TSTP Solution File: ITP073^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP073^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 13:24:06 EDT 2021
% Result : Unknown 0.78s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP073^1 : TPTP v7.5.0. Released v7.5.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Fri Mar 19 05:20:53 EDT 2021
% 0.13/0.34 % CPUTime :
% 0.13/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 0.47/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c368>, <kernel.Type object at 0x235cd40>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_J
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring set_se933006839lle_hf:Type
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2360d88>, <kernel.Type object at 0x235ccb0>) of role type named ty_n_t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring set_HF_Mirabelle_hf:Type
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c518>, <kernel.Type object at 0x235c1b8>) of role type named ty_n_t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring hF_Mirabelle_hf:Type
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c908>, <kernel.Type object at 0x235ccb0>) of role type named ty_n_t__Set__Oset_It__Nat__Onat_J
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring set_nat:Type
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c248>, <kernel.Type object at 0x235c098>) of role type named ty_n_t__Nat__Onat
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring nat:Type
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235cd40>, <kernel.DependentProduct object at 0x2339d40>) of role type named sy_c_Finite__Set_Ocard_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring finite1213132899lle_hf:(set_HF_Mirabelle_hf->nat)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c6c8>, <kernel.DependentProduct object at 0x2339e18>) of role type named sy_c_Finite__Set_Ocard_001t__Nat__Onat
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring finite_card_nat:(set_nat->nat)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c518>, <kernel.DependentProduct object at 0x2339c20>) of role type named sy_c_Finite__Set_Ocard_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring finite90088345lle_hf:(set_se933006839lle_hf->nat)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c6c8>, <kernel.DependentProduct object at 0x2339cb0>) of role type named sy_c_Finite__Set_Ofinite_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring finite586181922lle_hf:(set_HF_Mirabelle_hf->Prop)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c518>, <kernel.DependentProduct object at 0x2339998>) of role type named sy_c_Finite__Set_Ofinite_001t__Nat__Onat
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring finite_finite_nat:(set_nat->Prop)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c6c8>, <kernel.DependentProduct object at 0x2339a28>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring finite1450550360lle_hf:(set_se933006839lle_hf->Prop)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x235c6c8>, <kernel.DependentProduct object at 0x2339c20>) of role type named sy_c_Fun_Oinj__on_001t__HF____Mirabelle____glliljednj__Ohf_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring inj_on755450110lle_hf:((hF_Mirabelle_hf->hF_Mirabelle_hf)->(set_HF_Mirabelle_hf->Prop))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2339998>, <kernel.DependentProduct object at 0x2339e18>) of role type named sy_c_Fun_Oinj__on_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring inj_on1874279374hf_nat:((hF_Mirabelle_hf->nat)->(set_HF_Mirabelle_hf->Prop))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2339908>, <kernel.DependentProduct object at 0x2339a28>) of role type named sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring inj_on1988990670lle_hf:((nat->hF_Mirabelle_hf)->(set_nat->Prop))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2339dd0>, <kernel.DependentProduct object at 0x2339998>) of role type named sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring inj_on_nat_nat:((nat->nat)->(set_nat->Prop))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2339d88>, <kernel.DependentProduct object at 0x2339908>) of role type named sy_c_Fun_Oinj__on_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring inj_on811196232lle_hf:((set_HF_Mirabelle_hf->hF_Mirabelle_hf)->(set_se933006839lle_hf->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e7f5e9e0>, <kernel.Constant object at 0x2339d88>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring zero_z189798548lle_hf:hF_Mirabelle_hf
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e7f5e9e0>, <kernel.Constant object at 0x2339d88>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring zero_zero_nat:nat
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339d40>, <kernel.DependentProduct object at 0x2339dd0>) of role type named sy_c_HF__Mirabelle__glliljednj_OHCollect
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mir818139703ollect:((hF_Mirabelle_hf->Prop)->(hF_Mirabelle_hf->hF_Mirabelle_hf))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339e18>, <kernel.DependentProduct object at 0x2b24e048df38>) of role type named sy_c_HF__Mirabelle__glliljednj_OHF
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mirabelle_HF:(set_HF_Mirabelle_hf->hF_Mirabelle_hf)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339c20>, <kernel.DependentProduct object at 0x2b24e048df80>) of role type named sy_c_HF__Mirabelle__glliljednj_OHUnion
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mirabelle_HUnion:(hF_Mirabelle_hf->hF_Mirabelle_hf)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339dd0>, <kernel.DependentProduct object at 0x2b24e048df80>) of role type named sy_c_HF__Mirabelle__glliljednj_OPrimReplace
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mir1248913145eplace:(hF_Mirabelle_hf->((hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))->hF_Mirabelle_hf))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339c20>, <kernel.DependentProduct object at 0x2b24e048de18>) of role type named sy_c_HF__Mirabelle__glliljednj_ORepFun
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mirabelle_RepFun:(hF_Mirabelle_hf->((hF_Mirabelle_hf->hF_Mirabelle_hf)->hF_Mirabelle_hf))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339dd0>, <kernel.DependentProduct object at 0x2b24e048de18>) of role type named sy_c_HF__Mirabelle__glliljednj_OReplace
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mirabelle_Replace:(hF_Mirabelle_hf->((hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))->hF_Mirabelle_hf))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339e18>, <kernel.DependentProduct object at 0x2b24e048df38>) of role type named sy_c_HF__Mirabelle__glliljednj_Ohfset
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mirabelle_hfset:(hF_Mirabelle_hf->set_HF_Mirabelle_hf)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2339e18>, <kernel.DependentProduct object at 0x2b24e048df80>) of role type named sy_c_HF__Mirabelle__glliljednj_Ohmem
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring hF_Mirabelle_hmem:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048de18>, <kernel.DependentProduct object at 0x2b24e048dd40>) of role type named sy_c_Orderings_Oord__class_Oless_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_le1310584031lle_hf:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048df38>, <kernel.DependentProduct object at 0x2b24e048de60>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048df80>, <kernel.DependentProduct object at 0x2b24e048def0>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_le1344122901lle_hf:(set_HF_Mirabelle_hf->(set_HF_Mirabelle_hf->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048dd40>, <kernel.DependentProduct object at 0x2b24e048dcb0>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_less_set_nat:(set_nat->(set_nat->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048de60>, <kernel.DependentProduct object at 0x2b24e048db48>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__HF____Mirabelle____glliljednj__Ohf_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_le2017230260lle_hf:((Prop->hF_Mirabelle_hf)->((Prop->hF_Mirabelle_hf)->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048df80>, <kernel.DependentProduct object at 0x2b24e048da70>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Nat__Onat_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_less_eq_o_nat:((Prop->nat)->((Prop->nat)->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048dd40>, <kernel.DependentProduct object at 0x2b24e048db48>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_le976219883lle_hf:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048de18>, <kernel.DependentProduct object at 0x2b24e048df38>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048da70>, <kernel.DependentProduct object at 0x2b24e048de60>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_le432112161lle_hf:(set_HF_Mirabelle_hf->(set_HF_Mirabelle_hf->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048db48>, <kernel.DependentProduct object at 0x2b24e048df80>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ord_less_eq_set_nat:(set_nat->(set_nat->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048df38>, <kernel.DependentProduct object at 0x2b24e048dea8>) of role type named sy_c_Orderings_Oorder__class_OGreatest_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring order_1640852850lle_hf:((hF_Mirabelle_hf->Prop)->hF_Mirabelle_hf)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048de60>, <kernel.DependentProduct object at 0x2b24e048d998>) of role type named sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring order_Greatest_nat:((nat->Prop)->nat)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048d950>, <kernel.DependentProduct object at 0x2b24e048da70>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__HF____Mirabelle____glliljednj__Ohf_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring order_690706045lle_hf:((hF_Mirabelle_hf->hF_Mirabelle_hf)->Prop)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048dd40>, <kernel.DependentProduct object at 0x2b24e048db48>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring order_557194383hf_nat:((hF_Mirabelle_hf->nat)->Prop)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048d8c0>, <kernel.DependentProduct object at 0x2b24e048df38>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring order_671905679lle_hf:((nat->hF_Mirabelle_hf)->Prop)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048d908>, <kernel.DependentProduct object at 0x2b24e048de60>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring order_1631207636at_nat:((nat->nat)->Prop)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048d830>, <kernel.DependentProduct object at 0x2b24e048d950>) of role type named sy_c_Orderings_Oordering_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring orderi1737556723lle_hf:((hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))->((hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048d878>, <kernel.DependentProduct object at 0x2b24e048de60>) of role type named sy_c_Orderings_Oordering_001t__Nat__Onat
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ordering_nat:((nat->(nat->Prop))->((nat->(nat->Prop))->Prop))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048dd40>, <kernel.DependentProduct object at 0x2b24e048d7e8>) of role type named sy_c_Set_OCollect_001t__HF____Mirabelle____glliljednj__Ohf
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring collec2046588256lle_hf:((hF_Mirabelle_hf->Prop)->set_HF_Mirabelle_hf)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2b24e048d7a0>, <kernel.DependentProduct object at 0x2b24e048d5f0>) of role type named sy_c_Set_OCollect_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring collec1758573718lle_hf:((set_HF_Mirabelle_hf->Prop)->set_se933006839lle_hf)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d950>, <kernel.DependentProduct object at 0x2b24e048dd40>) of role type named sy_c_Set_Oimage_001t__HF____Mirabelle____glliljednj__Ohf_001t__HF____Mirabelle____glliljednj__Ohf
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring image_1743964010lle_hf:((hF_Mirabelle_hf->hF_Mirabelle_hf)->(set_HF_Mirabelle_hf->set_HF_Mirabelle_hf))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048df38>, <kernel.DependentProduct object at 0x2b24e048d7a0>) of role type named sy_c_Set_Oimage_001t__HF____Mirabelle____glliljednj__Ohf_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring image_131453538hf_nat:((hF_Mirabelle_hf->nat)->(set_HF_Mirabelle_hf->set_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d680>, <kernel.DependentProduct object at 0x2b24e048d950>) of role type named sy_c_Set_Oimage_001t__Nat__Onat_001t__HF____Mirabelle____glliljednj__Ohf
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring image_246164834lle_hf:((nat->hF_Mirabelle_hf)->(set_nat->set_HF_Mirabelle_hf))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d560>, <kernel.DependentProduct object at 0x2b24e048df38>) of role type named sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring image_nat_nat:((nat->nat)->(set_nat->set_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d5a8>, <kernel.DependentProduct object at 0x2b24e048d680>) of role type named sy_c_Set_Oimage_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J_001t__HF____Mirabelle____glliljednj__Ohf
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring image_899003828lle_hf:((set_HF_Mirabelle_hf->hF_Mirabelle_hf)->(set_se933006839lle_hf->set_HF_Mirabelle_hf))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d5f0>, <kernel.DependentProduct object at 0x2b24e048d878>) of role type named sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring set_or1544565540an_nat:(nat->(nat->set_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048dd40>, <kernel.DependentProduct object at 0x2b24e048d7a0>) of role type named sy_c_member_001t__HF____Mirabelle____glliljednj__Ohf
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring member1367349282lle_hf:(hF_Mirabelle_hf->(set_HF_Mirabelle_hf->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d680>, <kernel.DependentProduct object at 0x2b24e048df38>) of role type named sy_c_member_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring member_nat:(nat->(set_nat->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d878>, <kernel.DependentProduct object at 0x2b24e048d5a8>) of role type named sy_c_member_001t__Set__Oset_It__HF____Mirabelle____glliljednj__Ohf_J
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring member1490636632lle_hf:(set_HF_Mirabelle_hf->(set_se933006839lle_hf->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d7a0>, <kernel.Constant object at 0x2b24e048d5a8>) of role type named sy_v_A
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring a:hF_Mirabelle_hf
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b24e048d680>, <kernel.Constant object at 0x2b24e048d5a8>) of role type named sy_v_B
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring b:hF_Mirabelle_hf
% 0.48/0.64 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), ((forall (X:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X) A)) ((hF_Mirabelle_hmem X) B)))->(((eq hF_Mirabelle_hf) A) B))) of role axiom named fact_0_hf__equalityI
% 0.48/0.64 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), ((forall (X:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X) A)) ((hF_Mirabelle_hmem X) B)))->(((eq hF_Mirabelle_hf) A) B)))
% 0.48/0.64 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> (forall (X2:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X2) A2)) ((hF_Mirabelle_hmem X2) B2))))) of role axiom named fact_1_hf__ext
% 0.48/0.64 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> (forall (X2:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X2) A2)) ((hF_Mirabelle_hmem X2) B2)))))
% 0.48/0.65 FOF formula (forall (X3:hF_Mirabelle_hf) (R:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))), ((forall (U:hF_Mirabelle_hf) (V:hF_Mirabelle_hf) (V2:hF_Mirabelle_hf), (((hF_Mirabelle_hmem U) X3)->(((R U) V)->(((R U) V2)->(((eq hF_Mirabelle_hf) V2) V)))))->((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (V3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem V3) Z2)) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) X3)) ((R U2) V3)))))))))) of role axiom named fact_2_replacement
% 0.48/0.65 A new axiom: (forall (X3:hF_Mirabelle_hf) (R:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))), ((forall (U:hF_Mirabelle_hf) (V:hF_Mirabelle_hf) (V2:hF_Mirabelle_hf), (((hF_Mirabelle_hmem U) X3)->(((R U) V)->(((R U) V2)->(((eq hF_Mirabelle_hf) V2) V)))))->((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (V3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem V3) Z2)) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) X3)) ((R U2) V3))))))))))
% 0.48/0.65 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (U3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem U3) Z2)) ((or ((hF_Mirabelle_hmem U3) X3)) ((hF_Mirabelle_hmem U3) Y2))))))) of role axiom named fact_3_binary__union
% 0.48/0.65 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (U3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem U3) Z2)) ((or ((hF_Mirabelle_hmem U3) X3)) ((hF_Mirabelle_hmem U3) Y2)))))))
% 0.48/0.65 FOF formula (forall (X3:hF_Mirabelle_hf), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (U3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem U3) Z2)) ((ex hF_Mirabelle_hf) (fun (Y3:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem Y3) X3)) ((hF_Mirabelle_hmem U3) Y3))))))))) of role axiom named fact_4_union__of__set
% 0.48/0.65 A new axiom: (forall (X3:hF_Mirabelle_hf), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (U3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem U3) Z2)) ((ex hF_Mirabelle_hf) (fun (Y3:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem Y3) X3)) ((hF_Mirabelle_hmem U3) Y3)))))))))
% 0.48/0.65 FOF formula (forall (X3:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->Prop)), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (U3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem U3) Z2)) ((and ((hF_Mirabelle_hmem U3) X3)) (P U3))))))) of role axiom named fact_5_comprehension
% 0.48/0.65 A new axiom: (forall (X3:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->Prop)), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (U3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem U3) Z2)) ((and ((hF_Mirabelle_hmem U3) X3)) (P U3)))))))
% 0.48/0.65 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (A3:hF_Mirabelle_hf) (B3:hF_Mirabelle_hf)=> (forall (X2:hF_Mirabelle_hf), (((hF_Mirabelle_hmem X2) A3)->((hF_Mirabelle_hmem X2) B3))))) of role axiom named fact_6_less__eq__hf__def
% 0.48/0.65 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (A3:hF_Mirabelle_hf) (B3:hF_Mirabelle_hf)=> (forall (X2:hF_Mirabelle_hf), (((hF_Mirabelle_hmem X2) A3)->((hF_Mirabelle_hmem X2) B3)))))
% 0.48/0.65 FOF formula (forall (X3:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (V3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem V3) Z2)) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) X3)) (((eq hF_Mirabelle_hf) V3) (F U2)))))))))) of role axiom named fact_7_replacement__fun
% 0.48/0.65 A new axiom: (forall (X3:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)), ((ex hF_Mirabelle_hf) (fun (Z2:hF_Mirabelle_hf)=> (forall (V3:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem V3) Z2)) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) X3)) (((eq hF_Mirabelle_hf) V3) (F U2))))))))))
% 0.48/0.65 FOF formula (forall (X3:hF_Mirabelle_hf), ((ord_le976219883lle_hf X3) X3)) of role axiom named fact_8_order__refl
% 0.48/0.66 A new axiom: (forall (X3:hF_Mirabelle_hf), ((ord_le976219883lle_hf X3) X3))
% 0.48/0.66 FOF formula (forall (X3:nat), ((ord_less_eq_nat X3) X3)) of role axiom named fact_9_order__refl
% 0.48/0.66 A new axiom: (forall (X3:nat), ((ord_less_eq_nat X3) X3))
% 0.48/0.66 FOF formula (forall (A4:hF_Mirabelle_hf) (R:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (V4:hF_Mirabelle_hf), ((forall (U:hF_Mirabelle_hf) (V:hF_Mirabelle_hf) (V2:hF_Mirabelle_hf), (((hF_Mirabelle_hmem U) A4)->(((R U) V)->(((R U) V2)->(((eq hF_Mirabelle_hf) V2) V)))))->(((eq Prop) ((hF_Mirabelle_hmem V4) ((hF_Mir1248913145eplace A4) R))) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) A4)) ((R U2) V4))))))) of role axiom named fact_10_PrimReplace__iff
% 0.48/0.66 A new axiom: (forall (A4:hF_Mirabelle_hf) (R:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (V4:hF_Mirabelle_hf), ((forall (U:hF_Mirabelle_hf) (V:hF_Mirabelle_hf) (V2:hF_Mirabelle_hf), (((hF_Mirabelle_hmem U) A4)->(((R U) V)->(((R U) V2)->(((eq hF_Mirabelle_hf) V2) V)))))->(((eq Prop) ((hF_Mirabelle_hmem V4) ((hF_Mir1248913145eplace A4) R))) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) A4)) ((R U2) V4)))))))
% 0.48/0.66 FOF formula (forall (X3:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->Prop)) (A4:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X3) ((hF_Mir818139703ollect P) A4))) ((and (P X3)) ((hF_Mirabelle_hmem X3) A4)))) of role axiom named fact_11_HCollect__iff
% 0.48/0.66 A new axiom: (forall (X3:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->Prop)) (A4:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X3) ((hF_Mir818139703ollect P) A4))) ((and (P X3)) ((hF_Mirabelle_hmem X3) A4))))
% 0.48/0.66 FOF formula (forall (X3:hF_Mirabelle_hf) (A4:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X3) (hF_Mirabelle_HUnion A4))) ((ex hF_Mirabelle_hf) (fun (Y3:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem Y3) A4)) ((hF_Mirabelle_hmem X3) Y3)))))) of role axiom named fact_12_HUnion__iff
% 0.48/0.66 A new axiom: (forall (X3:hF_Mirabelle_hf) (A4:hF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X3) (hF_Mirabelle_HUnion A4))) ((ex hF_Mirabelle_hf) (fun (Y3:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem Y3) A4)) ((hF_Mirabelle_hmem X3) Y3))))))
% 0.48/0.66 FOF formula (forall (V4:hF_Mirabelle_hf) (A4:hF_Mirabelle_hf) (R:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))), (((eq Prop) ((hF_Mirabelle_hmem V4) ((hF_Mirabelle_Replace A4) R))) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((and ((hF_Mirabelle_hmem U2) A4)) ((R U2) V4))) (forall (Y3:hF_Mirabelle_hf), (((R U2) Y3)->(((eq hF_Mirabelle_hf) Y3) V4)))))))) of role axiom named fact_13_Replace__iff
% 0.48/0.66 A new axiom: (forall (V4:hF_Mirabelle_hf) (A4:hF_Mirabelle_hf) (R:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))), (((eq Prop) ((hF_Mirabelle_hmem V4) ((hF_Mirabelle_Replace A4) R))) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((and ((hF_Mirabelle_hmem U2) A4)) ((R U2) V4))) (forall (Y3:hF_Mirabelle_hf), (((R U2) Y3)->(((eq hF_Mirabelle_hf) Y3) V4))))))))
% 0.48/0.66 FOF formula (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C)))))) of role axiom named fact_14_order__subst1
% 0.48/0.66 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C))))))
% 0.48/0.66 FOF formula (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le976219883lle_hf A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C)))))) of role axiom named fact_15_order__subst1
% 0.48/0.66 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le976219883lle_hf A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C))))))
% 0.48/0.68 FOF formula (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_16_order__subst1
% 0.48/0.68 A new axiom: (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C))))))
% 0.48/0.68 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_17_order__subst1
% 0.48/0.68 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C))))))
% 0.48/0.68 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C))))) of role axiom named fact_18_order__subst2
% 0.48/0.68 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C)))))
% 0.48/0.68 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le976219883lle_hf A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_19_order__subst2
% 0.48/0.68 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le976219883lle_hf A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A)) C)))))
% 0.48/0.68 FOF formula (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C))))) of role axiom named fact_20_order__subst2
% 0.48/0.68 A new axiom: (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C)))))
% 0.48/0.68 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat (F B)) 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 A)) C))))) of role axiom named fact_21_order__subst2
% 0.48/0.68 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat (F B)) 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 A)) C)))))
% 0.48/0.68 FOF formula (forall (A:nat) (B:nat), ((or ((or (((eq nat) A) B)) (((ord_less_eq_nat A) B)->False))) (((ord_less_eq_nat B) A)->False))) of role axiom named fact_22_verit__la__disequality
% 0.48/0.68 A new axiom: (forall (A:nat) (B:nat), ((or ((or (((eq nat) A) B)) (((ord_less_eq_nat A) B)->False))) (((ord_less_eq_nat B) A)->False)))
% 0.48/0.69 FOF formula (forall (A4:hF_Mirabelle_hf) (B4:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (Q:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))), ((((eq hF_Mirabelle_hf) A4) B4)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((hF_Mirabelle_hmem X) B4)->(((eq Prop) ((P X) Y4)) ((Q X) Y4))))->(((eq hF_Mirabelle_hf) ((hF_Mirabelle_Replace A4) P)) ((hF_Mirabelle_Replace B4) Q))))) of role axiom named fact_23_Replace__cong
% 0.48/0.69 A new axiom: (forall (A4:hF_Mirabelle_hf) (B4:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (Q:(hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))), ((((eq hF_Mirabelle_hf) A4) B4)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((hF_Mirabelle_hmem X) B4)->(((eq Prop) ((P X) Y4)) ((Q X) Y4))))->(((eq hF_Mirabelle_hf) ((hF_Mirabelle_Replace A4) P)) ((hF_Mirabelle_Replace B4) Q)))))
% 0.48/0.69 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le976219883lle_hf B) A)->(((ord_le976219883lle_hf A) B)->(((eq hF_Mirabelle_hf) A) B)))) of role axiom named fact_24_dual__order_Oantisym
% 0.48/0.69 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le976219883lle_hf B) A)->(((ord_le976219883lle_hf A) B)->(((eq hF_Mirabelle_hf) A) B))))
% 0.48/0.69 FOF formula (forall (B:nat) (A:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat A) B)->(((eq nat) A) B)))) of role axiom named fact_25_dual__order_Oantisym
% 0.48/0.69 A new axiom: (forall (B:nat) (A:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat A) B)->(((eq nat) A) B))))
% 0.48/0.69 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf B2) A2)) ((ord_le976219883lle_hf A2) B2)))) of role axiom named fact_26_dual__order_Oeq__iff
% 0.48/0.69 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf B2) A2)) ((ord_le976219883lle_hf A2) B2))))
% 0.48/0.69 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2)))) of role axiom named fact_27_dual__order_Oeq__iff
% 0.48/0.69 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2))))
% 0.48/0.69 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf B) A)->(((ord_le976219883lle_hf C) B)->((ord_le976219883lle_hf C) A)))) of role axiom named fact_28_dual__order_Otrans
% 0.48/0.69 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf B) A)->(((ord_le976219883lle_hf C) B)->((ord_le976219883lle_hf C) A))))
% 0.48/0.69 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_eq_nat C) A)))) of role axiom named fact_29_dual__order_Otrans
% 0.48/0.69 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_eq_nat C) A))))
% 0.48/0.69 FOF formula (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A5:nat) (B5:nat), (((ord_less_eq_nat A5) B5)->((P A5) B5)))->((forall (A5:nat) (B5:nat), (((P B5) A5)->((P A5) B5)))->((P A) B)))) of role axiom named fact_30_linorder__wlog
% 0.48/0.69 A new axiom: (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A5:nat) (B5:nat), (((ord_less_eq_nat A5) B5)->((P A5) B5)))->((forall (A5:nat) (B5:nat), (((P B5) A5)->((P A5) B5)))->((P A) B))))
% 0.48/0.69 FOF formula (forall (A:hF_Mirabelle_hf), ((ord_le976219883lle_hf A) A)) of role axiom named fact_31_dual__order_Orefl
% 0.48/0.69 A new axiom: (forall (A:hF_Mirabelle_hf), ((ord_le976219883lle_hf A) A))
% 0.48/0.69 FOF formula (forall (A:nat), ((ord_less_eq_nat A) A)) of role axiom named fact_32_dual__order_Orefl
% 0.48/0.69 A new axiom: (forall (A:nat), ((ord_less_eq_nat A) A))
% 0.48/0.69 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((ord_le976219883lle_hf Y2) Z3)->((ord_le976219883lle_hf X3) Z3)))) of role axiom named fact_33_order__trans
% 0.48/0.71 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((ord_le976219883lle_hf Y2) Z3)->((ord_le976219883lle_hf X3) Z3))))
% 0.48/0.71 FOF formula (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z3)->((ord_less_eq_nat X3) Z3)))) of role axiom named fact_34_order__trans
% 0.48/0.71 A new axiom: (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z3)->((ord_less_eq_nat X3) Z3))))
% 0.48/0.71 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le976219883lle_hf B) A)->(((eq hF_Mirabelle_hf) A) B)))) of role axiom named fact_35_order__class_Oorder_Oantisym
% 0.48/0.71 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le976219883lle_hf B) A)->(((eq hF_Mirabelle_hf) A) B))))
% 0.48/0.71 FOF formula (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) A)->(((eq nat) A) B)))) of role axiom named fact_36_order__class_Oorder_Oantisym
% 0.48/0.71 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) A)->(((eq nat) A) B))))
% 0.48/0.71 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->((((eq hF_Mirabelle_hf) B) C)->((ord_le976219883lle_hf A) C)))) of role axiom named fact_37_ord__le__eq__trans
% 0.48/0.71 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->((((eq hF_Mirabelle_hf) B) C)->((ord_le976219883lle_hf A) C))))
% 0.48/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) B) C)->((ord_less_eq_nat A) C)))) of role axiom named fact_38_ord__le__eq__trans
% 0.48/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) B) C)->((ord_less_eq_nat A) C))))
% 0.48/0.71 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) B)->(((ord_le976219883lle_hf B) C)->((ord_le976219883lle_hf A) C)))) of role axiom named fact_39_ord__eq__le__trans
% 0.48/0.71 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) B)->(((ord_le976219883lle_hf B) C)->((ord_le976219883lle_hf A) C))))
% 0.48/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C)))) of role axiom named fact_40_ord__eq__le__trans
% 0.48/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C))))
% 0.48/0.71 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf A2) B2)) ((ord_le976219883lle_hf B2) A2)))) of role axiom named fact_41_order__class_Oorder_Oeq__iff
% 0.48/0.71 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf A2) B2)) ((ord_le976219883lle_hf B2) A2))))
% 0.48/0.71 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2)))) of role axiom named fact_42_order__class_Oorder_Oeq__iff
% 0.48/0.71 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2))))
% 0.48/0.71 FOF formula (forall (Y2:hF_Mirabelle_hf) (X3:hF_Mirabelle_hf), (((ord_le976219883lle_hf Y2) X3)->(((eq Prop) ((ord_le976219883lle_hf X3) Y2)) (((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_43_antisym__conv
% 0.48/0.71 A new axiom: (forall (Y2:hF_Mirabelle_hf) (X3:hF_Mirabelle_hf), (((ord_le976219883lle_hf Y2) X3)->(((eq Prop) ((ord_le976219883lle_hf X3) Y2)) (((eq hF_Mirabelle_hf) X3) Y2))))
% 0.48/0.71 FOF formula (forall (Y2:nat) (X3:nat), (((ord_less_eq_nat Y2) X3)->(((eq Prop) ((ord_less_eq_nat X3) Y2)) (((eq nat) X3) Y2)))) of role axiom named fact_44_antisym__conv
% 0.56/0.72 A new axiom: (forall (Y2:nat) (X3:nat), (((ord_less_eq_nat Y2) X3)->(((eq Prop) ((ord_less_eq_nat X3) Y2)) (((eq nat) X3) Y2))))
% 0.56/0.72 FOF formula (forall (X3:nat) (Y2:nat) (Z3:nat), ((((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z3)->False))->((((ord_less_eq_nat Y2) X3)->(((ord_less_eq_nat X3) Z3)->False))->((((ord_less_eq_nat X3) Z3)->(((ord_less_eq_nat Z3) Y2)->False))->((((ord_less_eq_nat Z3) Y2)->(((ord_less_eq_nat Y2) X3)->False))->((((ord_less_eq_nat Y2) Z3)->(((ord_less_eq_nat Z3) X3)->False))->((((ord_less_eq_nat Z3) X3)->(((ord_less_eq_nat X3) Y2)->False))->False))))))) of role axiom named fact_45_le__cases3
% 0.56/0.72 A new axiom: (forall (X3:nat) (Y2:nat) (Z3:nat), ((((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z3)->False))->((((ord_less_eq_nat Y2) X3)->(((ord_less_eq_nat X3) Z3)->False))->((((ord_less_eq_nat X3) Z3)->(((ord_less_eq_nat Z3) Y2)->False))->((((ord_less_eq_nat Z3) Y2)->(((ord_less_eq_nat Y2) X3)->False))->((((ord_less_eq_nat Y2) Z3)->(((ord_less_eq_nat Z3) X3)->False))->((((ord_less_eq_nat Z3) X3)->(((ord_less_eq_nat X3) Y2)->False))->False)))))))
% 0.56/0.72 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le976219883lle_hf B) C)->((ord_le976219883lle_hf A) C)))) of role axiom named fact_46_order_Otrans
% 0.56/0.72 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le976219883lle_hf B) C)->((ord_le976219883lle_hf A) C))))
% 0.56/0.72 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C)))) of role axiom named fact_47_order_Otrans
% 0.56/0.72 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C))))
% 0.56/0.72 FOF formula (forall (X3:nat) (Y2:nat), ((((ord_less_eq_nat X3) Y2)->False)->((ord_less_eq_nat Y2) X3))) of role axiom named fact_48_le__cases
% 0.56/0.72 A new axiom: (forall (X3:nat) (Y2:nat), ((((ord_less_eq_nat X3) Y2)->False)->((ord_less_eq_nat Y2) X3)))
% 0.56/0.72 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) X3) Y2)->((ord_le976219883lle_hf X3) Y2))) of role axiom named fact_49_eq__refl
% 0.56/0.72 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) X3) Y2)->((ord_le976219883lle_hf X3) Y2)))
% 0.56/0.72 FOF formula (forall (X3:nat) (Y2:nat), ((((eq nat) X3) Y2)->((ord_less_eq_nat X3) Y2))) of role axiom named fact_50_eq__refl
% 0.56/0.72 A new axiom: (forall (X3:nat) (Y2:nat), ((((eq nat) X3) Y2)->((ord_less_eq_nat X3) Y2)))
% 0.56/0.72 FOF formula (forall (X3:nat) (Y2:nat), ((or ((ord_less_eq_nat X3) Y2)) ((ord_less_eq_nat Y2) X3))) of role axiom named fact_51_linear
% 0.56/0.72 A new axiom: (forall (X3:nat) (Y2:nat), ((or ((ord_less_eq_nat X3) Y2)) ((ord_less_eq_nat Y2) X3)))
% 0.56/0.72 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((ord_le976219883lle_hf Y2) X3)->(((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_52_antisym
% 0.56/0.72 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((ord_le976219883lle_hf Y2) X3)->(((eq hF_Mirabelle_hf) X3) Y2))))
% 0.56/0.72 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) X3)->(((eq nat) X3) Y2)))) of role axiom named fact_53_antisym
% 0.56/0.72 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) X3)->(((eq nat) X3) Y2))))
% 0.56/0.72 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf X2) Y3)) ((ord_le976219883lle_hf Y3) X2)))) of role axiom named fact_54_eq__iff
% 0.56/0.72 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) (fun (Y:hF_Mirabelle_hf) (Z:hF_Mirabelle_hf)=> (((eq hF_Mirabelle_hf) Y) Z))) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf X2) Y3)) ((ord_le976219883lle_hf Y3) X2))))
% 0.56/0.74 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) ((ord_less_eq_nat Y3) X2)))) of role axiom named fact_55_eq__iff
% 0.56/0.74 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) ((ord_less_eq_nat Y3) X2))))
% 0.56/0.74 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C))))) of role axiom named fact_56_ord__le__eq__subst
% 0.56/0.74 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C)))))
% 0.56/0.74 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le976219883lle_hf A) B)->((((eq nat) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_57_ord__le__eq__subst
% 0.56/0.74 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le976219883lle_hf A) B)->((((eq nat) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A)) C)))))
% 0.56/0.74 FOF formula (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C))))) of role axiom named fact_58_ord__le__eq__subst
% 0.56/0.74 A new axiom: (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf (F A)) C)))))
% 0.56/0.74 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) (F B)) 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 A)) C))))) of role axiom named fact_59_ord__le__eq__subst
% 0.56/0.74 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) (F B)) 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 A)) C)))))
% 0.56/0.74 FOF formula (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C)))))) of role axiom named fact_60_ord__eq__le__subst
% 0.56/0.74 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C))))))
% 0.56/0.74 FOF formula (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq nat) A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_61_ord__eq__le__subst
% 0.56/0.74 A new axiom: (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq nat) A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C))))))
% 0.56/0.75 FOF formula (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C)))))) of role axiom named fact_62_ord__eq__le__subst
% 0.56/0.75 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le976219883lle_hf A) (F C))))))
% 0.56/0.75 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_63_ord__eq__le__subst
% 0.56/0.75 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A) (F C))))))
% 0.56/0.75 FOF formula (forall (P:(hF_Mirabelle_hf->Prop)) (X3:hF_Mirabelle_hf), ((P X3)->((forall (Y4:hF_Mirabelle_hf), ((P Y4)->((ord_le976219883lle_hf Y4) X3)))->(((eq hF_Mirabelle_hf) (order_1640852850lle_hf P)) X3)))) of role axiom named fact_64_Greatest__equality
% 0.56/0.75 A new axiom: (forall (P:(hF_Mirabelle_hf->Prop)) (X3:hF_Mirabelle_hf), ((P X3)->((forall (Y4:hF_Mirabelle_hf), ((P Y4)->((ord_le976219883lle_hf Y4) X3)))->(((eq hF_Mirabelle_hf) (order_1640852850lle_hf P)) X3))))
% 0.56/0.75 FOF formula (forall (P:(nat->Prop)) (X3:nat), ((P X3)->((forall (Y4:nat), ((P Y4)->((ord_less_eq_nat Y4) X3)))->(((eq nat) (order_Greatest_nat P)) X3)))) of role axiom named fact_65_Greatest__equality
% 0.56/0.75 A new axiom: (forall (P:(nat->Prop)) (X3:nat), ((P X3)->((forall (Y4:nat), ((P Y4)->((ord_less_eq_nat Y4) X3)))->(((eq nat) (order_Greatest_nat P)) X3))))
% 0.56/0.75 FOF formula (forall (P:(hF_Mirabelle_hf->Prop)) (X3:hF_Mirabelle_hf) (Q:(hF_Mirabelle_hf->Prop)), ((P X3)->((forall (Y4:hF_Mirabelle_hf), ((P Y4)->((ord_le976219883lle_hf Y4) X3)))->((forall (X:hF_Mirabelle_hf), ((P X)->((forall (Y5:hF_Mirabelle_hf), ((P Y5)->((ord_le976219883lle_hf Y5) X)))->(Q X))))->(Q (order_1640852850lle_hf P)))))) of role axiom named fact_66_GreatestI2__order
% 0.56/0.75 A new axiom: (forall (P:(hF_Mirabelle_hf->Prop)) (X3:hF_Mirabelle_hf) (Q:(hF_Mirabelle_hf->Prop)), ((P X3)->((forall (Y4:hF_Mirabelle_hf), ((P Y4)->((ord_le976219883lle_hf Y4) X3)))->((forall (X:hF_Mirabelle_hf), ((P X)->((forall (Y5:hF_Mirabelle_hf), ((P Y5)->((ord_le976219883lle_hf Y5) X)))->(Q X))))->(Q (order_1640852850lle_hf P))))))
% 0.56/0.75 FOF formula (forall (P:(nat->Prop)) (X3:nat) (Q:(nat->Prop)), ((P X3)->((forall (Y4:nat), ((P Y4)->((ord_less_eq_nat Y4) X3)))->((forall (X:nat), ((P X)->((forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X)))->(Q X))))->(Q (order_Greatest_nat P)))))) of role axiom named fact_67_GreatestI2__order
% 0.56/0.75 A new axiom: (forall (P:(nat->Prop)) (X3:nat) (Q:(nat->Prop)), ((P X3)->((forall (Y4:nat), ((P Y4)->((ord_less_eq_nat Y4) X3)))->((forall (X:nat), ((P X)->((forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X)))->(Q X))))->(Q (order_Greatest_nat P))))))
% 0.56/0.75 FOF formula (((eq ((Prop->hF_Mirabelle_hf)->((Prop->hF_Mirabelle_hf)->Prop))) ord_le2017230260lle_hf) (fun (X4:(Prop->hF_Mirabelle_hf)) (Y6:(Prop->hF_Mirabelle_hf))=> ((and ((ord_le976219883lle_hf (X4 False)) (Y6 False))) ((ord_le976219883lle_hf (X4 True)) (Y6 True))))) of role axiom named fact_68_le__rel__bool__arg__iff
% 0.56/0.75 A new axiom: (((eq ((Prop->hF_Mirabelle_hf)->((Prop->hF_Mirabelle_hf)->Prop))) ord_le2017230260lle_hf) (fun (X4:(Prop->hF_Mirabelle_hf)) (Y6:(Prop->hF_Mirabelle_hf))=> ((and ((ord_le976219883lle_hf (X4 False)) (Y6 False))) ((ord_le976219883lle_hf (X4 True)) (Y6 True)))))
% 0.56/0.75 FOF formula (((eq ((Prop->nat)->((Prop->nat)->Prop))) ord_less_eq_o_nat) (fun (X4:(Prop->nat)) (Y6:(Prop->nat))=> ((and ((ord_less_eq_nat (X4 False)) (Y6 False))) ((ord_less_eq_nat (X4 True)) (Y6 True))))) of role axiom named fact_69_le__rel__bool__arg__iff
% 0.56/0.76 A new axiom: (((eq ((Prop->nat)->((Prop->nat)->Prop))) ord_less_eq_o_nat) (fun (X4:(Prop->nat)) (Y6:(Prop->nat))=> ((and ((ord_less_eq_nat (X4 False)) (Y6 False))) ((ord_less_eq_nat (X4 True)) (Y6 True)))))
% 0.56/0.76 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) hF_Mirabelle_hmem) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((member1367349282lle_hf A2) (hF_Mirabelle_hfset B2)))) of role axiom named fact_70_hmem__def
% 0.56/0.76 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) hF_Mirabelle_hmem) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((member1367349282lle_hf A2) (hF_Mirabelle_hfset B2))))
% 0.56/0.76 FOF formula (forall (A:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->Prop)), (((eq Prop) ((member1367349282lle_hf A) (collec2046588256lle_hf P))) (P A))) of role axiom named fact_71_mem__Collect__eq
% 0.56/0.76 A new axiom: (forall (A:hF_Mirabelle_hf) (P:(hF_Mirabelle_hf->Prop)), (((eq Prop) ((member1367349282lle_hf A) (collec2046588256lle_hf P))) (P A)))
% 0.56/0.76 FOF formula (forall (A:set_HF_Mirabelle_hf) (P:(set_HF_Mirabelle_hf->Prop)), (((eq Prop) ((member1490636632lle_hf A) (collec1758573718lle_hf P))) (P A))) of role axiom named fact_72_mem__Collect__eq
% 0.56/0.76 A new axiom: (forall (A:set_HF_Mirabelle_hf) (P:(set_HF_Mirabelle_hf->Prop)), (((eq Prop) ((member1490636632lle_hf A) (collec1758573718lle_hf P))) (P A)))
% 0.56/0.76 FOF formula (forall (A4:set_HF_Mirabelle_hf), (((eq set_HF_Mirabelle_hf) (collec2046588256lle_hf (fun (X2:hF_Mirabelle_hf)=> ((member1367349282lle_hf X2) A4)))) A4)) of role axiom named fact_73_Collect__mem__eq
% 0.56/0.76 A new axiom: (forall (A4:set_HF_Mirabelle_hf), (((eq set_HF_Mirabelle_hf) (collec2046588256lle_hf (fun (X2:hF_Mirabelle_hf)=> ((member1367349282lle_hf X2) A4)))) A4))
% 0.56/0.76 FOF formula (forall (A4:set_se933006839lle_hf), (((eq set_se933006839lle_hf) (collec1758573718lle_hf (fun (X2:set_HF_Mirabelle_hf)=> ((member1490636632lle_hf X2) A4)))) A4)) of role axiom named fact_74_Collect__mem__eq
% 0.56/0.76 A new axiom: (forall (A4:set_se933006839lle_hf), (((eq set_se933006839lle_hf) (collec1758573718lle_hf (fun (X2:set_HF_Mirabelle_hf)=> ((member1490636632lle_hf X2) A4)))) A4))
% 0.56/0.76 FOF formula (forall (P:(set_HF_Mirabelle_hf->Prop)) (Q:(set_HF_Mirabelle_hf->Prop)), ((forall (X:set_HF_Mirabelle_hf), (((eq Prop) (P X)) (Q X)))->(((eq set_se933006839lle_hf) (collec1758573718lle_hf P)) (collec1758573718lle_hf Q)))) of role axiom named fact_75_Collect__cong
% 0.56/0.76 A new axiom: (forall (P:(set_HF_Mirabelle_hf->Prop)) (Q:(set_HF_Mirabelle_hf->Prop)), ((forall (X:set_HF_Mirabelle_hf), (((eq Prop) (P X)) (Q X)))->(((eq set_se933006839lle_hf) (collec1758573718lle_hf P)) (collec1758573718lle_hf Q))))
% 0.56/0.76 FOF formula (forall (V4:hF_Mirabelle_hf) (A4:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)), (((eq Prop) ((hF_Mirabelle_hmem V4) ((hF_Mirabelle_RepFun A4) F))) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) A4)) (((eq hF_Mirabelle_hf) V4) (F U2))))))) of role axiom named fact_76_RepFun__iff
% 0.56/0.76 A new axiom: (forall (V4:hF_Mirabelle_hf) (A4:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)), (((eq Prop) ((hF_Mirabelle_hmem V4) ((hF_Mirabelle_RepFun A4) F))) ((ex hF_Mirabelle_hf) (fun (U2:hF_Mirabelle_hf)=> ((and ((hF_Mirabelle_hmem U2) A4)) (((eq hF_Mirabelle_hf) V4) (F U2)))))))
% 0.56/0.76 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (A3:hF_Mirabelle_hf) (B3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf A3) B3)) (not (((eq hF_Mirabelle_hf) A3) B3))))) of role axiom named fact_77_less__hf__def
% 0.56/0.76 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (A3:hF_Mirabelle_hf) (B3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf A3) B3)) (not (((eq hF_Mirabelle_hf) A3) B3)))))
% 0.56/0.76 FOF formula (((eq ((hF_Mirabelle_hf->hF_Mirabelle_hf)->Prop)) order_690706045lle_hf) (fun (F2:(hF_Mirabelle_hf->hF_Mirabelle_hf))=> (forall (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X2) Y3)->((ord_le976219883lle_hf (F2 Y3)) (F2 X2)))))) of role axiom named fact_78_antimono__def
% 0.62/0.78 A new axiom: (((eq ((hF_Mirabelle_hf->hF_Mirabelle_hf)->Prop)) order_690706045lle_hf) (fun (F2:(hF_Mirabelle_hf->hF_Mirabelle_hf))=> (forall (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X2) Y3)->((ord_le976219883lle_hf (F2 Y3)) (F2 X2))))))
% 0.62/0.78 FOF formula (((eq ((hF_Mirabelle_hf->nat)->Prop)) order_557194383hf_nat) (fun (F2:(hF_Mirabelle_hf->nat))=> (forall (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X2) Y3)->((ord_less_eq_nat (F2 Y3)) (F2 X2)))))) of role axiom named fact_79_antimono__def
% 0.62/0.78 A new axiom: (((eq ((hF_Mirabelle_hf->nat)->Prop)) order_557194383hf_nat) (fun (F2:(hF_Mirabelle_hf->nat))=> (forall (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X2) Y3)->((ord_less_eq_nat (F2 Y3)) (F2 X2))))))
% 0.62/0.78 FOF formula (((eq ((nat->hF_Mirabelle_hf)->Prop)) order_671905679lle_hf) (fun (F2:(nat->hF_Mirabelle_hf))=> (forall (X2:nat) (Y3:nat), (((ord_less_eq_nat X2) Y3)->((ord_le976219883lle_hf (F2 Y3)) (F2 X2)))))) of role axiom named fact_80_antimono__def
% 0.62/0.78 A new axiom: (((eq ((nat->hF_Mirabelle_hf)->Prop)) order_671905679lle_hf) (fun (F2:(nat->hF_Mirabelle_hf))=> (forall (X2:nat) (Y3:nat), (((ord_less_eq_nat X2) Y3)->((ord_le976219883lle_hf (F2 Y3)) (F2 X2))))))
% 0.62/0.78 FOF formula (((eq ((nat->nat)->Prop)) order_1631207636at_nat) (fun (F2:(nat->nat))=> (forall (X2:nat) (Y3:nat), (((ord_less_eq_nat X2) Y3)->((ord_less_eq_nat (F2 Y3)) (F2 X2)))))) of role axiom named fact_81_antimono__def
% 0.62/0.78 A new axiom: (((eq ((nat->nat)->Prop)) order_1631207636at_nat) (fun (F2:(nat->nat))=> (forall (X2:nat) (Y3:nat), (((ord_less_eq_nat X2) Y3)->((ord_less_eq_nat (F2 Y3)) (F2 X2))))))
% 0.62/0.78 FOF formula (forall (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)), ((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F Y4)) (F X))))->(order_690706045lle_hf F))) of role axiom named fact_82_antimonoI
% 0.62/0.78 A new axiom: (forall (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)), ((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F Y4)) (F X))))->(order_690706045lle_hf F)))
% 0.62/0.78 FOF formula (forall (F:(hF_Mirabelle_hf->nat)), ((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F Y4)) (F X))))->(order_557194383hf_nat F))) of role axiom named fact_83_antimonoI
% 0.62/0.78 A new axiom: (forall (F:(hF_Mirabelle_hf->nat)), ((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F Y4)) (F X))))->(order_557194383hf_nat F)))
% 0.62/0.78 FOF formula (forall (F:(nat->hF_Mirabelle_hf)), ((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F Y4)) (F X))))->(order_671905679lle_hf F))) of role axiom named fact_84_antimonoI
% 0.62/0.78 A new axiom: (forall (F:(nat->hF_Mirabelle_hf)), ((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F Y4)) (F X))))->(order_671905679lle_hf F)))
% 0.62/0.78 FOF formula (forall (F:(nat->nat)), ((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F Y4)) (F X))))->(order_1631207636at_nat F))) of role axiom named fact_85_antimonoI
% 0.62/0.78 A new axiom: (forall (F:(nat->nat)), ((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F Y4)) (F X))))->(order_1631207636at_nat F)))
% 0.62/0.78 FOF formula (forall (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_690706045lle_hf F)->(((ord_le976219883lle_hf X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3))))) of role axiom named fact_86_antimonoE
% 0.62/0.78 A new axiom: (forall (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_690706045lle_hf F)->(((ord_le976219883lle_hf X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3)))))
% 0.62/0.78 FOF formula (forall (F:(hF_Mirabelle_hf->nat)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_557194383hf_nat F)->(((ord_le976219883lle_hf X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3))))) of role axiom named fact_87_antimonoE
% 0.62/0.78 A new axiom: (forall (F:(hF_Mirabelle_hf->nat)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_557194383hf_nat F)->(((ord_le976219883lle_hf X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (F:(nat->hF_Mirabelle_hf)) (X3:nat) (Y2:nat), ((order_671905679lle_hf F)->(((ord_less_eq_nat X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3))))) of role axiom named fact_88_antimonoE
% 0.62/0.79 A new axiom: (forall (F:(nat->hF_Mirabelle_hf)) (X3:nat) (Y2:nat), ((order_671905679lle_hf F)->(((ord_less_eq_nat X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (F:(nat->nat)) (X3:nat) (Y2:nat), ((order_1631207636at_nat F)->(((ord_less_eq_nat X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3))))) of role axiom named fact_89_antimonoE
% 0.62/0.79 A new axiom: (forall (F:(nat->nat)) (X3:nat) (Y2:nat), ((order_1631207636at_nat F)->(((ord_less_eq_nat X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_690706045lle_hf F)->(((ord_le976219883lle_hf X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3))))) of role axiom named fact_90_antimonoD
% 0.62/0.79 A new axiom: (forall (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_690706045lle_hf F)->(((ord_le976219883lle_hf X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (F:(hF_Mirabelle_hf->nat)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_557194383hf_nat F)->(((ord_le976219883lle_hf X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3))))) of role axiom named fact_91_antimonoD
% 0.62/0.79 A new axiom: (forall (F:(hF_Mirabelle_hf->nat)) (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((order_557194383hf_nat F)->(((ord_le976219883lle_hf X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (F:(nat->hF_Mirabelle_hf)) (X3:nat) (Y2:nat), ((order_671905679lle_hf F)->(((ord_less_eq_nat X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3))))) of role axiom named fact_92_antimonoD
% 0.62/0.79 A new axiom: (forall (F:(nat->hF_Mirabelle_hf)) (X3:nat) (Y2:nat), ((order_671905679lle_hf F)->(((ord_less_eq_nat X3) Y2)->((ord_le976219883lle_hf (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (F:(nat->nat)) (X3:nat) (Y2:nat), ((order_1631207636at_nat F)->(((ord_less_eq_nat X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3))))) of role axiom named fact_93_antimonoD
% 0.62/0.79 A new axiom: (forall (F:(nat->nat)) (X3:nat) (Y2:nat), ((order_1631207636at_nat F)->(((ord_less_eq_nat X3) Y2)->((ord_less_eq_nat (F Y2)) (F X3)))))
% 0.62/0.79 FOF formula (forall (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) A)->False)) of role axiom named fact_94_verit__comp__simplify1_I1_J
% 0.62/0.79 A new axiom: (forall (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) A)->False))
% 0.62/0.79 FOF formula (forall (A:nat), (((ord_less_nat A) A)->False)) of role axiom named fact_95_verit__comp__simplify1_I1_J
% 0.62/0.79 A new axiom: (forall (A:nat), (((ord_less_nat A) A)->False))
% 0.62/0.79 FOF formula (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_96_ord__eq__less__subst
% 0.62/0.79 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.62/0.79 FOF formula (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq nat) A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_97_ord__eq__less__subst
% 0.62/0.79 A new axiom: (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq nat) A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.62/0.81 FOF formula (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_98_ord__eq__less__subst
% 0.62/0.81 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), ((((eq hF_Mirabelle_hf) A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.62/0.81 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_99_ord__eq__less__subst
% 0.62/0.81 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.62/0.81 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_100_ord__less__eq__subst
% 0.62/0.81 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.62/0.81 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le1310584031lle_hf A) B)->((((eq nat) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_101_ord__less__eq__subst
% 0.62/0.81 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le1310584031lle_hf A) B)->((((eq nat) (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.62/0.81 FOF formula (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_nat A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_102_ord__less__eq__subst
% 0.62/0.81 A new axiom: (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_nat A) B)->((((eq hF_Mirabelle_hf) (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.62/0.81 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->((((eq nat) (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_103_ord__less__eq__subst
% 0.62/0.81 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->((((eq nat) (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.62/0.81 FOF formula (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_104_order__less__subst1
% 0.62/0.82 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.62/0.82 FOF formula (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le1310584031lle_hf A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_105_order__less__subst1
% 0.62/0.82 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le1310584031lle_hf A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.62/0.82 FOF formula (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_nat A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_106_order__less__subst1
% 0.62/0.82 A new axiom: (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_nat A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.62/0.82 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_107_order__less__subst1
% 0.62/0.82 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.62/0.82 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_108_order__less__subst2
% 0.62/0.82 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.62/0.82 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le1310584031lle_hf A) B)->(((ord_less_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_109_order__less__subst2
% 0.62/0.82 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le1310584031lle_hf A) B)->(((ord_less_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.62/0.82 FOF formula (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_nat A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_110_order__less__subst2
% 0.62/0.82 A new axiom: (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_nat A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.62/0.83 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_111_order__less__subst2
% 0.62/0.83 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.62/0.83 FOF formula (forall (X3:nat), ((ex nat) (fun (X_1:nat)=> ((ord_less_nat X3) X_1)))) of role axiom named fact_112_gt__ex
% 0.62/0.83 A new axiom: (forall (X3:nat), ((ex nat) (fun (X_1:nat)=> ((ord_less_nat X3) X_1))))
% 0.62/0.83 FOF formula (forall (X3:nat) (Y2:nat), ((not (((eq nat) X3) Y2))->((((ord_less_nat X3) Y2)->False)->((ord_less_nat Y2) X3)))) of role axiom named fact_113_neqE
% 0.62/0.83 A new axiom: (forall (X3:nat) (Y2:nat), ((not (((eq nat) X3) Y2))->((((ord_less_nat X3) Y2)->False)->((ord_less_nat Y2) X3))))
% 0.62/0.83 FOF formula (forall (X3:nat) (Y2:nat), (((eq Prop) (not (((eq nat) X3) Y2))) ((or ((ord_less_nat X3) Y2)) ((ord_less_nat Y2) X3)))) of role axiom named fact_114_neq__iff
% 0.62/0.83 A new axiom: (forall (X3:nat) (Y2:nat), (((eq Prop) (not (((eq nat) X3) Y2))) ((or ((ord_less_nat X3) Y2)) ((ord_less_nat Y2) X3))))
% 0.62/0.83 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf B) A)->False))) of role axiom named fact_115_order_Oasym
% 0.62/0.83 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf B) A)->False)))
% 0.62/0.83 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False))) of role axiom named fact_116_order_Oasym
% 0.62/0.83 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False)))
% 0.62/0.83 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(not (((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_117_less__imp__neq
% 0.62/0.83 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(not (((eq hF_Mirabelle_hf) X3) Y2))))
% 0.62/0.83 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(not (((eq nat) X3) Y2)))) of role axiom named fact_118_less__imp__neq
% 0.62/0.83 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(not (((eq nat) X3) Y2))))
% 0.62/0.83 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->False))) of role axiom named fact_119_less__asym
% 0.62/0.83 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->False)))
% 0.62/0.83 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->False))) of role axiom named fact_120_less__asym
% 0.62/0.83 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->False)))
% 0.62/0.83 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf B) A)->False))) of role axiom named fact_121_less__asym_H
% 0.62/0.83 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf B) A)->False)))
% 0.62/0.83 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False))) of role axiom named fact_122_less__asym_H
% 0.62/0.83 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False)))
% 0.62/0.83 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) Z3)->((ord_le1310584031lle_hf X3) Z3)))) of role axiom named fact_123_less__trans
% 0.62/0.83 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) Z3)->((ord_le1310584031lle_hf X3) Z3))))
% 0.62/0.83 FOF formula (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) Z3)->((ord_less_nat X3) Z3)))) of role axiom named fact_124_less__trans
% 0.62/0.84 A new axiom: (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) Z3)->((ord_less_nat X3) Z3))))
% 0.62/0.84 FOF formula (forall (X3:nat) (Y2:nat), ((or ((or ((ord_less_nat X3) Y2)) (((eq nat) X3) Y2))) ((ord_less_nat Y2) X3))) of role axiom named fact_125_less__linear
% 0.62/0.84 A new axiom: (forall (X3:nat) (Y2:nat), ((or ((or ((ord_less_nat X3) Y2)) (((eq nat) X3) Y2))) ((ord_less_nat Y2) X3)))
% 0.62/0.84 FOF formula (forall (X3:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) X3)->False)) of role axiom named fact_126_less__irrefl
% 0.62/0.84 A new axiom: (forall (X3:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) X3)->False))
% 0.62/0.84 FOF formula (forall (X3:nat), (((ord_less_nat X3) X3)->False)) of role axiom named fact_127_less__irrefl
% 0.62/0.84 A new axiom: (forall (X3:nat), (((ord_less_nat X3) X3)->False))
% 0.62/0.84 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) B)->(((ord_le1310584031lle_hf B) C)->((ord_le1310584031lle_hf A) C)))) of role axiom named fact_128_ord__eq__less__trans
% 0.62/0.84 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), ((((eq hF_Mirabelle_hf) A) B)->(((ord_le1310584031lle_hf B) C)->((ord_le1310584031lle_hf A) C))))
% 0.62/0.84 FOF formula (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_129_ord__eq__less__trans
% 0.62/0.84 A new axiom: (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C))))
% 0.62/0.84 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->((((eq hF_Mirabelle_hf) B) C)->((ord_le1310584031lle_hf A) C)))) of role axiom named fact_130_ord__less__eq__trans
% 0.62/0.84 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->((((eq hF_Mirabelle_hf) B) C)->((ord_le1310584031lle_hf A) C))))
% 0.62/0.84 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->((((eq nat) B) C)->((ord_less_nat A) C)))) of role axiom named fact_131_ord__less__eq__trans
% 0.62/0.84 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->((((eq nat) B) C)->((ord_less_nat A) C))))
% 0.62/0.84 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(((ord_le1310584031lle_hf A) B)->False))) of role axiom named fact_132_dual__order_Oasym
% 0.62/0.84 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(((ord_le1310584031lle_hf A) B)->False)))
% 0.62/0.84 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(((ord_less_nat A) B)->False))) of role axiom named fact_133_dual__order_Oasym
% 0.62/0.84 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(((ord_less_nat A) B)->False)))
% 0.62/0.84 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(not (((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_134_less__imp__not__eq
% 0.62/0.84 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(not (((eq hF_Mirabelle_hf) X3) Y2))))
% 0.62/0.84 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(not (((eq nat) X3) Y2)))) of role axiom named fact_135_less__imp__not__eq
% 0.62/0.84 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(not (((eq nat) X3) Y2))))
% 0.62/0.84 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->False))) of role axiom named fact_136_less__not__sym
% 0.62/0.84 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->False)))
% 0.62/0.84 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->False))) of role axiom named fact_137_less__not__sym
% 0.62/0.84 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->False)))
% 0.62/0.84 FOF formula (forall (P:(nat->Prop)) (A:nat), ((forall (X:nat), ((forall (Y5:nat), (((ord_less_nat Y5) X)->(P Y5)))->(P X)))->(P A))) of role axiom named fact_138_less__induct
% 0.62/0.84 A new axiom: (forall (P:(nat->Prop)) (A:nat), ((forall (X:nat), ((forall (Y5:nat), (((ord_less_nat Y5) X)->(P Y5)))->(P X)))->(P A)))
% 0.62/0.85 FOF formula (forall (Y2:nat) (X3:nat), ((((ord_less_nat Y2) X3)->False)->(((eq Prop) (((ord_less_nat X3) Y2)->False)) (((eq nat) X3) Y2)))) of role axiom named fact_139_antisym__conv3
% 0.62/0.85 A new axiom: (forall (Y2:nat) (X3:nat), ((((ord_less_nat Y2) X3)->False)->(((eq Prop) (((ord_less_nat X3) Y2)->False)) (((eq nat) X3) Y2))))
% 0.62/0.85 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(not (((eq hF_Mirabelle_hf) Y2) X3)))) of role axiom named fact_140_less__imp__not__eq2
% 0.62/0.85 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(not (((eq hF_Mirabelle_hf) Y2) X3))))
% 0.62/0.85 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(not (((eq nat) Y2) X3)))) of role axiom named fact_141_less__imp__not__eq2
% 0.62/0.85 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(not (((eq nat) Y2) X3))))
% 0.62/0.85 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (P:Prop), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->P))) of role axiom named fact_142_less__imp__triv
% 0.62/0.85 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (P:Prop), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->P)))
% 0.62/0.85 FOF formula (forall (X3:nat) (Y2:nat) (P:Prop), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->P))) of role axiom named fact_143_less__imp__triv
% 0.62/0.85 A new axiom: (forall (X3:nat) (Y2:nat) (P:Prop), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->P)))
% 0.62/0.85 FOF formula (forall (X3:nat) (Y2:nat), ((((ord_less_nat X3) Y2)->False)->((not (((eq nat) X3) Y2))->((ord_less_nat Y2) X3)))) of role axiom named fact_144_linorder__cases
% 0.62/0.85 A new axiom: (forall (X3:nat) (Y2:nat), ((((ord_less_nat X3) Y2)->False)->((not (((eq nat) X3) Y2))->((ord_less_nat Y2) X3))))
% 0.62/0.85 FOF formula (forall (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) A)->False)) of role axiom named fact_145_dual__order_Oirrefl
% 0.62/0.85 A new axiom: (forall (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) A)->False))
% 0.62/0.85 FOF formula (forall (A:nat), (((ord_less_nat A) A)->False)) of role axiom named fact_146_dual__order_Oirrefl
% 0.62/0.85 A new axiom: (forall (A:nat), (((ord_less_nat A) A)->False))
% 0.62/0.85 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf B) C)->((ord_le1310584031lle_hf A) C)))) of role axiom named fact_147_order_Ostrict__trans
% 0.62/0.85 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le1310584031lle_hf B) C)->((ord_le1310584031lle_hf A) C))))
% 0.62/0.85 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_148_order_Ostrict__trans
% 0.62/0.85 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C))))
% 0.62/0.85 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->False))) of role axiom named fact_149_less__imp__not__less
% 0.62/0.85 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) X3)->False)))
% 0.62/0.85 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->False))) of role axiom named fact_150_less__imp__not__less
% 0.62/0.85 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->(((ord_less_nat Y2) X3)->False)))
% 0.62/0.85 FOF formula (((eq ((nat->Prop)->Prop)) (fun (P2:(nat->Prop))=> ((ex nat) (fun (X5:nat)=> (P2 X5))))) (fun (P3:(nat->Prop))=> ((ex nat) (fun (N:nat)=> ((and (P3 N)) (forall (M:nat), (((ord_less_nat M) N)->((P3 M)->False)))))))) of role axiom named fact_151_exists__least__iff
% 0.62/0.85 A new axiom: (((eq ((nat->Prop)->Prop)) (fun (P2:(nat->Prop))=> ((ex nat) (fun (X5:nat)=> (P2 X5))))) (fun (P3:(nat->Prop))=> ((ex nat) (fun (N:nat)=> ((and (P3 N)) (forall (M:nat), (((ord_less_nat M) N)->((P3 M)->False))))))))
% 0.62/0.85 FOF formula (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A5:nat) (B5:nat), (((ord_less_nat A5) B5)->((P A5) B5)))->((forall (A5:nat), ((P A5) A5))->((forall (A5:nat) (B5:nat), (((P B5) A5)->((P A5) B5)))->((P A) B))))) of role axiom named fact_152_linorder__less__wlog
% 0.71/0.86 A new axiom: (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A5:nat) (B5:nat), (((ord_less_nat A5) B5)->((P A5) B5)))->((forall (A5:nat), ((P A5) A5))->((forall (A5:nat) (B5:nat), (((P B5) A5)->((P A5) B5)))->((P A) B)))))
% 0.71/0.86 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(((ord_le1310584031lle_hf C) B)->((ord_le1310584031lle_hf C) A)))) of role axiom named fact_153_dual__order_Ostrict__trans
% 0.71/0.86 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(((ord_le1310584031lle_hf C) B)->((ord_le1310584031lle_hf C) A))))
% 0.71/0.86 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A)))) of role axiom named fact_154_dual__order_Ostrict__trans
% 0.71/0.86 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A))))
% 0.71/0.86 FOF formula (forall (X3:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X3) Y2)->False)) ((or ((ord_less_nat Y2) X3)) (((eq nat) X3) Y2)))) of role axiom named fact_155_not__less__iff__gr__or__eq
% 0.71/0.86 A new axiom: (forall (X3:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X3) Y2)->False)) ((or ((ord_less_nat Y2) X3)) (((eq nat) X3) Y2))))
% 0.71/0.86 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(not (((eq hF_Mirabelle_hf) A) B)))) of role axiom named fact_156_order_Ostrict__implies__not__eq
% 0.71/0.86 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(not (((eq hF_Mirabelle_hf) A) B))))
% 0.71/0.86 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(not (((eq nat) A) B)))) of role axiom named fact_157_order_Ostrict__implies__not__eq
% 0.71/0.86 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(not (((eq nat) A) B))))
% 0.71/0.86 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(not (((eq hF_Mirabelle_hf) A) B)))) of role axiom named fact_158_dual__order_Ostrict__implies__not__eq
% 0.71/0.86 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(not (((eq hF_Mirabelle_hf) A) B))))
% 0.71/0.86 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(not (((eq nat) A) B)))) of role axiom named fact_159_dual__order_Ostrict__implies__not__eq
% 0.71/0.86 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(not (((eq nat) A) B))))
% 0.71/0.86 FOF formula (forall (B6:nat) (A6:nat), (((eq Prop) (((ord_less_eq_nat B6) A6)->False)) ((ord_less_nat A6) B6))) of role axiom named fact_160_verit__comp__simplify1_I3_J
% 0.71/0.86 A new axiom: (forall (B6:nat) (A6:nat), (((eq Prop) (((ord_less_eq_nat B6) A6)->False)) ((ord_less_nat A6) B6)))
% 0.71/0.86 FOF formula (forall (Y2:hF_Mirabelle_hf) (X3:hF_Mirabelle_hf), (((ord_le976219883lle_hf Y2) X3)->(((ord_le1310584031lle_hf X3) Y2)->False))) of role axiom named fact_161_leD
% 0.71/0.86 A new axiom: (forall (Y2:hF_Mirabelle_hf) (X3:hF_Mirabelle_hf), (((ord_le976219883lle_hf Y2) X3)->(((ord_le1310584031lle_hf X3) Y2)->False)))
% 0.71/0.86 FOF formula (forall (Y2:nat) (X3:nat), (((ord_less_eq_nat Y2) X3)->(((ord_less_nat X3) Y2)->False))) of role axiom named fact_162_leD
% 0.71/0.86 A new axiom: (forall (Y2:nat) (X3:nat), (((ord_less_eq_nat Y2) X3)->(((ord_less_nat X3) Y2)->False)))
% 0.71/0.86 FOF formula (forall (X3:nat) (Y2:nat), ((((ord_less_nat X3) Y2)->False)->((ord_less_eq_nat Y2) X3))) of role axiom named fact_163_leI
% 0.71/0.86 A new axiom: (forall (X3:nat) (Y2:nat), ((((ord_less_nat X3) Y2)->False)->((ord_less_eq_nat Y2) X3)))
% 0.71/0.86 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((or ((ord_le1310584031lle_hf X2) Y3)) (((eq hF_Mirabelle_hf) X2) Y3)))) of role axiom named fact_164_le__less
% 0.71/0.86 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((or ((ord_le1310584031lle_hf X2) Y3)) (((eq hF_Mirabelle_hf) X2) Y3))))
% 0.71/0.87 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X2:nat) (Y3:nat)=> ((or ((ord_less_nat X2) Y3)) (((eq nat) X2) Y3)))) of role axiom named fact_165_le__less
% 0.71/0.87 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X2:nat) (Y3:nat)=> ((or ((ord_less_nat X2) Y3)) (((eq nat) X2) Y3))))
% 0.71/0.87 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf X2) Y3)) (not (((eq hF_Mirabelle_hf) X2) Y3))))) of role axiom named fact_166_less__le
% 0.71/0.87 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf X2) Y3)) (not (((eq hF_Mirabelle_hf) X2) Y3)))))
% 0.71/0.87 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) (not (((eq nat) X2) Y3))))) of role axiom named fact_167_less__le
% 0.71/0.87 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) (not (((eq nat) X2) Y3)))))
% 0.71/0.87 FOF formula (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_168_order__le__less__subst1
% 0.71/0.87 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.71/0.87 FOF formula (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le976219883lle_hf A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_169_order__le__less__subst1
% 0.71/0.87 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le976219883lle_hf A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.71/0.87 FOF formula (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_170_order__le__less__subst1
% 0.71/0.87 A new axiom: (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) (F B))->(((ord_le1310584031lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.71/0.87 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_171_order__le__less__subst1
% 0.71/0.87 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.71/0.87 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_172_order__le__less__subst2
% 0.71/0.87 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.71/0.88 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le976219883lle_hf A) B)->(((ord_less_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_173_order__le__less__subst2
% 0.71/0.88 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le976219883lle_hf A) B)->(((ord_less_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.71/0.88 FOF formula (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_174_order__le__less__subst2
% 0.71/0.88 A new axiom: (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_eq_nat A) B)->(((ord_le1310584031lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.71/0.88 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_175_order__le__less__subst2
% 0.71/0.88 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.71/0.88 FOF formula (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_176_order__less__le__subst1
% 0.71/0.88 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.71/0.88 FOF formula (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_nat A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_177_order__less__le__subst1
% 0.71/0.88 A new axiom: (forall (A:nat) (F:(hF_Mirabelle_hf->nat)) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_less_nat A) (F B))->(((ord_le976219883lle_hf B) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le976219883lle_hf X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.71/0.88 FOF formula (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le1310584031lle_hf A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C)))))) of role axiom named fact_178_order__less__le__subst1
% 0.71/0.88 A new axiom: (forall (A:hF_Mirabelle_hf) (F:(nat->hF_Mirabelle_hf)) (B:nat) (C:nat), (((ord_le1310584031lle_hf A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le976219883lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf A) (F C))))))
% 0.73/0.89 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_179_order__less__le__subst1
% 0.73/0.89 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.73/0.89 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_180_order__less__le__subst2
% 0.73/0.89 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.73/0.89 FOF formula (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_nat A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C))))) of role axiom named fact_181_order__less__le__subst2
% 0.73/0.89 A new axiom: (forall (A:nat) (B:nat) (F:(nat->hF_Mirabelle_hf)) (C:hF_Mirabelle_hf), (((ord_less_nat A) B)->(((ord_le976219883lle_hf (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_le1310584031lle_hf (F X)) (F Y4))))->((ord_le1310584031lle_hf (F A)) C)))))
% 0.73/0.89 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le1310584031lle_hf A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_182_order__less__le__subst2
% 0.73/0.89 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->nat)) (C:nat), (((ord_le1310584031lle_hf A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X:hF_Mirabelle_hf) (Y4:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.73/0.89 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_183_order__less__le__subst2
% 0.73/0.89 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X:nat) (Y4:nat), (((ord_less_nat X) Y4)->((ord_less_nat (F X)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.73/0.89 FOF formula (forall (X3:nat) (Y2:nat), (((eq Prop) (((ord_less_eq_nat X3) Y2)->False)) ((ord_less_nat Y2) X3))) of role axiom named fact_184_not__le
% 0.73/0.89 A new axiom: (forall (X3:nat) (Y2:nat), (((eq Prop) (((ord_less_eq_nat X3) Y2)->False)) ((ord_less_nat Y2) X3)))
% 0.73/0.89 FOF formula (forall (X3:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X3) Y2)->False)) ((ord_less_eq_nat Y2) X3))) of role axiom named fact_185_not__less
% 0.73/0.89 A new axiom: (forall (X3:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X3) Y2)->False)) ((ord_less_eq_nat Y2) X3)))
% 0.73/0.89 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->((not (((eq hF_Mirabelle_hf) A) B))->((ord_le1310584031lle_hf A) B)))) of role axiom named fact_186_le__neq__trans
% 0.73/0.89 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->((not (((eq hF_Mirabelle_hf) A) B))->((ord_le1310584031lle_hf A) B))))
% 0.73/0.89 FOF formula (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->((not (((eq nat) A) B))->((ord_less_nat A) B)))) of role axiom named fact_187_le__neq__trans
% 0.73/0.90 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->((not (((eq nat) A) B))->((ord_less_nat A) B))))
% 0.73/0.90 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((((ord_le1310584031lle_hf X3) Y2)->False)->(((eq Prop) ((ord_le976219883lle_hf X3) Y2)) (((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_188_antisym__conv1
% 0.73/0.90 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), ((((ord_le1310584031lle_hf X3) Y2)->False)->(((eq Prop) ((ord_le976219883lle_hf X3) Y2)) (((eq hF_Mirabelle_hf) X3) Y2))))
% 0.73/0.90 FOF formula (forall (X3:nat) (Y2:nat), ((((ord_less_nat X3) Y2)->False)->(((eq Prop) ((ord_less_eq_nat X3) Y2)) (((eq nat) X3) Y2)))) of role axiom named fact_189_antisym__conv1
% 0.73/0.90 A new axiom: (forall (X3:nat) (Y2:nat), ((((ord_less_nat X3) Y2)->False)->(((eq Prop) ((ord_less_eq_nat X3) Y2)) (((eq nat) X3) Y2))))
% 0.73/0.90 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((eq Prop) (((ord_le1310584031lle_hf X3) Y2)->False)) (((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_190_antisym__conv2
% 0.73/0.90 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((eq Prop) (((ord_le1310584031lle_hf X3) Y2)->False)) (((eq hF_Mirabelle_hf) X3) Y2))))
% 0.73/0.90 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->(((eq Prop) (((ord_less_nat X3) Y2)->False)) (((eq nat) X3) Y2)))) of role axiom named fact_191_antisym__conv2
% 0.73/0.90 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->(((eq Prop) (((ord_less_nat X3) Y2)->False)) (((eq nat) X3) Y2))))
% 0.73/0.90 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->((ord_le976219883lle_hf X3) Y2))) of role axiom named fact_192_less__imp__le
% 0.73/0.90 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->((ord_le976219883lle_hf X3) Y2)))
% 0.73/0.90 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->((ord_less_eq_nat X3) Y2))) of role axiom named fact_193_less__imp__le
% 0.73/0.90 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_nat X3) Y2)->((ord_less_eq_nat X3) Y2)))
% 0.73/0.90 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) Z3)->((ord_le1310584031lle_hf X3) Z3)))) of role axiom named fact_194_le__less__trans
% 0.73/0.90 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->(((ord_le1310584031lle_hf Y2) Z3)->((ord_le1310584031lle_hf X3) Z3))))
% 0.73/0.90 FOF formula (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_nat Y2) Z3)->((ord_less_nat X3) Z3)))) of role axiom named fact_195_le__less__trans
% 0.73/0.90 A new axiom: (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_nat Y2) Z3)->((ord_less_nat X3) Z3))))
% 0.73/0.90 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le976219883lle_hf Y2) Z3)->((ord_le1310584031lle_hf X3) Z3)))) of role axiom named fact_196_less__le__trans
% 0.73/0.90 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf) (Z3:hF_Mirabelle_hf), (((ord_le1310584031lle_hf X3) Y2)->(((ord_le976219883lle_hf Y2) Z3)->((ord_le1310584031lle_hf X3) Z3))))
% 0.73/0.90 FOF formula (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_nat X3) Y2)->(((ord_less_eq_nat Y2) Z3)->((ord_less_nat X3) Z3)))) of role axiom named fact_197_less__le__trans
% 0.73/0.90 A new axiom: (forall (X3:nat) (Y2:nat) (Z3:nat), (((ord_less_nat X3) Y2)->(((ord_less_eq_nat Y2) Z3)->((ord_less_nat X3) Z3))))
% 0.73/0.90 FOF formula (forall (X3:nat) (Y2:nat), ((or ((ord_less_eq_nat X3) Y2)) ((ord_less_nat Y2) X3))) of role axiom named fact_198_le__less__linear
% 0.73/0.90 A new axiom: (forall (X3:nat) (Y2:nat), ((or ((ord_less_eq_nat X3) Y2)) ((ord_less_nat Y2) X3)))
% 0.73/0.90 FOF formula (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->((or ((ord_le1310584031lle_hf X3) Y2)) (((eq hF_Mirabelle_hf) X3) Y2)))) of role axiom named fact_199_le__imp__less__or__eq
% 0.73/0.90 A new axiom: (forall (X3:hF_Mirabelle_hf) (Y2:hF_Mirabelle_hf), (((ord_le976219883lle_hf X3) Y2)->((or ((ord_le1310584031lle_hf X3) Y2)) (((eq hF_Mirabelle_hf) X3) Y2))))
% 0.73/0.91 FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->((or ((ord_less_nat X3) Y2)) (((eq nat) X3) Y2)))) of role axiom named fact_200_le__imp__less__or__eq
% 0.73/0.91 A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->((or ((ord_less_nat X3) Y2)) (((eq nat) X3) Y2))))
% 0.73/0.91 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf X2) Y3)) (((ord_le976219883lle_hf Y3) X2)->False)))) of role axiom named fact_201_less__le__not__le
% 0.73/0.91 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (X2:hF_Mirabelle_hf) (Y3:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf X2) Y3)) (((ord_le976219883lle_hf Y3) X2)->False))))
% 0.73/0.91 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) (((ord_less_eq_nat Y3) X2)->False)))) of role axiom named fact_202_less__le__not__le
% 0.73/0.91 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) (((ord_less_eq_nat Y3) X2)->False))))
% 0.73/0.91 FOF formula (forall (Y2:nat) (X3:nat), ((((ord_less_eq_nat Y2) X3)->False)->((ord_less_nat X3) Y2))) of role axiom named fact_203_not__le__imp__less
% 0.73/0.91 A new axiom: (forall (Y2:nat) (X3:nat), ((((ord_less_eq_nat Y2) X3)->False)->((ord_less_nat X3) Y2)))
% 0.73/0.91 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le1310584031lle_hf B) C)->((ord_le1310584031lle_hf A) C)))) of role axiom named fact_204_order_Ostrict__trans1
% 0.73/0.91 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf A) B)->(((ord_le1310584031lle_hf B) C)->((ord_le1310584031lle_hf A) C))))
% 0.73/0.91 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_205_order_Ostrict__trans1
% 0.73/0.91 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C))))
% 0.73/0.91 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le976219883lle_hf B) C)->((ord_le1310584031lle_hf A) C)))) of role axiom named fact_206_order_Ostrict__trans2
% 0.73/0.91 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->(((ord_le976219883lle_hf B) C)->((ord_le1310584031lle_hf A) C))))
% 0.73/0.91 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_207_order_Ostrict__trans2
% 0.73/0.91 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_nat A) C))))
% 0.73/0.91 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((or ((ord_le1310584031lle_hf A2) B2)) (((eq hF_Mirabelle_hf) A2) B2)))) of role axiom named fact_208_order_Oorder__iff__strict
% 0.73/0.91 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((or ((ord_le1310584031lle_hf A2) B2)) (((eq hF_Mirabelle_hf) A2) B2))))
% 0.73/0.91 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A2:nat) (B2:nat)=> ((or ((ord_less_nat A2) B2)) (((eq nat) A2) B2)))) of role axiom named fact_209_order_Oorder__iff__strict
% 0.73/0.91 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A2:nat) (B2:nat)=> ((or ((ord_less_nat A2) B2)) (((eq nat) A2) B2))))
% 0.73/0.91 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf A2) B2)) (not (((eq hF_Mirabelle_hf) A2) B2))))) of role axiom named fact_210_order_Ostrict__iff__order
% 0.73/0.91 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (A2:hF_Mirabelle_hf) (B2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf A2) B2)) (not (((eq hF_Mirabelle_hf) A2) B2)))))
% 0.73/0.92 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) (not (((eq nat) A2) B2))))) of role axiom named fact_211_order_Ostrict__iff__order
% 0.73/0.92 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) (not (((eq nat) A2) B2)))))
% 0.73/0.92 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf B) A)->(((ord_le1310584031lle_hf C) B)->((ord_le1310584031lle_hf C) A)))) of role axiom named fact_212_dual__order_Ostrict__trans1
% 0.73/0.92 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le976219883lle_hf B) A)->(((ord_le1310584031lle_hf C) B)->((ord_le1310584031lle_hf C) A))))
% 0.73/0.92 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A)))) of role axiom named fact_213_dual__order_Ostrict__trans1
% 0.73/0.92 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A))))
% 0.73/0.92 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(((ord_le976219883lle_hf C) B)->((ord_le1310584031lle_hf C) A)))) of role axiom named fact_214_dual__order_Ostrict__trans2
% 0.73/0.92 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf) (C:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->(((ord_le976219883lle_hf C) B)->((ord_le1310584031lle_hf C) A))))
% 0.73/0.92 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_nat C) A)))) of role axiom named fact_215_dual__order_Ostrict__trans2
% 0.73/0.92 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_nat C) A))))
% 0.73/0.92 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->((ord_le976219883lle_hf A) B))) of role axiom named fact_216_order_Ostrict__implies__order
% 0.73/0.92 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), (((ord_le1310584031lle_hf A) B)->((ord_le976219883lle_hf A) B)))
% 0.73/0.92 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->((ord_less_eq_nat A) B))) of role axiom named fact_217_order_Ostrict__implies__order
% 0.73/0.92 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->((ord_less_eq_nat A) B)))
% 0.73/0.92 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (B2:hF_Mirabelle_hf) (A2:hF_Mirabelle_hf)=> ((or ((ord_le1310584031lle_hf B2) A2)) (((eq hF_Mirabelle_hf) A2) B2)))) of role axiom named fact_218_dual__order_Oorder__iff__strict
% 0.73/0.92 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le976219883lle_hf) (fun (B2:hF_Mirabelle_hf) (A2:hF_Mirabelle_hf)=> ((or ((ord_le1310584031lle_hf B2) A2)) (((eq hF_Mirabelle_hf) A2) B2))))
% 0.73/0.92 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (B2:nat) (A2:nat)=> ((or ((ord_less_nat B2) A2)) (((eq nat) A2) B2)))) of role axiom named fact_219_dual__order_Oorder__iff__strict
% 0.73/0.92 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (B2:nat) (A2:nat)=> ((or ((ord_less_nat B2) A2)) (((eq nat) A2) B2))))
% 0.73/0.92 FOF formula (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (B2:hF_Mirabelle_hf) (A2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf B2) A2)) (not (((eq hF_Mirabelle_hf) A2) B2))))) of role axiom named fact_220_dual__order_Ostrict__iff__order
% 0.73/0.92 A new axiom: (((eq (hF_Mirabelle_hf->(hF_Mirabelle_hf->Prop))) ord_le1310584031lle_hf) (fun (B2:hF_Mirabelle_hf) (A2:hF_Mirabelle_hf)=> ((and ((ord_le976219883lle_hf B2) A2)) (not (((eq hF_Mirabelle_hf) A2) B2)))))
% 0.73/0.92 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (B2:nat) (A2:nat)=> ((and ((ord_less_eq_nat B2) A2)) (not (((eq nat) A2) B2))))) of role axiom named fact_221_dual__order_Ostrict__iff__order
% 0.73/0.92 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (B2:nat) (A2:nat)=> ((and ((ord_less_eq_nat B2) A2)) (not (((eq nat) A2) B2)))))
% 0.73/0.92 FOF formula (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->((ord_le976219883lle_hf B) A))) of role axiom named fact_222_dual__order_Ostrict__implies__order
% 0.77/0.93 A new axiom: (forall (B:hF_Mirabelle_hf) (A:hF_Mirabelle_hf), (((ord_le1310584031lle_hf B) A)->((ord_le976219883lle_hf B) A)))
% 0.77/0.93 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->((ord_less_eq_nat B) A))) of role axiom named fact_223_dual__order_Ostrict__implies__order
% 0.77/0.93 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->((ord_less_eq_nat B) A)))
% 0.77/0.93 FOF formula (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), ((not (((eq hF_Mirabelle_hf) A) B))->(((ord_le976219883lle_hf A) B)->((ord_le1310584031lle_hf A) B)))) of role axiom named fact_224_order_Onot__eq__order__implies__strict
% 0.77/0.93 A new axiom: (forall (A:hF_Mirabelle_hf) (B:hF_Mirabelle_hf), ((not (((eq hF_Mirabelle_hf) A) B))->(((ord_le976219883lle_hf A) B)->((ord_le1310584031lle_hf A) B))))
% 0.77/0.93 FOF formula (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((ord_less_eq_nat A) B)->((ord_less_nat A) B)))) of role axiom named fact_225_order_Onot__eq__order__implies__strict
% 0.77/0.93 A new axiom: (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((ord_less_eq_nat A) B)->((ord_less_nat A) B))))
% 0.77/0.93 FOF formula (forall (A4:hF_Mirabelle_hf) (B4:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (G:(hF_Mirabelle_hf->hF_Mirabelle_hf)), ((((eq hF_Mirabelle_hf) A4) B4)->((forall (X:hF_Mirabelle_hf), (((hF_Mirabelle_hmem X) B4)->(((eq hF_Mirabelle_hf) (F X)) (G X))))->(((eq hF_Mirabelle_hf) ((hF_Mirabelle_RepFun A4) F)) ((hF_Mirabelle_RepFun B4) G))))) of role axiom named fact_226_RepFun__cong
% 0.77/0.93 A new axiom: (forall (A4:hF_Mirabelle_hf) (B4:hF_Mirabelle_hf) (F:(hF_Mirabelle_hf->hF_Mirabelle_hf)) (G:(hF_Mirabelle_hf->hF_Mirabelle_hf)), ((((eq hF_Mirabelle_hf) A4) B4)->((forall (X:hF_Mirabelle_hf), (((hF_Mirabelle_hmem X) B4)->(((eq hF_Mirabelle_hf) (F X)) (G X))))->(((eq hF_Mirabelle_hf) ((hF_Mirabelle_RepFun A4) F)) ((hF_Mirabelle_RepFun B4) G)))))
% 0.77/0.93 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((ord_less_eq_nat T) X6)->False)))))) of role axiom named fact_227_minf_I8_J
% 0.77/0.93 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((ord_less_eq_nat T) X6)->False))))))
% 0.77/0.93 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->((ord_less_eq_nat X6) T)))))) of role axiom named fact_228_minf_I6_J
% 0.77/0.93 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->((ord_less_eq_nat X6) T))))))
% 0.77/0.93 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->((ord_less_eq_nat T) X6)))))) of role axiom named fact_229_pinf_I8_J
% 0.77/0.93 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->((ord_less_eq_nat T) X6))))))
% 0.77/0.93 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((ord_less_eq_nat X6) T)->False)))))) of role axiom named fact_230_pinf_I6_J
% 0.77/0.93 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((ord_less_eq_nat X6) T)->False))))))
% 0.77/0.93 FOF formula (forall (A:nat) (B:nat) (P:(nat->Prop)), (((ord_less_nat A) B)->((P A)->(((P B)->False)->((ex nat) (fun (C2:nat)=> ((and ((and ((and ((ord_less_eq_nat A) C2)) ((ord_less_eq_nat C2) B))) (forall (X6:nat), (((and ((ord_less_eq_nat A) X6)) ((ord_less_nat X6) C2))->(P X6))))) (forall (D:nat), ((forall (X:nat), (((and ((ord_less_eq_nat A) X)) ((ord_less_nat X) D))->(P X)))->((ord_less_eq_nat D) C2)))))))))) of role axiom named fact_231_complete__interval
% 0.77/0.93 A new axiom: (forall (A:nat) (B:nat) (P:(nat->Prop)), (((ord_less_nat A) B)->((P A)->(((P B)->False)->((ex nat) (fun (C2:nat)=> ((and ((and ((and ((ord_less_eq_nat A) C2)) ((ord_less_eq_nat C2) B))) (forall (X6:nat), (((and ((ord_less_eq_nat A) X6)) ((ord_less_nat X6) C2))->(P X6))))) (forall (D:nat), ((forall (X:nat), (((and ((ord_less_eq_nat A) X)) ((ord_less_nat X) D))->(P X)))->((ord_less_eq_nat D) C2))))))))))
% 0.77/0.93 FOF formula (forall (A:hF_Mirabelle_hf), (((eq hF_Mirabelle_hf) (hF_Mirabelle_HF (hF_Mirabelle_hfset A))) A)) of role axiom named fact_232_HF__hfset
% 0.78/0.94 A new axiom: (forall (A:hF_Mirabelle_hf), (((eq hF_Mirabelle_hf) (hF_Mirabelle_HF (hF_Mirabelle_hfset A))) A))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((ord_less_nat T) X6)->False)))))) of role axiom named fact_233_minf_I7_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((ord_less_nat T) X6)->False))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->((ord_less_nat X6) T)))))) of role axiom named fact_234_minf_I5_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->((ord_less_nat X6) T))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(not (((eq nat) X6) T))))))) of role axiom named fact_235_minf_I4_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(not (((eq nat) X6) T)))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(not (((eq nat) X6) T))))))) of role axiom named fact_236_minf_I3_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(not (((eq nat) X6) T)))))))
% 0.78/0.94 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((eq Prop) ((or (P X6)) (Q X6))) ((or (P4 X6)) (Q2 X6)))))))))) of role axiom named fact_237_minf_I2_J
% 0.78/0.94 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((eq Prop) ((or (P X6)) (Q X6))) ((or (P4 X6)) (Q2 X6))))))))))
% 0.78/0.94 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((eq Prop) ((and (P X6)) (Q X6))) ((and (P4 X6)) (Q2 X6)))))))))) of role axiom named fact_238_minf_I1_J
% 0.78/0.94 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat X) Z4)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat X6) Z2)->(((eq Prop) ((and (P X6)) (Q X6))) ((and (P4 X6)) (Q2 X6))))))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->((ord_less_nat T) X6)))))) of role axiom named fact_239_pinf_I7_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->((ord_less_nat T) X6))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((ord_less_nat X6) T)->False)))))) of role axiom named fact_240_pinf_I5_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((ord_less_nat X6) T)->False))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(not (((eq nat) X6) T))))))) of role axiom named fact_241_pinf_I4_J
% 0.78/0.94 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(not (((eq nat) X6) T)))))))
% 0.78/0.94 FOF formula (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(not (((eq nat) X6) T))))))) of role axiom named fact_242_pinf_I3_J
% 0.78/0.95 A new axiom: (forall (T:nat), ((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(not (((eq nat) X6) T)))))))
% 0.78/0.95 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((eq Prop) ((or (P X6)) (Q X6))) ((or (P4 X6)) (Q2 X6)))))))))) of role axiom named fact_243_pinf_I2_J
% 0.78/0.95 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((eq Prop) ((or (P X6)) (Q X6))) ((or (P4 X6)) (Q2 X6))))))))))
% 0.78/0.95 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((eq Prop) ((and (P X6)) (Q X6))) ((and (P4 X6)) (Q2 X6)))))))))) of role axiom named fact_244_pinf_I1_J
% 0.78/0.95 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (P X)) (P4 X))))))->(((ex nat) (fun (Z4:nat)=> (forall (X:nat), (((ord_less_nat Z4) X)->(((eq Prop) (Q X)) (Q2 X))))))->((ex nat) (fun (Z2:nat)=> (forall (X6:nat), (((ord_less_nat Z2) X6)->(((eq Prop) ((and (P X6)) (Q X6))) ((and (P4 X6)) (Q2 X6))))))))))
% 0.78/0.95 FOF formula (forall (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf A4)->(((eq set_HF_Mirabelle_hf) (hF_Mirabelle_hfset (hF_Mirabelle_HF A4))) A4))) of role axiom named fact_245_hfset__HF
% 0.78/0.95 A new axiom: (forall (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf A4)->(((eq set_HF_Mirabelle_hf) (hF_Mirabelle_hfset (hF_Mirabelle_HF A4))) A4)))
% 0.78/0.95 FOF formula (forall (X3:hF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X3) (hF_Mirabelle_HF A4))) ((and ((member1367349282lle_hf X3) A4)) (finite586181922lle_hf A4)))) of role axiom named fact_246_hmem__HF__iff
% 0.78/0.95 A new axiom: (forall (X3:hF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), (((eq Prop) ((hF_Mirabelle_hmem X3) (hF_Mirabelle_HF A4))) ((and ((member1367349282lle_hf X3) A4)) (finite586181922lle_hf A4))))
% 0.78/0.95 FOF formula (forall (A:hF_Mirabelle_hf), (finite586181922lle_hf (hF_Mirabelle_hfset A))) of role axiom named fact_247_finite__hfset
% 0.78/0.95 A new axiom: (forall (A:hF_Mirabelle_hf), (finite586181922lle_hf (hF_Mirabelle_hfset A)))
% 0.78/0.95 FOF formula (forall (A4:set_HF_Mirabelle_hf) (A:hF_Mirabelle_hf), ((finite586181922lle_hf A4)->(((member1367349282lle_hf A) A4)->((ex hF_Mirabelle_hf) (fun (X:hF_Mirabelle_hf)=> ((and ((and ((member1367349282lle_hf X) A4)) ((ord_le976219883lle_hf X) A))) (forall (Xa:hF_Mirabelle_hf), (((member1367349282lle_hf Xa) A4)->(((ord_le976219883lle_hf Xa) X)->(((eq hF_Mirabelle_hf) X) Xa)))))))))) of role axiom named fact_248_finite__has__minimal2
% 0.78/0.95 A new axiom: (forall (A4:set_HF_Mirabelle_hf) (A:hF_Mirabelle_hf), ((finite586181922lle_hf A4)->(((member1367349282lle_hf A) A4)->((ex hF_Mirabelle_hf) (fun (X:hF_Mirabelle_hf)=> ((and ((and ((member1367349282lle_hf X) A4)) ((ord_le976219883lle_hf X) A))) (forall (Xa:hF_Mirabelle_hf), (((member1367349282lle_hf Xa) A4)->(((ord_le976219883lle_hf Xa) X)->(((eq hF_Mirabelle_hf) X) Xa))))))))))
% 0.78/0.95 FOF formula (forall (A4:set_nat) (A:nat), ((finite_finite_nat A4)->(((member_nat A) A4)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A4)) ((ord_less_eq_nat X) A))) (forall (Xa:nat), (((member_nat Xa) A4)->(((ord_less_eq_nat Xa) X)->(((eq nat) X) Xa)))))))))) of role axiom named fact_249_finite__has__minimal2
% 0.78/0.96 A new axiom: (forall (A4:set_nat) (A:nat), ((finite_finite_nat A4)->(((member_nat A) A4)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A4)) ((ord_less_eq_nat X) A))) (forall (Xa:nat), (((member_nat Xa) A4)->(((ord_less_eq_nat Xa) X)->(((eq nat) X) Xa))))))))))
% 0.78/0.96 FOF formula (forall (A4:set_HF_Mirabelle_hf) (A:hF_Mirabelle_hf), ((finite586181922lle_hf A4)->(((member1367349282lle_hf A) A4)->((ex hF_Mirabelle_hf) (fun (X:hF_Mirabelle_hf)=> ((and ((and ((member1367349282lle_hf X) A4)) ((ord_le976219883lle_hf A) X))) (forall (Xa:hF_Mirabelle_hf), (((member1367349282lle_hf Xa) A4)->(((ord_le976219883lle_hf X) Xa)->(((eq hF_Mirabelle_hf) X) Xa)))))))))) of role axiom named fact_250_finite__has__maximal2
% 0.78/0.96 A new axiom: (forall (A4:set_HF_Mirabelle_hf) (A:hF_Mirabelle_hf), ((finite586181922lle_hf A4)->(((member1367349282lle_hf A) A4)->((ex hF_Mirabelle_hf) (fun (X:hF_Mirabelle_hf)=> ((and ((and ((member1367349282lle_hf X) A4)) ((ord_le976219883lle_hf A) X))) (forall (Xa:hF_Mirabelle_hf), (((member1367349282lle_hf Xa) A4)->(((ord_le976219883lle_hf X) Xa)->(((eq hF_Mirabelle_hf) X) Xa))))))))))
% 0.78/0.96 FOF formula (forall (A4:set_nat) (A:nat), ((finite_finite_nat A4)->(((member_nat A) A4)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A4)) ((ord_less_eq_nat A) X))) (forall (Xa:nat), (((member_nat Xa) A4)->(((ord_less_eq_nat X) Xa)->(((eq nat) X) Xa)))))))))) of role axiom named fact_251_finite__has__maximal2
% 0.78/0.96 A new axiom: (forall (A4:set_nat) (A:nat), ((finite_finite_nat A4)->(((member_nat A) A4)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A4)) ((ord_less_eq_nat A) X))) (forall (Xa:nat), (((member_nat Xa) A4)->(((ord_less_eq_nat X) Xa)->(((eq nat) X) Xa))))))))))
% 0.78/0.96 FOF formula (forall (A4:set_HF_Mirabelle_hf) (B4:set_HF_Mirabelle_hf), (((ord_le432112161lle_hf A4) B4)->((finite586181922lle_hf B4)->(finite586181922lle_hf A4)))) of role axiom named fact_252_finite__subset
% 0.78/0.96 A new axiom: (forall (A4:set_HF_Mirabelle_hf) (B4:set_HF_Mirabelle_hf), (((ord_le432112161lle_hf A4) B4)->((finite586181922lle_hf B4)->(finite586181922lle_hf A4))))
% 0.78/0.96 FOF formula (forall (A4:set_nat) (B4:set_nat), (((ord_less_eq_set_nat A4) B4)->((finite_finite_nat B4)->(finite_finite_nat A4)))) of role axiom named fact_253_finite__subset
% 0.78/0.96 A new axiom: (forall (A4:set_nat) (B4:set_nat), (((ord_less_eq_set_nat A4) B4)->((finite_finite_nat B4)->(finite_finite_nat A4))))
% 0.78/0.96 FOF formula (forall (S:set_HF_Mirabelle_hf) (T2:set_HF_Mirabelle_hf), (((ord_le432112161lle_hf S) T2)->(((finite586181922lle_hf S)->False)->((finite586181922lle_hf T2)->False)))) of role axiom named fact_254_infinite__super
% 0.78/0.96 A new axiom: (forall (S:set_HF_Mirabelle_hf) (T2:set_HF_Mirabelle_hf), (((ord_le432112161lle_hf S) T2)->(((finite586181922lle_hf S)->False)->((finite586181922lle_hf T2)->False))))
% 0.78/0.96 FOF formula (forall (S:set_nat) (T2:set_nat), (((ord_less_eq_set_nat S) T2)->(((finite_finite_nat S)->False)->((finite_finite_nat T2)->False)))) of role axiom named fact_255_infinite__super
% 0.78/0.96 A new axiom: (forall (S:set_nat) (T2:set_nat), (((ord_less_eq_set_nat S) T2)->(((finite_finite_nat S)->False)->((finite_finite_nat T2)->False))))
% 0.78/0.96 FOF formula (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->(finite586181922lle_hf A4)))) of role axiom named fact_256_rev__finite__subset
% 0.78/0.96 A new axiom: (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->(finite586181922lle_hf A4))))
% 0.78/0.96 FOF formula (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->(finite_finite_nat A4)))) of role axiom named fact_257_rev__finite__subset
% 0.78/0.96 A new axiom: (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->(finite_finite_nat A4))))
% 0.78/0.96 FOF formula (forall (A4:set_HF_Mirabelle_hf) (P:(set_HF_Mirabelle_hf->Prop)), ((finite586181922lle_hf A4)->((forall (A7:set_HF_Mirabelle_hf), ((finite586181922lle_hf A7)->((forall (B7:set_HF_Mirabelle_hf), (((ord_le1344122901lle_hf B7) A7)->(P B7)))->(P A7))))->(P A4)))) of role axiom named fact_258_finite__psubset__induct
% 0.78/0.97 A new axiom: (forall (A4:set_HF_Mirabelle_hf) (P:(set_HF_Mirabelle_hf->Prop)), ((finite586181922lle_hf A4)->((forall (A7:set_HF_Mirabelle_hf), ((finite586181922lle_hf A7)->((forall (B7:set_HF_Mirabelle_hf), (((ord_le1344122901lle_hf B7) A7)->(P B7)))->(P A7))))->(P A4))))
% 0.78/0.97 FOF formula (forall (A4:set_nat) (P:(set_nat->Prop)), ((finite_finite_nat A4)->((forall (A7:set_nat), ((finite_finite_nat A7)->((forall (B7:set_nat), (((ord_less_set_nat B7) A7)->(P B7)))->(P A7))))->(P A4)))) of role axiom named fact_259_finite__psubset__induct
% 0.78/0.97 A new axiom: (forall (A4:set_nat) (P:(set_nat->Prop)), ((finite_finite_nat A4)->((forall (A7:set_nat), ((finite_finite_nat A7)->((forall (B7:set_nat), (((ord_less_set_nat B7) A7)->(P B7)))->(P A7))))->(P A4))))
% 0.78/0.97 FOF formula (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->(((ord_less_nat (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4))->((ord_le1344122901lle_hf A4) B4))))) of role axiom named fact_260_card__psubset
% 0.78/0.97 A new axiom: (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->(((ord_less_nat (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4))->((ord_le1344122901lle_hf A4) B4)))))
% 0.78/0.97 FOF formula (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->(((ord_less_nat (finite_card_nat A4)) (finite_card_nat B4))->((ord_less_set_nat A4) B4))))) of role axiom named fact_261_card__psubset
% 0.78/0.97 A new axiom: (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->(((ord_less_nat (finite_card_nat A4)) (finite_card_nat B4))->((ord_less_set_nat A4) B4)))))
% 0.78/0.97 FOF formula ((inj_on811196232lle_hf hF_Mirabelle_HF) (collec1758573718lle_hf finite586181922lle_hf)) of role axiom named fact_262_inj__on__HF
% 0.78/0.97 A new axiom: ((inj_on811196232lle_hf hF_Mirabelle_HF) (collec1758573718lle_hf finite586181922lle_hf))
% 0.78/0.97 FOF formula ((orderi1737556723lle_hf ord_le976219883lle_hf) ord_le1310584031lle_hf) of role axiom named fact_263_order_Oordering__axioms
% 0.78/0.97 A new axiom: ((orderi1737556723lle_hf ord_le976219883lle_hf) ord_le1310584031lle_hf)
% 0.78/0.97 FOF formula ((ordering_nat ord_less_eq_nat) ord_less_nat) of role axiom named fact_264_order_Oordering__axioms
% 0.78/0.97 A new axiom: ((ordering_nat ord_less_eq_nat) ord_less_nat)
% 0.78/0.97 FOF formula (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->((ord_less_eq_nat (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4))))) of role axiom named fact_265_card__mono
% 0.78/0.97 A new axiom: (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->((ord_less_eq_nat (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4)))))
% 0.78/0.97 FOF formula (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->((ord_less_eq_nat (finite_card_nat A4)) (finite_card_nat B4))))) of role axiom named fact_266_card__mono
% 0.78/0.97 A new axiom: (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->((ord_less_eq_nat (finite_card_nat A4)) (finite_card_nat B4)))))
% 0.78/0.97 FOF formula (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->(((ord_less_eq_nat (finite1213132899lle_hf B4)) (finite1213132899lle_hf A4))->(((eq set_HF_Mirabelle_hf) A4) B4))))) of role axiom named fact_267_card__seteq
% 0.78/0.97 A new axiom: (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->(((ord_less_eq_nat (finite1213132899lle_hf B4)) (finite1213132899lle_hf A4))->(((eq set_HF_Mirabelle_hf) A4) B4)))))
% 0.78/0.97 FOF formula (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->(((ord_less_eq_nat (finite_card_nat B4)) (finite_card_nat A4))->(((eq set_nat) A4) B4))))) of role axiom named fact_268_card__seteq
% 0.78/0.97 A new axiom: (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->(((ord_less_eq_nat (finite_card_nat B4)) (finite_card_nat A4))->(((eq set_nat) A4) B4)))))
% 0.78/0.98 FOF formula (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->((((eq nat) (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4))->(((eq set_HF_Mirabelle_hf) A4) B4))))) of role axiom named fact_269_card__subset__eq
% 0.78/0.98 A new axiom: (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le432112161lle_hf A4) B4)->((((eq nat) (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4))->(((eq set_HF_Mirabelle_hf) A4) B4)))))
% 0.78/0.98 FOF formula (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->((((eq nat) (finite_card_nat A4)) (finite_card_nat B4))->(((eq set_nat) A4) B4))))) of role axiom named fact_270_card__subset__eq
% 0.78/0.98 A new axiom: (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_eq_set_nat A4) B4)->((((eq nat) (finite_card_nat A4)) (finite_card_nat B4))->(((eq set_nat) A4) B4)))))
% 0.78/0.98 FOF formula (forall (A4:set_HF_Mirabelle_hf) (N2:nat), (((finite586181922lle_hf A4)->False)->((ex set_HF_Mirabelle_hf) (fun (B8:set_HF_Mirabelle_hf)=> ((and ((and (finite586181922lle_hf B8)) (((eq nat) (finite1213132899lle_hf B8)) N2))) ((ord_le432112161lle_hf B8) A4)))))) of role axiom named fact_271_infinite__arbitrarily__large
% 0.78/0.98 A new axiom: (forall (A4:set_HF_Mirabelle_hf) (N2:nat), (((finite586181922lle_hf A4)->False)->((ex set_HF_Mirabelle_hf) (fun (B8:set_HF_Mirabelle_hf)=> ((and ((and (finite586181922lle_hf B8)) (((eq nat) (finite1213132899lle_hf B8)) N2))) ((ord_le432112161lle_hf B8) A4))))))
% 0.78/0.98 FOF formula (forall (A4:set_nat) (N2:nat), (((finite_finite_nat A4)->False)->((ex set_nat) (fun (B8:set_nat)=> ((and ((and (finite_finite_nat B8)) (((eq nat) (finite_card_nat B8)) N2))) ((ord_less_eq_set_nat B8) A4)))))) of role axiom named fact_272_infinite__arbitrarily__large
% 0.78/0.98 A new axiom: (forall (A4:set_nat) (N2:nat), (((finite_finite_nat A4)->False)->((ex set_nat) (fun (B8:set_nat)=> ((and ((and (finite_finite_nat B8)) (((eq nat) (finite_card_nat B8)) N2))) ((ord_less_eq_set_nat B8) A4))))))
% 0.78/0.98 FOF formula (forall (F3:set_HF_Mirabelle_hf) (C3:nat), ((forall (G2:set_HF_Mirabelle_hf), (((ord_le432112161lle_hf G2) F3)->((finite586181922lle_hf G2)->((ord_less_eq_nat (finite1213132899lle_hf G2)) C3))))->((and (finite586181922lle_hf F3)) ((ord_less_eq_nat (finite1213132899lle_hf F3)) C3)))) of role axiom named fact_273_finite__if__finite__subsets__card__bdd
% 0.78/0.98 A new axiom: (forall (F3:set_HF_Mirabelle_hf) (C3:nat), ((forall (G2:set_HF_Mirabelle_hf), (((ord_le432112161lle_hf G2) F3)->((finite586181922lle_hf G2)->((ord_less_eq_nat (finite1213132899lle_hf G2)) C3))))->((and (finite586181922lle_hf F3)) ((ord_less_eq_nat (finite1213132899lle_hf F3)) C3))))
% 0.78/0.98 FOF formula (forall (F3:set_nat) (C3:nat), ((forall (G2:set_nat), (((ord_less_eq_set_nat G2) F3)->((finite_finite_nat G2)->((ord_less_eq_nat (finite_card_nat G2)) C3))))->((and (finite_finite_nat F3)) ((ord_less_eq_nat (finite_card_nat F3)) C3)))) of role axiom named fact_274_finite__if__finite__subsets__card__bdd
% 0.78/0.98 A new axiom: (forall (F3:set_nat) (C3:nat), ((forall (G2:set_nat), (((ord_less_eq_set_nat G2) F3)->((finite_finite_nat G2)->((ord_less_eq_nat (finite_card_nat G2)) C3))))->((and (finite_finite_nat F3)) ((ord_less_eq_nat (finite_card_nat F3)) C3))))
% 0.78/0.98 FOF formula (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le1344122901lle_hf A4) B4)->((ord_less_nat (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4))))) of role axiom named fact_275_psubset__card__mono
% 0.78/0.98 A new axiom: (forall (B4:set_HF_Mirabelle_hf) (A4:set_HF_Mirabelle_hf), ((finite586181922lle_hf B4)->(((ord_le1344122901lle_hf A4) B4)->((ord_less_nat (finite1213132899lle_hf A4)) (finite1213132899lle_hf B4)))))
% 0.78/0.98 FOF formula (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_set_nat A4) B4)->((ord_less_nat (finite_card_nat A4)) (finite_card_nat B4))))) of role axiom named fact_276_psubset__card__mono
% 0.78/0.98 A new axiom: (forall (B4:set_nat) (A4:set_nat), ((finite_finite_nat B4)->(((ord_less_set_nat A4) B4)->((ord_less_nat (finite_card_nat A4)) (finite_card_nat B4)))))
% 0.78/0.98 <<<abelle_hf] :
% 0.78/0.98 ( ( ord_less_eq_nat @ N2 @ ( finite1213132899lle_hf @ S ) )
% 0.78/0.98 => ~ !>>>!!!<<< [T3: set_HF_Mirabelle_hf] :
% 0.78/0.98 ( ( ord_le432112161lle_hf @ T3 @ S )
% 0.78/0.98 =>>>
% 0.78/0.98 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, 11, 22, 30, 36, 43, 50, 99, 113, 185, 229, 265, 285, 300, 221, 120, 187, 124]
% 0.78/0.98 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, 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, LexToken(THF,'thf',1,86514), LexToken(LPAR,'(',1,86517), name, LexToken(COMMA,',',1,86556), formula_role, LexToken(COMMA,',',1,86562), LexToken(LPAR,'(',1,86563), thf_quantified_formula_PRE, thf_quantifier, LexToken(LBRACKET,'[',1,86571), thf_variable_list, LexToken(RBRACKET,']',1,86602), LexToken(COLON,':',1,86604), LexToken(LPAR,'(',1,86612), thf_unitary_formula, thf_pair_connective, unary_connective]
% 0.78/0.98 Unexpected exception Syntax error at '!':BANG
% 0.78/0.98 Traceback (most recent call last):
% 0.78/0.98 File "CASC.py", line 79, in <module>
% 0.78/0.98 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.78/0.98 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 38, in __init__
% 0.78/0.98 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.78/0.98 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 265, in parse
% 0.78/0.98 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.78/0.98 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.78/0.98 tok = self.errorfunc(errtoken)
% 0.78/0.98 File "/export/starexec/sandbox2/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.78/0.98 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.78/0.98 TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------