: (forall (A:set_nat) (N:nat), (((finite_finite_nat A)->False)->((ex set_nat) (fun (B6:set_nat)=> ((and ((and (finite_finite_nat B6)) (((eq nat) (finite_card_nat B6)) N))) ((ord_less_eq_set_nat B6) A))))))
% 0.78/0.99 FOF formula (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->((((eq nat) (finite447719721at_nat A)) (finite447719721at_nat B))->(((eq set_Pr1986765409at_nat) A) B))))) of role axiom named fact_332_card__subset__eq
% 0.78/0.99 A new axiom: (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->((((eq nat) (finite447719721at_nat A)) (finite447719721at_nat B))->(((eq set_Pr1986765409at_nat) A) B)))))
% 0.78/0.99 FOF formula (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->((((eq nat) (finite_card_nat A)) (finite_card_nat B))->(((eq set_nat) A) B))))) of role axiom named fact_333_card__subset__eq
% 0.78/0.99 A new axiom: (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->((((eq nat) (finite_card_nat A)) (finite_card_nat B))->(((eq set_nat) A) B)))))
% 0.78/0.99 FOF formula (forall (F2:set_Pr1986765409at_nat) (C2:nat), ((forall (G2:set_Pr1986765409at_nat), (((ord_le841296385at_nat G2) F2)->((finite772653738at_nat G2)->((ord_less_eq_nat (finite447719721at_nat G2)) C2))))->((and (finite772653738at_nat F2)) ((ord_less_eq_nat (finite447719721at_nat F2)) C2)))) of role axiom named fact_334_finite__if__finite__subsets__card__bdd
% 0.78/0.99 A new axiom: (forall (F2:set_Pr1986765409at_nat) (C2:nat), ((forall (G2:set_Pr1986765409at_nat), (((ord_le841296385at_nat G2) F2)->((finite772653738at_nat G2)->((ord_less_eq_nat (finite447719721at_nat G2)) C2))))->((and (finite772653738at_nat F2)) ((ord_less_eq_nat (finite447719721at_nat F2)) C2))))
% 0.78/0.99 FOF formula (forall (F2:set_nat) (C2:nat), ((forall (G2:set_nat), (((ord_less_eq_set_nat G2) F2)->((finite_finite_nat G2)->((ord_less_eq_nat (finite_card_nat G2)) C2))))->((and (finite_finite_nat F2)) ((ord_less_eq_nat (finite_card_nat F2)) C2)))) of role axiom named fact_335_finite__if__finite__subsets__card__bdd
% 0.78/0.99 A new axiom: (forall (F2:set_nat) (C2:nat), ((forall (G2:set_nat), (((ord_less_eq_set_nat G2) F2)->((finite_finite_nat G2)->((ord_less_eq_nat (finite_card_nat G2)) C2))))->((and (finite_finite_nat F2)) ((ord_less_eq_nat (finite_card_nat F2)) C2))))
% 0.78/0.99 FOF formula (forall (U2:nat) (P:list_P559422087at_nat) (V:nat), (((member_nat U2) (v_a c))->(((((isPath_a c) U2) P) V)->((ord_less_eq_set_nat (set_nat2 ((pathVertices U2) P))) (v_a c))))) of role axiom named fact_336_pathVertices__edgeset
% 0.78/0.99 A new axiom: (forall (U2:nat) (P:list_P559422087at_nat) (V:nat), (((member_nat U2) (v_a c))->(((((isPath_a c) U2) P) V)->((ord_less_eq_set_nat (set_nat2 ((pathVertices U2) P))) (v_a c)))))
% 0.78/0.99 <<<5409at_nat] :
% 0.78/0.99 ( ( ord_less_eq_nat @ N @ ( finite447719721at_nat @ S2 ) )
% 0.78/0.99 => ~ !>>>!!!<<< [T4: set_Pr1986765409at_nat] :
% 0.78/0.99 ( ( ord_le841296385at_nat @ T4 @ S2 )
% 0.78/0.99 >>>
% 0.78/0.99 statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 11, 22, 30, 36, 43, 50, 99, 113, 185, 229, 265, 285, 300, 221, 120, 187, 124]
% 0.78/0.99 symstack=[$end, TPTP_file_pre, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, 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TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, LexToken(THF,'thf',1,93201), LexToken(LPAR,'(',1,93204), name, LexToken(COMMA,',',1,93243), formula_role, LexToken(COMMA,',',1,93249), LexToken(LPAR,'(',1,93250), thf_quantified_formula_PRE, thf_quantifier, LexToken(LBRACKET,'[',1,93258), thf_variable_list, LexToken(RBRACKET,']',1,93292), LexToken(COLON,':',1,93294), LexToken(LPAR,'(',1,93302), thf_unitary_formula, thf_pair_connective, unary_connective]
% 0.78/0.99 Unexpected exception Syntax error at '!':BANG
% 0.78/0.99 Traceback (most recent call last):
% 0.78/0.99 File "CASC.py", line 79, in <module>
% 0.78/0.99 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.78/0.99 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 38, in __init__
% 0.78/0.99 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.78/0.99 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 265, in parse
% 0.78/0.99 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.78/0.99 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.78/0.99 tok = self.errorfunc(errtoken)
% 0.78/0.99 File "/export/starexec/sandbox2/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.78/0.99 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.78/0.99 TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------